Project Promoter – Politechnika Śląska Norwegian Partner – University of Stavanger
Fundamentals of Electronics - Politechnika...
Transcript of Fundamentals of Electronics - Politechnika...
Fundamentals ofElectronics
Dr Artur Jędrusyna
1
2
CONTENTS
1 Basic Literature
2 Fundamental definitions
bull Electric voltage
bull Electric current
bull Resistance and Ohmrsquos Law
bull Current flow convention
bull Kirchhoffs circuit laws
bull Theacutevenins theorem
bull Electric power
bull Signals
bull Decibel gain
Contents ndash cont
3 Passive electronic components
bullResistors
bullCapacitors
bullInductors
bullTransformers
4Active electronic components
bullDiodes
bullBipolar transistors
bullBJT as a switch
bullCommon collector amplifier
bullCommon emitter amplifier
Contents ndash cont
5Operational amplifier
bullThe assumptions of an ideal operational amplifier
bullThe basic circuits
bullA hardware implementation of mathematical operations
bullA Wien sine wave oscillator
bullFunction generator
5
Basic Literature
[1] Horowitz P Hill Wndash The Art of Electronics
[2] Tietze U Schenk Ch Electronic Circuits --- Handbook for Design and Applications 2nd edition 2008 with CD-ROM ISBN 978-3-540-00429-5
[3] Op Amp Applications Handbook (Analog Devices Series) [Paperback] Walt Jung (Author)
[4] Various catalogues and application notes by the compomentsmanufacturers
Fundamental definitions
VoltageVEB ndash the difference of potentials between the points E and
B where VE potential is positive related to VB potential
An example UEB = 07 VUBE = - 07 V
where VE gt VBAn ideal voltage source symbol
Fundamental definitions (cont)
Electric Current ndasha flow of electric charge This flowing
electric charge is typically carried by moving electrons in a conductor such as wire
I
IdQ
dt=
where Q is the electric charge transferred through the surface over some time t If Q and t are measured in coulombs and seconds respectively I is in amperes
Fundamental definitions (cont)
E I
U1=IR1
U2=IR2
U3=IR3
R1
R2
R3
An electric current can flowonly through a closed path called an electric circuit
In order to produce a current flow at least one current source (eg a battery) must be present in the circuit
An ideal currentsource symbol
Fundamental definitions (cont)
Resistance and Ohmrsquos Law
Ohms law states that the current through a conductor between two points is directly proportional to the potential difference or voltage across the two points and inversely proportional to the resistance between them
The mathematical equation that describes this relationship is
R=UI
The unit is Ohm [ Ω ] = [ V ] [ A ]
10
Current flow convention
The electrons in a electrical circuit flow in the opposite direction of the conventional electric current
copyWikipedia
Fundamental definitions (cont)
Kirchhoffs circuit laws
Kirchhoffs current law (KCL)
At any node (junction) in an electrical circuit the sum of currents flowing into that node is equal to the sum of currents flowing out of that node
or
The algebraic sum of currents in a network of conductors meeting at a point is zero
I iisum = 0
Fundamental definitions (cont)
Kirchhoffs voltage law (KVL)
The directed sum of the electrical potential differences (voltage) around any closed circuit is zero
or
More simply the sum of the emfs in any closed loop is equivalent to the sum of the potential drops in that loop IR Ei
isum =
Fundamental definitions (cont)
In circuit theory Theacutevenins theorem for linear electrical networks states that any combination of voltage sources current sources and resistors with two terminals is electrically equivalent to a single voltage source V and a single series resistor R
Theacutevenins theorem
Where UT= open circuit voltage between points A and B
And RT = UTIT where IT is the short circuit current flowing between points A and B
Fundamental definitions (cont)
Electric power
An electric power P is the rate at which electrical energy is transferred by an electric circuit The SI unit of power is the watt In direct current resistive circuits electrical power is calculated using Joules law
P = UI
The unit
[W] = [J] [s] = ([J] [C]) ([C] [s]) [W] = [V][A]
Ohmrsquos law allows us to evaluate an electric power dissipated by a resistor
P = I2 R and respectively P = U2R
Fundamental definitions (cont)
SignalsIn electronics a signal is usually defined as a time-varying voltage or current that conveys information
Sinuisoidal signal
U = Umsin ω t
whereUm - amplitude ω =2πf ndash pulsation[rads]
t ndash time [s] f ndash frequency [Hz]
Other parameters
Vp-p = Peak-to-Peak value
Root-Mean_Square value (RMS)
For sinusoidal signal
Vp-p = 2Um
VRMS=0707Um
dttUT
UT
RMS int=0
2 )(1
Fundamental definitions (cont)
Square wave signal
For this signal URMS=UM
Other parameters
Risetime
Fall time
Highlow amplitude
Please note that real-life signal are not rectangular ie risetime and fall time are always greater than zero
For practical purposes risefall times are usually measured between 10 and 90 of the final value of the signal
Fundamental definitions (cont)
Sawtooth signal (sawtooth wave)
sawtooth wave ramps upward and then sharply drops
Pulses
A rapid transient changes in the amplitude of a signal
Step signals amp glitches
Useful mostly for theoretical analysis
Fundamental definitions (cont)
Decibel gain
The decibel (dB) is a logarithmic unit that indicates the ratio of a physical quantity (usually power or intensity) relative to a specified or implied reference level The decibel ratio of two signals can be expressed by a formula
ku[dB]=20log10(U2U1) where U2 and U1 are the amplitudes of the signals
Examples
ku ku [dB]
01 -20dB
0707 -3dB
1 0dB
141 3dB
10 20dB
100 40dB
1000 60dB
Passive components
Resistors
A resistor is a two-terminal electronic component that produces a voltage across its terminals that is proportional to the electric current through it in accordance with Ohms law
Generic graphic symbol
aMetalized resistor
bWirewound resistor
cCarbon resistor
dResistor ladder
eThick-film resistor
The primary characteristics of a resistor
Resistance (usually expressed in Ω kΩ and MΩ) Tolerance Maximal (rated) power Temperature coefficient of resistance (TCR) Maximal working voltage Parasitic inductance
Series and parallel resistors
The equivalent resistance of tworesistors in series connection
R=R1+R2
The equivalent resistance of tworesistors in parallel connection
1R=1R1+1R2
For n resistors
R=R1+R2+R3+Rn
For n resistors
1R=1R1+1R2+1R3+1Rn
Resistive divider
copy Wikipedia
If R1=R2 then Vout = Vin2
The voltage output of a voltage divider is not fixed but varies according to the load To obtain a reasonably stable output voltage the output current should be a small fraction of the input current
Loaded voltage divider
The voltage between points A and B
U = UT = UINmiddot [R2 (R1 + R2)]
According to Theveninrsquostheorem
RT = (R1 middot R2) (R1+ R2)
In practical projects we often
assume that RL should be 10 times higher than RT
Potentiometers
A potentiometer is a three-terminal resistor with a sliding contact acting as an adjustable voltage divider
Capacitors
copy Wikipedia
A capacitor is a passive electronic component consisting of a pair of conductors separated by a dielectric (insulator)
An ideal capacitor is characterized by a single constant value capacitance measured in farads This is the ratio of the electric charge on each conductor to the potential difference between them
The properties of capacitor are expressed by an equation
C=QU
Where C is capacitance Q is the electriccharge stored inside the capacitor and U is thevoltage between conductors (plates)
Capacitors ndashinternal structure
a) Film capacitor
b) Metalised plastic film capacitor
c) Ceramic disc capacitor
d) Tubular ceramic capacitor
e) Multilayer ceramic capacitor
Supercapacitors
Maxwell Technologies supercapacitors
Ultracapacitor (known also as anelectrochemical double layer capacitor) is an electrochemical capacitor that has a very high energy density when compared to common capacitors typically on the order of thousands of times greater than a high capacity electrolytic capacitor
They are characterized by a very shortcharging time (seconds to minutes)
Possible applications ndash electriccars power tools emergencypower supplies
Supercapacitors ndash cont
Pros very short charging time
Cons relatively high price
Supercapacitors vs standard capacitors
New generation of supercapacitotors
Second generation of supercapacitors by ioxuscom (2010)
From left 220F800F1000F Operating voltage 23V max
copy wwwioxuscom
Capacitors ndash cont
Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)
If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A
Capacitors ndash cont
Most imporant capacitor parameters
bullCapacitance [microF] [nF] or [pF]
bullTolerance []
bullRated voltage [V]
bullDischarge rate (leakage current)
bullTemperature coefficient of capacitance
bullEquivalent series resitance (ESR)
Capacitors ndash cont
a)Aluminium electrolytic capacitor
b)Tantalum electrolytic capacitor
c)Polyesther capacitor
d)Ceramic disc capacitor
e)Mylar capacitor
Capacitors ndash cont
Capacitors in series connection
For two capacitors in series the equivalent capacitance is
For parallel configuration
For two capacitors in parallel the equivalent capacitance is
C=C1+C2
For n capacitors (general case)
Capacitors ndash cont
Capacitor discharge through a resistor
If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge
The discharge rate is expressed by an equation
Where RC is called time constant
Capacitors ndash cont
Capacitor charging through a resistor
If a capacitor C will be charged from source of voltage UWE
through a resistor R the voltage change across its terminals will be described by the following equations
The final solution is
Inductors
An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it
An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material
Graphic symbola) Toroidal core inductor b)cylindrical core inductor
The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L
where L is expressed in H (Henryrsquos) but most often in mH or microH
Inductors ndash cont
Different variations of inductors
Surface mount(SMT) inductors
Cylindricalcoreinductors
Inductor parameters
bullInductance [H]
bullRated voltage [V]
bullTolerance []
bullSaturation DC current [A]
bullMaximal RMS current [A]
bullSelf-resonance frequency [Hz]
bullDC resistance [Ω]
Typical set of parameters
Coilcraft DO3340P-104M inductor
L-100microH tol-20 Isat-25A Irms-12A
SRF-5MHz(typ) RDC-022Ω
Transformers
A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation
Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio
Transformer ndash cont
The current I2 flowing in the secondary winding is inversely proportional
to the current I1 flowing in the primary winding
Moreover the impedance connected to the transformer is transformed by the square of the turns ratio
Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer
Transformers ndash cont
The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit
Examples of low power transformers
Toroidal coretransformer
Toroidal core variabletransformer
(autotransformer)
Laminatedcore EI transformers
Diodes
A diode is a two-terminal electronic component that conducts electric current in only one direction
When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)
Diodes ndash cont
The currentndashvoltage characteristic of a diodeWhere
ID is diode current
If is forward diode current
IFmax is maximum diode
current
UF is forward diode voltage
UR is reverse diode voltage
URmax is the maximum
reverse voltage diodevoltage
Diodes ndash cont
For common types of diodes the value of UF voltage is
bullFor Germanium junction diode 02 04V
bullFor Silicone junction diode 05 08V
bullFor Schottky diode 0204V
An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation
Where I is the diode current
IS is the reverse bias saturation current (or scale current)
VD is the voltage across the diode
VT is the thermal voltage and
n is the ideality factor also known as the quality factor
Diodes ndashcont
The thermal voltage VT is approximately 2585 mV at 300 K
At any other temperature it is given by an equation
where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)
Diodes ndash cont
The typical I-V characteristics of for germaniumand silicone junction diode
Diodes ndash cont
Diode as a switching element
Following the end of forward conduction in a PN type diode a
reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called
reverse recovery time and usually is between tens and hundreds of
ns (ie between 1e-8 and 1e-7 s)
Diodes ndash cont
Diode as a rectifier
A half wave rectifier
A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification
Diodes ndash cont
A full-wave rectifier
This kind of a circuit is also known as the bridge rectifier
Diodes ndash cont
A rectifier in a DC voltage supply
Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge
In general case the simple design rule should be followed
RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)
Diodes ndash cont
Another application ndash diode-based voltage limiter
The cathode of a diode has a potential equal to 4V
U out max = 4V + 06 V = 46 V
If UINlt46V then UOUT = UIN
Bipolar Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals
Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors
B=base C=collector E= emitter
Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases
Transistors ndash cont
The history of the transistor
The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work
The first silicon transistors were produced by Western Electric and TexasInstruments in 1954
Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)
copy wwwporticusorg
Transistors ndash cont
An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased
NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia
The first transistor
copy Bell Labs
Transistor ndash cont
Transistor as an amplifier
A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated
The relations between currents in BJT copy radartutorialeu
Transistor ndash cont
The most often used amplifier circuits
highmediumlowBandwidth4
00001800Phase Shift between input and output signals
3
lt 1highhighCurrent gain2
highlt 1highVoltage gain1
COMMON BASE
COMMON COLLECTOR
COMMON EMITTER
AMPLIFIER
Nr
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
2
CONTENTS
1 Basic Literature
2 Fundamental definitions
bull Electric voltage
bull Electric current
bull Resistance and Ohmrsquos Law
bull Current flow convention
bull Kirchhoffs circuit laws
bull Theacutevenins theorem
bull Electric power
bull Signals
bull Decibel gain
Contents ndash cont
3 Passive electronic components
bullResistors
bullCapacitors
bullInductors
bullTransformers
4Active electronic components
bullDiodes
bullBipolar transistors
bullBJT as a switch
bullCommon collector amplifier
bullCommon emitter amplifier
Contents ndash cont
5Operational amplifier
bullThe assumptions of an ideal operational amplifier
bullThe basic circuits
bullA hardware implementation of mathematical operations
bullA Wien sine wave oscillator
bullFunction generator
5
Basic Literature
[1] Horowitz P Hill Wndash The Art of Electronics
[2] Tietze U Schenk Ch Electronic Circuits --- Handbook for Design and Applications 2nd edition 2008 with CD-ROM ISBN 978-3-540-00429-5
[3] Op Amp Applications Handbook (Analog Devices Series) [Paperback] Walt Jung (Author)
[4] Various catalogues and application notes by the compomentsmanufacturers
Fundamental definitions
VoltageVEB ndash the difference of potentials between the points E and
B where VE potential is positive related to VB potential
An example UEB = 07 VUBE = - 07 V
where VE gt VBAn ideal voltage source symbol
Fundamental definitions (cont)
Electric Current ndasha flow of electric charge This flowing
electric charge is typically carried by moving electrons in a conductor such as wire
I
IdQ
dt=
where Q is the electric charge transferred through the surface over some time t If Q and t are measured in coulombs and seconds respectively I is in amperes
Fundamental definitions (cont)
E I
U1=IR1
U2=IR2
U3=IR3
R1
R2
R3
An electric current can flowonly through a closed path called an electric circuit
In order to produce a current flow at least one current source (eg a battery) must be present in the circuit
An ideal currentsource symbol
Fundamental definitions (cont)
Resistance and Ohmrsquos Law
Ohms law states that the current through a conductor between two points is directly proportional to the potential difference or voltage across the two points and inversely proportional to the resistance between them
The mathematical equation that describes this relationship is
R=UI
The unit is Ohm [ Ω ] = [ V ] [ A ]
10
Current flow convention
The electrons in a electrical circuit flow in the opposite direction of the conventional electric current
copyWikipedia
Fundamental definitions (cont)
Kirchhoffs circuit laws
Kirchhoffs current law (KCL)
At any node (junction) in an electrical circuit the sum of currents flowing into that node is equal to the sum of currents flowing out of that node
or
The algebraic sum of currents in a network of conductors meeting at a point is zero
I iisum = 0
Fundamental definitions (cont)
Kirchhoffs voltage law (KVL)
The directed sum of the electrical potential differences (voltage) around any closed circuit is zero
or
More simply the sum of the emfs in any closed loop is equivalent to the sum of the potential drops in that loop IR Ei
isum =
Fundamental definitions (cont)
In circuit theory Theacutevenins theorem for linear electrical networks states that any combination of voltage sources current sources and resistors with two terminals is electrically equivalent to a single voltage source V and a single series resistor R
Theacutevenins theorem
Where UT= open circuit voltage between points A and B
And RT = UTIT where IT is the short circuit current flowing between points A and B
Fundamental definitions (cont)
Electric power
An electric power P is the rate at which electrical energy is transferred by an electric circuit The SI unit of power is the watt In direct current resistive circuits electrical power is calculated using Joules law
P = UI
The unit
[W] = [J] [s] = ([J] [C]) ([C] [s]) [W] = [V][A]
Ohmrsquos law allows us to evaluate an electric power dissipated by a resistor
P = I2 R and respectively P = U2R
Fundamental definitions (cont)
SignalsIn electronics a signal is usually defined as a time-varying voltage or current that conveys information
Sinuisoidal signal
U = Umsin ω t
whereUm - amplitude ω =2πf ndash pulsation[rads]
t ndash time [s] f ndash frequency [Hz]
Other parameters
Vp-p = Peak-to-Peak value
Root-Mean_Square value (RMS)
For sinusoidal signal
Vp-p = 2Um
VRMS=0707Um
dttUT
UT
RMS int=0
2 )(1
Fundamental definitions (cont)
Square wave signal
For this signal URMS=UM
Other parameters
Risetime
Fall time
Highlow amplitude
Please note that real-life signal are not rectangular ie risetime and fall time are always greater than zero
For practical purposes risefall times are usually measured between 10 and 90 of the final value of the signal
Fundamental definitions (cont)
Sawtooth signal (sawtooth wave)
sawtooth wave ramps upward and then sharply drops
Pulses
A rapid transient changes in the amplitude of a signal
Step signals amp glitches
Useful mostly for theoretical analysis
Fundamental definitions (cont)
Decibel gain
The decibel (dB) is a logarithmic unit that indicates the ratio of a physical quantity (usually power or intensity) relative to a specified or implied reference level The decibel ratio of two signals can be expressed by a formula
ku[dB]=20log10(U2U1) where U2 and U1 are the amplitudes of the signals
Examples
ku ku [dB]
01 -20dB
0707 -3dB
1 0dB
141 3dB
10 20dB
100 40dB
1000 60dB
Passive components
Resistors
A resistor is a two-terminal electronic component that produces a voltage across its terminals that is proportional to the electric current through it in accordance with Ohms law
Generic graphic symbol
aMetalized resistor
bWirewound resistor
cCarbon resistor
dResistor ladder
eThick-film resistor
The primary characteristics of a resistor
Resistance (usually expressed in Ω kΩ and MΩ) Tolerance Maximal (rated) power Temperature coefficient of resistance (TCR) Maximal working voltage Parasitic inductance
Series and parallel resistors
The equivalent resistance of tworesistors in series connection
R=R1+R2
The equivalent resistance of tworesistors in parallel connection
1R=1R1+1R2
For n resistors
R=R1+R2+R3+Rn
For n resistors
1R=1R1+1R2+1R3+1Rn
Resistive divider
copy Wikipedia
If R1=R2 then Vout = Vin2
The voltage output of a voltage divider is not fixed but varies according to the load To obtain a reasonably stable output voltage the output current should be a small fraction of the input current
Loaded voltage divider
The voltage between points A and B
U = UT = UINmiddot [R2 (R1 + R2)]
According to Theveninrsquostheorem
RT = (R1 middot R2) (R1+ R2)
In practical projects we often
assume that RL should be 10 times higher than RT
Potentiometers
A potentiometer is a three-terminal resistor with a sliding contact acting as an adjustable voltage divider
Capacitors
copy Wikipedia
A capacitor is a passive electronic component consisting of a pair of conductors separated by a dielectric (insulator)
An ideal capacitor is characterized by a single constant value capacitance measured in farads This is the ratio of the electric charge on each conductor to the potential difference between them
The properties of capacitor are expressed by an equation
C=QU
Where C is capacitance Q is the electriccharge stored inside the capacitor and U is thevoltage between conductors (plates)
Capacitors ndashinternal structure
a) Film capacitor
b) Metalised plastic film capacitor
c) Ceramic disc capacitor
d) Tubular ceramic capacitor
e) Multilayer ceramic capacitor
Supercapacitors
Maxwell Technologies supercapacitors
Ultracapacitor (known also as anelectrochemical double layer capacitor) is an electrochemical capacitor that has a very high energy density when compared to common capacitors typically on the order of thousands of times greater than a high capacity electrolytic capacitor
They are characterized by a very shortcharging time (seconds to minutes)
Possible applications ndash electriccars power tools emergencypower supplies
Supercapacitors ndash cont
Pros very short charging time
Cons relatively high price
Supercapacitors vs standard capacitors
New generation of supercapacitotors
Second generation of supercapacitors by ioxuscom (2010)
From left 220F800F1000F Operating voltage 23V max
copy wwwioxuscom
Capacitors ndash cont
Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)
If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A
Capacitors ndash cont
Most imporant capacitor parameters
bullCapacitance [microF] [nF] or [pF]
bullTolerance []
bullRated voltage [V]
bullDischarge rate (leakage current)
bullTemperature coefficient of capacitance
bullEquivalent series resitance (ESR)
Capacitors ndash cont
a)Aluminium electrolytic capacitor
b)Tantalum electrolytic capacitor
c)Polyesther capacitor
d)Ceramic disc capacitor
e)Mylar capacitor
Capacitors ndash cont
Capacitors in series connection
For two capacitors in series the equivalent capacitance is
For parallel configuration
For two capacitors in parallel the equivalent capacitance is
C=C1+C2
For n capacitors (general case)
Capacitors ndash cont
Capacitor discharge through a resistor
If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge
The discharge rate is expressed by an equation
Where RC is called time constant
Capacitors ndash cont
Capacitor charging through a resistor
If a capacitor C will be charged from source of voltage UWE
through a resistor R the voltage change across its terminals will be described by the following equations
The final solution is
Inductors
An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it
An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material
Graphic symbola) Toroidal core inductor b)cylindrical core inductor
The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L
where L is expressed in H (Henryrsquos) but most often in mH or microH
Inductors ndash cont
Different variations of inductors
Surface mount(SMT) inductors
Cylindricalcoreinductors
Inductor parameters
bullInductance [H]
bullRated voltage [V]
bullTolerance []
bullSaturation DC current [A]
bullMaximal RMS current [A]
bullSelf-resonance frequency [Hz]
bullDC resistance [Ω]
Typical set of parameters
Coilcraft DO3340P-104M inductor
L-100microH tol-20 Isat-25A Irms-12A
SRF-5MHz(typ) RDC-022Ω
Transformers
A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation
Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio
Transformer ndash cont
The current I2 flowing in the secondary winding is inversely proportional
to the current I1 flowing in the primary winding
Moreover the impedance connected to the transformer is transformed by the square of the turns ratio
Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer
Transformers ndash cont
The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit
Examples of low power transformers
Toroidal coretransformer
Toroidal core variabletransformer
(autotransformer)
Laminatedcore EI transformers
Diodes
A diode is a two-terminal electronic component that conducts electric current in only one direction
When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)
Diodes ndash cont
The currentndashvoltage characteristic of a diodeWhere
ID is diode current
If is forward diode current
IFmax is maximum diode
current
UF is forward diode voltage
UR is reverse diode voltage
URmax is the maximum
reverse voltage diodevoltage
Diodes ndash cont
For common types of diodes the value of UF voltage is
bullFor Germanium junction diode 02 04V
bullFor Silicone junction diode 05 08V
bullFor Schottky diode 0204V
An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation
Where I is the diode current
IS is the reverse bias saturation current (or scale current)
VD is the voltage across the diode
VT is the thermal voltage and
n is the ideality factor also known as the quality factor
Diodes ndashcont
The thermal voltage VT is approximately 2585 mV at 300 K
At any other temperature it is given by an equation
where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)
Diodes ndash cont
The typical I-V characteristics of for germaniumand silicone junction diode
Diodes ndash cont
Diode as a switching element
Following the end of forward conduction in a PN type diode a
reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called
reverse recovery time and usually is between tens and hundreds of
ns (ie between 1e-8 and 1e-7 s)
Diodes ndash cont
Diode as a rectifier
A half wave rectifier
A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification
Diodes ndash cont
A full-wave rectifier
This kind of a circuit is also known as the bridge rectifier
Diodes ndash cont
A rectifier in a DC voltage supply
Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge
In general case the simple design rule should be followed
RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)
Diodes ndash cont
Another application ndash diode-based voltage limiter
The cathode of a diode has a potential equal to 4V
U out max = 4V + 06 V = 46 V
If UINlt46V then UOUT = UIN
Bipolar Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals
Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors
B=base C=collector E= emitter
Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases
Transistors ndash cont
The history of the transistor
The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work
The first silicon transistors were produced by Western Electric and TexasInstruments in 1954
Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)
copy wwwporticusorg
Transistors ndash cont
An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased
NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia
The first transistor
copy Bell Labs
Transistor ndash cont
Transistor as an amplifier
A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated
The relations between currents in BJT copy radartutorialeu
Transistor ndash cont
The most often used amplifier circuits
highmediumlowBandwidth4
00001800Phase Shift between input and output signals
3
lt 1highhighCurrent gain2
highlt 1highVoltage gain1
COMMON BASE
COMMON COLLECTOR
COMMON EMITTER
AMPLIFIER
Nr
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Contents ndash cont
3 Passive electronic components
bullResistors
bullCapacitors
bullInductors
bullTransformers
4Active electronic components
bullDiodes
bullBipolar transistors
bullBJT as a switch
bullCommon collector amplifier
bullCommon emitter amplifier
Contents ndash cont
5Operational amplifier
bullThe assumptions of an ideal operational amplifier
bullThe basic circuits
bullA hardware implementation of mathematical operations
bullA Wien sine wave oscillator
bullFunction generator
5
Basic Literature
[1] Horowitz P Hill Wndash The Art of Electronics
[2] Tietze U Schenk Ch Electronic Circuits --- Handbook for Design and Applications 2nd edition 2008 with CD-ROM ISBN 978-3-540-00429-5
[3] Op Amp Applications Handbook (Analog Devices Series) [Paperback] Walt Jung (Author)
[4] Various catalogues and application notes by the compomentsmanufacturers
Fundamental definitions
VoltageVEB ndash the difference of potentials between the points E and
B where VE potential is positive related to VB potential
An example UEB = 07 VUBE = - 07 V
where VE gt VBAn ideal voltage source symbol
Fundamental definitions (cont)
Electric Current ndasha flow of electric charge This flowing
electric charge is typically carried by moving electrons in a conductor such as wire
I
IdQ
dt=
where Q is the electric charge transferred through the surface over some time t If Q and t are measured in coulombs and seconds respectively I is in amperes
Fundamental definitions (cont)
E I
U1=IR1
U2=IR2
U3=IR3
R1
R2
R3
An electric current can flowonly through a closed path called an electric circuit
In order to produce a current flow at least one current source (eg a battery) must be present in the circuit
An ideal currentsource symbol
Fundamental definitions (cont)
Resistance and Ohmrsquos Law
Ohms law states that the current through a conductor between two points is directly proportional to the potential difference or voltage across the two points and inversely proportional to the resistance between them
The mathematical equation that describes this relationship is
R=UI
The unit is Ohm [ Ω ] = [ V ] [ A ]
10
Current flow convention
The electrons in a electrical circuit flow in the opposite direction of the conventional electric current
copyWikipedia
Fundamental definitions (cont)
Kirchhoffs circuit laws
Kirchhoffs current law (KCL)
At any node (junction) in an electrical circuit the sum of currents flowing into that node is equal to the sum of currents flowing out of that node
or
The algebraic sum of currents in a network of conductors meeting at a point is zero
I iisum = 0
Fundamental definitions (cont)
Kirchhoffs voltage law (KVL)
The directed sum of the electrical potential differences (voltage) around any closed circuit is zero
or
More simply the sum of the emfs in any closed loop is equivalent to the sum of the potential drops in that loop IR Ei
isum =
Fundamental definitions (cont)
In circuit theory Theacutevenins theorem for linear electrical networks states that any combination of voltage sources current sources and resistors with two terminals is electrically equivalent to a single voltage source V and a single series resistor R
Theacutevenins theorem
Where UT= open circuit voltage between points A and B
And RT = UTIT where IT is the short circuit current flowing between points A and B
Fundamental definitions (cont)
Electric power
An electric power P is the rate at which electrical energy is transferred by an electric circuit The SI unit of power is the watt In direct current resistive circuits electrical power is calculated using Joules law
P = UI
The unit
[W] = [J] [s] = ([J] [C]) ([C] [s]) [W] = [V][A]
Ohmrsquos law allows us to evaluate an electric power dissipated by a resistor
P = I2 R and respectively P = U2R
Fundamental definitions (cont)
SignalsIn electronics a signal is usually defined as a time-varying voltage or current that conveys information
Sinuisoidal signal
U = Umsin ω t
whereUm - amplitude ω =2πf ndash pulsation[rads]
t ndash time [s] f ndash frequency [Hz]
Other parameters
Vp-p = Peak-to-Peak value
Root-Mean_Square value (RMS)
For sinusoidal signal
Vp-p = 2Um
VRMS=0707Um
dttUT
UT
RMS int=0
2 )(1
Fundamental definitions (cont)
Square wave signal
For this signal URMS=UM
Other parameters
Risetime
Fall time
Highlow amplitude
Please note that real-life signal are not rectangular ie risetime and fall time are always greater than zero
For practical purposes risefall times are usually measured between 10 and 90 of the final value of the signal
Fundamental definitions (cont)
Sawtooth signal (sawtooth wave)
sawtooth wave ramps upward and then sharply drops
Pulses
A rapid transient changes in the amplitude of a signal
Step signals amp glitches
Useful mostly for theoretical analysis
Fundamental definitions (cont)
Decibel gain
The decibel (dB) is a logarithmic unit that indicates the ratio of a physical quantity (usually power or intensity) relative to a specified or implied reference level The decibel ratio of two signals can be expressed by a formula
ku[dB]=20log10(U2U1) where U2 and U1 are the amplitudes of the signals
Examples
ku ku [dB]
01 -20dB
0707 -3dB
1 0dB
141 3dB
10 20dB
100 40dB
1000 60dB
Passive components
Resistors
A resistor is a two-terminal electronic component that produces a voltage across its terminals that is proportional to the electric current through it in accordance with Ohms law
Generic graphic symbol
aMetalized resistor
bWirewound resistor
cCarbon resistor
dResistor ladder
eThick-film resistor
The primary characteristics of a resistor
Resistance (usually expressed in Ω kΩ and MΩ) Tolerance Maximal (rated) power Temperature coefficient of resistance (TCR) Maximal working voltage Parasitic inductance
Series and parallel resistors
The equivalent resistance of tworesistors in series connection
R=R1+R2
The equivalent resistance of tworesistors in parallel connection
1R=1R1+1R2
For n resistors
R=R1+R2+R3+Rn
For n resistors
1R=1R1+1R2+1R3+1Rn
Resistive divider
copy Wikipedia
If R1=R2 then Vout = Vin2
The voltage output of a voltage divider is not fixed but varies according to the load To obtain a reasonably stable output voltage the output current should be a small fraction of the input current
Loaded voltage divider
The voltage between points A and B
U = UT = UINmiddot [R2 (R1 + R2)]
According to Theveninrsquostheorem
RT = (R1 middot R2) (R1+ R2)
In practical projects we often
assume that RL should be 10 times higher than RT
Potentiometers
A potentiometer is a three-terminal resistor with a sliding contact acting as an adjustable voltage divider
Capacitors
copy Wikipedia
A capacitor is a passive electronic component consisting of a pair of conductors separated by a dielectric (insulator)
An ideal capacitor is characterized by a single constant value capacitance measured in farads This is the ratio of the electric charge on each conductor to the potential difference between them
The properties of capacitor are expressed by an equation
C=QU
Where C is capacitance Q is the electriccharge stored inside the capacitor and U is thevoltage between conductors (plates)
Capacitors ndashinternal structure
a) Film capacitor
b) Metalised plastic film capacitor
c) Ceramic disc capacitor
d) Tubular ceramic capacitor
e) Multilayer ceramic capacitor
Supercapacitors
Maxwell Technologies supercapacitors
Ultracapacitor (known also as anelectrochemical double layer capacitor) is an electrochemical capacitor that has a very high energy density when compared to common capacitors typically on the order of thousands of times greater than a high capacity electrolytic capacitor
They are characterized by a very shortcharging time (seconds to minutes)
Possible applications ndash electriccars power tools emergencypower supplies
Supercapacitors ndash cont
Pros very short charging time
Cons relatively high price
Supercapacitors vs standard capacitors
New generation of supercapacitotors
Second generation of supercapacitors by ioxuscom (2010)
From left 220F800F1000F Operating voltage 23V max
copy wwwioxuscom
Capacitors ndash cont
Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)
If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A
Capacitors ndash cont
Most imporant capacitor parameters
bullCapacitance [microF] [nF] or [pF]
bullTolerance []
bullRated voltage [V]
bullDischarge rate (leakage current)
bullTemperature coefficient of capacitance
bullEquivalent series resitance (ESR)
Capacitors ndash cont
a)Aluminium electrolytic capacitor
b)Tantalum electrolytic capacitor
c)Polyesther capacitor
d)Ceramic disc capacitor
e)Mylar capacitor
Capacitors ndash cont
Capacitors in series connection
For two capacitors in series the equivalent capacitance is
For parallel configuration
For two capacitors in parallel the equivalent capacitance is
C=C1+C2
For n capacitors (general case)
Capacitors ndash cont
Capacitor discharge through a resistor
If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge
The discharge rate is expressed by an equation
Where RC is called time constant
Capacitors ndash cont
Capacitor charging through a resistor
If a capacitor C will be charged from source of voltage UWE
through a resistor R the voltage change across its terminals will be described by the following equations
The final solution is
Inductors
An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it
An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material
Graphic symbola) Toroidal core inductor b)cylindrical core inductor
The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L
where L is expressed in H (Henryrsquos) but most often in mH or microH
Inductors ndash cont
Different variations of inductors
Surface mount(SMT) inductors
Cylindricalcoreinductors
Inductor parameters
bullInductance [H]
bullRated voltage [V]
bullTolerance []
bullSaturation DC current [A]
bullMaximal RMS current [A]
bullSelf-resonance frequency [Hz]
bullDC resistance [Ω]
Typical set of parameters
Coilcraft DO3340P-104M inductor
L-100microH tol-20 Isat-25A Irms-12A
SRF-5MHz(typ) RDC-022Ω
Transformers
A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation
Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio
Transformer ndash cont
The current I2 flowing in the secondary winding is inversely proportional
to the current I1 flowing in the primary winding
Moreover the impedance connected to the transformer is transformed by the square of the turns ratio
Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer
Transformers ndash cont
The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit
Examples of low power transformers
Toroidal coretransformer
Toroidal core variabletransformer
(autotransformer)
Laminatedcore EI transformers
Diodes
A diode is a two-terminal electronic component that conducts electric current in only one direction
When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)
Diodes ndash cont
The currentndashvoltage characteristic of a diodeWhere
ID is diode current
If is forward diode current
IFmax is maximum diode
current
UF is forward diode voltage
UR is reverse diode voltage
URmax is the maximum
reverse voltage diodevoltage
Diodes ndash cont
For common types of diodes the value of UF voltage is
bullFor Germanium junction diode 02 04V
bullFor Silicone junction diode 05 08V
bullFor Schottky diode 0204V
An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation
Where I is the diode current
IS is the reverse bias saturation current (or scale current)
VD is the voltage across the diode
VT is the thermal voltage and
n is the ideality factor also known as the quality factor
Diodes ndashcont
The thermal voltage VT is approximately 2585 mV at 300 K
At any other temperature it is given by an equation
where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)
Diodes ndash cont
The typical I-V characteristics of for germaniumand silicone junction diode
Diodes ndash cont
Diode as a switching element
Following the end of forward conduction in a PN type diode a
reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called
reverse recovery time and usually is between tens and hundreds of
ns (ie between 1e-8 and 1e-7 s)
Diodes ndash cont
Diode as a rectifier
A half wave rectifier
A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification
Diodes ndash cont
A full-wave rectifier
This kind of a circuit is also known as the bridge rectifier
Diodes ndash cont
A rectifier in a DC voltage supply
Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge
In general case the simple design rule should be followed
RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)
Diodes ndash cont
Another application ndash diode-based voltage limiter
The cathode of a diode has a potential equal to 4V
U out max = 4V + 06 V = 46 V
If UINlt46V then UOUT = UIN
Bipolar Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals
Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors
B=base C=collector E= emitter
Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases
Transistors ndash cont
The history of the transistor
The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work
The first silicon transistors were produced by Western Electric and TexasInstruments in 1954
Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)
copy wwwporticusorg
Transistors ndash cont
An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased
NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia
The first transistor
copy Bell Labs
Transistor ndash cont
Transistor as an amplifier
A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated
The relations between currents in BJT copy radartutorialeu
Transistor ndash cont
The most often used amplifier circuits
highmediumlowBandwidth4
00001800Phase Shift between input and output signals
3
lt 1highhighCurrent gain2
highlt 1highVoltage gain1
COMMON BASE
COMMON COLLECTOR
COMMON EMITTER
AMPLIFIER
Nr
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Contents ndash cont
5Operational amplifier
bullThe assumptions of an ideal operational amplifier
bullThe basic circuits
bullA hardware implementation of mathematical operations
bullA Wien sine wave oscillator
bullFunction generator
5
Basic Literature
[1] Horowitz P Hill Wndash The Art of Electronics
[2] Tietze U Schenk Ch Electronic Circuits --- Handbook for Design and Applications 2nd edition 2008 with CD-ROM ISBN 978-3-540-00429-5
[3] Op Amp Applications Handbook (Analog Devices Series) [Paperback] Walt Jung (Author)
[4] Various catalogues and application notes by the compomentsmanufacturers
Fundamental definitions
VoltageVEB ndash the difference of potentials between the points E and
B where VE potential is positive related to VB potential
An example UEB = 07 VUBE = - 07 V
where VE gt VBAn ideal voltage source symbol
Fundamental definitions (cont)
Electric Current ndasha flow of electric charge This flowing
electric charge is typically carried by moving electrons in a conductor such as wire
I
IdQ
dt=
where Q is the electric charge transferred through the surface over some time t If Q and t are measured in coulombs and seconds respectively I is in amperes
Fundamental definitions (cont)
E I
U1=IR1
U2=IR2
U3=IR3
R1
R2
R3
An electric current can flowonly through a closed path called an electric circuit
In order to produce a current flow at least one current source (eg a battery) must be present in the circuit
An ideal currentsource symbol
Fundamental definitions (cont)
Resistance and Ohmrsquos Law
Ohms law states that the current through a conductor between two points is directly proportional to the potential difference or voltage across the two points and inversely proportional to the resistance between them
The mathematical equation that describes this relationship is
R=UI
The unit is Ohm [ Ω ] = [ V ] [ A ]
10
Current flow convention
The electrons in a electrical circuit flow in the opposite direction of the conventional electric current
copyWikipedia
Fundamental definitions (cont)
Kirchhoffs circuit laws
Kirchhoffs current law (KCL)
At any node (junction) in an electrical circuit the sum of currents flowing into that node is equal to the sum of currents flowing out of that node
or
The algebraic sum of currents in a network of conductors meeting at a point is zero
I iisum = 0
Fundamental definitions (cont)
Kirchhoffs voltage law (KVL)
The directed sum of the electrical potential differences (voltage) around any closed circuit is zero
or
More simply the sum of the emfs in any closed loop is equivalent to the sum of the potential drops in that loop IR Ei
isum =
Fundamental definitions (cont)
In circuit theory Theacutevenins theorem for linear electrical networks states that any combination of voltage sources current sources and resistors with two terminals is electrically equivalent to a single voltage source V and a single series resistor R
Theacutevenins theorem
Where UT= open circuit voltage between points A and B
And RT = UTIT where IT is the short circuit current flowing between points A and B
Fundamental definitions (cont)
Electric power
An electric power P is the rate at which electrical energy is transferred by an electric circuit The SI unit of power is the watt In direct current resistive circuits electrical power is calculated using Joules law
P = UI
The unit
[W] = [J] [s] = ([J] [C]) ([C] [s]) [W] = [V][A]
Ohmrsquos law allows us to evaluate an electric power dissipated by a resistor
P = I2 R and respectively P = U2R
Fundamental definitions (cont)
SignalsIn electronics a signal is usually defined as a time-varying voltage or current that conveys information
Sinuisoidal signal
U = Umsin ω t
whereUm - amplitude ω =2πf ndash pulsation[rads]
t ndash time [s] f ndash frequency [Hz]
Other parameters
Vp-p = Peak-to-Peak value
Root-Mean_Square value (RMS)
For sinusoidal signal
Vp-p = 2Um
VRMS=0707Um
dttUT
UT
RMS int=0
2 )(1
Fundamental definitions (cont)
Square wave signal
For this signal URMS=UM
Other parameters
Risetime
Fall time
Highlow amplitude
Please note that real-life signal are not rectangular ie risetime and fall time are always greater than zero
For practical purposes risefall times are usually measured between 10 and 90 of the final value of the signal
Fundamental definitions (cont)
Sawtooth signal (sawtooth wave)
sawtooth wave ramps upward and then sharply drops
Pulses
A rapid transient changes in the amplitude of a signal
Step signals amp glitches
Useful mostly for theoretical analysis
Fundamental definitions (cont)
Decibel gain
The decibel (dB) is a logarithmic unit that indicates the ratio of a physical quantity (usually power or intensity) relative to a specified or implied reference level The decibel ratio of two signals can be expressed by a formula
ku[dB]=20log10(U2U1) where U2 and U1 are the amplitudes of the signals
Examples
ku ku [dB]
01 -20dB
0707 -3dB
1 0dB
141 3dB
10 20dB
100 40dB
1000 60dB
Passive components
Resistors
A resistor is a two-terminal electronic component that produces a voltage across its terminals that is proportional to the electric current through it in accordance with Ohms law
Generic graphic symbol
aMetalized resistor
bWirewound resistor
cCarbon resistor
dResistor ladder
eThick-film resistor
The primary characteristics of a resistor
Resistance (usually expressed in Ω kΩ and MΩ) Tolerance Maximal (rated) power Temperature coefficient of resistance (TCR) Maximal working voltage Parasitic inductance
Series and parallel resistors
The equivalent resistance of tworesistors in series connection
R=R1+R2
The equivalent resistance of tworesistors in parallel connection
1R=1R1+1R2
For n resistors
R=R1+R2+R3+Rn
For n resistors
1R=1R1+1R2+1R3+1Rn
Resistive divider
copy Wikipedia
If R1=R2 then Vout = Vin2
The voltage output of a voltage divider is not fixed but varies according to the load To obtain a reasonably stable output voltage the output current should be a small fraction of the input current
Loaded voltage divider
The voltage between points A and B
U = UT = UINmiddot [R2 (R1 + R2)]
According to Theveninrsquostheorem
RT = (R1 middot R2) (R1+ R2)
In practical projects we often
assume that RL should be 10 times higher than RT
Potentiometers
A potentiometer is a three-terminal resistor with a sliding contact acting as an adjustable voltage divider
Capacitors
copy Wikipedia
A capacitor is a passive electronic component consisting of a pair of conductors separated by a dielectric (insulator)
An ideal capacitor is characterized by a single constant value capacitance measured in farads This is the ratio of the electric charge on each conductor to the potential difference between them
The properties of capacitor are expressed by an equation
C=QU
Where C is capacitance Q is the electriccharge stored inside the capacitor and U is thevoltage between conductors (plates)
Capacitors ndashinternal structure
a) Film capacitor
b) Metalised plastic film capacitor
c) Ceramic disc capacitor
d) Tubular ceramic capacitor
e) Multilayer ceramic capacitor
Supercapacitors
Maxwell Technologies supercapacitors
Ultracapacitor (known also as anelectrochemical double layer capacitor) is an electrochemical capacitor that has a very high energy density when compared to common capacitors typically on the order of thousands of times greater than a high capacity electrolytic capacitor
They are characterized by a very shortcharging time (seconds to minutes)
Possible applications ndash electriccars power tools emergencypower supplies
Supercapacitors ndash cont
Pros very short charging time
Cons relatively high price
Supercapacitors vs standard capacitors
New generation of supercapacitotors
Second generation of supercapacitors by ioxuscom (2010)
From left 220F800F1000F Operating voltage 23V max
copy wwwioxuscom
Capacitors ndash cont
Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)
If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A
Capacitors ndash cont
Most imporant capacitor parameters
bullCapacitance [microF] [nF] or [pF]
bullTolerance []
bullRated voltage [V]
bullDischarge rate (leakage current)
bullTemperature coefficient of capacitance
bullEquivalent series resitance (ESR)
Capacitors ndash cont
a)Aluminium electrolytic capacitor
b)Tantalum electrolytic capacitor
c)Polyesther capacitor
d)Ceramic disc capacitor
e)Mylar capacitor
Capacitors ndash cont
Capacitors in series connection
For two capacitors in series the equivalent capacitance is
For parallel configuration
For two capacitors in parallel the equivalent capacitance is
C=C1+C2
For n capacitors (general case)
Capacitors ndash cont
Capacitor discharge through a resistor
If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge
The discharge rate is expressed by an equation
Where RC is called time constant
Capacitors ndash cont
Capacitor charging through a resistor
If a capacitor C will be charged from source of voltage UWE
through a resistor R the voltage change across its terminals will be described by the following equations
The final solution is
Inductors
An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it
An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material
Graphic symbola) Toroidal core inductor b)cylindrical core inductor
The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L
where L is expressed in H (Henryrsquos) but most often in mH or microH
Inductors ndash cont
Different variations of inductors
Surface mount(SMT) inductors
Cylindricalcoreinductors
Inductor parameters
bullInductance [H]
bullRated voltage [V]
bullTolerance []
bullSaturation DC current [A]
bullMaximal RMS current [A]
bullSelf-resonance frequency [Hz]
bullDC resistance [Ω]
Typical set of parameters
Coilcraft DO3340P-104M inductor
L-100microH tol-20 Isat-25A Irms-12A
SRF-5MHz(typ) RDC-022Ω
Transformers
A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation
Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio
Transformer ndash cont
The current I2 flowing in the secondary winding is inversely proportional
to the current I1 flowing in the primary winding
Moreover the impedance connected to the transformer is transformed by the square of the turns ratio
Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer
Transformers ndash cont
The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit
Examples of low power transformers
Toroidal coretransformer
Toroidal core variabletransformer
(autotransformer)
Laminatedcore EI transformers
Diodes
A diode is a two-terminal electronic component that conducts electric current in only one direction
When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)
Diodes ndash cont
The currentndashvoltage characteristic of a diodeWhere
ID is diode current
If is forward diode current
IFmax is maximum diode
current
UF is forward diode voltage
UR is reverse diode voltage
URmax is the maximum
reverse voltage diodevoltage
Diodes ndash cont
For common types of diodes the value of UF voltage is
bullFor Germanium junction diode 02 04V
bullFor Silicone junction diode 05 08V
bullFor Schottky diode 0204V
An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation
Where I is the diode current
IS is the reverse bias saturation current (or scale current)
VD is the voltage across the diode
VT is the thermal voltage and
n is the ideality factor also known as the quality factor
Diodes ndashcont
The thermal voltage VT is approximately 2585 mV at 300 K
At any other temperature it is given by an equation
where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)
Diodes ndash cont
The typical I-V characteristics of for germaniumand silicone junction diode
Diodes ndash cont
Diode as a switching element
Following the end of forward conduction in a PN type diode a
reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called
reverse recovery time and usually is between tens and hundreds of
ns (ie between 1e-8 and 1e-7 s)
Diodes ndash cont
Diode as a rectifier
A half wave rectifier
A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification
Diodes ndash cont
A full-wave rectifier
This kind of a circuit is also known as the bridge rectifier
Diodes ndash cont
A rectifier in a DC voltage supply
Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge
In general case the simple design rule should be followed
RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)
Diodes ndash cont
Another application ndash diode-based voltage limiter
The cathode of a diode has a potential equal to 4V
U out max = 4V + 06 V = 46 V
If UINlt46V then UOUT = UIN
Bipolar Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals
Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors
B=base C=collector E= emitter
Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases
Transistors ndash cont
The history of the transistor
The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work
The first silicon transistors were produced by Western Electric and TexasInstruments in 1954
Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)
copy wwwporticusorg
Transistors ndash cont
An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased
NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia
The first transistor
copy Bell Labs
Transistor ndash cont
Transistor as an amplifier
A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated
The relations between currents in BJT copy radartutorialeu
Transistor ndash cont
The most often used amplifier circuits
highmediumlowBandwidth4
00001800Phase Shift between input and output signals
3
lt 1highhighCurrent gain2
highlt 1highVoltage gain1
COMMON BASE
COMMON COLLECTOR
COMMON EMITTER
AMPLIFIER
Nr
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
5
Basic Literature
[1] Horowitz P Hill Wndash The Art of Electronics
[2] Tietze U Schenk Ch Electronic Circuits --- Handbook for Design and Applications 2nd edition 2008 with CD-ROM ISBN 978-3-540-00429-5
[3] Op Amp Applications Handbook (Analog Devices Series) [Paperback] Walt Jung (Author)
[4] Various catalogues and application notes by the compomentsmanufacturers
Fundamental definitions
VoltageVEB ndash the difference of potentials between the points E and
B where VE potential is positive related to VB potential
An example UEB = 07 VUBE = - 07 V
where VE gt VBAn ideal voltage source symbol
Fundamental definitions (cont)
Electric Current ndasha flow of electric charge This flowing
electric charge is typically carried by moving electrons in a conductor such as wire
I
IdQ
dt=
where Q is the electric charge transferred through the surface over some time t If Q and t are measured in coulombs and seconds respectively I is in amperes
Fundamental definitions (cont)
E I
U1=IR1
U2=IR2
U3=IR3
R1
R2
R3
An electric current can flowonly through a closed path called an electric circuit
In order to produce a current flow at least one current source (eg a battery) must be present in the circuit
An ideal currentsource symbol
Fundamental definitions (cont)
Resistance and Ohmrsquos Law
Ohms law states that the current through a conductor between two points is directly proportional to the potential difference or voltage across the two points and inversely proportional to the resistance between them
The mathematical equation that describes this relationship is
R=UI
The unit is Ohm [ Ω ] = [ V ] [ A ]
10
Current flow convention
The electrons in a electrical circuit flow in the opposite direction of the conventional electric current
copyWikipedia
Fundamental definitions (cont)
Kirchhoffs circuit laws
Kirchhoffs current law (KCL)
At any node (junction) in an electrical circuit the sum of currents flowing into that node is equal to the sum of currents flowing out of that node
or
The algebraic sum of currents in a network of conductors meeting at a point is zero
I iisum = 0
Fundamental definitions (cont)
Kirchhoffs voltage law (KVL)
The directed sum of the electrical potential differences (voltage) around any closed circuit is zero
or
More simply the sum of the emfs in any closed loop is equivalent to the sum of the potential drops in that loop IR Ei
isum =
Fundamental definitions (cont)
In circuit theory Theacutevenins theorem for linear electrical networks states that any combination of voltage sources current sources and resistors with two terminals is electrically equivalent to a single voltage source V and a single series resistor R
Theacutevenins theorem
Where UT= open circuit voltage between points A and B
And RT = UTIT where IT is the short circuit current flowing between points A and B
Fundamental definitions (cont)
Electric power
An electric power P is the rate at which electrical energy is transferred by an electric circuit The SI unit of power is the watt In direct current resistive circuits electrical power is calculated using Joules law
P = UI
The unit
[W] = [J] [s] = ([J] [C]) ([C] [s]) [W] = [V][A]
Ohmrsquos law allows us to evaluate an electric power dissipated by a resistor
P = I2 R and respectively P = U2R
Fundamental definitions (cont)
SignalsIn electronics a signal is usually defined as a time-varying voltage or current that conveys information
Sinuisoidal signal
U = Umsin ω t
whereUm - amplitude ω =2πf ndash pulsation[rads]
t ndash time [s] f ndash frequency [Hz]
Other parameters
Vp-p = Peak-to-Peak value
Root-Mean_Square value (RMS)
For sinusoidal signal
Vp-p = 2Um
VRMS=0707Um
dttUT
UT
RMS int=0
2 )(1
Fundamental definitions (cont)
Square wave signal
For this signal URMS=UM
Other parameters
Risetime
Fall time
Highlow amplitude
Please note that real-life signal are not rectangular ie risetime and fall time are always greater than zero
For practical purposes risefall times are usually measured between 10 and 90 of the final value of the signal
Fundamental definitions (cont)
Sawtooth signal (sawtooth wave)
sawtooth wave ramps upward and then sharply drops
Pulses
A rapid transient changes in the amplitude of a signal
Step signals amp glitches
Useful mostly for theoretical analysis
Fundamental definitions (cont)
Decibel gain
The decibel (dB) is a logarithmic unit that indicates the ratio of a physical quantity (usually power or intensity) relative to a specified or implied reference level The decibel ratio of two signals can be expressed by a formula
ku[dB]=20log10(U2U1) where U2 and U1 are the amplitudes of the signals
Examples
ku ku [dB]
01 -20dB
0707 -3dB
1 0dB
141 3dB
10 20dB
100 40dB
1000 60dB
Passive components
Resistors
A resistor is a two-terminal electronic component that produces a voltage across its terminals that is proportional to the electric current through it in accordance with Ohms law
Generic graphic symbol
aMetalized resistor
bWirewound resistor
cCarbon resistor
dResistor ladder
eThick-film resistor
The primary characteristics of a resistor
Resistance (usually expressed in Ω kΩ and MΩ) Tolerance Maximal (rated) power Temperature coefficient of resistance (TCR) Maximal working voltage Parasitic inductance
Series and parallel resistors
The equivalent resistance of tworesistors in series connection
R=R1+R2
The equivalent resistance of tworesistors in parallel connection
1R=1R1+1R2
For n resistors
R=R1+R2+R3+Rn
For n resistors
1R=1R1+1R2+1R3+1Rn
Resistive divider
copy Wikipedia
If R1=R2 then Vout = Vin2
The voltage output of a voltage divider is not fixed but varies according to the load To obtain a reasonably stable output voltage the output current should be a small fraction of the input current
Loaded voltage divider
The voltage between points A and B
U = UT = UINmiddot [R2 (R1 + R2)]
According to Theveninrsquostheorem
RT = (R1 middot R2) (R1+ R2)
In practical projects we often
assume that RL should be 10 times higher than RT
Potentiometers
A potentiometer is a three-terminal resistor with a sliding contact acting as an adjustable voltage divider
Capacitors
copy Wikipedia
A capacitor is a passive electronic component consisting of a pair of conductors separated by a dielectric (insulator)
An ideal capacitor is characterized by a single constant value capacitance measured in farads This is the ratio of the electric charge on each conductor to the potential difference between them
The properties of capacitor are expressed by an equation
C=QU
Where C is capacitance Q is the electriccharge stored inside the capacitor and U is thevoltage between conductors (plates)
Capacitors ndashinternal structure
a) Film capacitor
b) Metalised plastic film capacitor
c) Ceramic disc capacitor
d) Tubular ceramic capacitor
e) Multilayer ceramic capacitor
Supercapacitors
Maxwell Technologies supercapacitors
Ultracapacitor (known also as anelectrochemical double layer capacitor) is an electrochemical capacitor that has a very high energy density when compared to common capacitors typically on the order of thousands of times greater than a high capacity electrolytic capacitor
They are characterized by a very shortcharging time (seconds to minutes)
Possible applications ndash electriccars power tools emergencypower supplies
Supercapacitors ndash cont
Pros very short charging time
Cons relatively high price
Supercapacitors vs standard capacitors
New generation of supercapacitotors
Second generation of supercapacitors by ioxuscom (2010)
From left 220F800F1000F Operating voltage 23V max
copy wwwioxuscom
Capacitors ndash cont
Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)
If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A
Capacitors ndash cont
Most imporant capacitor parameters
bullCapacitance [microF] [nF] or [pF]
bullTolerance []
bullRated voltage [V]
bullDischarge rate (leakage current)
bullTemperature coefficient of capacitance
bullEquivalent series resitance (ESR)
Capacitors ndash cont
a)Aluminium electrolytic capacitor
b)Tantalum electrolytic capacitor
c)Polyesther capacitor
d)Ceramic disc capacitor
e)Mylar capacitor
Capacitors ndash cont
Capacitors in series connection
For two capacitors in series the equivalent capacitance is
For parallel configuration
For two capacitors in parallel the equivalent capacitance is
C=C1+C2
For n capacitors (general case)
Capacitors ndash cont
Capacitor discharge through a resistor
If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge
The discharge rate is expressed by an equation
Where RC is called time constant
Capacitors ndash cont
Capacitor charging through a resistor
If a capacitor C will be charged from source of voltage UWE
through a resistor R the voltage change across its terminals will be described by the following equations
The final solution is
Inductors
An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it
An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material
Graphic symbola) Toroidal core inductor b)cylindrical core inductor
The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L
where L is expressed in H (Henryrsquos) but most often in mH or microH
Inductors ndash cont
Different variations of inductors
Surface mount(SMT) inductors
Cylindricalcoreinductors
Inductor parameters
bullInductance [H]
bullRated voltage [V]
bullTolerance []
bullSaturation DC current [A]
bullMaximal RMS current [A]
bullSelf-resonance frequency [Hz]
bullDC resistance [Ω]
Typical set of parameters
Coilcraft DO3340P-104M inductor
L-100microH tol-20 Isat-25A Irms-12A
SRF-5MHz(typ) RDC-022Ω
Transformers
A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation
Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio
Transformer ndash cont
The current I2 flowing in the secondary winding is inversely proportional
to the current I1 flowing in the primary winding
Moreover the impedance connected to the transformer is transformed by the square of the turns ratio
Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer
Transformers ndash cont
The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit
Examples of low power transformers
Toroidal coretransformer
Toroidal core variabletransformer
(autotransformer)
Laminatedcore EI transformers
Diodes
A diode is a two-terminal electronic component that conducts electric current in only one direction
When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)
Diodes ndash cont
The currentndashvoltage characteristic of a diodeWhere
ID is diode current
If is forward diode current
IFmax is maximum diode
current
UF is forward diode voltage
UR is reverse diode voltage
URmax is the maximum
reverse voltage diodevoltage
Diodes ndash cont
For common types of diodes the value of UF voltage is
bullFor Germanium junction diode 02 04V
bullFor Silicone junction diode 05 08V
bullFor Schottky diode 0204V
An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation
Where I is the diode current
IS is the reverse bias saturation current (or scale current)
VD is the voltage across the diode
VT is the thermal voltage and
n is the ideality factor also known as the quality factor
Diodes ndashcont
The thermal voltage VT is approximately 2585 mV at 300 K
At any other temperature it is given by an equation
where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)
Diodes ndash cont
The typical I-V characteristics of for germaniumand silicone junction diode
Diodes ndash cont
Diode as a switching element
Following the end of forward conduction in a PN type diode a
reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called
reverse recovery time and usually is between tens and hundreds of
ns (ie between 1e-8 and 1e-7 s)
Diodes ndash cont
Diode as a rectifier
A half wave rectifier
A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification
Diodes ndash cont
A full-wave rectifier
This kind of a circuit is also known as the bridge rectifier
Diodes ndash cont
A rectifier in a DC voltage supply
Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge
In general case the simple design rule should be followed
RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)
Diodes ndash cont
Another application ndash diode-based voltage limiter
The cathode of a diode has a potential equal to 4V
U out max = 4V + 06 V = 46 V
If UINlt46V then UOUT = UIN
Bipolar Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals
Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors
B=base C=collector E= emitter
Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases
Transistors ndash cont
The history of the transistor
The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work
The first silicon transistors were produced by Western Electric and TexasInstruments in 1954
Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)
copy wwwporticusorg
Transistors ndash cont
An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased
NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia
The first transistor
copy Bell Labs
Transistor ndash cont
Transistor as an amplifier
A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated
The relations between currents in BJT copy radartutorialeu
Transistor ndash cont
The most often used amplifier circuits
highmediumlowBandwidth4
00001800Phase Shift between input and output signals
3
lt 1highhighCurrent gain2
highlt 1highVoltage gain1
COMMON BASE
COMMON COLLECTOR
COMMON EMITTER
AMPLIFIER
Nr
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Fundamental definitions
VoltageVEB ndash the difference of potentials between the points E and
B where VE potential is positive related to VB potential
An example UEB = 07 VUBE = - 07 V
where VE gt VBAn ideal voltage source symbol
Fundamental definitions (cont)
Electric Current ndasha flow of electric charge This flowing
electric charge is typically carried by moving electrons in a conductor such as wire
I
IdQ
dt=
where Q is the electric charge transferred through the surface over some time t If Q and t are measured in coulombs and seconds respectively I is in amperes
Fundamental definitions (cont)
E I
U1=IR1
U2=IR2
U3=IR3
R1
R2
R3
An electric current can flowonly through a closed path called an electric circuit
In order to produce a current flow at least one current source (eg a battery) must be present in the circuit
An ideal currentsource symbol
Fundamental definitions (cont)
Resistance and Ohmrsquos Law
Ohms law states that the current through a conductor between two points is directly proportional to the potential difference or voltage across the two points and inversely proportional to the resistance between them
The mathematical equation that describes this relationship is
R=UI
The unit is Ohm [ Ω ] = [ V ] [ A ]
10
Current flow convention
The electrons in a electrical circuit flow in the opposite direction of the conventional electric current
copyWikipedia
Fundamental definitions (cont)
Kirchhoffs circuit laws
Kirchhoffs current law (KCL)
At any node (junction) in an electrical circuit the sum of currents flowing into that node is equal to the sum of currents flowing out of that node
or
The algebraic sum of currents in a network of conductors meeting at a point is zero
I iisum = 0
Fundamental definitions (cont)
Kirchhoffs voltage law (KVL)
The directed sum of the electrical potential differences (voltage) around any closed circuit is zero
or
More simply the sum of the emfs in any closed loop is equivalent to the sum of the potential drops in that loop IR Ei
isum =
Fundamental definitions (cont)
In circuit theory Theacutevenins theorem for linear electrical networks states that any combination of voltage sources current sources and resistors with two terminals is electrically equivalent to a single voltage source V and a single series resistor R
Theacutevenins theorem
Where UT= open circuit voltage between points A and B
And RT = UTIT where IT is the short circuit current flowing between points A and B
Fundamental definitions (cont)
Electric power
An electric power P is the rate at which electrical energy is transferred by an electric circuit The SI unit of power is the watt In direct current resistive circuits electrical power is calculated using Joules law
P = UI
The unit
[W] = [J] [s] = ([J] [C]) ([C] [s]) [W] = [V][A]
Ohmrsquos law allows us to evaluate an electric power dissipated by a resistor
P = I2 R and respectively P = U2R
Fundamental definitions (cont)
SignalsIn electronics a signal is usually defined as a time-varying voltage or current that conveys information
Sinuisoidal signal
U = Umsin ω t
whereUm - amplitude ω =2πf ndash pulsation[rads]
t ndash time [s] f ndash frequency [Hz]
Other parameters
Vp-p = Peak-to-Peak value
Root-Mean_Square value (RMS)
For sinusoidal signal
Vp-p = 2Um
VRMS=0707Um
dttUT
UT
RMS int=0
2 )(1
Fundamental definitions (cont)
Square wave signal
For this signal URMS=UM
Other parameters
Risetime
Fall time
Highlow amplitude
Please note that real-life signal are not rectangular ie risetime and fall time are always greater than zero
For practical purposes risefall times are usually measured between 10 and 90 of the final value of the signal
Fundamental definitions (cont)
Sawtooth signal (sawtooth wave)
sawtooth wave ramps upward and then sharply drops
Pulses
A rapid transient changes in the amplitude of a signal
Step signals amp glitches
Useful mostly for theoretical analysis
Fundamental definitions (cont)
Decibel gain
The decibel (dB) is a logarithmic unit that indicates the ratio of a physical quantity (usually power or intensity) relative to a specified or implied reference level The decibel ratio of two signals can be expressed by a formula
ku[dB]=20log10(U2U1) where U2 and U1 are the amplitudes of the signals
Examples
ku ku [dB]
01 -20dB
0707 -3dB
1 0dB
141 3dB
10 20dB
100 40dB
1000 60dB
Passive components
Resistors
A resistor is a two-terminal electronic component that produces a voltage across its terminals that is proportional to the electric current through it in accordance with Ohms law
Generic graphic symbol
aMetalized resistor
bWirewound resistor
cCarbon resistor
dResistor ladder
eThick-film resistor
The primary characteristics of a resistor
Resistance (usually expressed in Ω kΩ and MΩ) Tolerance Maximal (rated) power Temperature coefficient of resistance (TCR) Maximal working voltage Parasitic inductance
Series and parallel resistors
The equivalent resistance of tworesistors in series connection
R=R1+R2
The equivalent resistance of tworesistors in parallel connection
1R=1R1+1R2
For n resistors
R=R1+R2+R3+Rn
For n resistors
1R=1R1+1R2+1R3+1Rn
Resistive divider
copy Wikipedia
If R1=R2 then Vout = Vin2
The voltage output of a voltage divider is not fixed but varies according to the load To obtain a reasonably stable output voltage the output current should be a small fraction of the input current
Loaded voltage divider
The voltage between points A and B
U = UT = UINmiddot [R2 (R1 + R2)]
According to Theveninrsquostheorem
RT = (R1 middot R2) (R1+ R2)
In practical projects we often
assume that RL should be 10 times higher than RT
Potentiometers
A potentiometer is a three-terminal resistor with a sliding contact acting as an adjustable voltage divider
Capacitors
copy Wikipedia
A capacitor is a passive electronic component consisting of a pair of conductors separated by a dielectric (insulator)
An ideal capacitor is characterized by a single constant value capacitance measured in farads This is the ratio of the electric charge on each conductor to the potential difference between them
The properties of capacitor are expressed by an equation
C=QU
Where C is capacitance Q is the electriccharge stored inside the capacitor and U is thevoltage between conductors (plates)
Capacitors ndashinternal structure
a) Film capacitor
b) Metalised plastic film capacitor
c) Ceramic disc capacitor
d) Tubular ceramic capacitor
e) Multilayer ceramic capacitor
Supercapacitors
Maxwell Technologies supercapacitors
Ultracapacitor (known also as anelectrochemical double layer capacitor) is an electrochemical capacitor that has a very high energy density when compared to common capacitors typically on the order of thousands of times greater than a high capacity electrolytic capacitor
They are characterized by a very shortcharging time (seconds to minutes)
Possible applications ndash electriccars power tools emergencypower supplies
Supercapacitors ndash cont
Pros very short charging time
Cons relatively high price
Supercapacitors vs standard capacitors
New generation of supercapacitotors
Second generation of supercapacitors by ioxuscom (2010)
From left 220F800F1000F Operating voltage 23V max
copy wwwioxuscom
Capacitors ndash cont
Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)
If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A
Capacitors ndash cont
Most imporant capacitor parameters
bullCapacitance [microF] [nF] or [pF]
bullTolerance []
bullRated voltage [V]
bullDischarge rate (leakage current)
bullTemperature coefficient of capacitance
bullEquivalent series resitance (ESR)
Capacitors ndash cont
a)Aluminium electrolytic capacitor
b)Tantalum electrolytic capacitor
c)Polyesther capacitor
d)Ceramic disc capacitor
e)Mylar capacitor
Capacitors ndash cont
Capacitors in series connection
For two capacitors in series the equivalent capacitance is
For parallel configuration
For two capacitors in parallel the equivalent capacitance is
C=C1+C2
For n capacitors (general case)
Capacitors ndash cont
Capacitor discharge through a resistor
If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge
The discharge rate is expressed by an equation
Where RC is called time constant
Capacitors ndash cont
Capacitor charging through a resistor
If a capacitor C will be charged from source of voltage UWE
through a resistor R the voltage change across its terminals will be described by the following equations
The final solution is
Inductors
An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it
An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material
Graphic symbola) Toroidal core inductor b)cylindrical core inductor
The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L
where L is expressed in H (Henryrsquos) but most often in mH or microH
Inductors ndash cont
Different variations of inductors
Surface mount(SMT) inductors
Cylindricalcoreinductors
Inductor parameters
bullInductance [H]
bullRated voltage [V]
bullTolerance []
bullSaturation DC current [A]
bullMaximal RMS current [A]
bullSelf-resonance frequency [Hz]
bullDC resistance [Ω]
Typical set of parameters
Coilcraft DO3340P-104M inductor
L-100microH tol-20 Isat-25A Irms-12A
SRF-5MHz(typ) RDC-022Ω
Transformers
A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation
Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio
Transformer ndash cont
The current I2 flowing in the secondary winding is inversely proportional
to the current I1 flowing in the primary winding
Moreover the impedance connected to the transformer is transformed by the square of the turns ratio
Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer
Transformers ndash cont
The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit
Examples of low power transformers
Toroidal coretransformer
Toroidal core variabletransformer
(autotransformer)
Laminatedcore EI transformers
Diodes
A diode is a two-terminal electronic component that conducts electric current in only one direction
When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)
Diodes ndash cont
The currentndashvoltage characteristic of a diodeWhere
ID is diode current
If is forward diode current
IFmax is maximum diode
current
UF is forward diode voltage
UR is reverse diode voltage
URmax is the maximum
reverse voltage diodevoltage
Diodes ndash cont
For common types of diodes the value of UF voltage is
bullFor Germanium junction diode 02 04V
bullFor Silicone junction diode 05 08V
bullFor Schottky diode 0204V
An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation
Where I is the diode current
IS is the reverse bias saturation current (or scale current)
VD is the voltage across the diode
VT is the thermal voltage and
n is the ideality factor also known as the quality factor
Diodes ndashcont
The thermal voltage VT is approximately 2585 mV at 300 K
At any other temperature it is given by an equation
where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)
Diodes ndash cont
The typical I-V characteristics of for germaniumand silicone junction diode
Diodes ndash cont
Diode as a switching element
Following the end of forward conduction in a PN type diode a
reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called
reverse recovery time and usually is between tens and hundreds of
ns (ie between 1e-8 and 1e-7 s)
Diodes ndash cont
Diode as a rectifier
A half wave rectifier
A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification
Diodes ndash cont
A full-wave rectifier
This kind of a circuit is also known as the bridge rectifier
Diodes ndash cont
A rectifier in a DC voltage supply
Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge
In general case the simple design rule should be followed
RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)
Diodes ndash cont
Another application ndash diode-based voltage limiter
The cathode of a diode has a potential equal to 4V
U out max = 4V + 06 V = 46 V
If UINlt46V then UOUT = UIN
Bipolar Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals
Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors
B=base C=collector E= emitter
Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases
Transistors ndash cont
The history of the transistor
The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work
The first silicon transistors were produced by Western Electric and TexasInstruments in 1954
Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)
copy wwwporticusorg
Transistors ndash cont
An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased
NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia
The first transistor
copy Bell Labs
Transistor ndash cont
Transistor as an amplifier
A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated
The relations between currents in BJT copy radartutorialeu
Transistor ndash cont
The most often used amplifier circuits
highmediumlowBandwidth4
00001800Phase Shift between input and output signals
3
lt 1highhighCurrent gain2
highlt 1highVoltage gain1
COMMON BASE
COMMON COLLECTOR
COMMON EMITTER
AMPLIFIER
Nr
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Fundamental definitions (cont)
Electric Current ndasha flow of electric charge This flowing
electric charge is typically carried by moving electrons in a conductor such as wire
I
IdQ
dt=
where Q is the electric charge transferred through the surface over some time t If Q and t are measured in coulombs and seconds respectively I is in amperes
Fundamental definitions (cont)
E I
U1=IR1
U2=IR2
U3=IR3
R1
R2
R3
An electric current can flowonly through a closed path called an electric circuit
In order to produce a current flow at least one current source (eg a battery) must be present in the circuit
An ideal currentsource symbol
Fundamental definitions (cont)
Resistance and Ohmrsquos Law
Ohms law states that the current through a conductor between two points is directly proportional to the potential difference or voltage across the two points and inversely proportional to the resistance between them
The mathematical equation that describes this relationship is
R=UI
The unit is Ohm [ Ω ] = [ V ] [ A ]
10
Current flow convention
The electrons in a electrical circuit flow in the opposite direction of the conventional electric current
copyWikipedia
Fundamental definitions (cont)
Kirchhoffs circuit laws
Kirchhoffs current law (KCL)
At any node (junction) in an electrical circuit the sum of currents flowing into that node is equal to the sum of currents flowing out of that node
or
The algebraic sum of currents in a network of conductors meeting at a point is zero
I iisum = 0
Fundamental definitions (cont)
Kirchhoffs voltage law (KVL)
The directed sum of the electrical potential differences (voltage) around any closed circuit is zero
or
More simply the sum of the emfs in any closed loop is equivalent to the sum of the potential drops in that loop IR Ei
isum =
Fundamental definitions (cont)
In circuit theory Theacutevenins theorem for linear electrical networks states that any combination of voltage sources current sources and resistors with two terminals is electrically equivalent to a single voltage source V and a single series resistor R
Theacutevenins theorem
Where UT= open circuit voltage between points A and B
And RT = UTIT where IT is the short circuit current flowing between points A and B
Fundamental definitions (cont)
Electric power
An electric power P is the rate at which electrical energy is transferred by an electric circuit The SI unit of power is the watt In direct current resistive circuits electrical power is calculated using Joules law
P = UI
The unit
[W] = [J] [s] = ([J] [C]) ([C] [s]) [W] = [V][A]
Ohmrsquos law allows us to evaluate an electric power dissipated by a resistor
P = I2 R and respectively P = U2R
Fundamental definitions (cont)
SignalsIn electronics a signal is usually defined as a time-varying voltage or current that conveys information
Sinuisoidal signal
U = Umsin ω t
whereUm - amplitude ω =2πf ndash pulsation[rads]
t ndash time [s] f ndash frequency [Hz]
Other parameters
Vp-p = Peak-to-Peak value
Root-Mean_Square value (RMS)
For sinusoidal signal
Vp-p = 2Um
VRMS=0707Um
dttUT
UT
RMS int=0
2 )(1
Fundamental definitions (cont)
Square wave signal
For this signal URMS=UM
Other parameters
Risetime
Fall time
Highlow amplitude
Please note that real-life signal are not rectangular ie risetime and fall time are always greater than zero
For practical purposes risefall times are usually measured between 10 and 90 of the final value of the signal
Fundamental definitions (cont)
Sawtooth signal (sawtooth wave)
sawtooth wave ramps upward and then sharply drops
Pulses
A rapid transient changes in the amplitude of a signal
Step signals amp glitches
Useful mostly for theoretical analysis
Fundamental definitions (cont)
Decibel gain
The decibel (dB) is a logarithmic unit that indicates the ratio of a physical quantity (usually power or intensity) relative to a specified or implied reference level The decibel ratio of two signals can be expressed by a formula
ku[dB]=20log10(U2U1) where U2 and U1 are the amplitudes of the signals
Examples
ku ku [dB]
01 -20dB
0707 -3dB
1 0dB
141 3dB
10 20dB
100 40dB
1000 60dB
Passive components
Resistors
A resistor is a two-terminal electronic component that produces a voltage across its terminals that is proportional to the electric current through it in accordance with Ohms law
Generic graphic symbol
aMetalized resistor
bWirewound resistor
cCarbon resistor
dResistor ladder
eThick-film resistor
The primary characteristics of a resistor
Resistance (usually expressed in Ω kΩ and MΩ) Tolerance Maximal (rated) power Temperature coefficient of resistance (TCR) Maximal working voltage Parasitic inductance
Series and parallel resistors
The equivalent resistance of tworesistors in series connection
R=R1+R2
The equivalent resistance of tworesistors in parallel connection
1R=1R1+1R2
For n resistors
R=R1+R2+R3+Rn
For n resistors
1R=1R1+1R2+1R3+1Rn
Resistive divider
copy Wikipedia
If R1=R2 then Vout = Vin2
The voltage output of a voltage divider is not fixed but varies according to the load To obtain a reasonably stable output voltage the output current should be a small fraction of the input current
Loaded voltage divider
The voltage between points A and B
U = UT = UINmiddot [R2 (R1 + R2)]
According to Theveninrsquostheorem
RT = (R1 middot R2) (R1+ R2)
In practical projects we often
assume that RL should be 10 times higher than RT
Potentiometers
A potentiometer is a three-terminal resistor with a sliding contact acting as an adjustable voltage divider
Capacitors
copy Wikipedia
A capacitor is a passive electronic component consisting of a pair of conductors separated by a dielectric (insulator)
An ideal capacitor is characterized by a single constant value capacitance measured in farads This is the ratio of the electric charge on each conductor to the potential difference between them
The properties of capacitor are expressed by an equation
C=QU
Where C is capacitance Q is the electriccharge stored inside the capacitor and U is thevoltage between conductors (plates)
Capacitors ndashinternal structure
a) Film capacitor
b) Metalised plastic film capacitor
c) Ceramic disc capacitor
d) Tubular ceramic capacitor
e) Multilayer ceramic capacitor
Supercapacitors
Maxwell Technologies supercapacitors
Ultracapacitor (known also as anelectrochemical double layer capacitor) is an electrochemical capacitor that has a very high energy density when compared to common capacitors typically on the order of thousands of times greater than a high capacity electrolytic capacitor
They are characterized by a very shortcharging time (seconds to minutes)
Possible applications ndash electriccars power tools emergencypower supplies
Supercapacitors ndash cont
Pros very short charging time
Cons relatively high price
Supercapacitors vs standard capacitors
New generation of supercapacitotors
Second generation of supercapacitors by ioxuscom (2010)
From left 220F800F1000F Operating voltage 23V max
copy wwwioxuscom
Capacitors ndash cont
Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)
If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A
Capacitors ndash cont
Most imporant capacitor parameters
bullCapacitance [microF] [nF] or [pF]
bullTolerance []
bullRated voltage [V]
bullDischarge rate (leakage current)
bullTemperature coefficient of capacitance
bullEquivalent series resitance (ESR)
Capacitors ndash cont
a)Aluminium electrolytic capacitor
b)Tantalum electrolytic capacitor
c)Polyesther capacitor
d)Ceramic disc capacitor
e)Mylar capacitor
Capacitors ndash cont
Capacitors in series connection
For two capacitors in series the equivalent capacitance is
For parallel configuration
For two capacitors in parallel the equivalent capacitance is
C=C1+C2
For n capacitors (general case)
Capacitors ndash cont
Capacitor discharge through a resistor
If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge
The discharge rate is expressed by an equation
Where RC is called time constant
Capacitors ndash cont
Capacitor charging through a resistor
If a capacitor C will be charged from source of voltage UWE
through a resistor R the voltage change across its terminals will be described by the following equations
The final solution is
Inductors
An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it
An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material
Graphic symbola) Toroidal core inductor b)cylindrical core inductor
The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L
where L is expressed in H (Henryrsquos) but most often in mH or microH
Inductors ndash cont
Different variations of inductors
Surface mount(SMT) inductors
Cylindricalcoreinductors
Inductor parameters
bullInductance [H]
bullRated voltage [V]
bullTolerance []
bullSaturation DC current [A]
bullMaximal RMS current [A]
bullSelf-resonance frequency [Hz]
bullDC resistance [Ω]
Typical set of parameters
Coilcraft DO3340P-104M inductor
L-100microH tol-20 Isat-25A Irms-12A
SRF-5MHz(typ) RDC-022Ω
Transformers
A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation
Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio
Transformer ndash cont
The current I2 flowing in the secondary winding is inversely proportional
to the current I1 flowing in the primary winding
Moreover the impedance connected to the transformer is transformed by the square of the turns ratio
Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer
Transformers ndash cont
The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit
Examples of low power transformers
Toroidal coretransformer
Toroidal core variabletransformer
(autotransformer)
Laminatedcore EI transformers
Diodes
A diode is a two-terminal electronic component that conducts electric current in only one direction
When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)
Diodes ndash cont
The currentndashvoltage characteristic of a diodeWhere
ID is diode current
If is forward diode current
IFmax is maximum diode
current
UF is forward diode voltage
UR is reverse diode voltage
URmax is the maximum
reverse voltage diodevoltage
Diodes ndash cont
For common types of diodes the value of UF voltage is
bullFor Germanium junction diode 02 04V
bullFor Silicone junction diode 05 08V
bullFor Schottky diode 0204V
An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation
Where I is the diode current
IS is the reverse bias saturation current (or scale current)
VD is the voltage across the diode
VT is the thermal voltage and
n is the ideality factor also known as the quality factor
Diodes ndashcont
The thermal voltage VT is approximately 2585 mV at 300 K
At any other temperature it is given by an equation
where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)
Diodes ndash cont
The typical I-V characteristics of for germaniumand silicone junction diode
Diodes ndash cont
Diode as a switching element
Following the end of forward conduction in a PN type diode a
reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called
reverse recovery time and usually is between tens and hundreds of
ns (ie between 1e-8 and 1e-7 s)
Diodes ndash cont
Diode as a rectifier
A half wave rectifier
A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification
Diodes ndash cont
A full-wave rectifier
This kind of a circuit is also known as the bridge rectifier
Diodes ndash cont
A rectifier in a DC voltage supply
Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge
In general case the simple design rule should be followed
RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)
Diodes ndash cont
Another application ndash diode-based voltage limiter
The cathode of a diode has a potential equal to 4V
U out max = 4V + 06 V = 46 V
If UINlt46V then UOUT = UIN
Bipolar Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals
Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors
B=base C=collector E= emitter
Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases
Transistors ndash cont
The history of the transistor
The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work
The first silicon transistors were produced by Western Electric and TexasInstruments in 1954
Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)
copy wwwporticusorg
Transistors ndash cont
An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased
NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia
The first transistor
copy Bell Labs
Transistor ndash cont
Transistor as an amplifier
A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated
The relations between currents in BJT copy radartutorialeu
Transistor ndash cont
The most often used amplifier circuits
highmediumlowBandwidth4
00001800Phase Shift between input and output signals
3
lt 1highhighCurrent gain2
highlt 1highVoltage gain1
COMMON BASE
COMMON COLLECTOR
COMMON EMITTER
AMPLIFIER
Nr
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Fundamental definitions (cont)
E I
U1=IR1
U2=IR2
U3=IR3
R1
R2
R3
An electric current can flowonly through a closed path called an electric circuit
In order to produce a current flow at least one current source (eg a battery) must be present in the circuit
An ideal currentsource symbol
Fundamental definitions (cont)
Resistance and Ohmrsquos Law
Ohms law states that the current through a conductor between two points is directly proportional to the potential difference or voltage across the two points and inversely proportional to the resistance between them
The mathematical equation that describes this relationship is
R=UI
The unit is Ohm [ Ω ] = [ V ] [ A ]
10
Current flow convention
The electrons in a electrical circuit flow in the opposite direction of the conventional electric current
copyWikipedia
Fundamental definitions (cont)
Kirchhoffs circuit laws
Kirchhoffs current law (KCL)
At any node (junction) in an electrical circuit the sum of currents flowing into that node is equal to the sum of currents flowing out of that node
or
The algebraic sum of currents in a network of conductors meeting at a point is zero
I iisum = 0
Fundamental definitions (cont)
Kirchhoffs voltage law (KVL)
The directed sum of the electrical potential differences (voltage) around any closed circuit is zero
or
More simply the sum of the emfs in any closed loop is equivalent to the sum of the potential drops in that loop IR Ei
isum =
Fundamental definitions (cont)
In circuit theory Theacutevenins theorem for linear electrical networks states that any combination of voltage sources current sources and resistors with two terminals is electrically equivalent to a single voltage source V and a single series resistor R
Theacutevenins theorem
Where UT= open circuit voltage between points A and B
And RT = UTIT where IT is the short circuit current flowing between points A and B
Fundamental definitions (cont)
Electric power
An electric power P is the rate at which electrical energy is transferred by an electric circuit The SI unit of power is the watt In direct current resistive circuits electrical power is calculated using Joules law
P = UI
The unit
[W] = [J] [s] = ([J] [C]) ([C] [s]) [W] = [V][A]
Ohmrsquos law allows us to evaluate an electric power dissipated by a resistor
P = I2 R and respectively P = U2R
Fundamental definitions (cont)
SignalsIn electronics a signal is usually defined as a time-varying voltage or current that conveys information
Sinuisoidal signal
U = Umsin ω t
whereUm - amplitude ω =2πf ndash pulsation[rads]
t ndash time [s] f ndash frequency [Hz]
Other parameters
Vp-p = Peak-to-Peak value
Root-Mean_Square value (RMS)
For sinusoidal signal
Vp-p = 2Um
VRMS=0707Um
dttUT
UT
RMS int=0
2 )(1
Fundamental definitions (cont)
Square wave signal
For this signal URMS=UM
Other parameters
Risetime
Fall time
Highlow amplitude
Please note that real-life signal are not rectangular ie risetime and fall time are always greater than zero
For practical purposes risefall times are usually measured between 10 and 90 of the final value of the signal
Fundamental definitions (cont)
Sawtooth signal (sawtooth wave)
sawtooth wave ramps upward and then sharply drops
Pulses
A rapid transient changes in the amplitude of a signal
Step signals amp glitches
Useful mostly for theoretical analysis
Fundamental definitions (cont)
Decibel gain
The decibel (dB) is a logarithmic unit that indicates the ratio of a physical quantity (usually power or intensity) relative to a specified or implied reference level The decibel ratio of two signals can be expressed by a formula
ku[dB]=20log10(U2U1) where U2 and U1 are the amplitudes of the signals
Examples
ku ku [dB]
01 -20dB
0707 -3dB
1 0dB
141 3dB
10 20dB
100 40dB
1000 60dB
Passive components
Resistors
A resistor is a two-terminal electronic component that produces a voltage across its terminals that is proportional to the electric current through it in accordance with Ohms law
Generic graphic symbol
aMetalized resistor
bWirewound resistor
cCarbon resistor
dResistor ladder
eThick-film resistor
The primary characteristics of a resistor
Resistance (usually expressed in Ω kΩ and MΩ) Tolerance Maximal (rated) power Temperature coefficient of resistance (TCR) Maximal working voltage Parasitic inductance
Series and parallel resistors
The equivalent resistance of tworesistors in series connection
R=R1+R2
The equivalent resistance of tworesistors in parallel connection
1R=1R1+1R2
For n resistors
R=R1+R2+R3+Rn
For n resistors
1R=1R1+1R2+1R3+1Rn
Resistive divider
copy Wikipedia
If R1=R2 then Vout = Vin2
The voltage output of a voltage divider is not fixed but varies according to the load To obtain a reasonably stable output voltage the output current should be a small fraction of the input current
Loaded voltage divider
The voltage between points A and B
U = UT = UINmiddot [R2 (R1 + R2)]
According to Theveninrsquostheorem
RT = (R1 middot R2) (R1+ R2)
In practical projects we often
assume that RL should be 10 times higher than RT
Potentiometers
A potentiometer is a three-terminal resistor with a sliding contact acting as an adjustable voltage divider
Capacitors
copy Wikipedia
A capacitor is a passive electronic component consisting of a pair of conductors separated by a dielectric (insulator)
An ideal capacitor is characterized by a single constant value capacitance measured in farads This is the ratio of the electric charge on each conductor to the potential difference between them
The properties of capacitor are expressed by an equation
C=QU
Where C is capacitance Q is the electriccharge stored inside the capacitor and U is thevoltage between conductors (plates)
Capacitors ndashinternal structure
a) Film capacitor
b) Metalised plastic film capacitor
c) Ceramic disc capacitor
d) Tubular ceramic capacitor
e) Multilayer ceramic capacitor
Supercapacitors
Maxwell Technologies supercapacitors
Ultracapacitor (known also as anelectrochemical double layer capacitor) is an electrochemical capacitor that has a very high energy density when compared to common capacitors typically on the order of thousands of times greater than a high capacity electrolytic capacitor
They are characterized by a very shortcharging time (seconds to minutes)
Possible applications ndash electriccars power tools emergencypower supplies
Supercapacitors ndash cont
Pros very short charging time
Cons relatively high price
Supercapacitors vs standard capacitors
New generation of supercapacitotors
Second generation of supercapacitors by ioxuscom (2010)
From left 220F800F1000F Operating voltage 23V max
copy wwwioxuscom
Capacitors ndash cont
Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)
If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A
Capacitors ndash cont
Most imporant capacitor parameters
bullCapacitance [microF] [nF] or [pF]
bullTolerance []
bullRated voltage [V]
bullDischarge rate (leakage current)
bullTemperature coefficient of capacitance
bullEquivalent series resitance (ESR)
Capacitors ndash cont
a)Aluminium electrolytic capacitor
b)Tantalum electrolytic capacitor
c)Polyesther capacitor
d)Ceramic disc capacitor
e)Mylar capacitor
Capacitors ndash cont
Capacitors in series connection
For two capacitors in series the equivalent capacitance is
For parallel configuration
For two capacitors in parallel the equivalent capacitance is
C=C1+C2
For n capacitors (general case)
Capacitors ndash cont
Capacitor discharge through a resistor
If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge
The discharge rate is expressed by an equation
Where RC is called time constant
Capacitors ndash cont
Capacitor charging through a resistor
If a capacitor C will be charged from source of voltage UWE
through a resistor R the voltage change across its terminals will be described by the following equations
The final solution is
Inductors
An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it
An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material
Graphic symbola) Toroidal core inductor b)cylindrical core inductor
The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L
where L is expressed in H (Henryrsquos) but most often in mH or microH
Inductors ndash cont
Different variations of inductors
Surface mount(SMT) inductors
Cylindricalcoreinductors
Inductor parameters
bullInductance [H]
bullRated voltage [V]
bullTolerance []
bullSaturation DC current [A]
bullMaximal RMS current [A]
bullSelf-resonance frequency [Hz]
bullDC resistance [Ω]
Typical set of parameters
Coilcraft DO3340P-104M inductor
L-100microH tol-20 Isat-25A Irms-12A
SRF-5MHz(typ) RDC-022Ω
Transformers
A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation
Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio
Transformer ndash cont
The current I2 flowing in the secondary winding is inversely proportional
to the current I1 flowing in the primary winding
Moreover the impedance connected to the transformer is transformed by the square of the turns ratio
Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer
Transformers ndash cont
The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit
Examples of low power transformers
Toroidal coretransformer
Toroidal core variabletransformer
(autotransformer)
Laminatedcore EI transformers
Diodes
A diode is a two-terminal electronic component that conducts electric current in only one direction
When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)
Diodes ndash cont
The currentndashvoltage characteristic of a diodeWhere
ID is diode current
If is forward diode current
IFmax is maximum diode
current
UF is forward diode voltage
UR is reverse diode voltage
URmax is the maximum
reverse voltage diodevoltage
Diodes ndash cont
For common types of diodes the value of UF voltage is
bullFor Germanium junction diode 02 04V
bullFor Silicone junction diode 05 08V
bullFor Schottky diode 0204V
An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation
Where I is the diode current
IS is the reverse bias saturation current (or scale current)
VD is the voltage across the diode
VT is the thermal voltage and
n is the ideality factor also known as the quality factor
Diodes ndashcont
The thermal voltage VT is approximately 2585 mV at 300 K
At any other temperature it is given by an equation
where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)
Diodes ndash cont
The typical I-V characteristics of for germaniumand silicone junction diode
Diodes ndash cont
Diode as a switching element
Following the end of forward conduction in a PN type diode a
reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called
reverse recovery time and usually is between tens and hundreds of
ns (ie between 1e-8 and 1e-7 s)
Diodes ndash cont
Diode as a rectifier
A half wave rectifier
A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification
Diodes ndash cont
A full-wave rectifier
This kind of a circuit is also known as the bridge rectifier
Diodes ndash cont
A rectifier in a DC voltage supply
Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge
In general case the simple design rule should be followed
RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)
Diodes ndash cont
Another application ndash diode-based voltage limiter
The cathode of a diode has a potential equal to 4V
U out max = 4V + 06 V = 46 V
If UINlt46V then UOUT = UIN
Bipolar Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals
Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors
B=base C=collector E= emitter
Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases
Transistors ndash cont
The history of the transistor
The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work
The first silicon transistors were produced by Western Electric and TexasInstruments in 1954
Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)
copy wwwporticusorg
Transistors ndash cont
An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased
NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia
The first transistor
copy Bell Labs
Transistor ndash cont
Transistor as an amplifier
A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated
The relations between currents in BJT copy radartutorialeu
Transistor ndash cont
The most often used amplifier circuits
highmediumlowBandwidth4
00001800Phase Shift between input and output signals
3
lt 1highhighCurrent gain2
highlt 1highVoltage gain1
COMMON BASE
COMMON COLLECTOR
COMMON EMITTER
AMPLIFIER
Nr
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Fundamental definitions (cont)
Resistance and Ohmrsquos Law
Ohms law states that the current through a conductor between two points is directly proportional to the potential difference or voltage across the two points and inversely proportional to the resistance between them
The mathematical equation that describes this relationship is
R=UI
The unit is Ohm [ Ω ] = [ V ] [ A ]
10
Current flow convention
The electrons in a electrical circuit flow in the opposite direction of the conventional electric current
copyWikipedia
Fundamental definitions (cont)
Kirchhoffs circuit laws
Kirchhoffs current law (KCL)
At any node (junction) in an electrical circuit the sum of currents flowing into that node is equal to the sum of currents flowing out of that node
or
The algebraic sum of currents in a network of conductors meeting at a point is zero
I iisum = 0
Fundamental definitions (cont)
Kirchhoffs voltage law (KVL)
The directed sum of the electrical potential differences (voltage) around any closed circuit is zero
or
More simply the sum of the emfs in any closed loop is equivalent to the sum of the potential drops in that loop IR Ei
isum =
Fundamental definitions (cont)
In circuit theory Theacutevenins theorem for linear electrical networks states that any combination of voltage sources current sources and resistors with two terminals is electrically equivalent to a single voltage source V and a single series resistor R
Theacutevenins theorem
Where UT= open circuit voltage between points A and B
And RT = UTIT where IT is the short circuit current flowing between points A and B
Fundamental definitions (cont)
Electric power
An electric power P is the rate at which electrical energy is transferred by an electric circuit The SI unit of power is the watt In direct current resistive circuits electrical power is calculated using Joules law
P = UI
The unit
[W] = [J] [s] = ([J] [C]) ([C] [s]) [W] = [V][A]
Ohmrsquos law allows us to evaluate an electric power dissipated by a resistor
P = I2 R and respectively P = U2R
Fundamental definitions (cont)
SignalsIn electronics a signal is usually defined as a time-varying voltage or current that conveys information
Sinuisoidal signal
U = Umsin ω t
whereUm - amplitude ω =2πf ndash pulsation[rads]
t ndash time [s] f ndash frequency [Hz]
Other parameters
Vp-p = Peak-to-Peak value
Root-Mean_Square value (RMS)
For sinusoidal signal
Vp-p = 2Um
VRMS=0707Um
dttUT
UT
RMS int=0
2 )(1
Fundamental definitions (cont)
Square wave signal
For this signal URMS=UM
Other parameters
Risetime
Fall time
Highlow amplitude
Please note that real-life signal are not rectangular ie risetime and fall time are always greater than zero
For practical purposes risefall times are usually measured between 10 and 90 of the final value of the signal
Fundamental definitions (cont)
Sawtooth signal (sawtooth wave)
sawtooth wave ramps upward and then sharply drops
Pulses
A rapid transient changes in the amplitude of a signal
Step signals amp glitches
Useful mostly for theoretical analysis
Fundamental definitions (cont)
Decibel gain
The decibel (dB) is a logarithmic unit that indicates the ratio of a physical quantity (usually power or intensity) relative to a specified or implied reference level The decibel ratio of two signals can be expressed by a formula
ku[dB]=20log10(U2U1) where U2 and U1 are the amplitudes of the signals
Examples
ku ku [dB]
01 -20dB
0707 -3dB
1 0dB
141 3dB
10 20dB
100 40dB
1000 60dB
Passive components
Resistors
A resistor is a two-terminal electronic component that produces a voltage across its terminals that is proportional to the electric current through it in accordance with Ohms law
Generic graphic symbol
aMetalized resistor
bWirewound resistor
cCarbon resistor
dResistor ladder
eThick-film resistor
The primary characteristics of a resistor
Resistance (usually expressed in Ω kΩ and MΩ) Tolerance Maximal (rated) power Temperature coefficient of resistance (TCR) Maximal working voltage Parasitic inductance
Series and parallel resistors
The equivalent resistance of tworesistors in series connection
R=R1+R2
The equivalent resistance of tworesistors in parallel connection
1R=1R1+1R2
For n resistors
R=R1+R2+R3+Rn
For n resistors
1R=1R1+1R2+1R3+1Rn
Resistive divider
copy Wikipedia
If R1=R2 then Vout = Vin2
The voltage output of a voltage divider is not fixed but varies according to the load To obtain a reasonably stable output voltage the output current should be a small fraction of the input current
Loaded voltage divider
The voltage between points A and B
U = UT = UINmiddot [R2 (R1 + R2)]
According to Theveninrsquostheorem
RT = (R1 middot R2) (R1+ R2)
In practical projects we often
assume that RL should be 10 times higher than RT
Potentiometers
A potentiometer is a three-terminal resistor with a sliding contact acting as an adjustable voltage divider
Capacitors
copy Wikipedia
A capacitor is a passive electronic component consisting of a pair of conductors separated by a dielectric (insulator)
An ideal capacitor is characterized by a single constant value capacitance measured in farads This is the ratio of the electric charge on each conductor to the potential difference between them
The properties of capacitor are expressed by an equation
C=QU
Where C is capacitance Q is the electriccharge stored inside the capacitor and U is thevoltage between conductors (plates)
Capacitors ndashinternal structure
a) Film capacitor
b) Metalised plastic film capacitor
c) Ceramic disc capacitor
d) Tubular ceramic capacitor
e) Multilayer ceramic capacitor
Supercapacitors
Maxwell Technologies supercapacitors
Ultracapacitor (known also as anelectrochemical double layer capacitor) is an electrochemical capacitor that has a very high energy density when compared to common capacitors typically on the order of thousands of times greater than a high capacity electrolytic capacitor
They are characterized by a very shortcharging time (seconds to minutes)
Possible applications ndash electriccars power tools emergencypower supplies
Supercapacitors ndash cont
Pros very short charging time
Cons relatively high price
Supercapacitors vs standard capacitors
New generation of supercapacitotors
Second generation of supercapacitors by ioxuscom (2010)
From left 220F800F1000F Operating voltage 23V max
copy wwwioxuscom
Capacitors ndash cont
Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)
If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A
Capacitors ndash cont
Most imporant capacitor parameters
bullCapacitance [microF] [nF] or [pF]
bullTolerance []
bullRated voltage [V]
bullDischarge rate (leakage current)
bullTemperature coefficient of capacitance
bullEquivalent series resitance (ESR)
Capacitors ndash cont
a)Aluminium electrolytic capacitor
b)Tantalum electrolytic capacitor
c)Polyesther capacitor
d)Ceramic disc capacitor
e)Mylar capacitor
Capacitors ndash cont
Capacitors in series connection
For two capacitors in series the equivalent capacitance is
For parallel configuration
For two capacitors in parallel the equivalent capacitance is
C=C1+C2
For n capacitors (general case)
Capacitors ndash cont
Capacitor discharge through a resistor
If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge
The discharge rate is expressed by an equation
Where RC is called time constant
Capacitors ndash cont
Capacitor charging through a resistor
If a capacitor C will be charged from source of voltage UWE
through a resistor R the voltage change across its terminals will be described by the following equations
The final solution is
Inductors
An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it
An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material
Graphic symbola) Toroidal core inductor b)cylindrical core inductor
The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L
where L is expressed in H (Henryrsquos) but most often in mH or microH
Inductors ndash cont
Different variations of inductors
Surface mount(SMT) inductors
Cylindricalcoreinductors
Inductor parameters
bullInductance [H]
bullRated voltage [V]
bullTolerance []
bullSaturation DC current [A]
bullMaximal RMS current [A]
bullSelf-resonance frequency [Hz]
bullDC resistance [Ω]
Typical set of parameters
Coilcraft DO3340P-104M inductor
L-100microH tol-20 Isat-25A Irms-12A
SRF-5MHz(typ) RDC-022Ω
Transformers
A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation
Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio
Transformer ndash cont
The current I2 flowing in the secondary winding is inversely proportional
to the current I1 flowing in the primary winding
Moreover the impedance connected to the transformer is transformed by the square of the turns ratio
Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer
Transformers ndash cont
The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit
Examples of low power transformers
Toroidal coretransformer
Toroidal core variabletransformer
(autotransformer)
Laminatedcore EI transformers
Diodes
A diode is a two-terminal electronic component that conducts electric current in only one direction
When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)
Diodes ndash cont
The currentndashvoltage characteristic of a diodeWhere
ID is diode current
If is forward diode current
IFmax is maximum diode
current
UF is forward diode voltage
UR is reverse diode voltage
URmax is the maximum
reverse voltage diodevoltage
Diodes ndash cont
For common types of diodes the value of UF voltage is
bullFor Germanium junction diode 02 04V
bullFor Silicone junction diode 05 08V
bullFor Schottky diode 0204V
An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation
Where I is the diode current
IS is the reverse bias saturation current (or scale current)
VD is the voltage across the diode
VT is the thermal voltage and
n is the ideality factor also known as the quality factor
Diodes ndashcont
The thermal voltage VT is approximately 2585 mV at 300 K
At any other temperature it is given by an equation
where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)
Diodes ndash cont
The typical I-V characteristics of for germaniumand silicone junction diode
Diodes ndash cont
Diode as a switching element
Following the end of forward conduction in a PN type diode a
reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called
reverse recovery time and usually is between tens and hundreds of
ns (ie between 1e-8 and 1e-7 s)
Diodes ndash cont
Diode as a rectifier
A half wave rectifier
A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification
Diodes ndash cont
A full-wave rectifier
This kind of a circuit is also known as the bridge rectifier
Diodes ndash cont
A rectifier in a DC voltage supply
Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge
In general case the simple design rule should be followed
RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)
Diodes ndash cont
Another application ndash diode-based voltage limiter
The cathode of a diode has a potential equal to 4V
U out max = 4V + 06 V = 46 V
If UINlt46V then UOUT = UIN
Bipolar Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals
Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors
B=base C=collector E= emitter
Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases
Transistors ndash cont
The history of the transistor
The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work
The first silicon transistors were produced by Western Electric and TexasInstruments in 1954
Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)
copy wwwporticusorg
Transistors ndash cont
An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased
NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia
The first transistor
copy Bell Labs
Transistor ndash cont
Transistor as an amplifier
A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated
The relations between currents in BJT copy radartutorialeu
Transistor ndash cont
The most often used amplifier circuits
highmediumlowBandwidth4
00001800Phase Shift between input and output signals
3
lt 1highhighCurrent gain2
highlt 1highVoltage gain1
COMMON BASE
COMMON COLLECTOR
COMMON EMITTER
AMPLIFIER
Nr
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
10
Current flow convention
The electrons in a electrical circuit flow in the opposite direction of the conventional electric current
copyWikipedia
Fundamental definitions (cont)
Kirchhoffs circuit laws
Kirchhoffs current law (KCL)
At any node (junction) in an electrical circuit the sum of currents flowing into that node is equal to the sum of currents flowing out of that node
or
The algebraic sum of currents in a network of conductors meeting at a point is zero
I iisum = 0
Fundamental definitions (cont)
Kirchhoffs voltage law (KVL)
The directed sum of the electrical potential differences (voltage) around any closed circuit is zero
or
More simply the sum of the emfs in any closed loop is equivalent to the sum of the potential drops in that loop IR Ei
isum =
Fundamental definitions (cont)
In circuit theory Theacutevenins theorem for linear electrical networks states that any combination of voltage sources current sources and resistors with two terminals is electrically equivalent to a single voltage source V and a single series resistor R
Theacutevenins theorem
Where UT= open circuit voltage between points A and B
And RT = UTIT where IT is the short circuit current flowing between points A and B
Fundamental definitions (cont)
Electric power
An electric power P is the rate at which electrical energy is transferred by an electric circuit The SI unit of power is the watt In direct current resistive circuits electrical power is calculated using Joules law
P = UI
The unit
[W] = [J] [s] = ([J] [C]) ([C] [s]) [W] = [V][A]
Ohmrsquos law allows us to evaluate an electric power dissipated by a resistor
P = I2 R and respectively P = U2R
Fundamental definitions (cont)
SignalsIn electronics a signal is usually defined as a time-varying voltage or current that conveys information
Sinuisoidal signal
U = Umsin ω t
whereUm - amplitude ω =2πf ndash pulsation[rads]
t ndash time [s] f ndash frequency [Hz]
Other parameters
Vp-p = Peak-to-Peak value
Root-Mean_Square value (RMS)
For sinusoidal signal
Vp-p = 2Um
VRMS=0707Um
dttUT
UT
RMS int=0
2 )(1
Fundamental definitions (cont)
Square wave signal
For this signal URMS=UM
Other parameters
Risetime
Fall time
Highlow amplitude
Please note that real-life signal are not rectangular ie risetime and fall time are always greater than zero
For practical purposes risefall times are usually measured between 10 and 90 of the final value of the signal
Fundamental definitions (cont)
Sawtooth signal (sawtooth wave)
sawtooth wave ramps upward and then sharply drops
Pulses
A rapid transient changes in the amplitude of a signal
Step signals amp glitches
Useful mostly for theoretical analysis
Fundamental definitions (cont)
Decibel gain
The decibel (dB) is a logarithmic unit that indicates the ratio of a physical quantity (usually power or intensity) relative to a specified or implied reference level The decibel ratio of two signals can be expressed by a formula
ku[dB]=20log10(U2U1) where U2 and U1 are the amplitudes of the signals
Examples
ku ku [dB]
01 -20dB
0707 -3dB
1 0dB
141 3dB
10 20dB
100 40dB
1000 60dB
Passive components
Resistors
A resistor is a two-terminal electronic component that produces a voltage across its terminals that is proportional to the electric current through it in accordance with Ohms law
Generic graphic symbol
aMetalized resistor
bWirewound resistor
cCarbon resistor
dResistor ladder
eThick-film resistor
The primary characteristics of a resistor
Resistance (usually expressed in Ω kΩ and MΩ) Tolerance Maximal (rated) power Temperature coefficient of resistance (TCR) Maximal working voltage Parasitic inductance
Series and parallel resistors
The equivalent resistance of tworesistors in series connection
R=R1+R2
The equivalent resistance of tworesistors in parallel connection
1R=1R1+1R2
For n resistors
R=R1+R2+R3+Rn
For n resistors
1R=1R1+1R2+1R3+1Rn
Resistive divider
copy Wikipedia
If R1=R2 then Vout = Vin2
The voltage output of a voltage divider is not fixed but varies according to the load To obtain a reasonably stable output voltage the output current should be a small fraction of the input current
Loaded voltage divider
The voltage between points A and B
U = UT = UINmiddot [R2 (R1 + R2)]
According to Theveninrsquostheorem
RT = (R1 middot R2) (R1+ R2)
In practical projects we often
assume that RL should be 10 times higher than RT
Potentiometers
A potentiometer is a three-terminal resistor with a sliding contact acting as an adjustable voltage divider
Capacitors
copy Wikipedia
A capacitor is a passive electronic component consisting of a pair of conductors separated by a dielectric (insulator)
An ideal capacitor is characterized by a single constant value capacitance measured in farads This is the ratio of the electric charge on each conductor to the potential difference between them
The properties of capacitor are expressed by an equation
C=QU
Where C is capacitance Q is the electriccharge stored inside the capacitor and U is thevoltage between conductors (plates)
Capacitors ndashinternal structure
a) Film capacitor
b) Metalised plastic film capacitor
c) Ceramic disc capacitor
d) Tubular ceramic capacitor
e) Multilayer ceramic capacitor
Supercapacitors
Maxwell Technologies supercapacitors
Ultracapacitor (known also as anelectrochemical double layer capacitor) is an electrochemical capacitor that has a very high energy density when compared to common capacitors typically on the order of thousands of times greater than a high capacity electrolytic capacitor
They are characterized by a very shortcharging time (seconds to minutes)
Possible applications ndash electriccars power tools emergencypower supplies
Supercapacitors ndash cont
Pros very short charging time
Cons relatively high price
Supercapacitors vs standard capacitors
New generation of supercapacitotors
Second generation of supercapacitors by ioxuscom (2010)
From left 220F800F1000F Operating voltage 23V max
copy wwwioxuscom
Capacitors ndash cont
Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)
If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A
Capacitors ndash cont
Most imporant capacitor parameters
bullCapacitance [microF] [nF] or [pF]
bullTolerance []
bullRated voltage [V]
bullDischarge rate (leakage current)
bullTemperature coefficient of capacitance
bullEquivalent series resitance (ESR)
Capacitors ndash cont
a)Aluminium electrolytic capacitor
b)Tantalum electrolytic capacitor
c)Polyesther capacitor
d)Ceramic disc capacitor
e)Mylar capacitor
Capacitors ndash cont
Capacitors in series connection
For two capacitors in series the equivalent capacitance is
For parallel configuration
For two capacitors in parallel the equivalent capacitance is
C=C1+C2
For n capacitors (general case)
Capacitors ndash cont
Capacitor discharge through a resistor
If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge
The discharge rate is expressed by an equation
Where RC is called time constant
Capacitors ndash cont
Capacitor charging through a resistor
If a capacitor C will be charged from source of voltage UWE
through a resistor R the voltage change across its terminals will be described by the following equations
The final solution is
Inductors
An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it
An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material
Graphic symbola) Toroidal core inductor b)cylindrical core inductor
The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L
where L is expressed in H (Henryrsquos) but most often in mH or microH
Inductors ndash cont
Different variations of inductors
Surface mount(SMT) inductors
Cylindricalcoreinductors
Inductor parameters
bullInductance [H]
bullRated voltage [V]
bullTolerance []
bullSaturation DC current [A]
bullMaximal RMS current [A]
bullSelf-resonance frequency [Hz]
bullDC resistance [Ω]
Typical set of parameters
Coilcraft DO3340P-104M inductor
L-100microH tol-20 Isat-25A Irms-12A
SRF-5MHz(typ) RDC-022Ω
Transformers
A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation
Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio
Transformer ndash cont
The current I2 flowing in the secondary winding is inversely proportional
to the current I1 flowing in the primary winding
Moreover the impedance connected to the transformer is transformed by the square of the turns ratio
Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer
Transformers ndash cont
The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit
Examples of low power transformers
Toroidal coretransformer
Toroidal core variabletransformer
(autotransformer)
Laminatedcore EI transformers
Diodes
A diode is a two-terminal electronic component that conducts electric current in only one direction
When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)
Diodes ndash cont
The currentndashvoltage characteristic of a diodeWhere
ID is diode current
If is forward diode current
IFmax is maximum diode
current
UF is forward diode voltage
UR is reverse diode voltage
URmax is the maximum
reverse voltage diodevoltage
Diodes ndash cont
For common types of diodes the value of UF voltage is
bullFor Germanium junction diode 02 04V
bullFor Silicone junction diode 05 08V
bullFor Schottky diode 0204V
An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation
Where I is the diode current
IS is the reverse bias saturation current (or scale current)
VD is the voltage across the diode
VT is the thermal voltage and
n is the ideality factor also known as the quality factor
Diodes ndashcont
The thermal voltage VT is approximately 2585 mV at 300 K
At any other temperature it is given by an equation
where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)
Diodes ndash cont
The typical I-V characteristics of for germaniumand silicone junction diode
Diodes ndash cont
Diode as a switching element
Following the end of forward conduction in a PN type diode a
reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called
reverse recovery time and usually is between tens and hundreds of
ns (ie between 1e-8 and 1e-7 s)
Diodes ndash cont
Diode as a rectifier
A half wave rectifier
A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification
Diodes ndash cont
A full-wave rectifier
This kind of a circuit is also known as the bridge rectifier
Diodes ndash cont
A rectifier in a DC voltage supply
Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge
In general case the simple design rule should be followed
RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)
Diodes ndash cont
Another application ndash diode-based voltage limiter
The cathode of a diode has a potential equal to 4V
U out max = 4V + 06 V = 46 V
If UINlt46V then UOUT = UIN
Bipolar Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals
Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors
B=base C=collector E= emitter
Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases
Transistors ndash cont
The history of the transistor
The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work
The first silicon transistors were produced by Western Electric and TexasInstruments in 1954
Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)
copy wwwporticusorg
Transistors ndash cont
An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased
NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia
The first transistor
copy Bell Labs
Transistor ndash cont
Transistor as an amplifier
A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated
The relations between currents in BJT copy radartutorialeu
Transistor ndash cont
The most often used amplifier circuits
highmediumlowBandwidth4
00001800Phase Shift between input and output signals
3
lt 1highhighCurrent gain2
highlt 1highVoltage gain1
COMMON BASE
COMMON COLLECTOR
COMMON EMITTER
AMPLIFIER
Nr
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Fundamental definitions (cont)
Kirchhoffs circuit laws
Kirchhoffs current law (KCL)
At any node (junction) in an electrical circuit the sum of currents flowing into that node is equal to the sum of currents flowing out of that node
or
The algebraic sum of currents in a network of conductors meeting at a point is zero
I iisum = 0
Fundamental definitions (cont)
Kirchhoffs voltage law (KVL)
The directed sum of the electrical potential differences (voltage) around any closed circuit is zero
or
More simply the sum of the emfs in any closed loop is equivalent to the sum of the potential drops in that loop IR Ei
isum =
Fundamental definitions (cont)
In circuit theory Theacutevenins theorem for linear electrical networks states that any combination of voltage sources current sources and resistors with two terminals is electrically equivalent to a single voltage source V and a single series resistor R
Theacutevenins theorem
Where UT= open circuit voltage between points A and B
And RT = UTIT where IT is the short circuit current flowing between points A and B
Fundamental definitions (cont)
Electric power
An electric power P is the rate at which electrical energy is transferred by an electric circuit The SI unit of power is the watt In direct current resistive circuits electrical power is calculated using Joules law
P = UI
The unit
[W] = [J] [s] = ([J] [C]) ([C] [s]) [W] = [V][A]
Ohmrsquos law allows us to evaluate an electric power dissipated by a resistor
P = I2 R and respectively P = U2R
Fundamental definitions (cont)
SignalsIn electronics a signal is usually defined as a time-varying voltage or current that conveys information
Sinuisoidal signal
U = Umsin ω t
whereUm - amplitude ω =2πf ndash pulsation[rads]
t ndash time [s] f ndash frequency [Hz]
Other parameters
Vp-p = Peak-to-Peak value
Root-Mean_Square value (RMS)
For sinusoidal signal
Vp-p = 2Um
VRMS=0707Um
dttUT
UT
RMS int=0
2 )(1
Fundamental definitions (cont)
Square wave signal
For this signal URMS=UM
Other parameters
Risetime
Fall time
Highlow amplitude
Please note that real-life signal are not rectangular ie risetime and fall time are always greater than zero
For practical purposes risefall times are usually measured between 10 and 90 of the final value of the signal
Fundamental definitions (cont)
Sawtooth signal (sawtooth wave)
sawtooth wave ramps upward and then sharply drops
Pulses
A rapid transient changes in the amplitude of a signal
Step signals amp glitches
Useful mostly for theoretical analysis
Fundamental definitions (cont)
Decibel gain
The decibel (dB) is a logarithmic unit that indicates the ratio of a physical quantity (usually power or intensity) relative to a specified or implied reference level The decibel ratio of two signals can be expressed by a formula
ku[dB]=20log10(U2U1) where U2 and U1 are the amplitudes of the signals
Examples
ku ku [dB]
01 -20dB
0707 -3dB
1 0dB
141 3dB
10 20dB
100 40dB
1000 60dB
Passive components
Resistors
A resistor is a two-terminal electronic component that produces a voltage across its terminals that is proportional to the electric current through it in accordance with Ohms law
Generic graphic symbol
aMetalized resistor
bWirewound resistor
cCarbon resistor
dResistor ladder
eThick-film resistor
The primary characteristics of a resistor
Resistance (usually expressed in Ω kΩ and MΩ) Tolerance Maximal (rated) power Temperature coefficient of resistance (TCR) Maximal working voltage Parasitic inductance
Series and parallel resistors
The equivalent resistance of tworesistors in series connection
R=R1+R2
The equivalent resistance of tworesistors in parallel connection
1R=1R1+1R2
For n resistors
R=R1+R2+R3+Rn
For n resistors
1R=1R1+1R2+1R3+1Rn
Resistive divider
copy Wikipedia
If R1=R2 then Vout = Vin2
The voltage output of a voltage divider is not fixed but varies according to the load To obtain a reasonably stable output voltage the output current should be a small fraction of the input current
Loaded voltage divider
The voltage between points A and B
U = UT = UINmiddot [R2 (R1 + R2)]
According to Theveninrsquostheorem
RT = (R1 middot R2) (R1+ R2)
In practical projects we often
assume that RL should be 10 times higher than RT
Potentiometers
A potentiometer is a three-terminal resistor with a sliding contact acting as an adjustable voltage divider
Capacitors
copy Wikipedia
A capacitor is a passive electronic component consisting of a pair of conductors separated by a dielectric (insulator)
An ideal capacitor is characterized by a single constant value capacitance measured in farads This is the ratio of the electric charge on each conductor to the potential difference between them
The properties of capacitor are expressed by an equation
C=QU
Where C is capacitance Q is the electriccharge stored inside the capacitor and U is thevoltage between conductors (plates)
Capacitors ndashinternal structure
a) Film capacitor
b) Metalised plastic film capacitor
c) Ceramic disc capacitor
d) Tubular ceramic capacitor
e) Multilayer ceramic capacitor
Supercapacitors
Maxwell Technologies supercapacitors
Ultracapacitor (known also as anelectrochemical double layer capacitor) is an electrochemical capacitor that has a very high energy density when compared to common capacitors typically on the order of thousands of times greater than a high capacity electrolytic capacitor
They are characterized by a very shortcharging time (seconds to minutes)
Possible applications ndash electriccars power tools emergencypower supplies
Supercapacitors ndash cont
Pros very short charging time
Cons relatively high price
Supercapacitors vs standard capacitors
New generation of supercapacitotors
Second generation of supercapacitors by ioxuscom (2010)
From left 220F800F1000F Operating voltage 23V max
copy wwwioxuscom
Capacitors ndash cont
Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)
If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A
Capacitors ndash cont
Most imporant capacitor parameters
bullCapacitance [microF] [nF] or [pF]
bullTolerance []
bullRated voltage [V]
bullDischarge rate (leakage current)
bullTemperature coefficient of capacitance
bullEquivalent series resitance (ESR)
Capacitors ndash cont
a)Aluminium electrolytic capacitor
b)Tantalum electrolytic capacitor
c)Polyesther capacitor
d)Ceramic disc capacitor
e)Mylar capacitor
Capacitors ndash cont
Capacitors in series connection
For two capacitors in series the equivalent capacitance is
For parallel configuration
For two capacitors in parallel the equivalent capacitance is
C=C1+C2
For n capacitors (general case)
Capacitors ndash cont
Capacitor discharge through a resistor
If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge
The discharge rate is expressed by an equation
Where RC is called time constant
Capacitors ndash cont
Capacitor charging through a resistor
If a capacitor C will be charged from source of voltage UWE
through a resistor R the voltage change across its terminals will be described by the following equations
The final solution is
Inductors
An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it
An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material
Graphic symbola) Toroidal core inductor b)cylindrical core inductor
The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L
where L is expressed in H (Henryrsquos) but most often in mH or microH
Inductors ndash cont
Different variations of inductors
Surface mount(SMT) inductors
Cylindricalcoreinductors
Inductor parameters
bullInductance [H]
bullRated voltage [V]
bullTolerance []
bullSaturation DC current [A]
bullMaximal RMS current [A]
bullSelf-resonance frequency [Hz]
bullDC resistance [Ω]
Typical set of parameters
Coilcraft DO3340P-104M inductor
L-100microH tol-20 Isat-25A Irms-12A
SRF-5MHz(typ) RDC-022Ω
Transformers
A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation
Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio
Transformer ndash cont
The current I2 flowing in the secondary winding is inversely proportional
to the current I1 flowing in the primary winding
Moreover the impedance connected to the transformer is transformed by the square of the turns ratio
Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer
Transformers ndash cont
The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit
Examples of low power transformers
Toroidal coretransformer
Toroidal core variabletransformer
(autotransformer)
Laminatedcore EI transformers
Diodes
A diode is a two-terminal electronic component that conducts electric current in only one direction
When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)
Diodes ndash cont
The currentndashvoltage characteristic of a diodeWhere
ID is diode current
If is forward diode current
IFmax is maximum diode
current
UF is forward diode voltage
UR is reverse diode voltage
URmax is the maximum
reverse voltage diodevoltage
Diodes ndash cont
For common types of diodes the value of UF voltage is
bullFor Germanium junction diode 02 04V
bullFor Silicone junction diode 05 08V
bullFor Schottky diode 0204V
An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation
Where I is the diode current
IS is the reverse bias saturation current (or scale current)
VD is the voltage across the diode
VT is the thermal voltage and
n is the ideality factor also known as the quality factor
Diodes ndashcont
The thermal voltage VT is approximately 2585 mV at 300 K
At any other temperature it is given by an equation
where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)
Diodes ndash cont
The typical I-V characteristics of for germaniumand silicone junction diode
Diodes ndash cont
Diode as a switching element
Following the end of forward conduction in a PN type diode a
reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called
reverse recovery time and usually is between tens and hundreds of
ns (ie between 1e-8 and 1e-7 s)
Diodes ndash cont
Diode as a rectifier
A half wave rectifier
A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification
Diodes ndash cont
A full-wave rectifier
This kind of a circuit is also known as the bridge rectifier
Diodes ndash cont
A rectifier in a DC voltage supply
Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge
In general case the simple design rule should be followed
RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)
Diodes ndash cont
Another application ndash diode-based voltage limiter
The cathode of a diode has a potential equal to 4V
U out max = 4V + 06 V = 46 V
If UINlt46V then UOUT = UIN
Bipolar Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals
Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors
B=base C=collector E= emitter
Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases
Transistors ndash cont
The history of the transistor
The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work
The first silicon transistors were produced by Western Electric and TexasInstruments in 1954
Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)
copy wwwporticusorg
Transistors ndash cont
An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased
NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia
The first transistor
copy Bell Labs
Transistor ndash cont
Transistor as an amplifier
A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated
The relations between currents in BJT copy radartutorialeu
Transistor ndash cont
The most often used amplifier circuits
highmediumlowBandwidth4
00001800Phase Shift between input and output signals
3
lt 1highhighCurrent gain2
highlt 1highVoltage gain1
COMMON BASE
COMMON COLLECTOR
COMMON EMITTER
AMPLIFIER
Nr
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Fundamental definitions (cont)
Kirchhoffs voltage law (KVL)
The directed sum of the electrical potential differences (voltage) around any closed circuit is zero
or
More simply the sum of the emfs in any closed loop is equivalent to the sum of the potential drops in that loop IR Ei
isum =
Fundamental definitions (cont)
In circuit theory Theacutevenins theorem for linear electrical networks states that any combination of voltage sources current sources and resistors with two terminals is electrically equivalent to a single voltage source V and a single series resistor R
Theacutevenins theorem
Where UT= open circuit voltage between points A and B
And RT = UTIT where IT is the short circuit current flowing between points A and B
Fundamental definitions (cont)
Electric power
An electric power P is the rate at which electrical energy is transferred by an electric circuit The SI unit of power is the watt In direct current resistive circuits electrical power is calculated using Joules law
P = UI
The unit
[W] = [J] [s] = ([J] [C]) ([C] [s]) [W] = [V][A]
Ohmrsquos law allows us to evaluate an electric power dissipated by a resistor
P = I2 R and respectively P = U2R
Fundamental definitions (cont)
SignalsIn electronics a signal is usually defined as a time-varying voltage or current that conveys information
Sinuisoidal signal
U = Umsin ω t
whereUm - amplitude ω =2πf ndash pulsation[rads]
t ndash time [s] f ndash frequency [Hz]
Other parameters
Vp-p = Peak-to-Peak value
Root-Mean_Square value (RMS)
For sinusoidal signal
Vp-p = 2Um
VRMS=0707Um
dttUT
UT
RMS int=0
2 )(1
Fundamental definitions (cont)
Square wave signal
For this signal URMS=UM
Other parameters
Risetime
Fall time
Highlow amplitude
Please note that real-life signal are not rectangular ie risetime and fall time are always greater than zero
For practical purposes risefall times are usually measured between 10 and 90 of the final value of the signal
Fundamental definitions (cont)
Sawtooth signal (sawtooth wave)
sawtooth wave ramps upward and then sharply drops
Pulses
A rapid transient changes in the amplitude of a signal
Step signals amp glitches
Useful mostly for theoretical analysis
Fundamental definitions (cont)
Decibel gain
The decibel (dB) is a logarithmic unit that indicates the ratio of a physical quantity (usually power or intensity) relative to a specified or implied reference level The decibel ratio of two signals can be expressed by a formula
ku[dB]=20log10(U2U1) where U2 and U1 are the amplitudes of the signals
Examples
ku ku [dB]
01 -20dB
0707 -3dB
1 0dB
141 3dB
10 20dB
100 40dB
1000 60dB
Passive components
Resistors
A resistor is a two-terminal electronic component that produces a voltage across its terminals that is proportional to the electric current through it in accordance with Ohms law
Generic graphic symbol
aMetalized resistor
bWirewound resistor
cCarbon resistor
dResistor ladder
eThick-film resistor
The primary characteristics of a resistor
Resistance (usually expressed in Ω kΩ and MΩ) Tolerance Maximal (rated) power Temperature coefficient of resistance (TCR) Maximal working voltage Parasitic inductance
Series and parallel resistors
The equivalent resistance of tworesistors in series connection
R=R1+R2
The equivalent resistance of tworesistors in parallel connection
1R=1R1+1R2
For n resistors
R=R1+R2+R3+Rn
For n resistors
1R=1R1+1R2+1R3+1Rn
Resistive divider
copy Wikipedia
If R1=R2 then Vout = Vin2
The voltage output of a voltage divider is not fixed but varies according to the load To obtain a reasonably stable output voltage the output current should be a small fraction of the input current
Loaded voltage divider
The voltage between points A and B
U = UT = UINmiddot [R2 (R1 + R2)]
According to Theveninrsquostheorem
RT = (R1 middot R2) (R1+ R2)
In practical projects we often
assume that RL should be 10 times higher than RT
Potentiometers
A potentiometer is a three-terminal resistor with a sliding contact acting as an adjustable voltage divider
Capacitors
copy Wikipedia
A capacitor is a passive electronic component consisting of a pair of conductors separated by a dielectric (insulator)
An ideal capacitor is characterized by a single constant value capacitance measured in farads This is the ratio of the electric charge on each conductor to the potential difference between them
The properties of capacitor are expressed by an equation
C=QU
Where C is capacitance Q is the electriccharge stored inside the capacitor and U is thevoltage between conductors (plates)
Capacitors ndashinternal structure
a) Film capacitor
b) Metalised plastic film capacitor
c) Ceramic disc capacitor
d) Tubular ceramic capacitor
e) Multilayer ceramic capacitor
Supercapacitors
Maxwell Technologies supercapacitors
Ultracapacitor (known also as anelectrochemical double layer capacitor) is an electrochemical capacitor that has a very high energy density when compared to common capacitors typically on the order of thousands of times greater than a high capacity electrolytic capacitor
They are characterized by a very shortcharging time (seconds to minutes)
Possible applications ndash electriccars power tools emergencypower supplies
Supercapacitors ndash cont
Pros very short charging time
Cons relatively high price
Supercapacitors vs standard capacitors
New generation of supercapacitotors
Second generation of supercapacitors by ioxuscom (2010)
From left 220F800F1000F Operating voltage 23V max
copy wwwioxuscom
Capacitors ndash cont
Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)
If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A
Capacitors ndash cont
Most imporant capacitor parameters
bullCapacitance [microF] [nF] or [pF]
bullTolerance []
bullRated voltage [V]
bullDischarge rate (leakage current)
bullTemperature coefficient of capacitance
bullEquivalent series resitance (ESR)
Capacitors ndash cont
a)Aluminium electrolytic capacitor
b)Tantalum electrolytic capacitor
c)Polyesther capacitor
d)Ceramic disc capacitor
e)Mylar capacitor
Capacitors ndash cont
Capacitors in series connection
For two capacitors in series the equivalent capacitance is
For parallel configuration
For two capacitors in parallel the equivalent capacitance is
C=C1+C2
For n capacitors (general case)
Capacitors ndash cont
Capacitor discharge through a resistor
If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge
The discharge rate is expressed by an equation
Where RC is called time constant
Capacitors ndash cont
Capacitor charging through a resistor
If a capacitor C will be charged from source of voltage UWE
through a resistor R the voltage change across its terminals will be described by the following equations
The final solution is
Inductors
An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it
An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material
Graphic symbola) Toroidal core inductor b)cylindrical core inductor
The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L
where L is expressed in H (Henryrsquos) but most often in mH or microH
Inductors ndash cont
Different variations of inductors
Surface mount(SMT) inductors
Cylindricalcoreinductors
Inductor parameters
bullInductance [H]
bullRated voltage [V]
bullTolerance []
bullSaturation DC current [A]
bullMaximal RMS current [A]
bullSelf-resonance frequency [Hz]
bullDC resistance [Ω]
Typical set of parameters
Coilcraft DO3340P-104M inductor
L-100microH tol-20 Isat-25A Irms-12A
SRF-5MHz(typ) RDC-022Ω
Transformers
A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation
Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio
Transformer ndash cont
The current I2 flowing in the secondary winding is inversely proportional
to the current I1 flowing in the primary winding
Moreover the impedance connected to the transformer is transformed by the square of the turns ratio
Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer
Transformers ndash cont
The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit
Examples of low power transformers
Toroidal coretransformer
Toroidal core variabletransformer
(autotransformer)
Laminatedcore EI transformers
Diodes
A diode is a two-terminal electronic component that conducts electric current in only one direction
When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)
Diodes ndash cont
The currentndashvoltage characteristic of a diodeWhere
ID is diode current
If is forward diode current
IFmax is maximum diode
current
UF is forward diode voltage
UR is reverse diode voltage
URmax is the maximum
reverse voltage diodevoltage
Diodes ndash cont
For common types of diodes the value of UF voltage is
bullFor Germanium junction diode 02 04V
bullFor Silicone junction diode 05 08V
bullFor Schottky diode 0204V
An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation
Where I is the diode current
IS is the reverse bias saturation current (or scale current)
VD is the voltage across the diode
VT is the thermal voltage and
n is the ideality factor also known as the quality factor
Diodes ndashcont
The thermal voltage VT is approximately 2585 mV at 300 K
At any other temperature it is given by an equation
where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)
Diodes ndash cont
The typical I-V characteristics of for germaniumand silicone junction diode
Diodes ndash cont
Diode as a switching element
Following the end of forward conduction in a PN type diode a
reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called
reverse recovery time and usually is between tens and hundreds of
ns (ie between 1e-8 and 1e-7 s)
Diodes ndash cont
Diode as a rectifier
A half wave rectifier
A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification
Diodes ndash cont
A full-wave rectifier
This kind of a circuit is also known as the bridge rectifier
Diodes ndash cont
A rectifier in a DC voltage supply
Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge
In general case the simple design rule should be followed
RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)
Diodes ndash cont
Another application ndash diode-based voltage limiter
The cathode of a diode has a potential equal to 4V
U out max = 4V + 06 V = 46 V
If UINlt46V then UOUT = UIN
Bipolar Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals
Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors
B=base C=collector E= emitter
Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases
Transistors ndash cont
The history of the transistor
The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work
The first silicon transistors were produced by Western Electric and TexasInstruments in 1954
Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)
copy wwwporticusorg
Transistors ndash cont
An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased
NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia
The first transistor
copy Bell Labs
Transistor ndash cont
Transistor as an amplifier
A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated
The relations between currents in BJT copy radartutorialeu
Transistor ndash cont
The most often used amplifier circuits
highmediumlowBandwidth4
00001800Phase Shift between input and output signals
3
lt 1highhighCurrent gain2
highlt 1highVoltage gain1
COMMON BASE
COMMON COLLECTOR
COMMON EMITTER
AMPLIFIER
Nr
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Fundamental definitions (cont)
In circuit theory Theacutevenins theorem for linear electrical networks states that any combination of voltage sources current sources and resistors with two terminals is electrically equivalent to a single voltage source V and a single series resistor R
Theacutevenins theorem
Where UT= open circuit voltage between points A and B
And RT = UTIT where IT is the short circuit current flowing between points A and B
Fundamental definitions (cont)
Electric power
An electric power P is the rate at which electrical energy is transferred by an electric circuit The SI unit of power is the watt In direct current resistive circuits electrical power is calculated using Joules law
P = UI
The unit
[W] = [J] [s] = ([J] [C]) ([C] [s]) [W] = [V][A]
Ohmrsquos law allows us to evaluate an electric power dissipated by a resistor
P = I2 R and respectively P = U2R
Fundamental definitions (cont)
SignalsIn electronics a signal is usually defined as a time-varying voltage or current that conveys information
Sinuisoidal signal
U = Umsin ω t
whereUm - amplitude ω =2πf ndash pulsation[rads]
t ndash time [s] f ndash frequency [Hz]
Other parameters
Vp-p = Peak-to-Peak value
Root-Mean_Square value (RMS)
For sinusoidal signal
Vp-p = 2Um
VRMS=0707Um
dttUT
UT
RMS int=0
2 )(1
Fundamental definitions (cont)
Square wave signal
For this signal URMS=UM
Other parameters
Risetime
Fall time
Highlow amplitude
Please note that real-life signal are not rectangular ie risetime and fall time are always greater than zero
For practical purposes risefall times are usually measured between 10 and 90 of the final value of the signal
Fundamental definitions (cont)
Sawtooth signal (sawtooth wave)
sawtooth wave ramps upward and then sharply drops
Pulses
A rapid transient changes in the amplitude of a signal
Step signals amp glitches
Useful mostly for theoretical analysis
Fundamental definitions (cont)
Decibel gain
The decibel (dB) is a logarithmic unit that indicates the ratio of a physical quantity (usually power or intensity) relative to a specified or implied reference level The decibel ratio of two signals can be expressed by a formula
ku[dB]=20log10(U2U1) where U2 and U1 are the amplitudes of the signals
Examples
ku ku [dB]
01 -20dB
0707 -3dB
1 0dB
141 3dB
10 20dB
100 40dB
1000 60dB
Passive components
Resistors
A resistor is a two-terminal electronic component that produces a voltage across its terminals that is proportional to the electric current through it in accordance with Ohms law
Generic graphic symbol
aMetalized resistor
bWirewound resistor
cCarbon resistor
dResistor ladder
eThick-film resistor
The primary characteristics of a resistor
Resistance (usually expressed in Ω kΩ and MΩ) Tolerance Maximal (rated) power Temperature coefficient of resistance (TCR) Maximal working voltage Parasitic inductance
Series and parallel resistors
The equivalent resistance of tworesistors in series connection
R=R1+R2
The equivalent resistance of tworesistors in parallel connection
1R=1R1+1R2
For n resistors
R=R1+R2+R3+Rn
For n resistors
1R=1R1+1R2+1R3+1Rn
Resistive divider
copy Wikipedia
If R1=R2 then Vout = Vin2
The voltage output of a voltage divider is not fixed but varies according to the load To obtain a reasonably stable output voltage the output current should be a small fraction of the input current
Loaded voltage divider
The voltage between points A and B
U = UT = UINmiddot [R2 (R1 + R2)]
According to Theveninrsquostheorem
RT = (R1 middot R2) (R1+ R2)
In practical projects we often
assume that RL should be 10 times higher than RT
Potentiometers
A potentiometer is a three-terminal resistor with a sliding contact acting as an adjustable voltage divider
Capacitors
copy Wikipedia
A capacitor is a passive electronic component consisting of a pair of conductors separated by a dielectric (insulator)
An ideal capacitor is characterized by a single constant value capacitance measured in farads This is the ratio of the electric charge on each conductor to the potential difference between them
The properties of capacitor are expressed by an equation
C=QU
Where C is capacitance Q is the electriccharge stored inside the capacitor and U is thevoltage between conductors (plates)
Capacitors ndashinternal structure
a) Film capacitor
b) Metalised plastic film capacitor
c) Ceramic disc capacitor
d) Tubular ceramic capacitor
e) Multilayer ceramic capacitor
Supercapacitors
Maxwell Technologies supercapacitors
Ultracapacitor (known also as anelectrochemical double layer capacitor) is an electrochemical capacitor that has a very high energy density when compared to common capacitors typically on the order of thousands of times greater than a high capacity electrolytic capacitor
They are characterized by a very shortcharging time (seconds to minutes)
Possible applications ndash electriccars power tools emergencypower supplies
Supercapacitors ndash cont
Pros very short charging time
Cons relatively high price
Supercapacitors vs standard capacitors
New generation of supercapacitotors
Second generation of supercapacitors by ioxuscom (2010)
From left 220F800F1000F Operating voltage 23V max
copy wwwioxuscom
Capacitors ndash cont
Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)
If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A
Capacitors ndash cont
Most imporant capacitor parameters
bullCapacitance [microF] [nF] or [pF]
bullTolerance []
bullRated voltage [V]
bullDischarge rate (leakage current)
bullTemperature coefficient of capacitance
bullEquivalent series resitance (ESR)
Capacitors ndash cont
a)Aluminium electrolytic capacitor
b)Tantalum electrolytic capacitor
c)Polyesther capacitor
d)Ceramic disc capacitor
e)Mylar capacitor
Capacitors ndash cont
Capacitors in series connection
For two capacitors in series the equivalent capacitance is
For parallel configuration
For two capacitors in parallel the equivalent capacitance is
C=C1+C2
For n capacitors (general case)
Capacitors ndash cont
Capacitor discharge through a resistor
If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge
The discharge rate is expressed by an equation
Where RC is called time constant
Capacitors ndash cont
Capacitor charging through a resistor
If a capacitor C will be charged from source of voltage UWE
through a resistor R the voltage change across its terminals will be described by the following equations
The final solution is
Inductors
An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it
An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material
Graphic symbola) Toroidal core inductor b)cylindrical core inductor
The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L
where L is expressed in H (Henryrsquos) but most often in mH or microH
Inductors ndash cont
Different variations of inductors
Surface mount(SMT) inductors
Cylindricalcoreinductors
Inductor parameters
bullInductance [H]
bullRated voltage [V]
bullTolerance []
bullSaturation DC current [A]
bullMaximal RMS current [A]
bullSelf-resonance frequency [Hz]
bullDC resistance [Ω]
Typical set of parameters
Coilcraft DO3340P-104M inductor
L-100microH tol-20 Isat-25A Irms-12A
SRF-5MHz(typ) RDC-022Ω
Transformers
A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation
Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio
Transformer ndash cont
The current I2 flowing in the secondary winding is inversely proportional
to the current I1 flowing in the primary winding
Moreover the impedance connected to the transformer is transformed by the square of the turns ratio
Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer
Transformers ndash cont
The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit
Examples of low power transformers
Toroidal coretransformer
Toroidal core variabletransformer
(autotransformer)
Laminatedcore EI transformers
Diodes
A diode is a two-terminal electronic component that conducts electric current in only one direction
When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)
Diodes ndash cont
The currentndashvoltage characteristic of a diodeWhere
ID is diode current
If is forward diode current
IFmax is maximum diode
current
UF is forward diode voltage
UR is reverse diode voltage
URmax is the maximum
reverse voltage diodevoltage
Diodes ndash cont
For common types of diodes the value of UF voltage is
bullFor Germanium junction diode 02 04V
bullFor Silicone junction diode 05 08V
bullFor Schottky diode 0204V
An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation
Where I is the diode current
IS is the reverse bias saturation current (or scale current)
VD is the voltage across the diode
VT is the thermal voltage and
n is the ideality factor also known as the quality factor
Diodes ndashcont
The thermal voltage VT is approximately 2585 mV at 300 K
At any other temperature it is given by an equation
where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)
Diodes ndash cont
The typical I-V characteristics of for germaniumand silicone junction diode
Diodes ndash cont
Diode as a switching element
Following the end of forward conduction in a PN type diode a
reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called
reverse recovery time and usually is between tens and hundreds of
ns (ie between 1e-8 and 1e-7 s)
Diodes ndash cont
Diode as a rectifier
A half wave rectifier
A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification
Diodes ndash cont
A full-wave rectifier
This kind of a circuit is also known as the bridge rectifier
Diodes ndash cont
A rectifier in a DC voltage supply
Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge
In general case the simple design rule should be followed
RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)
Diodes ndash cont
Another application ndash diode-based voltage limiter
The cathode of a diode has a potential equal to 4V
U out max = 4V + 06 V = 46 V
If UINlt46V then UOUT = UIN
Bipolar Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals
Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors
B=base C=collector E= emitter
Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases
Transistors ndash cont
The history of the transistor
The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work
The first silicon transistors were produced by Western Electric and TexasInstruments in 1954
Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)
copy wwwporticusorg
Transistors ndash cont
An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased
NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia
The first transistor
copy Bell Labs
Transistor ndash cont
Transistor as an amplifier
A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated
The relations between currents in BJT copy radartutorialeu
Transistor ndash cont
The most often used amplifier circuits
highmediumlowBandwidth4
00001800Phase Shift between input and output signals
3
lt 1highhighCurrent gain2
highlt 1highVoltage gain1
COMMON BASE
COMMON COLLECTOR
COMMON EMITTER
AMPLIFIER
Nr
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Fundamental definitions (cont)
Electric power
An electric power P is the rate at which electrical energy is transferred by an electric circuit The SI unit of power is the watt In direct current resistive circuits electrical power is calculated using Joules law
P = UI
The unit
[W] = [J] [s] = ([J] [C]) ([C] [s]) [W] = [V][A]
Ohmrsquos law allows us to evaluate an electric power dissipated by a resistor
P = I2 R and respectively P = U2R
Fundamental definitions (cont)
SignalsIn electronics a signal is usually defined as a time-varying voltage or current that conveys information
Sinuisoidal signal
U = Umsin ω t
whereUm - amplitude ω =2πf ndash pulsation[rads]
t ndash time [s] f ndash frequency [Hz]
Other parameters
Vp-p = Peak-to-Peak value
Root-Mean_Square value (RMS)
For sinusoidal signal
Vp-p = 2Um
VRMS=0707Um
dttUT
UT
RMS int=0
2 )(1
Fundamental definitions (cont)
Square wave signal
For this signal URMS=UM
Other parameters
Risetime
Fall time
Highlow amplitude
Please note that real-life signal are not rectangular ie risetime and fall time are always greater than zero
For practical purposes risefall times are usually measured between 10 and 90 of the final value of the signal
Fundamental definitions (cont)
Sawtooth signal (sawtooth wave)
sawtooth wave ramps upward and then sharply drops
Pulses
A rapid transient changes in the amplitude of a signal
Step signals amp glitches
Useful mostly for theoretical analysis
Fundamental definitions (cont)
Decibel gain
The decibel (dB) is a logarithmic unit that indicates the ratio of a physical quantity (usually power or intensity) relative to a specified or implied reference level The decibel ratio of two signals can be expressed by a formula
ku[dB]=20log10(U2U1) where U2 and U1 are the amplitudes of the signals
Examples
ku ku [dB]
01 -20dB
0707 -3dB
1 0dB
141 3dB
10 20dB
100 40dB
1000 60dB
Passive components
Resistors
A resistor is a two-terminal electronic component that produces a voltage across its terminals that is proportional to the electric current through it in accordance with Ohms law
Generic graphic symbol
aMetalized resistor
bWirewound resistor
cCarbon resistor
dResistor ladder
eThick-film resistor
The primary characteristics of a resistor
Resistance (usually expressed in Ω kΩ and MΩ) Tolerance Maximal (rated) power Temperature coefficient of resistance (TCR) Maximal working voltage Parasitic inductance
Series and parallel resistors
The equivalent resistance of tworesistors in series connection
R=R1+R2
The equivalent resistance of tworesistors in parallel connection
1R=1R1+1R2
For n resistors
R=R1+R2+R3+Rn
For n resistors
1R=1R1+1R2+1R3+1Rn
Resistive divider
copy Wikipedia
If R1=R2 then Vout = Vin2
The voltage output of a voltage divider is not fixed but varies according to the load To obtain a reasonably stable output voltage the output current should be a small fraction of the input current
Loaded voltage divider
The voltage between points A and B
U = UT = UINmiddot [R2 (R1 + R2)]
According to Theveninrsquostheorem
RT = (R1 middot R2) (R1+ R2)
In practical projects we often
assume that RL should be 10 times higher than RT
Potentiometers
A potentiometer is a three-terminal resistor with a sliding contact acting as an adjustable voltage divider
Capacitors
copy Wikipedia
A capacitor is a passive electronic component consisting of a pair of conductors separated by a dielectric (insulator)
An ideal capacitor is characterized by a single constant value capacitance measured in farads This is the ratio of the electric charge on each conductor to the potential difference between them
The properties of capacitor are expressed by an equation
C=QU
Where C is capacitance Q is the electriccharge stored inside the capacitor and U is thevoltage between conductors (plates)
Capacitors ndashinternal structure
a) Film capacitor
b) Metalised plastic film capacitor
c) Ceramic disc capacitor
d) Tubular ceramic capacitor
e) Multilayer ceramic capacitor
Supercapacitors
Maxwell Technologies supercapacitors
Ultracapacitor (known also as anelectrochemical double layer capacitor) is an electrochemical capacitor that has a very high energy density when compared to common capacitors typically on the order of thousands of times greater than a high capacity electrolytic capacitor
They are characterized by a very shortcharging time (seconds to minutes)
Possible applications ndash electriccars power tools emergencypower supplies
Supercapacitors ndash cont
Pros very short charging time
Cons relatively high price
Supercapacitors vs standard capacitors
New generation of supercapacitotors
Second generation of supercapacitors by ioxuscom (2010)
From left 220F800F1000F Operating voltage 23V max
copy wwwioxuscom
Capacitors ndash cont
Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)
If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A
Capacitors ndash cont
Most imporant capacitor parameters
bullCapacitance [microF] [nF] or [pF]
bullTolerance []
bullRated voltage [V]
bullDischarge rate (leakage current)
bullTemperature coefficient of capacitance
bullEquivalent series resitance (ESR)
Capacitors ndash cont
a)Aluminium electrolytic capacitor
b)Tantalum electrolytic capacitor
c)Polyesther capacitor
d)Ceramic disc capacitor
e)Mylar capacitor
Capacitors ndash cont
Capacitors in series connection
For two capacitors in series the equivalent capacitance is
For parallel configuration
For two capacitors in parallel the equivalent capacitance is
C=C1+C2
For n capacitors (general case)
Capacitors ndash cont
Capacitor discharge through a resistor
If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge
The discharge rate is expressed by an equation
Where RC is called time constant
Capacitors ndash cont
Capacitor charging through a resistor
If a capacitor C will be charged from source of voltage UWE
through a resistor R the voltage change across its terminals will be described by the following equations
The final solution is
Inductors
An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it
An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material
Graphic symbola) Toroidal core inductor b)cylindrical core inductor
The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L
where L is expressed in H (Henryrsquos) but most often in mH or microH
Inductors ndash cont
Different variations of inductors
Surface mount(SMT) inductors
Cylindricalcoreinductors
Inductor parameters
bullInductance [H]
bullRated voltage [V]
bullTolerance []
bullSaturation DC current [A]
bullMaximal RMS current [A]
bullSelf-resonance frequency [Hz]
bullDC resistance [Ω]
Typical set of parameters
Coilcraft DO3340P-104M inductor
L-100microH tol-20 Isat-25A Irms-12A
SRF-5MHz(typ) RDC-022Ω
Transformers
A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation
Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio
Transformer ndash cont
The current I2 flowing in the secondary winding is inversely proportional
to the current I1 flowing in the primary winding
Moreover the impedance connected to the transformer is transformed by the square of the turns ratio
Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer
Transformers ndash cont
The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit
Examples of low power transformers
Toroidal coretransformer
Toroidal core variabletransformer
(autotransformer)
Laminatedcore EI transformers
Diodes
A diode is a two-terminal electronic component that conducts electric current in only one direction
When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)
Diodes ndash cont
The currentndashvoltage characteristic of a diodeWhere
ID is diode current
If is forward diode current
IFmax is maximum diode
current
UF is forward diode voltage
UR is reverse diode voltage
URmax is the maximum
reverse voltage diodevoltage
Diodes ndash cont
For common types of diodes the value of UF voltage is
bullFor Germanium junction diode 02 04V
bullFor Silicone junction diode 05 08V
bullFor Schottky diode 0204V
An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation
Where I is the diode current
IS is the reverse bias saturation current (or scale current)
VD is the voltage across the diode
VT is the thermal voltage and
n is the ideality factor also known as the quality factor
Diodes ndashcont
The thermal voltage VT is approximately 2585 mV at 300 K
At any other temperature it is given by an equation
where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)
Diodes ndash cont
The typical I-V characteristics of for germaniumand silicone junction diode
Diodes ndash cont
Diode as a switching element
Following the end of forward conduction in a PN type diode a
reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called
reverse recovery time and usually is between tens and hundreds of
ns (ie between 1e-8 and 1e-7 s)
Diodes ndash cont
Diode as a rectifier
A half wave rectifier
A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification
Diodes ndash cont
A full-wave rectifier
This kind of a circuit is also known as the bridge rectifier
Diodes ndash cont
A rectifier in a DC voltage supply
Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge
In general case the simple design rule should be followed
RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)
Diodes ndash cont
Another application ndash diode-based voltage limiter
The cathode of a diode has a potential equal to 4V
U out max = 4V + 06 V = 46 V
If UINlt46V then UOUT = UIN
Bipolar Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals
Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors
B=base C=collector E= emitter
Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases
Transistors ndash cont
The history of the transistor
The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work
The first silicon transistors were produced by Western Electric and TexasInstruments in 1954
Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)
copy wwwporticusorg
Transistors ndash cont
An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased
NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia
The first transistor
copy Bell Labs
Transistor ndash cont
Transistor as an amplifier
A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated
The relations between currents in BJT copy radartutorialeu
Transistor ndash cont
The most often used amplifier circuits
highmediumlowBandwidth4
00001800Phase Shift between input and output signals
3
lt 1highhighCurrent gain2
highlt 1highVoltage gain1
COMMON BASE
COMMON COLLECTOR
COMMON EMITTER
AMPLIFIER
Nr
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Fundamental definitions (cont)
SignalsIn electronics a signal is usually defined as a time-varying voltage or current that conveys information
Sinuisoidal signal
U = Umsin ω t
whereUm - amplitude ω =2πf ndash pulsation[rads]
t ndash time [s] f ndash frequency [Hz]
Other parameters
Vp-p = Peak-to-Peak value
Root-Mean_Square value (RMS)
For sinusoidal signal
Vp-p = 2Um
VRMS=0707Um
dttUT
UT
RMS int=0
2 )(1
Fundamental definitions (cont)
Square wave signal
For this signal URMS=UM
Other parameters
Risetime
Fall time
Highlow amplitude
Please note that real-life signal are not rectangular ie risetime and fall time are always greater than zero
For practical purposes risefall times are usually measured between 10 and 90 of the final value of the signal
Fundamental definitions (cont)
Sawtooth signal (sawtooth wave)
sawtooth wave ramps upward and then sharply drops
Pulses
A rapid transient changes in the amplitude of a signal
Step signals amp glitches
Useful mostly for theoretical analysis
Fundamental definitions (cont)
Decibel gain
The decibel (dB) is a logarithmic unit that indicates the ratio of a physical quantity (usually power or intensity) relative to a specified or implied reference level The decibel ratio of two signals can be expressed by a formula
ku[dB]=20log10(U2U1) where U2 and U1 are the amplitudes of the signals
Examples
ku ku [dB]
01 -20dB
0707 -3dB
1 0dB
141 3dB
10 20dB
100 40dB
1000 60dB
Passive components
Resistors
A resistor is a two-terminal electronic component that produces a voltage across its terminals that is proportional to the electric current through it in accordance with Ohms law
Generic graphic symbol
aMetalized resistor
bWirewound resistor
cCarbon resistor
dResistor ladder
eThick-film resistor
The primary characteristics of a resistor
Resistance (usually expressed in Ω kΩ and MΩ) Tolerance Maximal (rated) power Temperature coefficient of resistance (TCR) Maximal working voltage Parasitic inductance
Series and parallel resistors
The equivalent resistance of tworesistors in series connection
R=R1+R2
The equivalent resistance of tworesistors in parallel connection
1R=1R1+1R2
For n resistors
R=R1+R2+R3+Rn
For n resistors
1R=1R1+1R2+1R3+1Rn
Resistive divider
copy Wikipedia
If R1=R2 then Vout = Vin2
The voltage output of a voltage divider is not fixed but varies according to the load To obtain a reasonably stable output voltage the output current should be a small fraction of the input current
Loaded voltage divider
The voltage between points A and B
U = UT = UINmiddot [R2 (R1 + R2)]
According to Theveninrsquostheorem
RT = (R1 middot R2) (R1+ R2)
In practical projects we often
assume that RL should be 10 times higher than RT
Potentiometers
A potentiometer is a three-terminal resistor with a sliding contact acting as an adjustable voltage divider
Capacitors
copy Wikipedia
A capacitor is a passive electronic component consisting of a pair of conductors separated by a dielectric (insulator)
An ideal capacitor is characterized by a single constant value capacitance measured in farads This is the ratio of the electric charge on each conductor to the potential difference between them
The properties of capacitor are expressed by an equation
C=QU
Where C is capacitance Q is the electriccharge stored inside the capacitor and U is thevoltage between conductors (plates)
Capacitors ndashinternal structure
a) Film capacitor
b) Metalised plastic film capacitor
c) Ceramic disc capacitor
d) Tubular ceramic capacitor
e) Multilayer ceramic capacitor
Supercapacitors
Maxwell Technologies supercapacitors
Ultracapacitor (known also as anelectrochemical double layer capacitor) is an electrochemical capacitor that has a very high energy density when compared to common capacitors typically on the order of thousands of times greater than a high capacity electrolytic capacitor
They are characterized by a very shortcharging time (seconds to minutes)
Possible applications ndash electriccars power tools emergencypower supplies
Supercapacitors ndash cont
Pros very short charging time
Cons relatively high price
Supercapacitors vs standard capacitors
New generation of supercapacitotors
Second generation of supercapacitors by ioxuscom (2010)
From left 220F800F1000F Operating voltage 23V max
copy wwwioxuscom
Capacitors ndash cont
Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)
If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A
Capacitors ndash cont
Most imporant capacitor parameters
bullCapacitance [microF] [nF] or [pF]
bullTolerance []
bullRated voltage [V]
bullDischarge rate (leakage current)
bullTemperature coefficient of capacitance
bullEquivalent series resitance (ESR)
Capacitors ndash cont
a)Aluminium electrolytic capacitor
b)Tantalum electrolytic capacitor
c)Polyesther capacitor
d)Ceramic disc capacitor
e)Mylar capacitor
Capacitors ndash cont
Capacitors in series connection
For two capacitors in series the equivalent capacitance is
For parallel configuration
For two capacitors in parallel the equivalent capacitance is
C=C1+C2
For n capacitors (general case)
Capacitors ndash cont
Capacitor discharge through a resistor
If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge
The discharge rate is expressed by an equation
Where RC is called time constant
Capacitors ndash cont
Capacitor charging through a resistor
If a capacitor C will be charged from source of voltage UWE
through a resistor R the voltage change across its terminals will be described by the following equations
The final solution is
Inductors
An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it
An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material
Graphic symbola) Toroidal core inductor b)cylindrical core inductor
The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L
where L is expressed in H (Henryrsquos) but most often in mH or microH
Inductors ndash cont
Different variations of inductors
Surface mount(SMT) inductors
Cylindricalcoreinductors
Inductor parameters
bullInductance [H]
bullRated voltage [V]
bullTolerance []
bullSaturation DC current [A]
bullMaximal RMS current [A]
bullSelf-resonance frequency [Hz]
bullDC resistance [Ω]
Typical set of parameters
Coilcraft DO3340P-104M inductor
L-100microH tol-20 Isat-25A Irms-12A
SRF-5MHz(typ) RDC-022Ω
Transformers
A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation
Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio
Transformer ndash cont
The current I2 flowing in the secondary winding is inversely proportional
to the current I1 flowing in the primary winding
Moreover the impedance connected to the transformer is transformed by the square of the turns ratio
Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer
Transformers ndash cont
The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit
Examples of low power transformers
Toroidal coretransformer
Toroidal core variabletransformer
(autotransformer)
Laminatedcore EI transformers
Diodes
A diode is a two-terminal electronic component that conducts electric current in only one direction
When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)
Diodes ndash cont
The currentndashvoltage characteristic of a diodeWhere
ID is diode current
If is forward diode current
IFmax is maximum diode
current
UF is forward diode voltage
UR is reverse diode voltage
URmax is the maximum
reverse voltage diodevoltage
Diodes ndash cont
For common types of diodes the value of UF voltage is
bullFor Germanium junction diode 02 04V
bullFor Silicone junction diode 05 08V
bullFor Schottky diode 0204V
An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation
Where I is the diode current
IS is the reverse bias saturation current (or scale current)
VD is the voltage across the diode
VT is the thermal voltage and
n is the ideality factor also known as the quality factor
Diodes ndashcont
The thermal voltage VT is approximately 2585 mV at 300 K
At any other temperature it is given by an equation
where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)
Diodes ndash cont
The typical I-V characteristics of for germaniumand silicone junction diode
Diodes ndash cont
Diode as a switching element
Following the end of forward conduction in a PN type diode a
reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called
reverse recovery time and usually is between tens and hundreds of
ns (ie between 1e-8 and 1e-7 s)
Diodes ndash cont
Diode as a rectifier
A half wave rectifier
A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification
Diodes ndash cont
A full-wave rectifier
This kind of a circuit is also known as the bridge rectifier
Diodes ndash cont
A rectifier in a DC voltage supply
Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge
In general case the simple design rule should be followed
RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)
Diodes ndash cont
Another application ndash diode-based voltage limiter
The cathode of a diode has a potential equal to 4V
U out max = 4V + 06 V = 46 V
If UINlt46V then UOUT = UIN
Bipolar Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals
Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors
B=base C=collector E= emitter
Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases
Transistors ndash cont
The history of the transistor
The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work
The first silicon transistors were produced by Western Electric and TexasInstruments in 1954
Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)
copy wwwporticusorg
Transistors ndash cont
An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased
NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia
The first transistor
copy Bell Labs
Transistor ndash cont
Transistor as an amplifier
A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated
The relations between currents in BJT copy radartutorialeu
Transistor ndash cont
The most often used amplifier circuits
highmediumlowBandwidth4
00001800Phase Shift between input and output signals
3
lt 1highhighCurrent gain2
highlt 1highVoltage gain1
COMMON BASE
COMMON COLLECTOR
COMMON EMITTER
AMPLIFIER
Nr
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Fundamental definitions (cont)
Square wave signal
For this signal URMS=UM
Other parameters
Risetime
Fall time
Highlow amplitude
Please note that real-life signal are not rectangular ie risetime and fall time are always greater than zero
For practical purposes risefall times are usually measured between 10 and 90 of the final value of the signal
Fundamental definitions (cont)
Sawtooth signal (sawtooth wave)
sawtooth wave ramps upward and then sharply drops
Pulses
A rapid transient changes in the amplitude of a signal
Step signals amp glitches
Useful mostly for theoretical analysis
Fundamental definitions (cont)
Decibel gain
The decibel (dB) is a logarithmic unit that indicates the ratio of a physical quantity (usually power or intensity) relative to a specified or implied reference level The decibel ratio of two signals can be expressed by a formula
ku[dB]=20log10(U2U1) where U2 and U1 are the amplitudes of the signals
Examples
ku ku [dB]
01 -20dB
0707 -3dB
1 0dB
141 3dB
10 20dB
100 40dB
1000 60dB
Passive components
Resistors
A resistor is a two-terminal electronic component that produces a voltage across its terminals that is proportional to the electric current through it in accordance with Ohms law
Generic graphic symbol
aMetalized resistor
bWirewound resistor
cCarbon resistor
dResistor ladder
eThick-film resistor
The primary characteristics of a resistor
Resistance (usually expressed in Ω kΩ and MΩ) Tolerance Maximal (rated) power Temperature coefficient of resistance (TCR) Maximal working voltage Parasitic inductance
Series and parallel resistors
The equivalent resistance of tworesistors in series connection
R=R1+R2
The equivalent resistance of tworesistors in parallel connection
1R=1R1+1R2
For n resistors
R=R1+R2+R3+Rn
For n resistors
1R=1R1+1R2+1R3+1Rn
Resistive divider
copy Wikipedia
If R1=R2 then Vout = Vin2
The voltage output of a voltage divider is not fixed but varies according to the load To obtain a reasonably stable output voltage the output current should be a small fraction of the input current
Loaded voltage divider
The voltage between points A and B
U = UT = UINmiddot [R2 (R1 + R2)]
According to Theveninrsquostheorem
RT = (R1 middot R2) (R1+ R2)
In practical projects we often
assume that RL should be 10 times higher than RT
Potentiometers
A potentiometer is a three-terminal resistor with a sliding contact acting as an adjustable voltage divider
Capacitors
copy Wikipedia
A capacitor is a passive electronic component consisting of a pair of conductors separated by a dielectric (insulator)
An ideal capacitor is characterized by a single constant value capacitance measured in farads This is the ratio of the electric charge on each conductor to the potential difference between them
The properties of capacitor are expressed by an equation
C=QU
Where C is capacitance Q is the electriccharge stored inside the capacitor and U is thevoltage between conductors (plates)
Capacitors ndashinternal structure
a) Film capacitor
b) Metalised plastic film capacitor
c) Ceramic disc capacitor
d) Tubular ceramic capacitor
e) Multilayer ceramic capacitor
Supercapacitors
Maxwell Technologies supercapacitors
Ultracapacitor (known also as anelectrochemical double layer capacitor) is an electrochemical capacitor that has a very high energy density when compared to common capacitors typically on the order of thousands of times greater than a high capacity electrolytic capacitor
They are characterized by a very shortcharging time (seconds to minutes)
Possible applications ndash electriccars power tools emergencypower supplies
Supercapacitors ndash cont
Pros very short charging time
Cons relatively high price
Supercapacitors vs standard capacitors
New generation of supercapacitotors
Second generation of supercapacitors by ioxuscom (2010)
From left 220F800F1000F Operating voltage 23V max
copy wwwioxuscom
Capacitors ndash cont
Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)
If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A
Capacitors ndash cont
Most imporant capacitor parameters
bullCapacitance [microF] [nF] or [pF]
bullTolerance []
bullRated voltage [V]
bullDischarge rate (leakage current)
bullTemperature coefficient of capacitance
bullEquivalent series resitance (ESR)
Capacitors ndash cont
a)Aluminium electrolytic capacitor
b)Tantalum electrolytic capacitor
c)Polyesther capacitor
d)Ceramic disc capacitor
e)Mylar capacitor
Capacitors ndash cont
Capacitors in series connection
For two capacitors in series the equivalent capacitance is
For parallel configuration
For two capacitors in parallel the equivalent capacitance is
C=C1+C2
For n capacitors (general case)
Capacitors ndash cont
Capacitor discharge through a resistor
If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge
The discharge rate is expressed by an equation
Where RC is called time constant
Capacitors ndash cont
Capacitor charging through a resistor
If a capacitor C will be charged from source of voltage UWE
through a resistor R the voltage change across its terminals will be described by the following equations
The final solution is
Inductors
An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it
An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material
Graphic symbola) Toroidal core inductor b)cylindrical core inductor
The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L
where L is expressed in H (Henryrsquos) but most often in mH or microH
Inductors ndash cont
Different variations of inductors
Surface mount(SMT) inductors
Cylindricalcoreinductors
Inductor parameters
bullInductance [H]
bullRated voltage [V]
bullTolerance []
bullSaturation DC current [A]
bullMaximal RMS current [A]
bullSelf-resonance frequency [Hz]
bullDC resistance [Ω]
Typical set of parameters
Coilcraft DO3340P-104M inductor
L-100microH tol-20 Isat-25A Irms-12A
SRF-5MHz(typ) RDC-022Ω
Transformers
A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation
Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio
Transformer ndash cont
The current I2 flowing in the secondary winding is inversely proportional
to the current I1 flowing in the primary winding
Moreover the impedance connected to the transformer is transformed by the square of the turns ratio
Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer
Transformers ndash cont
The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit
Examples of low power transformers
Toroidal coretransformer
Toroidal core variabletransformer
(autotransformer)
Laminatedcore EI transformers
Diodes
A diode is a two-terminal electronic component that conducts electric current in only one direction
When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)
Diodes ndash cont
The currentndashvoltage characteristic of a diodeWhere
ID is diode current
If is forward diode current
IFmax is maximum diode
current
UF is forward diode voltage
UR is reverse diode voltage
URmax is the maximum
reverse voltage diodevoltage
Diodes ndash cont
For common types of diodes the value of UF voltage is
bullFor Germanium junction diode 02 04V
bullFor Silicone junction diode 05 08V
bullFor Schottky diode 0204V
An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation
Where I is the diode current
IS is the reverse bias saturation current (or scale current)
VD is the voltage across the diode
VT is the thermal voltage and
n is the ideality factor also known as the quality factor
Diodes ndashcont
The thermal voltage VT is approximately 2585 mV at 300 K
At any other temperature it is given by an equation
where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)
Diodes ndash cont
The typical I-V characteristics of for germaniumand silicone junction diode
Diodes ndash cont
Diode as a switching element
Following the end of forward conduction in a PN type diode a
reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called
reverse recovery time and usually is between tens and hundreds of
ns (ie between 1e-8 and 1e-7 s)
Diodes ndash cont
Diode as a rectifier
A half wave rectifier
A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification
Diodes ndash cont
A full-wave rectifier
This kind of a circuit is also known as the bridge rectifier
Diodes ndash cont
A rectifier in a DC voltage supply
Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge
In general case the simple design rule should be followed
RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)
Diodes ndash cont
Another application ndash diode-based voltage limiter
The cathode of a diode has a potential equal to 4V
U out max = 4V + 06 V = 46 V
If UINlt46V then UOUT = UIN
Bipolar Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals
Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors
B=base C=collector E= emitter
Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases
Transistors ndash cont
The history of the transistor
The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work
The first silicon transistors were produced by Western Electric and TexasInstruments in 1954
Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)
copy wwwporticusorg
Transistors ndash cont
An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased
NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia
The first transistor
copy Bell Labs
Transistor ndash cont
Transistor as an amplifier
A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated
The relations between currents in BJT copy radartutorialeu
Transistor ndash cont
The most often used amplifier circuits
highmediumlowBandwidth4
00001800Phase Shift between input and output signals
3
lt 1highhighCurrent gain2
highlt 1highVoltage gain1
COMMON BASE
COMMON COLLECTOR
COMMON EMITTER
AMPLIFIER
Nr
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Fundamental definitions (cont)
Sawtooth signal (sawtooth wave)
sawtooth wave ramps upward and then sharply drops
Pulses
A rapid transient changes in the amplitude of a signal
Step signals amp glitches
Useful mostly for theoretical analysis
Fundamental definitions (cont)
Decibel gain
The decibel (dB) is a logarithmic unit that indicates the ratio of a physical quantity (usually power or intensity) relative to a specified or implied reference level The decibel ratio of two signals can be expressed by a formula
ku[dB]=20log10(U2U1) where U2 and U1 are the amplitudes of the signals
Examples
ku ku [dB]
01 -20dB
0707 -3dB
1 0dB
141 3dB
10 20dB
100 40dB
1000 60dB
Passive components
Resistors
A resistor is a two-terminal electronic component that produces a voltage across its terminals that is proportional to the electric current through it in accordance with Ohms law
Generic graphic symbol
aMetalized resistor
bWirewound resistor
cCarbon resistor
dResistor ladder
eThick-film resistor
The primary characteristics of a resistor
Resistance (usually expressed in Ω kΩ and MΩ) Tolerance Maximal (rated) power Temperature coefficient of resistance (TCR) Maximal working voltage Parasitic inductance
Series and parallel resistors
The equivalent resistance of tworesistors in series connection
R=R1+R2
The equivalent resistance of tworesistors in parallel connection
1R=1R1+1R2
For n resistors
R=R1+R2+R3+Rn
For n resistors
1R=1R1+1R2+1R3+1Rn
Resistive divider
copy Wikipedia
If R1=R2 then Vout = Vin2
The voltage output of a voltage divider is not fixed but varies according to the load To obtain a reasonably stable output voltage the output current should be a small fraction of the input current
Loaded voltage divider
The voltage between points A and B
U = UT = UINmiddot [R2 (R1 + R2)]
According to Theveninrsquostheorem
RT = (R1 middot R2) (R1+ R2)
In practical projects we often
assume that RL should be 10 times higher than RT
Potentiometers
A potentiometer is a three-terminal resistor with a sliding contact acting as an adjustable voltage divider
Capacitors
copy Wikipedia
A capacitor is a passive electronic component consisting of a pair of conductors separated by a dielectric (insulator)
An ideal capacitor is characterized by a single constant value capacitance measured in farads This is the ratio of the electric charge on each conductor to the potential difference between them
The properties of capacitor are expressed by an equation
C=QU
Where C is capacitance Q is the electriccharge stored inside the capacitor and U is thevoltage between conductors (plates)
Capacitors ndashinternal structure
a) Film capacitor
b) Metalised plastic film capacitor
c) Ceramic disc capacitor
d) Tubular ceramic capacitor
e) Multilayer ceramic capacitor
Supercapacitors
Maxwell Technologies supercapacitors
Ultracapacitor (known also as anelectrochemical double layer capacitor) is an electrochemical capacitor that has a very high energy density when compared to common capacitors typically on the order of thousands of times greater than a high capacity electrolytic capacitor
They are characterized by a very shortcharging time (seconds to minutes)
Possible applications ndash electriccars power tools emergencypower supplies
Supercapacitors ndash cont
Pros very short charging time
Cons relatively high price
Supercapacitors vs standard capacitors
New generation of supercapacitotors
Second generation of supercapacitors by ioxuscom (2010)
From left 220F800F1000F Operating voltage 23V max
copy wwwioxuscom
Capacitors ndash cont
Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)
If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A
Capacitors ndash cont
Most imporant capacitor parameters
bullCapacitance [microF] [nF] or [pF]
bullTolerance []
bullRated voltage [V]
bullDischarge rate (leakage current)
bullTemperature coefficient of capacitance
bullEquivalent series resitance (ESR)
Capacitors ndash cont
a)Aluminium electrolytic capacitor
b)Tantalum electrolytic capacitor
c)Polyesther capacitor
d)Ceramic disc capacitor
e)Mylar capacitor
Capacitors ndash cont
Capacitors in series connection
For two capacitors in series the equivalent capacitance is
For parallel configuration
For two capacitors in parallel the equivalent capacitance is
C=C1+C2
For n capacitors (general case)
Capacitors ndash cont
Capacitor discharge through a resistor
If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge
The discharge rate is expressed by an equation
Where RC is called time constant
Capacitors ndash cont
Capacitor charging through a resistor
If a capacitor C will be charged from source of voltage UWE
through a resistor R the voltage change across its terminals will be described by the following equations
The final solution is
Inductors
An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it
An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material
Graphic symbola) Toroidal core inductor b)cylindrical core inductor
The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L
where L is expressed in H (Henryrsquos) but most often in mH or microH
Inductors ndash cont
Different variations of inductors
Surface mount(SMT) inductors
Cylindricalcoreinductors
Inductor parameters
bullInductance [H]
bullRated voltage [V]
bullTolerance []
bullSaturation DC current [A]
bullMaximal RMS current [A]
bullSelf-resonance frequency [Hz]
bullDC resistance [Ω]
Typical set of parameters
Coilcraft DO3340P-104M inductor
L-100microH tol-20 Isat-25A Irms-12A
SRF-5MHz(typ) RDC-022Ω
Transformers
A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation
Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio
Transformer ndash cont
The current I2 flowing in the secondary winding is inversely proportional
to the current I1 flowing in the primary winding
Moreover the impedance connected to the transformer is transformed by the square of the turns ratio
Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer
Transformers ndash cont
The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit
Examples of low power transformers
Toroidal coretransformer
Toroidal core variabletransformer
(autotransformer)
Laminatedcore EI transformers
Diodes
A diode is a two-terminal electronic component that conducts electric current in only one direction
When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)
Diodes ndash cont
The currentndashvoltage characteristic of a diodeWhere
ID is diode current
If is forward diode current
IFmax is maximum diode
current
UF is forward diode voltage
UR is reverse diode voltage
URmax is the maximum
reverse voltage diodevoltage
Diodes ndash cont
For common types of diodes the value of UF voltage is
bullFor Germanium junction diode 02 04V
bullFor Silicone junction diode 05 08V
bullFor Schottky diode 0204V
An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation
Where I is the diode current
IS is the reverse bias saturation current (or scale current)
VD is the voltage across the diode
VT is the thermal voltage and
n is the ideality factor also known as the quality factor
Diodes ndashcont
The thermal voltage VT is approximately 2585 mV at 300 K
At any other temperature it is given by an equation
where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)
Diodes ndash cont
The typical I-V characteristics of for germaniumand silicone junction diode
Diodes ndash cont
Diode as a switching element
Following the end of forward conduction in a PN type diode a
reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called
reverse recovery time and usually is between tens and hundreds of
ns (ie between 1e-8 and 1e-7 s)
Diodes ndash cont
Diode as a rectifier
A half wave rectifier
A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification
Diodes ndash cont
A full-wave rectifier
This kind of a circuit is also known as the bridge rectifier
Diodes ndash cont
A rectifier in a DC voltage supply
Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge
In general case the simple design rule should be followed
RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)
Diodes ndash cont
Another application ndash diode-based voltage limiter
The cathode of a diode has a potential equal to 4V
U out max = 4V + 06 V = 46 V
If UINlt46V then UOUT = UIN
Bipolar Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals
Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors
B=base C=collector E= emitter
Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases
Transistors ndash cont
The history of the transistor
The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work
The first silicon transistors were produced by Western Electric and TexasInstruments in 1954
Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)
copy wwwporticusorg
Transistors ndash cont
An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased
NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia
The first transistor
copy Bell Labs
Transistor ndash cont
Transistor as an amplifier
A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated
The relations between currents in BJT copy radartutorialeu
Transistor ndash cont
The most often used amplifier circuits
highmediumlowBandwidth4
00001800Phase Shift between input and output signals
3
lt 1highhighCurrent gain2
highlt 1highVoltage gain1
COMMON BASE
COMMON COLLECTOR
COMMON EMITTER
AMPLIFIER
Nr
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Fundamental definitions (cont)
Decibel gain
The decibel (dB) is a logarithmic unit that indicates the ratio of a physical quantity (usually power or intensity) relative to a specified or implied reference level The decibel ratio of two signals can be expressed by a formula
ku[dB]=20log10(U2U1) where U2 and U1 are the amplitudes of the signals
Examples
ku ku [dB]
01 -20dB
0707 -3dB
1 0dB
141 3dB
10 20dB
100 40dB
1000 60dB
Passive components
Resistors
A resistor is a two-terminal electronic component that produces a voltage across its terminals that is proportional to the electric current through it in accordance with Ohms law
Generic graphic symbol
aMetalized resistor
bWirewound resistor
cCarbon resistor
dResistor ladder
eThick-film resistor
The primary characteristics of a resistor
Resistance (usually expressed in Ω kΩ and MΩ) Tolerance Maximal (rated) power Temperature coefficient of resistance (TCR) Maximal working voltage Parasitic inductance
Series and parallel resistors
The equivalent resistance of tworesistors in series connection
R=R1+R2
The equivalent resistance of tworesistors in parallel connection
1R=1R1+1R2
For n resistors
R=R1+R2+R3+Rn
For n resistors
1R=1R1+1R2+1R3+1Rn
Resistive divider
copy Wikipedia
If R1=R2 then Vout = Vin2
The voltage output of a voltage divider is not fixed but varies according to the load To obtain a reasonably stable output voltage the output current should be a small fraction of the input current
Loaded voltage divider
The voltage between points A and B
U = UT = UINmiddot [R2 (R1 + R2)]
According to Theveninrsquostheorem
RT = (R1 middot R2) (R1+ R2)
In practical projects we often
assume that RL should be 10 times higher than RT
Potentiometers
A potentiometer is a three-terminal resistor with a sliding contact acting as an adjustable voltage divider
Capacitors
copy Wikipedia
A capacitor is a passive electronic component consisting of a pair of conductors separated by a dielectric (insulator)
An ideal capacitor is characterized by a single constant value capacitance measured in farads This is the ratio of the electric charge on each conductor to the potential difference between them
The properties of capacitor are expressed by an equation
C=QU
Where C is capacitance Q is the electriccharge stored inside the capacitor and U is thevoltage between conductors (plates)
Capacitors ndashinternal structure
a) Film capacitor
b) Metalised plastic film capacitor
c) Ceramic disc capacitor
d) Tubular ceramic capacitor
e) Multilayer ceramic capacitor
Supercapacitors
Maxwell Technologies supercapacitors
Ultracapacitor (known also as anelectrochemical double layer capacitor) is an electrochemical capacitor that has a very high energy density when compared to common capacitors typically on the order of thousands of times greater than a high capacity electrolytic capacitor
They are characterized by a very shortcharging time (seconds to minutes)
Possible applications ndash electriccars power tools emergencypower supplies
Supercapacitors ndash cont
Pros very short charging time
Cons relatively high price
Supercapacitors vs standard capacitors
New generation of supercapacitotors
Second generation of supercapacitors by ioxuscom (2010)
From left 220F800F1000F Operating voltage 23V max
copy wwwioxuscom
Capacitors ndash cont
Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)
If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A
Capacitors ndash cont
Most imporant capacitor parameters
bullCapacitance [microF] [nF] or [pF]
bullTolerance []
bullRated voltage [V]
bullDischarge rate (leakage current)
bullTemperature coefficient of capacitance
bullEquivalent series resitance (ESR)
Capacitors ndash cont
a)Aluminium electrolytic capacitor
b)Tantalum electrolytic capacitor
c)Polyesther capacitor
d)Ceramic disc capacitor
e)Mylar capacitor
Capacitors ndash cont
Capacitors in series connection
For two capacitors in series the equivalent capacitance is
For parallel configuration
For two capacitors in parallel the equivalent capacitance is
C=C1+C2
For n capacitors (general case)
Capacitors ndash cont
Capacitor discharge through a resistor
If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge
The discharge rate is expressed by an equation
Where RC is called time constant
Capacitors ndash cont
Capacitor charging through a resistor
If a capacitor C will be charged from source of voltage UWE
through a resistor R the voltage change across its terminals will be described by the following equations
The final solution is
Inductors
An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it
An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material
Graphic symbola) Toroidal core inductor b)cylindrical core inductor
The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L
where L is expressed in H (Henryrsquos) but most often in mH or microH
Inductors ndash cont
Different variations of inductors
Surface mount(SMT) inductors
Cylindricalcoreinductors
Inductor parameters
bullInductance [H]
bullRated voltage [V]
bullTolerance []
bullSaturation DC current [A]
bullMaximal RMS current [A]
bullSelf-resonance frequency [Hz]
bullDC resistance [Ω]
Typical set of parameters
Coilcraft DO3340P-104M inductor
L-100microH tol-20 Isat-25A Irms-12A
SRF-5MHz(typ) RDC-022Ω
Transformers
A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation
Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio
Transformer ndash cont
The current I2 flowing in the secondary winding is inversely proportional
to the current I1 flowing in the primary winding
Moreover the impedance connected to the transformer is transformed by the square of the turns ratio
Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer
Transformers ndash cont
The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit
Examples of low power transformers
Toroidal coretransformer
Toroidal core variabletransformer
(autotransformer)
Laminatedcore EI transformers
Diodes
A diode is a two-terminal electronic component that conducts electric current in only one direction
When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)
Diodes ndash cont
The currentndashvoltage characteristic of a diodeWhere
ID is diode current
If is forward diode current
IFmax is maximum diode
current
UF is forward diode voltage
UR is reverse diode voltage
URmax is the maximum
reverse voltage diodevoltage
Diodes ndash cont
For common types of diodes the value of UF voltage is
bullFor Germanium junction diode 02 04V
bullFor Silicone junction diode 05 08V
bullFor Schottky diode 0204V
An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation
Where I is the diode current
IS is the reverse bias saturation current (or scale current)
VD is the voltage across the diode
VT is the thermal voltage and
n is the ideality factor also known as the quality factor
Diodes ndashcont
The thermal voltage VT is approximately 2585 mV at 300 K
At any other temperature it is given by an equation
where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)
Diodes ndash cont
The typical I-V characteristics of for germaniumand silicone junction diode
Diodes ndash cont
Diode as a switching element
Following the end of forward conduction in a PN type diode a
reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called
reverse recovery time and usually is between tens and hundreds of
ns (ie between 1e-8 and 1e-7 s)
Diodes ndash cont
Diode as a rectifier
A half wave rectifier
A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification
Diodes ndash cont
A full-wave rectifier
This kind of a circuit is also known as the bridge rectifier
Diodes ndash cont
A rectifier in a DC voltage supply
Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge
In general case the simple design rule should be followed
RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)
Diodes ndash cont
Another application ndash diode-based voltage limiter
The cathode of a diode has a potential equal to 4V
U out max = 4V + 06 V = 46 V
If UINlt46V then UOUT = UIN
Bipolar Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals
Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors
B=base C=collector E= emitter
Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases
Transistors ndash cont
The history of the transistor
The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work
The first silicon transistors were produced by Western Electric and TexasInstruments in 1954
Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)
copy wwwporticusorg
Transistors ndash cont
An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased
NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia
The first transistor
copy Bell Labs
Transistor ndash cont
Transistor as an amplifier
A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated
The relations between currents in BJT copy radartutorialeu
Transistor ndash cont
The most often used amplifier circuits
highmediumlowBandwidth4
00001800Phase Shift between input and output signals
3
lt 1highhighCurrent gain2
highlt 1highVoltage gain1
COMMON BASE
COMMON COLLECTOR
COMMON EMITTER
AMPLIFIER
Nr
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Passive components
Resistors
A resistor is a two-terminal electronic component that produces a voltage across its terminals that is proportional to the electric current through it in accordance with Ohms law
Generic graphic symbol
aMetalized resistor
bWirewound resistor
cCarbon resistor
dResistor ladder
eThick-film resistor
The primary characteristics of a resistor
Resistance (usually expressed in Ω kΩ and MΩ) Tolerance Maximal (rated) power Temperature coefficient of resistance (TCR) Maximal working voltage Parasitic inductance
Series and parallel resistors
The equivalent resistance of tworesistors in series connection
R=R1+R2
The equivalent resistance of tworesistors in parallel connection
1R=1R1+1R2
For n resistors
R=R1+R2+R3+Rn
For n resistors
1R=1R1+1R2+1R3+1Rn
Resistive divider
copy Wikipedia
If R1=R2 then Vout = Vin2
The voltage output of a voltage divider is not fixed but varies according to the load To obtain a reasonably stable output voltage the output current should be a small fraction of the input current
Loaded voltage divider
The voltage between points A and B
U = UT = UINmiddot [R2 (R1 + R2)]
According to Theveninrsquostheorem
RT = (R1 middot R2) (R1+ R2)
In practical projects we often
assume that RL should be 10 times higher than RT
Potentiometers
A potentiometer is a three-terminal resistor with a sliding contact acting as an adjustable voltage divider
Capacitors
copy Wikipedia
A capacitor is a passive electronic component consisting of a pair of conductors separated by a dielectric (insulator)
An ideal capacitor is characterized by a single constant value capacitance measured in farads This is the ratio of the electric charge on each conductor to the potential difference between them
The properties of capacitor are expressed by an equation
C=QU
Where C is capacitance Q is the electriccharge stored inside the capacitor and U is thevoltage between conductors (plates)
Capacitors ndashinternal structure
a) Film capacitor
b) Metalised plastic film capacitor
c) Ceramic disc capacitor
d) Tubular ceramic capacitor
e) Multilayer ceramic capacitor
Supercapacitors
Maxwell Technologies supercapacitors
Ultracapacitor (known also as anelectrochemical double layer capacitor) is an electrochemical capacitor that has a very high energy density when compared to common capacitors typically on the order of thousands of times greater than a high capacity electrolytic capacitor
They are characterized by a very shortcharging time (seconds to minutes)
Possible applications ndash electriccars power tools emergencypower supplies
Supercapacitors ndash cont
Pros very short charging time
Cons relatively high price
Supercapacitors vs standard capacitors
New generation of supercapacitotors
Second generation of supercapacitors by ioxuscom (2010)
From left 220F800F1000F Operating voltage 23V max
copy wwwioxuscom
Capacitors ndash cont
Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)
If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A
Capacitors ndash cont
Most imporant capacitor parameters
bullCapacitance [microF] [nF] or [pF]
bullTolerance []
bullRated voltage [V]
bullDischarge rate (leakage current)
bullTemperature coefficient of capacitance
bullEquivalent series resitance (ESR)
Capacitors ndash cont
a)Aluminium electrolytic capacitor
b)Tantalum electrolytic capacitor
c)Polyesther capacitor
d)Ceramic disc capacitor
e)Mylar capacitor
Capacitors ndash cont
Capacitors in series connection
For two capacitors in series the equivalent capacitance is
For parallel configuration
For two capacitors in parallel the equivalent capacitance is
C=C1+C2
For n capacitors (general case)
Capacitors ndash cont
Capacitor discharge through a resistor
If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge
The discharge rate is expressed by an equation
Where RC is called time constant
Capacitors ndash cont
Capacitor charging through a resistor
If a capacitor C will be charged from source of voltage UWE
through a resistor R the voltage change across its terminals will be described by the following equations
The final solution is
Inductors
An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it
An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material
Graphic symbola) Toroidal core inductor b)cylindrical core inductor
The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L
where L is expressed in H (Henryrsquos) but most often in mH or microH
Inductors ndash cont
Different variations of inductors
Surface mount(SMT) inductors
Cylindricalcoreinductors
Inductor parameters
bullInductance [H]
bullRated voltage [V]
bullTolerance []
bullSaturation DC current [A]
bullMaximal RMS current [A]
bullSelf-resonance frequency [Hz]
bullDC resistance [Ω]
Typical set of parameters
Coilcraft DO3340P-104M inductor
L-100microH tol-20 Isat-25A Irms-12A
SRF-5MHz(typ) RDC-022Ω
Transformers
A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation
Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio
Transformer ndash cont
The current I2 flowing in the secondary winding is inversely proportional
to the current I1 flowing in the primary winding
Moreover the impedance connected to the transformer is transformed by the square of the turns ratio
Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer
Transformers ndash cont
The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit
Examples of low power transformers
Toroidal coretransformer
Toroidal core variabletransformer
(autotransformer)
Laminatedcore EI transformers
Diodes
A diode is a two-terminal electronic component that conducts electric current in only one direction
When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)
Diodes ndash cont
The currentndashvoltage characteristic of a diodeWhere
ID is diode current
If is forward diode current
IFmax is maximum diode
current
UF is forward diode voltage
UR is reverse diode voltage
URmax is the maximum
reverse voltage diodevoltage
Diodes ndash cont
For common types of diodes the value of UF voltage is
bullFor Germanium junction diode 02 04V
bullFor Silicone junction diode 05 08V
bullFor Schottky diode 0204V
An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation
Where I is the diode current
IS is the reverse bias saturation current (or scale current)
VD is the voltage across the diode
VT is the thermal voltage and
n is the ideality factor also known as the quality factor
Diodes ndashcont
The thermal voltage VT is approximately 2585 mV at 300 K
At any other temperature it is given by an equation
where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)
Diodes ndash cont
The typical I-V characteristics of for germaniumand silicone junction diode
Diodes ndash cont
Diode as a switching element
Following the end of forward conduction in a PN type diode a
reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called
reverse recovery time and usually is between tens and hundreds of
ns (ie between 1e-8 and 1e-7 s)
Diodes ndash cont
Diode as a rectifier
A half wave rectifier
A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification
Diodes ndash cont
A full-wave rectifier
This kind of a circuit is also known as the bridge rectifier
Diodes ndash cont
A rectifier in a DC voltage supply
Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge
In general case the simple design rule should be followed
RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)
Diodes ndash cont
Another application ndash diode-based voltage limiter
The cathode of a diode has a potential equal to 4V
U out max = 4V + 06 V = 46 V
If UINlt46V then UOUT = UIN
Bipolar Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals
Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors
B=base C=collector E= emitter
Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases
Transistors ndash cont
The history of the transistor
The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work
The first silicon transistors were produced by Western Electric and TexasInstruments in 1954
Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)
copy wwwporticusorg
Transistors ndash cont
An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased
NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia
The first transistor
copy Bell Labs
Transistor ndash cont
Transistor as an amplifier
A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated
The relations between currents in BJT copy radartutorialeu
Transistor ndash cont
The most often used amplifier circuits
highmediumlowBandwidth4
00001800Phase Shift between input and output signals
3
lt 1highhighCurrent gain2
highlt 1highVoltage gain1
COMMON BASE
COMMON COLLECTOR
COMMON EMITTER
AMPLIFIER
Nr
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
The primary characteristics of a resistor
Resistance (usually expressed in Ω kΩ and MΩ) Tolerance Maximal (rated) power Temperature coefficient of resistance (TCR) Maximal working voltage Parasitic inductance
Series and parallel resistors
The equivalent resistance of tworesistors in series connection
R=R1+R2
The equivalent resistance of tworesistors in parallel connection
1R=1R1+1R2
For n resistors
R=R1+R2+R3+Rn
For n resistors
1R=1R1+1R2+1R3+1Rn
Resistive divider
copy Wikipedia
If R1=R2 then Vout = Vin2
The voltage output of a voltage divider is not fixed but varies according to the load To obtain a reasonably stable output voltage the output current should be a small fraction of the input current
Loaded voltage divider
The voltage between points A and B
U = UT = UINmiddot [R2 (R1 + R2)]
According to Theveninrsquostheorem
RT = (R1 middot R2) (R1+ R2)
In practical projects we often
assume that RL should be 10 times higher than RT
Potentiometers
A potentiometer is a three-terminal resistor with a sliding contact acting as an adjustable voltage divider
Capacitors
copy Wikipedia
A capacitor is a passive electronic component consisting of a pair of conductors separated by a dielectric (insulator)
An ideal capacitor is characterized by a single constant value capacitance measured in farads This is the ratio of the electric charge on each conductor to the potential difference between them
The properties of capacitor are expressed by an equation
C=QU
Where C is capacitance Q is the electriccharge stored inside the capacitor and U is thevoltage between conductors (plates)
Capacitors ndashinternal structure
a) Film capacitor
b) Metalised plastic film capacitor
c) Ceramic disc capacitor
d) Tubular ceramic capacitor
e) Multilayer ceramic capacitor
Supercapacitors
Maxwell Technologies supercapacitors
Ultracapacitor (known also as anelectrochemical double layer capacitor) is an electrochemical capacitor that has a very high energy density when compared to common capacitors typically on the order of thousands of times greater than a high capacity electrolytic capacitor
They are characterized by a very shortcharging time (seconds to minutes)
Possible applications ndash electriccars power tools emergencypower supplies
Supercapacitors ndash cont
Pros very short charging time
Cons relatively high price
Supercapacitors vs standard capacitors
New generation of supercapacitotors
Second generation of supercapacitors by ioxuscom (2010)
From left 220F800F1000F Operating voltage 23V max
copy wwwioxuscom
Capacitors ndash cont
Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)
If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A
Capacitors ndash cont
Most imporant capacitor parameters
bullCapacitance [microF] [nF] or [pF]
bullTolerance []
bullRated voltage [V]
bullDischarge rate (leakage current)
bullTemperature coefficient of capacitance
bullEquivalent series resitance (ESR)
Capacitors ndash cont
a)Aluminium electrolytic capacitor
b)Tantalum electrolytic capacitor
c)Polyesther capacitor
d)Ceramic disc capacitor
e)Mylar capacitor
Capacitors ndash cont
Capacitors in series connection
For two capacitors in series the equivalent capacitance is
For parallel configuration
For two capacitors in parallel the equivalent capacitance is
C=C1+C2
For n capacitors (general case)
Capacitors ndash cont
Capacitor discharge through a resistor
If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge
The discharge rate is expressed by an equation
Where RC is called time constant
Capacitors ndash cont
Capacitor charging through a resistor
If a capacitor C will be charged from source of voltage UWE
through a resistor R the voltage change across its terminals will be described by the following equations
The final solution is
Inductors
An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it
An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material
Graphic symbola) Toroidal core inductor b)cylindrical core inductor
The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L
where L is expressed in H (Henryrsquos) but most often in mH or microH
Inductors ndash cont
Different variations of inductors
Surface mount(SMT) inductors
Cylindricalcoreinductors
Inductor parameters
bullInductance [H]
bullRated voltage [V]
bullTolerance []
bullSaturation DC current [A]
bullMaximal RMS current [A]
bullSelf-resonance frequency [Hz]
bullDC resistance [Ω]
Typical set of parameters
Coilcraft DO3340P-104M inductor
L-100microH tol-20 Isat-25A Irms-12A
SRF-5MHz(typ) RDC-022Ω
Transformers
A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation
Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio
Transformer ndash cont
The current I2 flowing in the secondary winding is inversely proportional
to the current I1 flowing in the primary winding
Moreover the impedance connected to the transformer is transformed by the square of the turns ratio
Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer
Transformers ndash cont
The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit
Examples of low power transformers
Toroidal coretransformer
Toroidal core variabletransformer
(autotransformer)
Laminatedcore EI transformers
Diodes
A diode is a two-terminal electronic component that conducts electric current in only one direction
When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)
Diodes ndash cont
The currentndashvoltage characteristic of a diodeWhere
ID is diode current
If is forward diode current
IFmax is maximum diode
current
UF is forward diode voltage
UR is reverse diode voltage
URmax is the maximum
reverse voltage diodevoltage
Diodes ndash cont
For common types of diodes the value of UF voltage is
bullFor Germanium junction diode 02 04V
bullFor Silicone junction diode 05 08V
bullFor Schottky diode 0204V
An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation
Where I is the diode current
IS is the reverse bias saturation current (or scale current)
VD is the voltage across the diode
VT is the thermal voltage and
n is the ideality factor also known as the quality factor
Diodes ndashcont
The thermal voltage VT is approximately 2585 mV at 300 K
At any other temperature it is given by an equation
where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)
Diodes ndash cont
The typical I-V characteristics of for germaniumand silicone junction diode
Diodes ndash cont
Diode as a switching element
Following the end of forward conduction in a PN type diode a
reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called
reverse recovery time and usually is between tens and hundreds of
ns (ie between 1e-8 and 1e-7 s)
Diodes ndash cont
Diode as a rectifier
A half wave rectifier
A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification
Diodes ndash cont
A full-wave rectifier
This kind of a circuit is also known as the bridge rectifier
Diodes ndash cont
A rectifier in a DC voltage supply
Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge
In general case the simple design rule should be followed
RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)
Diodes ndash cont
Another application ndash diode-based voltage limiter
The cathode of a diode has a potential equal to 4V
U out max = 4V + 06 V = 46 V
If UINlt46V then UOUT = UIN
Bipolar Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals
Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors
B=base C=collector E= emitter
Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases
Transistors ndash cont
The history of the transistor
The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work
The first silicon transistors were produced by Western Electric and TexasInstruments in 1954
Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)
copy wwwporticusorg
Transistors ndash cont
An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased
NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia
The first transistor
copy Bell Labs
Transistor ndash cont
Transistor as an amplifier
A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated
The relations between currents in BJT copy radartutorialeu
Transistor ndash cont
The most often used amplifier circuits
highmediumlowBandwidth4
00001800Phase Shift between input and output signals
3
lt 1highhighCurrent gain2
highlt 1highVoltage gain1
COMMON BASE
COMMON COLLECTOR
COMMON EMITTER
AMPLIFIER
Nr
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Series and parallel resistors
The equivalent resistance of tworesistors in series connection
R=R1+R2
The equivalent resistance of tworesistors in parallel connection
1R=1R1+1R2
For n resistors
R=R1+R2+R3+Rn
For n resistors
1R=1R1+1R2+1R3+1Rn
Resistive divider
copy Wikipedia
If R1=R2 then Vout = Vin2
The voltage output of a voltage divider is not fixed but varies according to the load To obtain a reasonably stable output voltage the output current should be a small fraction of the input current
Loaded voltage divider
The voltage between points A and B
U = UT = UINmiddot [R2 (R1 + R2)]
According to Theveninrsquostheorem
RT = (R1 middot R2) (R1+ R2)
In practical projects we often
assume that RL should be 10 times higher than RT
Potentiometers
A potentiometer is a three-terminal resistor with a sliding contact acting as an adjustable voltage divider
Capacitors
copy Wikipedia
A capacitor is a passive electronic component consisting of a pair of conductors separated by a dielectric (insulator)
An ideal capacitor is characterized by a single constant value capacitance measured in farads This is the ratio of the electric charge on each conductor to the potential difference between them
The properties of capacitor are expressed by an equation
C=QU
Where C is capacitance Q is the electriccharge stored inside the capacitor and U is thevoltage between conductors (plates)
Capacitors ndashinternal structure
a) Film capacitor
b) Metalised plastic film capacitor
c) Ceramic disc capacitor
d) Tubular ceramic capacitor
e) Multilayer ceramic capacitor
Supercapacitors
Maxwell Technologies supercapacitors
Ultracapacitor (known also as anelectrochemical double layer capacitor) is an electrochemical capacitor that has a very high energy density when compared to common capacitors typically on the order of thousands of times greater than a high capacity electrolytic capacitor
They are characterized by a very shortcharging time (seconds to minutes)
Possible applications ndash electriccars power tools emergencypower supplies
Supercapacitors ndash cont
Pros very short charging time
Cons relatively high price
Supercapacitors vs standard capacitors
New generation of supercapacitotors
Second generation of supercapacitors by ioxuscom (2010)
From left 220F800F1000F Operating voltage 23V max
copy wwwioxuscom
Capacitors ndash cont
Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)
If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A
Capacitors ndash cont
Most imporant capacitor parameters
bullCapacitance [microF] [nF] or [pF]
bullTolerance []
bullRated voltage [V]
bullDischarge rate (leakage current)
bullTemperature coefficient of capacitance
bullEquivalent series resitance (ESR)
Capacitors ndash cont
a)Aluminium electrolytic capacitor
b)Tantalum electrolytic capacitor
c)Polyesther capacitor
d)Ceramic disc capacitor
e)Mylar capacitor
Capacitors ndash cont
Capacitors in series connection
For two capacitors in series the equivalent capacitance is
For parallel configuration
For two capacitors in parallel the equivalent capacitance is
C=C1+C2
For n capacitors (general case)
Capacitors ndash cont
Capacitor discharge through a resistor
If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge
The discharge rate is expressed by an equation
Where RC is called time constant
Capacitors ndash cont
Capacitor charging through a resistor
If a capacitor C will be charged from source of voltage UWE
through a resistor R the voltage change across its terminals will be described by the following equations
The final solution is
Inductors
An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it
An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material
Graphic symbola) Toroidal core inductor b)cylindrical core inductor
The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L
where L is expressed in H (Henryrsquos) but most often in mH or microH
Inductors ndash cont
Different variations of inductors
Surface mount(SMT) inductors
Cylindricalcoreinductors
Inductor parameters
bullInductance [H]
bullRated voltage [V]
bullTolerance []
bullSaturation DC current [A]
bullMaximal RMS current [A]
bullSelf-resonance frequency [Hz]
bullDC resistance [Ω]
Typical set of parameters
Coilcraft DO3340P-104M inductor
L-100microH tol-20 Isat-25A Irms-12A
SRF-5MHz(typ) RDC-022Ω
Transformers
A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation
Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio
Transformer ndash cont
The current I2 flowing in the secondary winding is inversely proportional
to the current I1 flowing in the primary winding
Moreover the impedance connected to the transformer is transformed by the square of the turns ratio
Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer
Transformers ndash cont
The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit
Examples of low power transformers
Toroidal coretransformer
Toroidal core variabletransformer
(autotransformer)
Laminatedcore EI transformers
Diodes
A diode is a two-terminal electronic component that conducts electric current in only one direction
When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)
Diodes ndash cont
The currentndashvoltage characteristic of a diodeWhere
ID is diode current
If is forward diode current
IFmax is maximum diode
current
UF is forward diode voltage
UR is reverse diode voltage
URmax is the maximum
reverse voltage diodevoltage
Diodes ndash cont
For common types of diodes the value of UF voltage is
bullFor Germanium junction diode 02 04V
bullFor Silicone junction diode 05 08V
bullFor Schottky diode 0204V
An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation
Where I is the diode current
IS is the reverse bias saturation current (or scale current)
VD is the voltage across the diode
VT is the thermal voltage and
n is the ideality factor also known as the quality factor
Diodes ndashcont
The thermal voltage VT is approximately 2585 mV at 300 K
At any other temperature it is given by an equation
where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)
Diodes ndash cont
The typical I-V characteristics of for germaniumand silicone junction diode
Diodes ndash cont
Diode as a switching element
Following the end of forward conduction in a PN type diode a
reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called
reverse recovery time and usually is between tens and hundreds of
ns (ie between 1e-8 and 1e-7 s)
Diodes ndash cont
Diode as a rectifier
A half wave rectifier
A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification
Diodes ndash cont
A full-wave rectifier
This kind of a circuit is also known as the bridge rectifier
Diodes ndash cont
A rectifier in a DC voltage supply
Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge
In general case the simple design rule should be followed
RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)
Diodes ndash cont
Another application ndash diode-based voltage limiter
The cathode of a diode has a potential equal to 4V
U out max = 4V + 06 V = 46 V
If UINlt46V then UOUT = UIN
Bipolar Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals
Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors
B=base C=collector E= emitter
Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases
Transistors ndash cont
The history of the transistor
The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work
The first silicon transistors were produced by Western Electric and TexasInstruments in 1954
Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)
copy wwwporticusorg
Transistors ndash cont
An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased
NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia
The first transistor
copy Bell Labs
Transistor ndash cont
Transistor as an amplifier
A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated
The relations between currents in BJT copy radartutorialeu
Transistor ndash cont
The most often used amplifier circuits
highmediumlowBandwidth4
00001800Phase Shift between input and output signals
3
lt 1highhighCurrent gain2
highlt 1highVoltage gain1
COMMON BASE
COMMON COLLECTOR
COMMON EMITTER
AMPLIFIER
Nr
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Resistive divider
copy Wikipedia
If R1=R2 then Vout = Vin2
The voltage output of a voltage divider is not fixed but varies according to the load To obtain a reasonably stable output voltage the output current should be a small fraction of the input current
Loaded voltage divider
The voltage between points A and B
U = UT = UINmiddot [R2 (R1 + R2)]
According to Theveninrsquostheorem
RT = (R1 middot R2) (R1+ R2)
In practical projects we often
assume that RL should be 10 times higher than RT
Potentiometers
A potentiometer is a three-terminal resistor with a sliding contact acting as an adjustable voltage divider
Capacitors
copy Wikipedia
A capacitor is a passive electronic component consisting of a pair of conductors separated by a dielectric (insulator)
An ideal capacitor is characterized by a single constant value capacitance measured in farads This is the ratio of the electric charge on each conductor to the potential difference between them
The properties of capacitor are expressed by an equation
C=QU
Where C is capacitance Q is the electriccharge stored inside the capacitor and U is thevoltage between conductors (plates)
Capacitors ndashinternal structure
a) Film capacitor
b) Metalised plastic film capacitor
c) Ceramic disc capacitor
d) Tubular ceramic capacitor
e) Multilayer ceramic capacitor
Supercapacitors
Maxwell Technologies supercapacitors
Ultracapacitor (known also as anelectrochemical double layer capacitor) is an electrochemical capacitor that has a very high energy density when compared to common capacitors typically on the order of thousands of times greater than a high capacity electrolytic capacitor
They are characterized by a very shortcharging time (seconds to minutes)
Possible applications ndash electriccars power tools emergencypower supplies
Supercapacitors ndash cont
Pros very short charging time
Cons relatively high price
Supercapacitors vs standard capacitors
New generation of supercapacitotors
Second generation of supercapacitors by ioxuscom (2010)
From left 220F800F1000F Operating voltage 23V max
copy wwwioxuscom
Capacitors ndash cont
Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)
If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A
Capacitors ndash cont
Most imporant capacitor parameters
bullCapacitance [microF] [nF] or [pF]
bullTolerance []
bullRated voltage [V]
bullDischarge rate (leakage current)
bullTemperature coefficient of capacitance
bullEquivalent series resitance (ESR)
Capacitors ndash cont
a)Aluminium electrolytic capacitor
b)Tantalum electrolytic capacitor
c)Polyesther capacitor
d)Ceramic disc capacitor
e)Mylar capacitor
Capacitors ndash cont
Capacitors in series connection
For two capacitors in series the equivalent capacitance is
For parallel configuration
For two capacitors in parallel the equivalent capacitance is
C=C1+C2
For n capacitors (general case)
Capacitors ndash cont
Capacitor discharge through a resistor
If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge
The discharge rate is expressed by an equation
Where RC is called time constant
Capacitors ndash cont
Capacitor charging through a resistor
If a capacitor C will be charged from source of voltage UWE
through a resistor R the voltage change across its terminals will be described by the following equations
The final solution is
Inductors
An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it
An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material
Graphic symbola) Toroidal core inductor b)cylindrical core inductor
The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L
where L is expressed in H (Henryrsquos) but most often in mH or microH
Inductors ndash cont
Different variations of inductors
Surface mount(SMT) inductors
Cylindricalcoreinductors
Inductor parameters
bullInductance [H]
bullRated voltage [V]
bullTolerance []
bullSaturation DC current [A]
bullMaximal RMS current [A]
bullSelf-resonance frequency [Hz]
bullDC resistance [Ω]
Typical set of parameters
Coilcraft DO3340P-104M inductor
L-100microH tol-20 Isat-25A Irms-12A
SRF-5MHz(typ) RDC-022Ω
Transformers
A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation
Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio
Transformer ndash cont
The current I2 flowing in the secondary winding is inversely proportional
to the current I1 flowing in the primary winding
Moreover the impedance connected to the transformer is transformed by the square of the turns ratio
Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer
Transformers ndash cont
The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit
Examples of low power transformers
Toroidal coretransformer
Toroidal core variabletransformer
(autotransformer)
Laminatedcore EI transformers
Diodes
A diode is a two-terminal electronic component that conducts electric current in only one direction
When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)
Diodes ndash cont
The currentndashvoltage characteristic of a diodeWhere
ID is diode current
If is forward diode current
IFmax is maximum diode
current
UF is forward diode voltage
UR is reverse diode voltage
URmax is the maximum
reverse voltage diodevoltage
Diodes ndash cont
For common types of diodes the value of UF voltage is
bullFor Germanium junction diode 02 04V
bullFor Silicone junction diode 05 08V
bullFor Schottky diode 0204V
An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation
Where I is the diode current
IS is the reverse bias saturation current (or scale current)
VD is the voltage across the diode
VT is the thermal voltage and
n is the ideality factor also known as the quality factor
Diodes ndashcont
The thermal voltage VT is approximately 2585 mV at 300 K
At any other temperature it is given by an equation
where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)
Diodes ndash cont
The typical I-V characteristics of for germaniumand silicone junction diode
Diodes ndash cont
Diode as a switching element
Following the end of forward conduction in a PN type diode a
reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called
reverse recovery time and usually is between tens and hundreds of
ns (ie between 1e-8 and 1e-7 s)
Diodes ndash cont
Diode as a rectifier
A half wave rectifier
A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification
Diodes ndash cont
A full-wave rectifier
This kind of a circuit is also known as the bridge rectifier
Diodes ndash cont
A rectifier in a DC voltage supply
Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge
In general case the simple design rule should be followed
RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)
Diodes ndash cont
Another application ndash diode-based voltage limiter
The cathode of a diode has a potential equal to 4V
U out max = 4V + 06 V = 46 V
If UINlt46V then UOUT = UIN
Bipolar Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals
Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors
B=base C=collector E= emitter
Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases
Transistors ndash cont
The history of the transistor
The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work
The first silicon transistors were produced by Western Electric and TexasInstruments in 1954
Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)
copy wwwporticusorg
Transistors ndash cont
An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased
NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia
The first transistor
copy Bell Labs
Transistor ndash cont
Transistor as an amplifier
A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated
The relations between currents in BJT copy radartutorialeu
Transistor ndash cont
The most often used amplifier circuits
highmediumlowBandwidth4
00001800Phase Shift between input and output signals
3
lt 1highhighCurrent gain2
highlt 1highVoltage gain1
COMMON BASE
COMMON COLLECTOR
COMMON EMITTER
AMPLIFIER
Nr
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Loaded voltage divider
The voltage between points A and B
U = UT = UINmiddot [R2 (R1 + R2)]
According to Theveninrsquostheorem
RT = (R1 middot R2) (R1+ R2)
In practical projects we often
assume that RL should be 10 times higher than RT
Potentiometers
A potentiometer is a three-terminal resistor with a sliding contact acting as an adjustable voltage divider
Capacitors
copy Wikipedia
A capacitor is a passive electronic component consisting of a pair of conductors separated by a dielectric (insulator)
An ideal capacitor is characterized by a single constant value capacitance measured in farads This is the ratio of the electric charge on each conductor to the potential difference between them
The properties of capacitor are expressed by an equation
C=QU
Where C is capacitance Q is the electriccharge stored inside the capacitor and U is thevoltage between conductors (plates)
Capacitors ndashinternal structure
a) Film capacitor
b) Metalised plastic film capacitor
c) Ceramic disc capacitor
d) Tubular ceramic capacitor
e) Multilayer ceramic capacitor
Supercapacitors
Maxwell Technologies supercapacitors
Ultracapacitor (known also as anelectrochemical double layer capacitor) is an electrochemical capacitor that has a very high energy density when compared to common capacitors typically on the order of thousands of times greater than a high capacity electrolytic capacitor
They are characterized by a very shortcharging time (seconds to minutes)
Possible applications ndash electriccars power tools emergencypower supplies
Supercapacitors ndash cont
Pros very short charging time
Cons relatively high price
Supercapacitors vs standard capacitors
New generation of supercapacitotors
Second generation of supercapacitors by ioxuscom (2010)
From left 220F800F1000F Operating voltage 23V max
copy wwwioxuscom
Capacitors ndash cont
Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)
If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A
Capacitors ndash cont
Most imporant capacitor parameters
bullCapacitance [microF] [nF] or [pF]
bullTolerance []
bullRated voltage [V]
bullDischarge rate (leakage current)
bullTemperature coefficient of capacitance
bullEquivalent series resitance (ESR)
Capacitors ndash cont
a)Aluminium electrolytic capacitor
b)Tantalum electrolytic capacitor
c)Polyesther capacitor
d)Ceramic disc capacitor
e)Mylar capacitor
Capacitors ndash cont
Capacitors in series connection
For two capacitors in series the equivalent capacitance is
For parallel configuration
For two capacitors in parallel the equivalent capacitance is
C=C1+C2
For n capacitors (general case)
Capacitors ndash cont
Capacitor discharge through a resistor
If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge
The discharge rate is expressed by an equation
Where RC is called time constant
Capacitors ndash cont
Capacitor charging through a resistor
If a capacitor C will be charged from source of voltage UWE
through a resistor R the voltage change across its terminals will be described by the following equations
The final solution is
Inductors
An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it
An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material
Graphic symbola) Toroidal core inductor b)cylindrical core inductor
The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L
where L is expressed in H (Henryrsquos) but most often in mH or microH
Inductors ndash cont
Different variations of inductors
Surface mount(SMT) inductors
Cylindricalcoreinductors
Inductor parameters
bullInductance [H]
bullRated voltage [V]
bullTolerance []
bullSaturation DC current [A]
bullMaximal RMS current [A]
bullSelf-resonance frequency [Hz]
bullDC resistance [Ω]
Typical set of parameters
Coilcraft DO3340P-104M inductor
L-100microH tol-20 Isat-25A Irms-12A
SRF-5MHz(typ) RDC-022Ω
Transformers
A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation
Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio
Transformer ndash cont
The current I2 flowing in the secondary winding is inversely proportional
to the current I1 flowing in the primary winding
Moreover the impedance connected to the transformer is transformed by the square of the turns ratio
Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer
Transformers ndash cont
The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit
Examples of low power transformers
Toroidal coretransformer
Toroidal core variabletransformer
(autotransformer)
Laminatedcore EI transformers
Diodes
A diode is a two-terminal electronic component that conducts electric current in only one direction
When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)
Diodes ndash cont
The currentndashvoltage characteristic of a diodeWhere
ID is diode current
If is forward diode current
IFmax is maximum diode
current
UF is forward diode voltage
UR is reverse diode voltage
URmax is the maximum
reverse voltage diodevoltage
Diodes ndash cont
For common types of diodes the value of UF voltage is
bullFor Germanium junction diode 02 04V
bullFor Silicone junction diode 05 08V
bullFor Schottky diode 0204V
An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation
Where I is the diode current
IS is the reverse bias saturation current (or scale current)
VD is the voltage across the diode
VT is the thermal voltage and
n is the ideality factor also known as the quality factor
Diodes ndashcont
The thermal voltage VT is approximately 2585 mV at 300 K
At any other temperature it is given by an equation
where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)
Diodes ndash cont
The typical I-V characteristics of for germaniumand silicone junction diode
Diodes ndash cont
Diode as a switching element
Following the end of forward conduction in a PN type diode a
reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called
reverse recovery time and usually is between tens and hundreds of
ns (ie between 1e-8 and 1e-7 s)
Diodes ndash cont
Diode as a rectifier
A half wave rectifier
A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification
Diodes ndash cont
A full-wave rectifier
This kind of a circuit is also known as the bridge rectifier
Diodes ndash cont
A rectifier in a DC voltage supply
Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge
In general case the simple design rule should be followed
RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)
Diodes ndash cont
Another application ndash diode-based voltage limiter
The cathode of a diode has a potential equal to 4V
U out max = 4V + 06 V = 46 V
If UINlt46V then UOUT = UIN
Bipolar Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals
Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors
B=base C=collector E= emitter
Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases
Transistors ndash cont
The history of the transistor
The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work
The first silicon transistors were produced by Western Electric and TexasInstruments in 1954
Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)
copy wwwporticusorg
Transistors ndash cont
An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased
NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia
The first transistor
copy Bell Labs
Transistor ndash cont
Transistor as an amplifier
A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated
The relations between currents in BJT copy radartutorialeu
Transistor ndash cont
The most often used amplifier circuits
highmediumlowBandwidth4
00001800Phase Shift between input and output signals
3
lt 1highhighCurrent gain2
highlt 1highVoltage gain1
COMMON BASE
COMMON COLLECTOR
COMMON EMITTER
AMPLIFIER
Nr
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Potentiometers
A potentiometer is a three-terminal resistor with a sliding contact acting as an adjustable voltage divider
Capacitors
copy Wikipedia
A capacitor is a passive electronic component consisting of a pair of conductors separated by a dielectric (insulator)
An ideal capacitor is characterized by a single constant value capacitance measured in farads This is the ratio of the electric charge on each conductor to the potential difference between them
The properties of capacitor are expressed by an equation
C=QU
Where C is capacitance Q is the electriccharge stored inside the capacitor and U is thevoltage between conductors (plates)
Capacitors ndashinternal structure
a) Film capacitor
b) Metalised plastic film capacitor
c) Ceramic disc capacitor
d) Tubular ceramic capacitor
e) Multilayer ceramic capacitor
Supercapacitors
Maxwell Technologies supercapacitors
Ultracapacitor (known also as anelectrochemical double layer capacitor) is an electrochemical capacitor that has a very high energy density when compared to common capacitors typically on the order of thousands of times greater than a high capacity electrolytic capacitor
They are characterized by a very shortcharging time (seconds to minutes)
Possible applications ndash electriccars power tools emergencypower supplies
Supercapacitors ndash cont
Pros very short charging time
Cons relatively high price
Supercapacitors vs standard capacitors
New generation of supercapacitotors
Second generation of supercapacitors by ioxuscom (2010)
From left 220F800F1000F Operating voltage 23V max
copy wwwioxuscom
Capacitors ndash cont
Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)
If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A
Capacitors ndash cont
Most imporant capacitor parameters
bullCapacitance [microF] [nF] or [pF]
bullTolerance []
bullRated voltage [V]
bullDischarge rate (leakage current)
bullTemperature coefficient of capacitance
bullEquivalent series resitance (ESR)
Capacitors ndash cont
a)Aluminium electrolytic capacitor
b)Tantalum electrolytic capacitor
c)Polyesther capacitor
d)Ceramic disc capacitor
e)Mylar capacitor
Capacitors ndash cont
Capacitors in series connection
For two capacitors in series the equivalent capacitance is
For parallel configuration
For two capacitors in parallel the equivalent capacitance is
C=C1+C2
For n capacitors (general case)
Capacitors ndash cont
Capacitor discharge through a resistor
If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge
The discharge rate is expressed by an equation
Where RC is called time constant
Capacitors ndash cont
Capacitor charging through a resistor
If a capacitor C will be charged from source of voltage UWE
through a resistor R the voltage change across its terminals will be described by the following equations
The final solution is
Inductors
An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it
An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material
Graphic symbola) Toroidal core inductor b)cylindrical core inductor
The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L
where L is expressed in H (Henryrsquos) but most often in mH or microH
Inductors ndash cont
Different variations of inductors
Surface mount(SMT) inductors
Cylindricalcoreinductors
Inductor parameters
bullInductance [H]
bullRated voltage [V]
bullTolerance []
bullSaturation DC current [A]
bullMaximal RMS current [A]
bullSelf-resonance frequency [Hz]
bullDC resistance [Ω]
Typical set of parameters
Coilcraft DO3340P-104M inductor
L-100microH tol-20 Isat-25A Irms-12A
SRF-5MHz(typ) RDC-022Ω
Transformers
A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation
Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio
Transformer ndash cont
The current I2 flowing in the secondary winding is inversely proportional
to the current I1 flowing in the primary winding
Moreover the impedance connected to the transformer is transformed by the square of the turns ratio
Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer
Transformers ndash cont
The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit
Examples of low power transformers
Toroidal coretransformer
Toroidal core variabletransformer
(autotransformer)
Laminatedcore EI transformers
Diodes
A diode is a two-terminal electronic component that conducts electric current in only one direction
When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)
Diodes ndash cont
The currentndashvoltage characteristic of a diodeWhere
ID is diode current
If is forward diode current
IFmax is maximum diode
current
UF is forward diode voltage
UR is reverse diode voltage
URmax is the maximum
reverse voltage diodevoltage
Diodes ndash cont
For common types of diodes the value of UF voltage is
bullFor Germanium junction diode 02 04V
bullFor Silicone junction diode 05 08V
bullFor Schottky diode 0204V
An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation
Where I is the diode current
IS is the reverse bias saturation current (or scale current)
VD is the voltage across the diode
VT is the thermal voltage and
n is the ideality factor also known as the quality factor
Diodes ndashcont
The thermal voltage VT is approximately 2585 mV at 300 K
At any other temperature it is given by an equation
where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)
Diodes ndash cont
The typical I-V characteristics of for germaniumand silicone junction diode
Diodes ndash cont
Diode as a switching element
Following the end of forward conduction in a PN type diode a
reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called
reverse recovery time and usually is between tens and hundreds of
ns (ie between 1e-8 and 1e-7 s)
Diodes ndash cont
Diode as a rectifier
A half wave rectifier
A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification
Diodes ndash cont
A full-wave rectifier
This kind of a circuit is also known as the bridge rectifier
Diodes ndash cont
A rectifier in a DC voltage supply
Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge
In general case the simple design rule should be followed
RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)
Diodes ndash cont
Another application ndash diode-based voltage limiter
The cathode of a diode has a potential equal to 4V
U out max = 4V + 06 V = 46 V
If UINlt46V then UOUT = UIN
Bipolar Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals
Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors
B=base C=collector E= emitter
Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases
Transistors ndash cont
The history of the transistor
The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work
The first silicon transistors were produced by Western Electric and TexasInstruments in 1954
Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)
copy wwwporticusorg
Transistors ndash cont
An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased
NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia
The first transistor
copy Bell Labs
Transistor ndash cont
Transistor as an amplifier
A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated
The relations between currents in BJT copy radartutorialeu
Transistor ndash cont
The most often used amplifier circuits
highmediumlowBandwidth4
00001800Phase Shift between input and output signals
3
lt 1highhighCurrent gain2
highlt 1highVoltage gain1
COMMON BASE
COMMON COLLECTOR
COMMON EMITTER
AMPLIFIER
Nr
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Capacitors
copy Wikipedia
A capacitor is a passive electronic component consisting of a pair of conductors separated by a dielectric (insulator)
An ideal capacitor is characterized by a single constant value capacitance measured in farads This is the ratio of the electric charge on each conductor to the potential difference between them
The properties of capacitor are expressed by an equation
C=QU
Where C is capacitance Q is the electriccharge stored inside the capacitor and U is thevoltage between conductors (plates)
Capacitors ndashinternal structure
a) Film capacitor
b) Metalised plastic film capacitor
c) Ceramic disc capacitor
d) Tubular ceramic capacitor
e) Multilayer ceramic capacitor
Supercapacitors
Maxwell Technologies supercapacitors
Ultracapacitor (known also as anelectrochemical double layer capacitor) is an electrochemical capacitor that has a very high energy density when compared to common capacitors typically on the order of thousands of times greater than a high capacity electrolytic capacitor
They are characterized by a very shortcharging time (seconds to minutes)
Possible applications ndash electriccars power tools emergencypower supplies
Supercapacitors ndash cont
Pros very short charging time
Cons relatively high price
Supercapacitors vs standard capacitors
New generation of supercapacitotors
Second generation of supercapacitors by ioxuscom (2010)
From left 220F800F1000F Operating voltage 23V max
copy wwwioxuscom
Capacitors ndash cont
Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)
If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A
Capacitors ndash cont
Most imporant capacitor parameters
bullCapacitance [microF] [nF] or [pF]
bullTolerance []
bullRated voltage [V]
bullDischarge rate (leakage current)
bullTemperature coefficient of capacitance
bullEquivalent series resitance (ESR)
Capacitors ndash cont
a)Aluminium electrolytic capacitor
b)Tantalum electrolytic capacitor
c)Polyesther capacitor
d)Ceramic disc capacitor
e)Mylar capacitor
Capacitors ndash cont
Capacitors in series connection
For two capacitors in series the equivalent capacitance is
For parallel configuration
For two capacitors in parallel the equivalent capacitance is
C=C1+C2
For n capacitors (general case)
Capacitors ndash cont
Capacitor discharge through a resistor
If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge
The discharge rate is expressed by an equation
Where RC is called time constant
Capacitors ndash cont
Capacitor charging through a resistor
If a capacitor C will be charged from source of voltage UWE
through a resistor R the voltage change across its terminals will be described by the following equations
The final solution is
Inductors
An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it
An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material
Graphic symbola) Toroidal core inductor b)cylindrical core inductor
The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L
where L is expressed in H (Henryrsquos) but most often in mH or microH
Inductors ndash cont
Different variations of inductors
Surface mount(SMT) inductors
Cylindricalcoreinductors
Inductor parameters
bullInductance [H]
bullRated voltage [V]
bullTolerance []
bullSaturation DC current [A]
bullMaximal RMS current [A]
bullSelf-resonance frequency [Hz]
bullDC resistance [Ω]
Typical set of parameters
Coilcraft DO3340P-104M inductor
L-100microH tol-20 Isat-25A Irms-12A
SRF-5MHz(typ) RDC-022Ω
Transformers
A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation
Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio
Transformer ndash cont
The current I2 flowing in the secondary winding is inversely proportional
to the current I1 flowing in the primary winding
Moreover the impedance connected to the transformer is transformed by the square of the turns ratio
Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer
Transformers ndash cont
The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit
Examples of low power transformers
Toroidal coretransformer
Toroidal core variabletransformer
(autotransformer)
Laminatedcore EI transformers
Diodes
A diode is a two-terminal electronic component that conducts electric current in only one direction
When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)
Diodes ndash cont
The currentndashvoltage characteristic of a diodeWhere
ID is diode current
If is forward diode current
IFmax is maximum diode
current
UF is forward diode voltage
UR is reverse diode voltage
URmax is the maximum
reverse voltage diodevoltage
Diodes ndash cont
For common types of diodes the value of UF voltage is
bullFor Germanium junction diode 02 04V
bullFor Silicone junction diode 05 08V
bullFor Schottky diode 0204V
An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation
Where I is the diode current
IS is the reverse bias saturation current (or scale current)
VD is the voltage across the diode
VT is the thermal voltage and
n is the ideality factor also known as the quality factor
Diodes ndashcont
The thermal voltage VT is approximately 2585 mV at 300 K
At any other temperature it is given by an equation
where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)
Diodes ndash cont
The typical I-V characteristics of for germaniumand silicone junction diode
Diodes ndash cont
Diode as a switching element
Following the end of forward conduction in a PN type diode a
reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called
reverse recovery time and usually is between tens and hundreds of
ns (ie between 1e-8 and 1e-7 s)
Diodes ndash cont
Diode as a rectifier
A half wave rectifier
A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification
Diodes ndash cont
A full-wave rectifier
This kind of a circuit is also known as the bridge rectifier
Diodes ndash cont
A rectifier in a DC voltage supply
Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge
In general case the simple design rule should be followed
RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)
Diodes ndash cont
Another application ndash diode-based voltage limiter
The cathode of a diode has a potential equal to 4V
U out max = 4V + 06 V = 46 V
If UINlt46V then UOUT = UIN
Bipolar Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals
Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors
B=base C=collector E= emitter
Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases
Transistors ndash cont
The history of the transistor
The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work
The first silicon transistors were produced by Western Electric and TexasInstruments in 1954
Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)
copy wwwporticusorg
Transistors ndash cont
An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased
NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia
The first transistor
copy Bell Labs
Transistor ndash cont
Transistor as an amplifier
A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated
The relations between currents in BJT copy radartutorialeu
Transistor ndash cont
The most often used amplifier circuits
highmediumlowBandwidth4
00001800Phase Shift between input and output signals
3
lt 1highhighCurrent gain2
highlt 1highVoltage gain1
COMMON BASE
COMMON COLLECTOR
COMMON EMITTER
AMPLIFIER
Nr
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Capacitors ndashinternal structure
a) Film capacitor
b) Metalised plastic film capacitor
c) Ceramic disc capacitor
d) Tubular ceramic capacitor
e) Multilayer ceramic capacitor
Supercapacitors
Maxwell Technologies supercapacitors
Ultracapacitor (known also as anelectrochemical double layer capacitor) is an electrochemical capacitor that has a very high energy density when compared to common capacitors typically on the order of thousands of times greater than a high capacity electrolytic capacitor
They are characterized by a very shortcharging time (seconds to minutes)
Possible applications ndash electriccars power tools emergencypower supplies
Supercapacitors ndash cont
Pros very short charging time
Cons relatively high price
Supercapacitors vs standard capacitors
New generation of supercapacitotors
Second generation of supercapacitors by ioxuscom (2010)
From left 220F800F1000F Operating voltage 23V max
copy wwwioxuscom
Capacitors ndash cont
Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)
If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A
Capacitors ndash cont
Most imporant capacitor parameters
bullCapacitance [microF] [nF] or [pF]
bullTolerance []
bullRated voltage [V]
bullDischarge rate (leakage current)
bullTemperature coefficient of capacitance
bullEquivalent series resitance (ESR)
Capacitors ndash cont
a)Aluminium electrolytic capacitor
b)Tantalum electrolytic capacitor
c)Polyesther capacitor
d)Ceramic disc capacitor
e)Mylar capacitor
Capacitors ndash cont
Capacitors in series connection
For two capacitors in series the equivalent capacitance is
For parallel configuration
For two capacitors in parallel the equivalent capacitance is
C=C1+C2
For n capacitors (general case)
Capacitors ndash cont
Capacitor discharge through a resistor
If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge
The discharge rate is expressed by an equation
Where RC is called time constant
Capacitors ndash cont
Capacitor charging through a resistor
If a capacitor C will be charged from source of voltage UWE
through a resistor R the voltage change across its terminals will be described by the following equations
The final solution is
Inductors
An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it
An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material
Graphic symbola) Toroidal core inductor b)cylindrical core inductor
The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L
where L is expressed in H (Henryrsquos) but most often in mH or microH
Inductors ndash cont
Different variations of inductors
Surface mount(SMT) inductors
Cylindricalcoreinductors
Inductor parameters
bullInductance [H]
bullRated voltage [V]
bullTolerance []
bullSaturation DC current [A]
bullMaximal RMS current [A]
bullSelf-resonance frequency [Hz]
bullDC resistance [Ω]
Typical set of parameters
Coilcraft DO3340P-104M inductor
L-100microH tol-20 Isat-25A Irms-12A
SRF-5MHz(typ) RDC-022Ω
Transformers
A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation
Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio
Transformer ndash cont
The current I2 flowing in the secondary winding is inversely proportional
to the current I1 flowing in the primary winding
Moreover the impedance connected to the transformer is transformed by the square of the turns ratio
Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer
Transformers ndash cont
The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit
Examples of low power transformers
Toroidal coretransformer
Toroidal core variabletransformer
(autotransformer)
Laminatedcore EI transformers
Diodes
A diode is a two-terminal electronic component that conducts electric current in only one direction
When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)
Diodes ndash cont
The currentndashvoltage characteristic of a diodeWhere
ID is diode current
If is forward diode current
IFmax is maximum diode
current
UF is forward diode voltage
UR is reverse diode voltage
URmax is the maximum
reverse voltage diodevoltage
Diodes ndash cont
For common types of diodes the value of UF voltage is
bullFor Germanium junction diode 02 04V
bullFor Silicone junction diode 05 08V
bullFor Schottky diode 0204V
An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation
Where I is the diode current
IS is the reverse bias saturation current (or scale current)
VD is the voltage across the diode
VT is the thermal voltage and
n is the ideality factor also known as the quality factor
Diodes ndashcont
The thermal voltage VT is approximately 2585 mV at 300 K
At any other temperature it is given by an equation
where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)
Diodes ndash cont
The typical I-V characteristics of for germaniumand silicone junction diode
Diodes ndash cont
Diode as a switching element
Following the end of forward conduction in a PN type diode a
reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called
reverse recovery time and usually is between tens and hundreds of
ns (ie between 1e-8 and 1e-7 s)
Diodes ndash cont
Diode as a rectifier
A half wave rectifier
A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification
Diodes ndash cont
A full-wave rectifier
This kind of a circuit is also known as the bridge rectifier
Diodes ndash cont
A rectifier in a DC voltage supply
Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge
In general case the simple design rule should be followed
RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)
Diodes ndash cont
Another application ndash diode-based voltage limiter
The cathode of a diode has a potential equal to 4V
U out max = 4V + 06 V = 46 V
If UINlt46V then UOUT = UIN
Bipolar Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals
Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors
B=base C=collector E= emitter
Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases
Transistors ndash cont
The history of the transistor
The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work
The first silicon transistors were produced by Western Electric and TexasInstruments in 1954
Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)
copy wwwporticusorg
Transistors ndash cont
An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased
NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia
The first transistor
copy Bell Labs
Transistor ndash cont
Transistor as an amplifier
A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated
The relations between currents in BJT copy radartutorialeu
Transistor ndash cont
The most often used amplifier circuits
highmediumlowBandwidth4
00001800Phase Shift between input and output signals
3
lt 1highhighCurrent gain2
highlt 1highVoltage gain1
COMMON BASE
COMMON COLLECTOR
COMMON EMITTER
AMPLIFIER
Nr
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Supercapacitors
Maxwell Technologies supercapacitors
Ultracapacitor (known also as anelectrochemical double layer capacitor) is an electrochemical capacitor that has a very high energy density when compared to common capacitors typically on the order of thousands of times greater than a high capacity electrolytic capacitor
They are characterized by a very shortcharging time (seconds to minutes)
Possible applications ndash electriccars power tools emergencypower supplies
Supercapacitors ndash cont
Pros very short charging time
Cons relatively high price
Supercapacitors vs standard capacitors
New generation of supercapacitotors
Second generation of supercapacitors by ioxuscom (2010)
From left 220F800F1000F Operating voltage 23V max
copy wwwioxuscom
Capacitors ndash cont
Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)
If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A
Capacitors ndash cont
Most imporant capacitor parameters
bullCapacitance [microF] [nF] or [pF]
bullTolerance []
bullRated voltage [V]
bullDischarge rate (leakage current)
bullTemperature coefficient of capacitance
bullEquivalent series resitance (ESR)
Capacitors ndash cont
a)Aluminium electrolytic capacitor
b)Tantalum electrolytic capacitor
c)Polyesther capacitor
d)Ceramic disc capacitor
e)Mylar capacitor
Capacitors ndash cont
Capacitors in series connection
For two capacitors in series the equivalent capacitance is
For parallel configuration
For two capacitors in parallel the equivalent capacitance is
C=C1+C2
For n capacitors (general case)
Capacitors ndash cont
Capacitor discharge through a resistor
If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge
The discharge rate is expressed by an equation
Where RC is called time constant
Capacitors ndash cont
Capacitor charging through a resistor
If a capacitor C will be charged from source of voltage UWE
through a resistor R the voltage change across its terminals will be described by the following equations
The final solution is
Inductors
An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it
An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material
Graphic symbola) Toroidal core inductor b)cylindrical core inductor
The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L
where L is expressed in H (Henryrsquos) but most often in mH or microH
Inductors ndash cont
Different variations of inductors
Surface mount(SMT) inductors
Cylindricalcoreinductors
Inductor parameters
bullInductance [H]
bullRated voltage [V]
bullTolerance []
bullSaturation DC current [A]
bullMaximal RMS current [A]
bullSelf-resonance frequency [Hz]
bullDC resistance [Ω]
Typical set of parameters
Coilcraft DO3340P-104M inductor
L-100microH tol-20 Isat-25A Irms-12A
SRF-5MHz(typ) RDC-022Ω
Transformers
A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation
Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio
Transformer ndash cont
The current I2 flowing in the secondary winding is inversely proportional
to the current I1 flowing in the primary winding
Moreover the impedance connected to the transformer is transformed by the square of the turns ratio
Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer
Transformers ndash cont
The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit
Examples of low power transformers
Toroidal coretransformer
Toroidal core variabletransformer
(autotransformer)
Laminatedcore EI transformers
Diodes
A diode is a two-terminal electronic component that conducts electric current in only one direction
When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)
Diodes ndash cont
The currentndashvoltage characteristic of a diodeWhere
ID is diode current
If is forward diode current
IFmax is maximum diode
current
UF is forward diode voltage
UR is reverse diode voltage
URmax is the maximum
reverse voltage diodevoltage
Diodes ndash cont
For common types of diodes the value of UF voltage is
bullFor Germanium junction diode 02 04V
bullFor Silicone junction diode 05 08V
bullFor Schottky diode 0204V
An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation
Where I is the diode current
IS is the reverse bias saturation current (or scale current)
VD is the voltage across the diode
VT is the thermal voltage and
n is the ideality factor also known as the quality factor
Diodes ndashcont
The thermal voltage VT is approximately 2585 mV at 300 K
At any other temperature it is given by an equation
where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)
Diodes ndash cont
The typical I-V characteristics of for germaniumand silicone junction diode
Diodes ndash cont
Diode as a switching element
Following the end of forward conduction in a PN type diode a
reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called
reverse recovery time and usually is between tens and hundreds of
ns (ie between 1e-8 and 1e-7 s)
Diodes ndash cont
Diode as a rectifier
A half wave rectifier
A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification
Diodes ndash cont
A full-wave rectifier
This kind of a circuit is also known as the bridge rectifier
Diodes ndash cont
A rectifier in a DC voltage supply
Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge
In general case the simple design rule should be followed
RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)
Diodes ndash cont
Another application ndash diode-based voltage limiter
The cathode of a diode has a potential equal to 4V
U out max = 4V + 06 V = 46 V
If UINlt46V then UOUT = UIN
Bipolar Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals
Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors
B=base C=collector E= emitter
Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases
Transistors ndash cont
The history of the transistor
The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work
The first silicon transistors were produced by Western Electric and TexasInstruments in 1954
Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)
copy wwwporticusorg
Transistors ndash cont
An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased
NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia
The first transistor
copy Bell Labs
Transistor ndash cont
Transistor as an amplifier
A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated
The relations between currents in BJT copy radartutorialeu
Transistor ndash cont
The most often used amplifier circuits
highmediumlowBandwidth4
00001800Phase Shift between input and output signals
3
lt 1highhighCurrent gain2
highlt 1highVoltage gain1
COMMON BASE
COMMON COLLECTOR
COMMON EMITTER
AMPLIFIER
Nr
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Supercapacitors ndash cont
Pros very short charging time
Cons relatively high price
Supercapacitors vs standard capacitors
New generation of supercapacitotors
Second generation of supercapacitors by ioxuscom (2010)
From left 220F800F1000F Operating voltage 23V max
copy wwwioxuscom
Capacitors ndash cont
Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)
If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A
Capacitors ndash cont
Most imporant capacitor parameters
bullCapacitance [microF] [nF] or [pF]
bullTolerance []
bullRated voltage [V]
bullDischarge rate (leakage current)
bullTemperature coefficient of capacitance
bullEquivalent series resitance (ESR)
Capacitors ndash cont
a)Aluminium electrolytic capacitor
b)Tantalum electrolytic capacitor
c)Polyesther capacitor
d)Ceramic disc capacitor
e)Mylar capacitor
Capacitors ndash cont
Capacitors in series connection
For two capacitors in series the equivalent capacitance is
For parallel configuration
For two capacitors in parallel the equivalent capacitance is
C=C1+C2
For n capacitors (general case)
Capacitors ndash cont
Capacitor discharge through a resistor
If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge
The discharge rate is expressed by an equation
Where RC is called time constant
Capacitors ndash cont
Capacitor charging through a resistor
If a capacitor C will be charged from source of voltage UWE
through a resistor R the voltage change across its terminals will be described by the following equations
The final solution is
Inductors
An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it
An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material
Graphic symbola) Toroidal core inductor b)cylindrical core inductor
The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L
where L is expressed in H (Henryrsquos) but most often in mH or microH
Inductors ndash cont
Different variations of inductors
Surface mount(SMT) inductors
Cylindricalcoreinductors
Inductor parameters
bullInductance [H]
bullRated voltage [V]
bullTolerance []
bullSaturation DC current [A]
bullMaximal RMS current [A]
bullSelf-resonance frequency [Hz]
bullDC resistance [Ω]
Typical set of parameters
Coilcraft DO3340P-104M inductor
L-100microH tol-20 Isat-25A Irms-12A
SRF-5MHz(typ) RDC-022Ω
Transformers
A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation
Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio
Transformer ndash cont
The current I2 flowing in the secondary winding is inversely proportional
to the current I1 flowing in the primary winding
Moreover the impedance connected to the transformer is transformed by the square of the turns ratio
Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer
Transformers ndash cont
The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit
Examples of low power transformers
Toroidal coretransformer
Toroidal core variabletransformer
(autotransformer)
Laminatedcore EI transformers
Diodes
A diode is a two-terminal electronic component that conducts electric current in only one direction
When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)
Diodes ndash cont
The currentndashvoltage characteristic of a diodeWhere
ID is diode current
If is forward diode current
IFmax is maximum diode
current
UF is forward diode voltage
UR is reverse diode voltage
URmax is the maximum
reverse voltage diodevoltage
Diodes ndash cont
For common types of diodes the value of UF voltage is
bullFor Germanium junction diode 02 04V
bullFor Silicone junction diode 05 08V
bullFor Schottky diode 0204V
An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation
Where I is the diode current
IS is the reverse bias saturation current (or scale current)
VD is the voltage across the diode
VT is the thermal voltage and
n is the ideality factor also known as the quality factor
Diodes ndashcont
The thermal voltage VT is approximately 2585 mV at 300 K
At any other temperature it is given by an equation
where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)
Diodes ndash cont
The typical I-V characteristics of for germaniumand silicone junction diode
Diodes ndash cont
Diode as a switching element
Following the end of forward conduction in a PN type diode a
reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called
reverse recovery time and usually is between tens and hundreds of
ns (ie between 1e-8 and 1e-7 s)
Diodes ndash cont
Diode as a rectifier
A half wave rectifier
A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification
Diodes ndash cont
A full-wave rectifier
This kind of a circuit is also known as the bridge rectifier
Diodes ndash cont
A rectifier in a DC voltage supply
Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge
In general case the simple design rule should be followed
RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)
Diodes ndash cont
Another application ndash diode-based voltage limiter
The cathode of a diode has a potential equal to 4V
U out max = 4V + 06 V = 46 V
If UINlt46V then UOUT = UIN
Bipolar Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals
Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors
B=base C=collector E= emitter
Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases
Transistors ndash cont
The history of the transistor
The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work
The first silicon transistors were produced by Western Electric and TexasInstruments in 1954
Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)
copy wwwporticusorg
Transistors ndash cont
An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased
NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia
The first transistor
copy Bell Labs
Transistor ndash cont
Transistor as an amplifier
A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated
The relations between currents in BJT copy radartutorialeu
Transistor ndash cont
The most often used amplifier circuits
highmediumlowBandwidth4
00001800Phase Shift between input and output signals
3
lt 1highhighCurrent gain2
highlt 1highVoltage gain1
COMMON BASE
COMMON COLLECTOR
COMMON EMITTER
AMPLIFIER
Nr
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
New generation of supercapacitotors
Second generation of supercapacitors by ioxuscom (2010)
From left 220F800F1000F Operating voltage 23V max
copy wwwioxuscom
Capacitors ndash cont
Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)
If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A
Capacitors ndash cont
Most imporant capacitor parameters
bullCapacitance [microF] [nF] or [pF]
bullTolerance []
bullRated voltage [V]
bullDischarge rate (leakage current)
bullTemperature coefficient of capacitance
bullEquivalent series resitance (ESR)
Capacitors ndash cont
a)Aluminium electrolytic capacitor
b)Tantalum electrolytic capacitor
c)Polyesther capacitor
d)Ceramic disc capacitor
e)Mylar capacitor
Capacitors ndash cont
Capacitors in series connection
For two capacitors in series the equivalent capacitance is
For parallel configuration
For two capacitors in parallel the equivalent capacitance is
C=C1+C2
For n capacitors (general case)
Capacitors ndash cont
Capacitor discharge through a resistor
If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge
The discharge rate is expressed by an equation
Where RC is called time constant
Capacitors ndash cont
Capacitor charging through a resistor
If a capacitor C will be charged from source of voltage UWE
through a resistor R the voltage change across its terminals will be described by the following equations
The final solution is
Inductors
An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it
An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material
Graphic symbola) Toroidal core inductor b)cylindrical core inductor
The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L
where L is expressed in H (Henryrsquos) but most often in mH or microH
Inductors ndash cont
Different variations of inductors
Surface mount(SMT) inductors
Cylindricalcoreinductors
Inductor parameters
bullInductance [H]
bullRated voltage [V]
bullTolerance []
bullSaturation DC current [A]
bullMaximal RMS current [A]
bullSelf-resonance frequency [Hz]
bullDC resistance [Ω]
Typical set of parameters
Coilcraft DO3340P-104M inductor
L-100microH tol-20 Isat-25A Irms-12A
SRF-5MHz(typ) RDC-022Ω
Transformers
A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation
Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio
Transformer ndash cont
The current I2 flowing in the secondary winding is inversely proportional
to the current I1 flowing in the primary winding
Moreover the impedance connected to the transformer is transformed by the square of the turns ratio
Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer
Transformers ndash cont
The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit
Examples of low power transformers
Toroidal coretransformer
Toroidal core variabletransformer
(autotransformer)
Laminatedcore EI transformers
Diodes
A diode is a two-terminal electronic component that conducts electric current in only one direction
When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)
Diodes ndash cont
The currentndashvoltage characteristic of a diodeWhere
ID is diode current
If is forward diode current
IFmax is maximum diode
current
UF is forward diode voltage
UR is reverse diode voltage
URmax is the maximum
reverse voltage diodevoltage
Diodes ndash cont
For common types of diodes the value of UF voltage is
bullFor Germanium junction diode 02 04V
bullFor Silicone junction diode 05 08V
bullFor Schottky diode 0204V
An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation
Where I is the diode current
IS is the reverse bias saturation current (or scale current)
VD is the voltage across the diode
VT is the thermal voltage and
n is the ideality factor also known as the quality factor
Diodes ndashcont
The thermal voltage VT is approximately 2585 mV at 300 K
At any other temperature it is given by an equation
where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)
Diodes ndash cont
The typical I-V characteristics of for germaniumand silicone junction diode
Diodes ndash cont
Diode as a switching element
Following the end of forward conduction in a PN type diode a
reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called
reverse recovery time and usually is between tens and hundreds of
ns (ie between 1e-8 and 1e-7 s)
Diodes ndash cont
Diode as a rectifier
A half wave rectifier
A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification
Diodes ndash cont
A full-wave rectifier
This kind of a circuit is also known as the bridge rectifier
Diodes ndash cont
A rectifier in a DC voltage supply
Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge
In general case the simple design rule should be followed
RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)
Diodes ndash cont
Another application ndash diode-based voltage limiter
The cathode of a diode has a potential equal to 4V
U out max = 4V + 06 V = 46 V
If UINlt46V then UOUT = UIN
Bipolar Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals
Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors
B=base C=collector E= emitter
Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases
Transistors ndash cont
The history of the transistor
The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work
The first silicon transistors were produced by Western Electric and TexasInstruments in 1954
Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)
copy wwwporticusorg
Transistors ndash cont
An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased
NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia
The first transistor
copy Bell Labs
Transistor ndash cont
Transistor as an amplifier
A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated
The relations between currents in BJT copy radartutorialeu
Transistor ndash cont
The most often used amplifier circuits
highmediumlowBandwidth4
00001800Phase Shift between input and output signals
3
lt 1highhighCurrent gain2
highlt 1highVoltage gain1
COMMON BASE
COMMON COLLECTOR
COMMON EMITTER
AMPLIFIER
Nr
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Capacitors ndash cont
Current flowing across the capacitor is proportionalto the speed of voltage change present on itsterminals (rate of charge flow through thecapacitor)
If voltage change rate across 1F capacitor equals to 1Vs then the current flowing through it is 1A
Capacitors ndash cont
Most imporant capacitor parameters
bullCapacitance [microF] [nF] or [pF]
bullTolerance []
bullRated voltage [V]
bullDischarge rate (leakage current)
bullTemperature coefficient of capacitance
bullEquivalent series resitance (ESR)
Capacitors ndash cont
a)Aluminium electrolytic capacitor
b)Tantalum electrolytic capacitor
c)Polyesther capacitor
d)Ceramic disc capacitor
e)Mylar capacitor
Capacitors ndash cont
Capacitors in series connection
For two capacitors in series the equivalent capacitance is
For parallel configuration
For two capacitors in parallel the equivalent capacitance is
C=C1+C2
For n capacitors (general case)
Capacitors ndash cont
Capacitor discharge through a resistor
If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge
The discharge rate is expressed by an equation
Where RC is called time constant
Capacitors ndash cont
Capacitor charging through a resistor
If a capacitor C will be charged from source of voltage UWE
through a resistor R the voltage change across its terminals will be described by the following equations
The final solution is
Inductors
An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it
An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material
Graphic symbola) Toroidal core inductor b)cylindrical core inductor
The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L
where L is expressed in H (Henryrsquos) but most often in mH or microH
Inductors ndash cont
Different variations of inductors
Surface mount(SMT) inductors
Cylindricalcoreinductors
Inductor parameters
bullInductance [H]
bullRated voltage [V]
bullTolerance []
bullSaturation DC current [A]
bullMaximal RMS current [A]
bullSelf-resonance frequency [Hz]
bullDC resistance [Ω]
Typical set of parameters
Coilcraft DO3340P-104M inductor
L-100microH tol-20 Isat-25A Irms-12A
SRF-5MHz(typ) RDC-022Ω
Transformers
A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation
Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio
Transformer ndash cont
The current I2 flowing in the secondary winding is inversely proportional
to the current I1 flowing in the primary winding
Moreover the impedance connected to the transformer is transformed by the square of the turns ratio
Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer
Transformers ndash cont
The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit
Examples of low power transformers
Toroidal coretransformer
Toroidal core variabletransformer
(autotransformer)
Laminatedcore EI transformers
Diodes
A diode is a two-terminal electronic component that conducts electric current in only one direction
When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)
Diodes ndash cont
The currentndashvoltage characteristic of a diodeWhere
ID is diode current
If is forward diode current
IFmax is maximum diode
current
UF is forward diode voltage
UR is reverse diode voltage
URmax is the maximum
reverse voltage diodevoltage
Diodes ndash cont
For common types of diodes the value of UF voltage is
bullFor Germanium junction diode 02 04V
bullFor Silicone junction diode 05 08V
bullFor Schottky diode 0204V
An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation
Where I is the diode current
IS is the reverse bias saturation current (or scale current)
VD is the voltage across the diode
VT is the thermal voltage and
n is the ideality factor also known as the quality factor
Diodes ndashcont
The thermal voltage VT is approximately 2585 mV at 300 K
At any other temperature it is given by an equation
where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)
Diodes ndash cont
The typical I-V characteristics of for germaniumand silicone junction diode
Diodes ndash cont
Diode as a switching element
Following the end of forward conduction in a PN type diode a
reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called
reverse recovery time and usually is between tens and hundreds of
ns (ie between 1e-8 and 1e-7 s)
Diodes ndash cont
Diode as a rectifier
A half wave rectifier
A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification
Diodes ndash cont
A full-wave rectifier
This kind of a circuit is also known as the bridge rectifier
Diodes ndash cont
A rectifier in a DC voltage supply
Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge
In general case the simple design rule should be followed
RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)
Diodes ndash cont
Another application ndash diode-based voltage limiter
The cathode of a diode has a potential equal to 4V
U out max = 4V + 06 V = 46 V
If UINlt46V then UOUT = UIN
Bipolar Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals
Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors
B=base C=collector E= emitter
Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases
Transistors ndash cont
The history of the transistor
The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work
The first silicon transistors were produced by Western Electric and TexasInstruments in 1954
Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)
copy wwwporticusorg
Transistors ndash cont
An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased
NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia
The first transistor
copy Bell Labs
Transistor ndash cont
Transistor as an amplifier
A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated
The relations between currents in BJT copy radartutorialeu
Transistor ndash cont
The most often used amplifier circuits
highmediumlowBandwidth4
00001800Phase Shift between input and output signals
3
lt 1highhighCurrent gain2
highlt 1highVoltage gain1
COMMON BASE
COMMON COLLECTOR
COMMON EMITTER
AMPLIFIER
Nr
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Capacitors ndash cont
Most imporant capacitor parameters
bullCapacitance [microF] [nF] or [pF]
bullTolerance []
bullRated voltage [V]
bullDischarge rate (leakage current)
bullTemperature coefficient of capacitance
bullEquivalent series resitance (ESR)
Capacitors ndash cont
a)Aluminium electrolytic capacitor
b)Tantalum electrolytic capacitor
c)Polyesther capacitor
d)Ceramic disc capacitor
e)Mylar capacitor
Capacitors ndash cont
Capacitors in series connection
For two capacitors in series the equivalent capacitance is
For parallel configuration
For two capacitors in parallel the equivalent capacitance is
C=C1+C2
For n capacitors (general case)
Capacitors ndash cont
Capacitor discharge through a resistor
If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge
The discharge rate is expressed by an equation
Where RC is called time constant
Capacitors ndash cont
Capacitor charging through a resistor
If a capacitor C will be charged from source of voltage UWE
through a resistor R the voltage change across its terminals will be described by the following equations
The final solution is
Inductors
An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it
An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material
Graphic symbola) Toroidal core inductor b)cylindrical core inductor
The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L
where L is expressed in H (Henryrsquos) but most often in mH or microH
Inductors ndash cont
Different variations of inductors
Surface mount(SMT) inductors
Cylindricalcoreinductors
Inductor parameters
bullInductance [H]
bullRated voltage [V]
bullTolerance []
bullSaturation DC current [A]
bullMaximal RMS current [A]
bullSelf-resonance frequency [Hz]
bullDC resistance [Ω]
Typical set of parameters
Coilcraft DO3340P-104M inductor
L-100microH tol-20 Isat-25A Irms-12A
SRF-5MHz(typ) RDC-022Ω
Transformers
A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation
Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio
Transformer ndash cont
The current I2 flowing in the secondary winding is inversely proportional
to the current I1 flowing in the primary winding
Moreover the impedance connected to the transformer is transformed by the square of the turns ratio
Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer
Transformers ndash cont
The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit
Examples of low power transformers
Toroidal coretransformer
Toroidal core variabletransformer
(autotransformer)
Laminatedcore EI transformers
Diodes
A diode is a two-terminal electronic component that conducts electric current in only one direction
When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)
Diodes ndash cont
The currentndashvoltage characteristic of a diodeWhere
ID is diode current
If is forward diode current
IFmax is maximum diode
current
UF is forward diode voltage
UR is reverse diode voltage
URmax is the maximum
reverse voltage diodevoltage
Diodes ndash cont
For common types of diodes the value of UF voltage is
bullFor Germanium junction diode 02 04V
bullFor Silicone junction diode 05 08V
bullFor Schottky diode 0204V
An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation
Where I is the diode current
IS is the reverse bias saturation current (or scale current)
VD is the voltage across the diode
VT is the thermal voltage and
n is the ideality factor also known as the quality factor
Diodes ndashcont
The thermal voltage VT is approximately 2585 mV at 300 K
At any other temperature it is given by an equation
where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)
Diodes ndash cont
The typical I-V characteristics of for germaniumand silicone junction diode
Diodes ndash cont
Diode as a switching element
Following the end of forward conduction in a PN type diode a
reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called
reverse recovery time and usually is between tens and hundreds of
ns (ie between 1e-8 and 1e-7 s)
Diodes ndash cont
Diode as a rectifier
A half wave rectifier
A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification
Diodes ndash cont
A full-wave rectifier
This kind of a circuit is also known as the bridge rectifier
Diodes ndash cont
A rectifier in a DC voltage supply
Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge
In general case the simple design rule should be followed
RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)
Diodes ndash cont
Another application ndash diode-based voltage limiter
The cathode of a diode has a potential equal to 4V
U out max = 4V + 06 V = 46 V
If UINlt46V then UOUT = UIN
Bipolar Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals
Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors
B=base C=collector E= emitter
Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases
Transistors ndash cont
The history of the transistor
The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work
The first silicon transistors were produced by Western Electric and TexasInstruments in 1954
Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)
copy wwwporticusorg
Transistors ndash cont
An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased
NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia
The first transistor
copy Bell Labs
Transistor ndash cont
Transistor as an amplifier
A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated
The relations between currents in BJT copy radartutorialeu
Transistor ndash cont
The most often used amplifier circuits
highmediumlowBandwidth4
00001800Phase Shift between input and output signals
3
lt 1highhighCurrent gain2
highlt 1highVoltage gain1
COMMON BASE
COMMON COLLECTOR
COMMON EMITTER
AMPLIFIER
Nr
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Capacitors ndash cont
a)Aluminium electrolytic capacitor
b)Tantalum electrolytic capacitor
c)Polyesther capacitor
d)Ceramic disc capacitor
e)Mylar capacitor
Capacitors ndash cont
Capacitors in series connection
For two capacitors in series the equivalent capacitance is
For parallel configuration
For two capacitors in parallel the equivalent capacitance is
C=C1+C2
For n capacitors (general case)
Capacitors ndash cont
Capacitor discharge through a resistor
If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge
The discharge rate is expressed by an equation
Where RC is called time constant
Capacitors ndash cont
Capacitor charging through a resistor
If a capacitor C will be charged from source of voltage UWE
through a resistor R the voltage change across its terminals will be described by the following equations
The final solution is
Inductors
An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it
An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material
Graphic symbola) Toroidal core inductor b)cylindrical core inductor
The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L
where L is expressed in H (Henryrsquos) but most often in mH or microH
Inductors ndash cont
Different variations of inductors
Surface mount(SMT) inductors
Cylindricalcoreinductors
Inductor parameters
bullInductance [H]
bullRated voltage [V]
bullTolerance []
bullSaturation DC current [A]
bullMaximal RMS current [A]
bullSelf-resonance frequency [Hz]
bullDC resistance [Ω]
Typical set of parameters
Coilcraft DO3340P-104M inductor
L-100microH tol-20 Isat-25A Irms-12A
SRF-5MHz(typ) RDC-022Ω
Transformers
A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation
Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio
Transformer ndash cont
The current I2 flowing in the secondary winding is inversely proportional
to the current I1 flowing in the primary winding
Moreover the impedance connected to the transformer is transformed by the square of the turns ratio
Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer
Transformers ndash cont
The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit
Examples of low power transformers
Toroidal coretransformer
Toroidal core variabletransformer
(autotransformer)
Laminatedcore EI transformers
Diodes
A diode is a two-terminal electronic component that conducts electric current in only one direction
When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)
Diodes ndash cont
The currentndashvoltage characteristic of a diodeWhere
ID is diode current
If is forward diode current
IFmax is maximum diode
current
UF is forward diode voltage
UR is reverse diode voltage
URmax is the maximum
reverse voltage diodevoltage
Diodes ndash cont
For common types of diodes the value of UF voltage is
bullFor Germanium junction diode 02 04V
bullFor Silicone junction diode 05 08V
bullFor Schottky diode 0204V
An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation
Where I is the diode current
IS is the reverse bias saturation current (or scale current)
VD is the voltage across the diode
VT is the thermal voltage and
n is the ideality factor also known as the quality factor
Diodes ndashcont
The thermal voltage VT is approximately 2585 mV at 300 K
At any other temperature it is given by an equation
where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)
Diodes ndash cont
The typical I-V characteristics of for germaniumand silicone junction diode
Diodes ndash cont
Diode as a switching element
Following the end of forward conduction in a PN type diode a
reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called
reverse recovery time and usually is between tens and hundreds of
ns (ie between 1e-8 and 1e-7 s)
Diodes ndash cont
Diode as a rectifier
A half wave rectifier
A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification
Diodes ndash cont
A full-wave rectifier
This kind of a circuit is also known as the bridge rectifier
Diodes ndash cont
A rectifier in a DC voltage supply
Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge
In general case the simple design rule should be followed
RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)
Diodes ndash cont
Another application ndash diode-based voltage limiter
The cathode of a diode has a potential equal to 4V
U out max = 4V + 06 V = 46 V
If UINlt46V then UOUT = UIN
Bipolar Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals
Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors
B=base C=collector E= emitter
Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases
Transistors ndash cont
The history of the transistor
The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work
The first silicon transistors were produced by Western Electric and TexasInstruments in 1954
Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)
copy wwwporticusorg
Transistors ndash cont
An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased
NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia
The first transistor
copy Bell Labs
Transistor ndash cont
Transistor as an amplifier
A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated
The relations between currents in BJT copy radartutorialeu
Transistor ndash cont
The most often used amplifier circuits
highmediumlowBandwidth4
00001800Phase Shift between input and output signals
3
lt 1highhighCurrent gain2
highlt 1highVoltage gain1
COMMON BASE
COMMON COLLECTOR
COMMON EMITTER
AMPLIFIER
Nr
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Capacitors ndash cont
Capacitors in series connection
For two capacitors in series the equivalent capacitance is
For parallel configuration
For two capacitors in parallel the equivalent capacitance is
C=C1+C2
For n capacitors (general case)
Capacitors ndash cont
Capacitor discharge through a resistor
If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge
The discharge rate is expressed by an equation
Where RC is called time constant
Capacitors ndash cont
Capacitor charging through a resistor
If a capacitor C will be charged from source of voltage UWE
through a resistor R the voltage change across its terminals will be described by the following equations
The final solution is
Inductors
An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it
An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material
Graphic symbola) Toroidal core inductor b)cylindrical core inductor
The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L
where L is expressed in H (Henryrsquos) but most often in mH or microH
Inductors ndash cont
Different variations of inductors
Surface mount(SMT) inductors
Cylindricalcoreinductors
Inductor parameters
bullInductance [H]
bullRated voltage [V]
bullTolerance []
bullSaturation DC current [A]
bullMaximal RMS current [A]
bullSelf-resonance frequency [Hz]
bullDC resistance [Ω]
Typical set of parameters
Coilcraft DO3340P-104M inductor
L-100microH tol-20 Isat-25A Irms-12A
SRF-5MHz(typ) RDC-022Ω
Transformers
A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation
Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio
Transformer ndash cont
The current I2 flowing in the secondary winding is inversely proportional
to the current I1 flowing in the primary winding
Moreover the impedance connected to the transformer is transformed by the square of the turns ratio
Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer
Transformers ndash cont
The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit
Examples of low power transformers
Toroidal coretransformer
Toroidal core variabletransformer
(autotransformer)
Laminatedcore EI transformers
Diodes
A diode is a two-terminal electronic component that conducts electric current in only one direction
When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)
Diodes ndash cont
The currentndashvoltage characteristic of a diodeWhere
ID is diode current
If is forward diode current
IFmax is maximum diode
current
UF is forward diode voltage
UR is reverse diode voltage
URmax is the maximum
reverse voltage diodevoltage
Diodes ndash cont
For common types of diodes the value of UF voltage is
bullFor Germanium junction diode 02 04V
bullFor Silicone junction diode 05 08V
bullFor Schottky diode 0204V
An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation
Where I is the diode current
IS is the reverse bias saturation current (or scale current)
VD is the voltage across the diode
VT is the thermal voltage and
n is the ideality factor also known as the quality factor
Diodes ndashcont
The thermal voltage VT is approximately 2585 mV at 300 K
At any other temperature it is given by an equation
where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)
Diodes ndash cont
The typical I-V characteristics of for germaniumand silicone junction diode
Diodes ndash cont
Diode as a switching element
Following the end of forward conduction in a PN type diode a
reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called
reverse recovery time and usually is between tens and hundreds of
ns (ie between 1e-8 and 1e-7 s)
Diodes ndash cont
Diode as a rectifier
A half wave rectifier
A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification
Diodes ndash cont
A full-wave rectifier
This kind of a circuit is also known as the bridge rectifier
Diodes ndash cont
A rectifier in a DC voltage supply
Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge
In general case the simple design rule should be followed
RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)
Diodes ndash cont
Another application ndash diode-based voltage limiter
The cathode of a diode has a potential equal to 4V
U out max = 4V + 06 V = 46 V
If UINlt46V then UOUT = UIN
Bipolar Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals
Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors
B=base C=collector E= emitter
Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases
Transistors ndash cont
The history of the transistor
The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work
The first silicon transistors were produced by Western Electric and TexasInstruments in 1954
Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)
copy wwwporticusorg
Transistors ndash cont
An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased
NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia
The first transistor
copy Bell Labs
Transistor ndash cont
Transistor as an amplifier
A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated
The relations between currents in BJT copy radartutorialeu
Transistor ndash cont
The most often used amplifier circuits
highmediumlowBandwidth4
00001800Phase Shift between input and output signals
3
lt 1highhighCurrent gain2
highlt 1highVoltage gain1
COMMON BASE
COMMON COLLECTOR
COMMON EMITTER
AMPLIFIER
Nr
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Capacitors ndash cont
Capacitor discharge through a resistor
If a capacitor C charged to voltage U0 will be connected to a resistor R it will gradually discharge
The discharge rate is expressed by an equation
Where RC is called time constant
Capacitors ndash cont
Capacitor charging through a resistor
If a capacitor C will be charged from source of voltage UWE
through a resistor R the voltage change across its terminals will be described by the following equations
The final solution is
Inductors
An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it
An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material
Graphic symbola) Toroidal core inductor b)cylindrical core inductor
The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L
where L is expressed in H (Henryrsquos) but most often in mH or microH
Inductors ndash cont
Different variations of inductors
Surface mount(SMT) inductors
Cylindricalcoreinductors
Inductor parameters
bullInductance [H]
bullRated voltage [V]
bullTolerance []
bullSaturation DC current [A]
bullMaximal RMS current [A]
bullSelf-resonance frequency [Hz]
bullDC resistance [Ω]
Typical set of parameters
Coilcraft DO3340P-104M inductor
L-100microH tol-20 Isat-25A Irms-12A
SRF-5MHz(typ) RDC-022Ω
Transformers
A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation
Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio
Transformer ndash cont
The current I2 flowing in the secondary winding is inversely proportional
to the current I1 flowing in the primary winding
Moreover the impedance connected to the transformer is transformed by the square of the turns ratio
Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer
Transformers ndash cont
The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit
Examples of low power transformers
Toroidal coretransformer
Toroidal core variabletransformer
(autotransformer)
Laminatedcore EI transformers
Diodes
A diode is a two-terminal electronic component that conducts electric current in only one direction
When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)
Diodes ndash cont
The currentndashvoltage characteristic of a diodeWhere
ID is diode current
If is forward diode current
IFmax is maximum diode
current
UF is forward diode voltage
UR is reverse diode voltage
URmax is the maximum
reverse voltage diodevoltage
Diodes ndash cont
For common types of diodes the value of UF voltage is
bullFor Germanium junction diode 02 04V
bullFor Silicone junction diode 05 08V
bullFor Schottky diode 0204V
An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation
Where I is the diode current
IS is the reverse bias saturation current (or scale current)
VD is the voltage across the diode
VT is the thermal voltage and
n is the ideality factor also known as the quality factor
Diodes ndashcont
The thermal voltage VT is approximately 2585 mV at 300 K
At any other temperature it is given by an equation
where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)
Diodes ndash cont
The typical I-V characteristics of for germaniumand silicone junction diode
Diodes ndash cont
Diode as a switching element
Following the end of forward conduction in a PN type diode a
reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called
reverse recovery time and usually is between tens and hundreds of
ns (ie between 1e-8 and 1e-7 s)
Diodes ndash cont
Diode as a rectifier
A half wave rectifier
A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification
Diodes ndash cont
A full-wave rectifier
This kind of a circuit is also known as the bridge rectifier
Diodes ndash cont
A rectifier in a DC voltage supply
Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge
In general case the simple design rule should be followed
RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)
Diodes ndash cont
Another application ndash diode-based voltage limiter
The cathode of a diode has a potential equal to 4V
U out max = 4V + 06 V = 46 V
If UINlt46V then UOUT = UIN
Bipolar Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals
Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors
B=base C=collector E= emitter
Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases
Transistors ndash cont
The history of the transistor
The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work
The first silicon transistors were produced by Western Electric and TexasInstruments in 1954
Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)
copy wwwporticusorg
Transistors ndash cont
An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased
NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia
The first transistor
copy Bell Labs
Transistor ndash cont
Transistor as an amplifier
A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated
The relations between currents in BJT copy radartutorialeu
Transistor ndash cont
The most often used amplifier circuits
highmediumlowBandwidth4
00001800Phase Shift between input and output signals
3
lt 1highhighCurrent gain2
highlt 1highVoltage gain1
COMMON BASE
COMMON COLLECTOR
COMMON EMITTER
AMPLIFIER
Nr
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Capacitors ndash cont
Capacitor charging through a resistor
If a capacitor C will be charged from source of voltage UWE
through a resistor R the voltage change across its terminals will be described by the following equations
The final solution is
Inductors
An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it
An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material
Graphic symbola) Toroidal core inductor b)cylindrical core inductor
The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L
where L is expressed in H (Henryrsquos) but most often in mH or microH
Inductors ndash cont
Different variations of inductors
Surface mount(SMT) inductors
Cylindricalcoreinductors
Inductor parameters
bullInductance [H]
bullRated voltage [V]
bullTolerance []
bullSaturation DC current [A]
bullMaximal RMS current [A]
bullSelf-resonance frequency [Hz]
bullDC resistance [Ω]
Typical set of parameters
Coilcraft DO3340P-104M inductor
L-100microH tol-20 Isat-25A Irms-12A
SRF-5MHz(typ) RDC-022Ω
Transformers
A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation
Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio
Transformer ndash cont
The current I2 flowing in the secondary winding is inversely proportional
to the current I1 flowing in the primary winding
Moreover the impedance connected to the transformer is transformed by the square of the turns ratio
Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer
Transformers ndash cont
The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit
Examples of low power transformers
Toroidal coretransformer
Toroidal core variabletransformer
(autotransformer)
Laminatedcore EI transformers
Diodes
A diode is a two-terminal electronic component that conducts electric current in only one direction
When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)
Diodes ndash cont
The currentndashvoltage characteristic of a diodeWhere
ID is diode current
If is forward diode current
IFmax is maximum diode
current
UF is forward diode voltage
UR is reverse diode voltage
URmax is the maximum
reverse voltage diodevoltage
Diodes ndash cont
For common types of diodes the value of UF voltage is
bullFor Germanium junction diode 02 04V
bullFor Silicone junction diode 05 08V
bullFor Schottky diode 0204V
An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation
Where I is the diode current
IS is the reverse bias saturation current (or scale current)
VD is the voltage across the diode
VT is the thermal voltage and
n is the ideality factor also known as the quality factor
Diodes ndashcont
The thermal voltage VT is approximately 2585 mV at 300 K
At any other temperature it is given by an equation
where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)
Diodes ndash cont
The typical I-V characteristics of for germaniumand silicone junction diode
Diodes ndash cont
Diode as a switching element
Following the end of forward conduction in a PN type diode a
reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called
reverse recovery time and usually is between tens and hundreds of
ns (ie between 1e-8 and 1e-7 s)
Diodes ndash cont
Diode as a rectifier
A half wave rectifier
A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification
Diodes ndash cont
A full-wave rectifier
This kind of a circuit is also known as the bridge rectifier
Diodes ndash cont
A rectifier in a DC voltage supply
Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge
In general case the simple design rule should be followed
RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)
Diodes ndash cont
Another application ndash diode-based voltage limiter
The cathode of a diode has a potential equal to 4V
U out max = 4V + 06 V = 46 V
If UINlt46V then UOUT = UIN
Bipolar Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals
Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors
B=base C=collector E= emitter
Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases
Transistors ndash cont
The history of the transistor
The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work
The first silicon transistors were produced by Western Electric and TexasInstruments in 1954
Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)
copy wwwporticusorg
Transistors ndash cont
An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased
NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia
The first transistor
copy Bell Labs
Transistor ndash cont
Transistor as an amplifier
A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated
The relations between currents in BJT copy radartutorialeu
Transistor ndash cont
The most often used amplifier circuits
highmediumlowBandwidth4
00001800Phase Shift between input and output signals
3
lt 1highhighCurrent gain2
highlt 1highVoltage gain1
COMMON BASE
COMMON COLLECTOR
COMMON EMITTER
AMPLIFIER
Nr
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Inductors
An inductor is a passive electronic component that can store energy in a magnetic field created by currents flowing through it
An inductor is usually constructed as a coil of conducting material typically copper wire wrapped around a core either of air or of ferromagnetic material
Graphic symbola) Toroidal core inductor b)cylindrical core inductor
The voltage U across the terminal of an inductor is proportional to therate of current change (I) flowing through it and the inductance L
where L is expressed in H (Henryrsquos) but most often in mH or microH
Inductors ndash cont
Different variations of inductors
Surface mount(SMT) inductors
Cylindricalcoreinductors
Inductor parameters
bullInductance [H]
bullRated voltage [V]
bullTolerance []
bullSaturation DC current [A]
bullMaximal RMS current [A]
bullSelf-resonance frequency [Hz]
bullDC resistance [Ω]
Typical set of parameters
Coilcraft DO3340P-104M inductor
L-100microH tol-20 Isat-25A Irms-12A
SRF-5MHz(typ) RDC-022Ω
Transformers
A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation
Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio
Transformer ndash cont
The current I2 flowing in the secondary winding is inversely proportional
to the current I1 flowing in the primary winding
Moreover the impedance connected to the transformer is transformed by the square of the turns ratio
Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer
Transformers ndash cont
The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit
Examples of low power transformers
Toroidal coretransformer
Toroidal core variabletransformer
(autotransformer)
Laminatedcore EI transformers
Diodes
A diode is a two-terminal electronic component that conducts electric current in only one direction
When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)
Diodes ndash cont
The currentndashvoltage characteristic of a diodeWhere
ID is diode current
If is forward diode current
IFmax is maximum diode
current
UF is forward diode voltage
UR is reverse diode voltage
URmax is the maximum
reverse voltage diodevoltage
Diodes ndash cont
For common types of diodes the value of UF voltage is
bullFor Germanium junction diode 02 04V
bullFor Silicone junction diode 05 08V
bullFor Schottky diode 0204V
An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation
Where I is the diode current
IS is the reverse bias saturation current (or scale current)
VD is the voltage across the diode
VT is the thermal voltage and
n is the ideality factor also known as the quality factor
Diodes ndashcont
The thermal voltage VT is approximately 2585 mV at 300 K
At any other temperature it is given by an equation
where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)
Diodes ndash cont
The typical I-V characteristics of for germaniumand silicone junction diode
Diodes ndash cont
Diode as a switching element
Following the end of forward conduction in a PN type diode a
reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called
reverse recovery time and usually is between tens and hundreds of
ns (ie between 1e-8 and 1e-7 s)
Diodes ndash cont
Diode as a rectifier
A half wave rectifier
A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification
Diodes ndash cont
A full-wave rectifier
This kind of a circuit is also known as the bridge rectifier
Diodes ndash cont
A rectifier in a DC voltage supply
Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge
In general case the simple design rule should be followed
RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)
Diodes ndash cont
Another application ndash diode-based voltage limiter
The cathode of a diode has a potential equal to 4V
U out max = 4V + 06 V = 46 V
If UINlt46V then UOUT = UIN
Bipolar Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals
Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors
B=base C=collector E= emitter
Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases
Transistors ndash cont
The history of the transistor
The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work
The first silicon transistors were produced by Western Electric and TexasInstruments in 1954
Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)
copy wwwporticusorg
Transistors ndash cont
An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased
NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia
The first transistor
copy Bell Labs
Transistor ndash cont
Transistor as an amplifier
A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated
The relations between currents in BJT copy radartutorialeu
Transistor ndash cont
The most often used amplifier circuits
highmediumlowBandwidth4
00001800Phase Shift between input and output signals
3
lt 1highhighCurrent gain2
highlt 1highVoltage gain1
COMMON BASE
COMMON COLLECTOR
COMMON EMITTER
AMPLIFIER
Nr
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Inductors ndash cont
Different variations of inductors
Surface mount(SMT) inductors
Cylindricalcoreinductors
Inductor parameters
bullInductance [H]
bullRated voltage [V]
bullTolerance []
bullSaturation DC current [A]
bullMaximal RMS current [A]
bullSelf-resonance frequency [Hz]
bullDC resistance [Ω]
Typical set of parameters
Coilcraft DO3340P-104M inductor
L-100microH tol-20 Isat-25A Irms-12A
SRF-5MHz(typ) RDC-022Ω
Transformers
A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation
Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio
Transformer ndash cont
The current I2 flowing in the secondary winding is inversely proportional
to the current I1 flowing in the primary winding
Moreover the impedance connected to the transformer is transformed by the square of the turns ratio
Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer
Transformers ndash cont
The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit
Examples of low power transformers
Toroidal coretransformer
Toroidal core variabletransformer
(autotransformer)
Laminatedcore EI transformers
Diodes
A diode is a two-terminal electronic component that conducts electric current in only one direction
When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)
Diodes ndash cont
The currentndashvoltage characteristic of a diodeWhere
ID is diode current
If is forward diode current
IFmax is maximum diode
current
UF is forward diode voltage
UR is reverse diode voltage
URmax is the maximum
reverse voltage diodevoltage
Diodes ndash cont
For common types of diodes the value of UF voltage is
bullFor Germanium junction diode 02 04V
bullFor Silicone junction diode 05 08V
bullFor Schottky diode 0204V
An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation
Where I is the diode current
IS is the reverse bias saturation current (or scale current)
VD is the voltage across the diode
VT is the thermal voltage and
n is the ideality factor also known as the quality factor
Diodes ndashcont
The thermal voltage VT is approximately 2585 mV at 300 K
At any other temperature it is given by an equation
where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)
Diodes ndash cont
The typical I-V characteristics of for germaniumand silicone junction diode
Diodes ndash cont
Diode as a switching element
Following the end of forward conduction in a PN type diode a
reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called
reverse recovery time and usually is between tens and hundreds of
ns (ie between 1e-8 and 1e-7 s)
Diodes ndash cont
Diode as a rectifier
A half wave rectifier
A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification
Diodes ndash cont
A full-wave rectifier
This kind of a circuit is also known as the bridge rectifier
Diodes ndash cont
A rectifier in a DC voltage supply
Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge
In general case the simple design rule should be followed
RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)
Diodes ndash cont
Another application ndash diode-based voltage limiter
The cathode of a diode has a potential equal to 4V
U out max = 4V + 06 V = 46 V
If UINlt46V then UOUT = UIN
Bipolar Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals
Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors
B=base C=collector E= emitter
Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases
Transistors ndash cont
The history of the transistor
The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work
The first silicon transistors were produced by Western Electric and TexasInstruments in 1954
Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)
copy wwwporticusorg
Transistors ndash cont
An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased
NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia
The first transistor
copy Bell Labs
Transistor ndash cont
Transistor as an amplifier
A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated
The relations between currents in BJT copy radartutorialeu
Transistor ndash cont
The most often used amplifier circuits
highmediumlowBandwidth4
00001800Phase Shift between input and output signals
3
lt 1highhighCurrent gain2
highlt 1highVoltage gain1
COMMON BASE
COMMON COLLECTOR
COMMON EMITTER
AMPLIFIER
Nr
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Inductor parameters
bullInductance [H]
bullRated voltage [V]
bullTolerance []
bullSaturation DC current [A]
bullMaximal RMS current [A]
bullSelf-resonance frequency [Hz]
bullDC resistance [Ω]
Typical set of parameters
Coilcraft DO3340P-104M inductor
L-100microH tol-20 Isat-25A Irms-12A
SRF-5MHz(typ) RDC-022Ω
Transformers
A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation
Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio
Transformer ndash cont
The current I2 flowing in the secondary winding is inversely proportional
to the current I1 flowing in the primary winding
Moreover the impedance connected to the transformer is transformed by the square of the turns ratio
Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer
Transformers ndash cont
The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit
Examples of low power transformers
Toroidal coretransformer
Toroidal core variabletransformer
(autotransformer)
Laminatedcore EI transformers
Diodes
A diode is a two-terminal electronic component that conducts electric current in only one direction
When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)
Diodes ndash cont
The currentndashvoltage characteristic of a diodeWhere
ID is diode current
If is forward diode current
IFmax is maximum diode
current
UF is forward diode voltage
UR is reverse diode voltage
URmax is the maximum
reverse voltage diodevoltage
Diodes ndash cont
For common types of diodes the value of UF voltage is
bullFor Germanium junction diode 02 04V
bullFor Silicone junction diode 05 08V
bullFor Schottky diode 0204V
An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation
Where I is the diode current
IS is the reverse bias saturation current (or scale current)
VD is the voltage across the diode
VT is the thermal voltage and
n is the ideality factor also known as the quality factor
Diodes ndashcont
The thermal voltage VT is approximately 2585 mV at 300 K
At any other temperature it is given by an equation
where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)
Diodes ndash cont
The typical I-V characteristics of for germaniumand silicone junction diode
Diodes ndash cont
Diode as a switching element
Following the end of forward conduction in a PN type diode a
reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called
reverse recovery time and usually is between tens and hundreds of
ns (ie between 1e-8 and 1e-7 s)
Diodes ndash cont
Diode as a rectifier
A half wave rectifier
A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification
Diodes ndash cont
A full-wave rectifier
This kind of a circuit is also known as the bridge rectifier
Diodes ndash cont
A rectifier in a DC voltage supply
Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge
In general case the simple design rule should be followed
RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)
Diodes ndash cont
Another application ndash diode-based voltage limiter
The cathode of a diode has a potential equal to 4V
U out max = 4V + 06 V = 46 V
If UINlt46V then UOUT = UIN
Bipolar Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals
Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors
B=base C=collector E= emitter
Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases
Transistors ndash cont
The history of the transistor
The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work
The first silicon transistors were produced by Western Electric and TexasInstruments in 1954
Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)
copy wwwporticusorg
Transistors ndash cont
An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased
NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia
The first transistor
copy Bell Labs
Transistor ndash cont
Transistor as an amplifier
A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated
The relations between currents in BJT copy radartutorialeu
Transistor ndash cont
The most often used amplifier circuits
highmediumlowBandwidth4
00001800Phase Shift between input and output signals
3
lt 1highhighCurrent gain2
highlt 1highVoltage gain1
COMMON BASE
COMMON COLLECTOR
COMMON EMITTER
AMPLIFIER
Nr
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Transformers
A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsmdashthe transformers coils A varying current in the first or primary winding creates a varying magnetic flux in the transformers core and thus a varying magnetic field through the secondary winding The relation between voltages in primary and secondary windings aredescribed by the following equation
Where U1 ndash voltage across the primary winding n1- number of turns inthe primary winding U2 ndash voltage across the secondary winding and n2 ndashnumber of turns in the secondary winding n=turn ratio
Transformer ndash cont
The current I2 flowing in the secondary winding is inversely proportional
to the current I1 flowing in the primary winding
Moreover the impedance connected to the transformer is transformed by the square of the turns ratio
Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer
Transformers ndash cont
The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit
Examples of low power transformers
Toroidal coretransformer
Toroidal core variabletransformer
(autotransformer)
Laminatedcore EI transformers
Diodes
A diode is a two-terminal electronic component that conducts electric current in only one direction
When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)
Diodes ndash cont
The currentndashvoltage characteristic of a diodeWhere
ID is diode current
If is forward diode current
IFmax is maximum diode
current
UF is forward diode voltage
UR is reverse diode voltage
URmax is the maximum
reverse voltage diodevoltage
Diodes ndash cont
For common types of diodes the value of UF voltage is
bullFor Germanium junction diode 02 04V
bullFor Silicone junction diode 05 08V
bullFor Schottky diode 0204V
An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation
Where I is the diode current
IS is the reverse bias saturation current (or scale current)
VD is the voltage across the diode
VT is the thermal voltage and
n is the ideality factor also known as the quality factor
Diodes ndashcont
The thermal voltage VT is approximately 2585 mV at 300 K
At any other temperature it is given by an equation
where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)
Diodes ndash cont
The typical I-V characteristics of for germaniumand silicone junction diode
Diodes ndash cont
Diode as a switching element
Following the end of forward conduction in a PN type diode a
reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called
reverse recovery time and usually is between tens and hundreds of
ns (ie between 1e-8 and 1e-7 s)
Diodes ndash cont
Diode as a rectifier
A half wave rectifier
A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification
Diodes ndash cont
A full-wave rectifier
This kind of a circuit is also known as the bridge rectifier
Diodes ndash cont
A rectifier in a DC voltage supply
Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge
In general case the simple design rule should be followed
RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)
Diodes ndash cont
Another application ndash diode-based voltage limiter
The cathode of a diode has a potential equal to 4V
U out max = 4V + 06 V = 46 V
If UINlt46V then UOUT = UIN
Bipolar Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals
Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors
B=base C=collector E= emitter
Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases
Transistors ndash cont
The history of the transistor
The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work
The first silicon transistors were produced by Western Electric and TexasInstruments in 1954
Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)
copy wwwporticusorg
Transistors ndash cont
An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased
NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia
The first transistor
copy Bell Labs
Transistor ndash cont
Transistor as an amplifier
A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated
The relations between currents in BJT copy radartutorialeu
Transistor ndash cont
The most often used amplifier circuits
highmediumlowBandwidth4
00001800Phase Shift between input and output signals
3
lt 1highhighCurrent gain2
highlt 1highVoltage gain1
COMMON BASE
COMMON COLLECTOR
COMMON EMITTER
AMPLIFIER
Nr
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Transformer ndash cont
The current I2 flowing in the secondary winding is inversely proportional
to the current I1 flowing in the primary winding
Moreover the impedance connected to the transformer is transformed by the square of the turns ratio
Where Z1 and Z2 are the impedances on the primary and secondary side ofthe transformer
Transformers ndash cont
The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit
Examples of low power transformers
Toroidal coretransformer
Toroidal core variabletransformer
(autotransformer)
Laminatedcore EI transformers
Diodes
A diode is a two-terminal electronic component that conducts electric current in only one direction
When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)
Diodes ndash cont
The currentndashvoltage characteristic of a diodeWhere
ID is diode current
If is forward diode current
IFmax is maximum diode
current
UF is forward diode voltage
UR is reverse diode voltage
URmax is the maximum
reverse voltage diodevoltage
Diodes ndash cont
For common types of diodes the value of UF voltage is
bullFor Germanium junction diode 02 04V
bullFor Silicone junction diode 05 08V
bullFor Schottky diode 0204V
An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation
Where I is the diode current
IS is the reverse bias saturation current (or scale current)
VD is the voltage across the diode
VT is the thermal voltage and
n is the ideality factor also known as the quality factor
Diodes ndashcont
The thermal voltage VT is approximately 2585 mV at 300 K
At any other temperature it is given by an equation
where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)
Diodes ndash cont
The typical I-V characteristics of for germaniumand silicone junction diode
Diodes ndash cont
Diode as a switching element
Following the end of forward conduction in a PN type diode a
reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called
reverse recovery time and usually is between tens and hundreds of
ns (ie between 1e-8 and 1e-7 s)
Diodes ndash cont
Diode as a rectifier
A half wave rectifier
A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification
Diodes ndash cont
A full-wave rectifier
This kind of a circuit is also known as the bridge rectifier
Diodes ndash cont
A rectifier in a DC voltage supply
Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge
In general case the simple design rule should be followed
RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)
Diodes ndash cont
Another application ndash diode-based voltage limiter
The cathode of a diode has a potential equal to 4V
U out max = 4V + 06 V = 46 V
If UINlt46V then UOUT = UIN
Bipolar Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals
Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors
B=base C=collector E= emitter
Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases
Transistors ndash cont
The history of the transistor
The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work
The first silicon transistors were produced by Western Electric and TexasInstruments in 1954
Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)
copy wwwporticusorg
Transistors ndash cont
An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased
NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia
The first transistor
copy Bell Labs
Transistor ndash cont
Transistor as an amplifier
A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated
The relations between currents in BJT copy radartutorialeu
Transistor ndash cont
The most often used amplifier circuits
highmediumlowBandwidth4
00001800Phase Shift between input and output signals
3
lt 1highhighCurrent gain2
highlt 1highVoltage gain1
COMMON BASE
COMMON COLLECTOR
COMMON EMITTER
AMPLIFIER
Nr
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Transformers ndash cont
The transformers used in electronics circuits are most often power line transformersworking with 50 or 60 Hz power line AC voltage They are used for lowering powerline voltage to the more convenient low voltage used by DC power supply Theyalso provide galvanic separation between power line and the electronic circuit
Examples of low power transformers
Toroidal coretransformer
Toroidal core variabletransformer
(autotransformer)
Laminatedcore EI transformers
Diodes
A diode is a two-terminal electronic component that conducts electric current in only one direction
When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)
Diodes ndash cont
The currentndashvoltage characteristic of a diodeWhere
ID is diode current
If is forward diode current
IFmax is maximum diode
current
UF is forward diode voltage
UR is reverse diode voltage
URmax is the maximum
reverse voltage diodevoltage
Diodes ndash cont
For common types of diodes the value of UF voltage is
bullFor Germanium junction diode 02 04V
bullFor Silicone junction diode 05 08V
bullFor Schottky diode 0204V
An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation
Where I is the diode current
IS is the reverse bias saturation current (or scale current)
VD is the voltage across the diode
VT is the thermal voltage and
n is the ideality factor also known as the quality factor
Diodes ndashcont
The thermal voltage VT is approximately 2585 mV at 300 K
At any other temperature it is given by an equation
where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)
Diodes ndash cont
The typical I-V characteristics of for germaniumand silicone junction diode
Diodes ndash cont
Diode as a switching element
Following the end of forward conduction in a PN type diode a
reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called
reverse recovery time and usually is between tens and hundreds of
ns (ie between 1e-8 and 1e-7 s)
Diodes ndash cont
Diode as a rectifier
A half wave rectifier
A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification
Diodes ndash cont
A full-wave rectifier
This kind of a circuit is also known as the bridge rectifier
Diodes ndash cont
A rectifier in a DC voltage supply
Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge
In general case the simple design rule should be followed
RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)
Diodes ndash cont
Another application ndash diode-based voltage limiter
The cathode of a diode has a potential equal to 4V
U out max = 4V + 06 V = 46 V
If UINlt46V then UOUT = UIN
Bipolar Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals
Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors
B=base C=collector E= emitter
Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases
Transistors ndash cont
The history of the transistor
The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work
The first silicon transistors were produced by Western Electric and TexasInstruments in 1954
Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)
copy wwwporticusorg
Transistors ndash cont
An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased
NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia
The first transistor
copy Bell Labs
Transistor ndash cont
Transistor as an amplifier
A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated
The relations between currents in BJT copy radartutorialeu
Transistor ndash cont
The most often used amplifier circuits
highmediumlowBandwidth4
00001800Phase Shift between input and output signals
3
lt 1highhighCurrent gain2
highlt 1highVoltage gain1
COMMON BASE
COMMON COLLECTOR
COMMON EMITTER
AMPLIFIER
Nr
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Diodes
A diode is a two-terminal electronic component that conducts electric current in only one direction
When a positive voltage is applied to anode (A) against the cathode (K) then diode allows an electric current to pass in one direction (called the diodes forward direction) while blocking current in the opposite direction (the reverse direction)
Diodes ndash cont
The currentndashvoltage characteristic of a diodeWhere
ID is diode current
If is forward diode current
IFmax is maximum diode
current
UF is forward diode voltage
UR is reverse diode voltage
URmax is the maximum
reverse voltage diodevoltage
Diodes ndash cont
For common types of diodes the value of UF voltage is
bullFor Germanium junction diode 02 04V
bullFor Silicone junction diode 05 08V
bullFor Schottky diode 0204V
An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation
Where I is the diode current
IS is the reverse bias saturation current (or scale current)
VD is the voltage across the diode
VT is the thermal voltage and
n is the ideality factor also known as the quality factor
Diodes ndashcont
The thermal voltage VT is approximately 2585 mV at 300 K
At any other temperature it is given by an equation
where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)
Diodes ndash cont
The typical I-V characteristics of for germaniumand silicone junction diode
Diodes ndash cont
Diode as a switching element
Following the end of forward conduction in a PN type diode a
reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called
reverse recovery time and usually is between tens and hundreds of
ns (ie between 1e-8 and 1e-7 s)
Diodes ndash cont
Diode as a rectifier
A half wave rectifier
A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification
Diodes ndash cont
A full-wave rectifier
This kind of a circuit is also known as the bridge rectifier
Diodes ndash cont
A rectifier in a DC voltage supply
Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge
In general case the simple design rule should be followed
RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)
Diodes ndash cont
Another application ndash diode-based voltage limiter
The cathode of a diode has a potential equal to 4V
U out max = 4V + 06 V = 46 V
If UINlt46V then UOUT = UIN
Bipolar Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals
Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors
B=base C=collector E= emitter
Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases
Transistors ndash cont
The history of the transistor
The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work
The first silicon transistors were produced by Western Electric and TexasInstruments in 1954
Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)
copy wwwporticusorg
Transistors ndash cont
An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased
NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia
The first transistor
copy Bell Labs
Transistor ndash cont
Transistor as an amplifier
A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated
The relations between currents in BJT copy radartutorialeu
Transistor ndash cont
The most often used amplifier circuits
highmediumlowBandwidth4
00001800Phase Shift between input and output signals
3
lt 1highhighCurrent gain2
highlt 1highVoltage gain1
COMMON BASE
COMMON COLLECTOR
COMMON EMITTER
AMPLIFIER
Nr
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Diodes ndash cont
The currentndashvoltage characteristic of a diodeWhere
ID is diode current
If is forward diode current
IFmax is maximum diode
current
UF is forward diode voltage
UR is reverse diode voltage
URmax is the maximum
reverse voltage diodevoltage
Diodes ndash cont
For common types of diodes the value of UF voltage is
bullFor Germanium junction diode 02 04V
bullFor Silicone junction diode 05 08V
bullFor Schottky diode 0204V
An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation
Where I is the diode current
IS is the reverse bias saturation current (or scale current)
VD is the voltage across the diode
VT is the thermal voltage and
n is the ideality factor also known as the quality factor
Diodes ndashcont
The thermal voltage VT is approximately 2585 mV at 300 K
At any other temperature it is given by an equation
where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)
Diodes ndash cont
The typical I-V characteristics of for germaniumand silicone junction diode
Diodes ndash cont
Diode as a switching element
Following the end of forward conduction in a PN type diode a
reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called
reverse recovery time and usually is between tens and hundreds of
ns (ie between 1e-8 and 1e-7 s)
Diodes ndash cont
Diode as a rectifier
A half wave rectifier
A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification
Diodes ndash cont
A full-wave rectifier
This kind of a circuit is also known as the bridge rectifier
Diodes ndash cont
A rectifier in a DC voltage supply
Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge
In general case the simple design rule should be followed
RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)
Diodes ndash cont
Another application ndash diode-based voltage limiter
The cathode of a diode has a potential equal to 4V
U out max = 4V + 06 V = 46 V
If UINlt46V then UOUT = UIN
Bipolar Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals
Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors
B=base C=collector E= emitter
Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases
Transistors ndash cont
The history of the transistor
The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work
The first silicon transistors were produced by Western Electric and TexasInstruments in 1954
Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)
copy wwwporticusorg
Transistors ndash cont
An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased
NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia
The first transistor
copy Bell Labs
Transistor ndash cont
Transistor as an amplifier
A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated
The relations between currents in BJT copy radartutorialeu
Transistor ndash cont
The most often used amplifier circuits
highmediumlowBandwidth4
00001800Phase Shift between input and output signals
3
lt 1highhighCurrent gain2
highlt 1highVoltage gain1
COMMON BASE
COMMON COLLECTOR
COMMON EMITTER
AMPLIFIER
Nr
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Diodes ndash cont
For common types of diodes the value of UF voltage is
bullFor Germanium junction diode 02 04V
bullFor Silicone junction diode 05 08V
bullFor Schottky diode 0204V
An IndashV characteristic of an ideal diode is given by the Shockley ideal diodeequation
Where I is the diode current
IS is the reverse bias saturation current (or scale current)
VD is the voltage across the diode
VT is the thermal voltage and
n is the ideality factor also known as the quality factor
Diodes ndashcont
The thermal voltage VT is approximately 2585 mV at 300 K
At any other temperature it is given by an equation
where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)
Diodes ndash cont
The typical I-V characteristics of for germaniumand silicone junction diode
Diodes ndash cont
Diode as a switching element
Following the end of forward conduction in a PN type diode a
reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called
reverse recovery time and usually is between tens and hundreds of
ns (ie between 1e-8 and 1e-7 s)
Diodes ndash cont
Diode as a rectifier
A half wave rectifier
A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification
Diodes ndash cont
A full-wave rectifier
This kind of a circuit is also known as the bridge rectifier
Diodes ndash cont
A rectifier in a DC voltage supply
Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge
In general case the simple design rule should be followed
RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)
Diodes ndash cont
Another application ndash diode-based voltage limiter
The cathode of a diode has a potential equal to 4V
U out max = 4V + 06 V = 46 V
If UINlt46V then UOUT = UIN
Bipolar Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals
Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors
B=base C=collector E= emitter
Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases
Transistors ndash cont
The history of the transistor
The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work
The first silicon transistors were produced by Western Electric and TexasInstruments in 1954
Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)
copy wwwporticusorg
Transistors ndash cont
An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased
NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia
The first transistor
copy Bell Labs
Transistor ndash cont
Transistor as an amplifier
A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated
The relations between currents in BJT copy radartutorialeu
Transistor ndash cont
The most often used amplifier circuits
highmediumlowBandwidth4
00001800Phase Shift between input and output signals
3
lt 1highhighCurrent gain2
highlt 1highVoltage gain1
COMMON BASE
COMMON COLLECTOR
COMMON EMITTER
AMPLIFIER
Nr
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Diodes ndashcont
The thermal voltage VT is approximately 2585 mV at 300 K
At any other temperature it is given by an equation
where k is the Boltzmann constant T is the absolute temperature of the p-n junction and q is the magnitude of charge on an electron (the elementary charge q= 160210e-19 C)
Diodes ndash cont
The typical I-V characteristics of for germaniumand silicone junction diode
Diodes ndash cont
Diode as a switching element
Following the end of forward conduction in a PN type diode a
reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called
reverse recovery time and usually is between tens and hundreds of
ns (ie between 1e-8 and 1e-7 s)
Diodes ndash cont
Diode as a rectifier
A half wave rectifier
A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification
Diodes ndash cont
A full-wave rectifier
This kind of a circuit is also known as the bridge rectifier
Diodes ndash cont
A rectifier in a DC voltage supply
Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge
In general case the simple design rule should be followed
RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)
Diodes ndash cont
Another application ndash diode-based voltage limiter
The cathode of a diode has a potential equal to 4V
U out max = 4V + 06 V = 46 V
If UINlt46V then UOUT = UIN
Bipolar Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals
Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors
B=base C=collector E= emitter
Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases
Transistors ndash cont
The history of the transistor
The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work
The first silicon transistors were produced by Western Electric and TexasInstruments in 1954
Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)
copy wwwporticusorg
Transistors ndash cont
An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased
NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia
The first transistor
copy Bell Labs
Transistor ndash cont
Transistor as an amplifier
A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated
The relations between currents in BJT copy radartutorialeu
Transistor ndash cont
The most often used amplifier circuits
highmediumlowBandwidth4
00001800Phase Shift between input and output signals
3
lt 1highhighCurrent gain2
highlt 1highVoltage gain1
COMMON BASE
COMMON COLLECTOR
COMMON EMITTER
AMPLIFIER
Nr
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Diodes ndash cont
The typical I-V characteristics of for germaniumand silicone junction diode
Diodes ndash cont
Diode as a switching element
Following the end of forward conduction in a PN type diode a
reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called
reverse recovery time and usually is between tens and hundreds of
ns (ie between 1e-8 and 1e-7 s)
Diodes ndash cont
Diode as a rectifier
A half wave rectifier
A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification
Diodes ndash cont
A full-wave rectifier
This kind of a circuit is also known as the bridge rectifier
Diodes ndash cont
A rectifier in a DC voltage supply
Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge
In general case the simple design rule should be followed
RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)
Diodes ndash cont
Another application ndash diode-based voltage limiter
The cathode of a diode has a potential equal to 4V
U out max = 4V + 06 V = 46 V
If UINlt46V then UOUT = UIN
Bipolar Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals
Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors
B=base C=collector E= emitter
Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases
Transistors ndash cont
The history of the transistor
The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work
The first silicon transistors were produced by Western Electric and TexasInstruments in 1954
Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)
copy wwwporticusorg
Transistors ndash cont
An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased
NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia
The first transistor
copy Bell Labs
Transistor ndash cont
Transistor as an amplifier
A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated
The relations between currents in BJT copy radartutorialeu
Transistor ndash cont
The most often used amplifier circuits
highmediumlowBandwidth4
00001800Phase Shift between input and output signals
3
lt 1highhighCurrent gain2
highlt 1highVoltage gain1
COMMON BASE
COMMON COLLECTOR
COMMON EMITTER
AMPLIFIER
Nr
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Diodes ndash cont
Diode as a switching element
Following the end of forward conduction in a PN type diode a
reverse current flows for a short time The device does not attain its full blocking capability until the reverse current ceases Trr is called
reverse recovery time and usually is between tens and hundreds of
ns (ie between 1e-8 and 1e-7 s)
Diodes ndash cont
Diode as a rectifier
A half wave rectifier
A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification
Diodes ndash cont
A full-wave rectifier
This kind of a circuit is also known as the bridge rectifier
Diodes ndash cont
A rectifier in a DC voltage supply
Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge
In general case the simple design rule should be followed
RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)
Diodes ndash cont
Another application ndash diode-based voltage limiter
The cathode of a diode has a potential equal to 4V
U out max = 4V + 06 V = 46 V
If UINlt46V then UOUT = UIN
Bipolar Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals
Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors
B=base C=collector E= emitter
Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases
Transistors ndash cont
The history of the transistor
The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work
The first silicon transistors were produced by Western Electric and TexasInstruments in 1954
Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)
copy wwwporticusorg
Transistors ndash cont
An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased
NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia
The first transistor
copy Bell Labs
Transistor ndash cont
Transistor as an amplifier
A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated
The relations between currents in BJT copy radartutorialeu
Transistor ndash cont
The most often used amplifier circuits
highmediumlowBandwidth4
00001800Phase Shift between input and output signals
3
lt 1highhighCurrent gain2
highlt 1highVoltage gain1
COMMON BASE
COMMON COLLECTOR
COMMON EMITTER
AMPLIFIER
Nr
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Diodes ndash cont
Diode as a rectifier
A half wave rectifier
A rectifier is an electrical device that converts alternating current (AC) which periodically reverses direction to direct current (DC) which is in only one direction such a process is known as rectification
Diodes ndash cont
A full-wave rectifier
This kind of a circuit is also known as the bridge rectifier
Diodes ndash cont
A rectifier in a DC voltage supply
Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge
In general case the simple design rule should be followed
RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)
Diodes ndash cont
Another application ndash diode-based voltage limiter
The cathode of a diode has a potential equal to 4V
U out max = 4V + 06 V = 46 V
If UINlt46V then UOUT = UIN
Bipolar Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals
Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors
B=base C=collector E= emitter
Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases
Transistors ndash cont
The history of the transistor
The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work
The first silicon transistors were produced by Western Electric and TexasInstruments in 1954
Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)
copy wwwporticusorg
Transistors ndash cont
An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased
NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia
The first transistor
copy Bell Labs
Transistor ndash cont
Transistor as an amplifier
A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated
The relations between currents in BJT copy radartutorialeu
Transistor ndash cont
The most often used amplifier circuits
highmediumlowBandwidth4
00001800Phase Shift between input and output signals
3
lt 1highhighCurrent gain2
highlt 1highVoltage gain1
COMMON BASE
COMMON COLLECTOR
COMMON EMITTER
AMPLIFIER
Nr
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Diodes ndash cont
A full-wave rectifier
This kind of a circuit is also known as the bridge rectifier
Diodes ndash cont
A rectifier in a DC voltage supply
Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge
In general case the simple design rule should be followed
RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)
Diodes ndash cont
Another application ndash diode-based voltage limiter
The cathode of a diode has a potential equal to 4V
U out max = 4V + 06 V = 46 V
If UINlt46V then UOUT = UIN
Bipolar Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals
Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors
B=base C=collector E= emitter
Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases
Transistors ndash cont
The history of the transistor
The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work
The first silicon transistors were produced by Western Electric and TexasInstruments in 1954
Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)
copy wwwporticusorg
Transistors ndash cont
An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased
NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia
The first transistor
copy Bell Labs
Transistor ndash cont
Transistor as an amplifier
A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated
The relations between currents in BJT copy radartutorialeu
Transistor ndash cont
The most often used amplifier circuits
highmediumlowBandwidth4
00001800Phase Shift between input and output signals
3
lt 1highhighCurrent gain2
highlt 1highVoltage gain1
COMMON BASE
COMMON COLLECTOR
COMMON EMITTER
AMPLIFIER
Nr
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Diodes ndash cont
A rectifier in a DC voltage supply
Both single- and full-wave rectifier produce a large amount of ripple voltageon its output In order to produce direct current (DC) voltage from ripplevoltage a smoothing circuit (a filter) is required The most common versioncalled RC filter includes a capacitor placed at the output of the rectifier Thiselement act as an energy reservoir storing electric charge
In general case the simple design rule should be followed
RLmiddotCgtgt1f where f is the ripple voltage frequency (100 Hz)
Diodes ndash cont
Another application ndash diode-based voltage limiter
The cathode of a diode has a potential equal to 4V
U out max = 4V + 06 V = 46 V
If UINlt46V then UOUT = UIN
Bipolar Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals
Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors
B=base C=collector E= emitter
Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases
Transistors ndash cont
The history of the transistor
The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work
The first silicon transistors were produced by Western Electric and TexasInstruments in 1954
Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)
copy wwwporticusorg
Transistors ndash cont
An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased
NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia
The first transistor
copy Bell Labs
Transistor ndash cont
Transistor as an amplifier
A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated
The relations between currents in BJT copy radartutorialeu
Transistor ndash cont
The most often used amplifier circuits
highmediumlowBandwidth4
00001800Phase Shift between input and output signals
3
lt 1highhighCurrent gain2
highlt 1highVoltage gain1
COMMON BASE
COMMON COLLECTOR
COMMON EMITTER
AMPLIFIER
Nr
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Diodes ndash cont
Another application ndash diode-based voltage limiter
The cathode of a diode has a potential equal to 4V
U out max = 4V + 06 V = 46 V
If UINlt46V then UOUT = UIN
Bipolar Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals
Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors
B=base C=collector E= emitter
Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases
Transistors ndash cont
The history of the transistor
The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work
The first silicon transistors were produced by Western Electric and TexasInstruments in 1954
Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)
copy wwwporticusorg
Transistors ndash cont
An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased
NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia
The first transistor
copy Bell Labs
Transistor ndash cont
Transistor as an amplifier
A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated
The relations between currents in BJT copy radartutorialeu
Transistor ndash cont
The most often used amplifier circuits
highmediumlowBandwidth4
00001800Phase Shift between input and output signals
3
lt 1highhighCurrent gain2
highlt 1highVoltage gain1
COMMON BASE
COMMON COLLECTOR
COMMON EMITTER
AMPLIFIER
Nr
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Bipolar Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals
Schematic symbols and internal structureof NPN (left) and PNP bipolar transistors
B=base C=collector E= emitter
Bipolar junction transistors(BJTs) from the left TO-72 TO-220 and TO-3 cases
Transistors ndash cont
The history of the transistor
The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work
The first silicon transistors were produced by Western Electric and TexasInstruments in 1954
Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)
copy wwwporticusorg
Transistors ndash cont
An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased
NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia
The first transistor
copy Bell Labs
Transistor ndash cont
Transistor as an amplifier
A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated
The relations between currents in BJT copy radartutorialeu
Transistor ndash cont
The most often used amplifier circuits
highmediumlowBandwidth4
00001800Phase Shift between input and output signals
3
lt 1highhighCurrent gain2
highlt 1highVoltage gain1
COMMON BASE
COMMON COLLECTOR
COMMON EMITTER
AMPLIFIER
Nr
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Transistors ndash cont
The history of the transistor
The first working transistor was built in 1947 by J Bardeen W Brattainand W Shockley from Bell Labs In 1956 they were awarded Nobel Prizefor their work
The first silicon transistors were produced by Western Electric and TexasInstruments in 1954
Left An early 2N23 bipolar junctiontransistor (Western Electric 1954)
copy wwwporticusorg
Transistors ndash cont
An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased
NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia
The first transistor
copy Bell Labs
Transistor ndash cont
Transistor as an amplifier
A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated
The relations between currents in BJT copy radartutorialeu
Transistor ndash cont
The most often used amplifier circuits
highmediumlowBandwidth4
00001800Phase Shift between input and output signals
3
lt 1highhighCurrent gain2
highlt 1highVoltage gain1
COMMON BASE
COMMON COLLECTOR
COMMON EMITTER
AMPLIFIER
Nr
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Transistors ndash cont
An NPN transistor can be considered as two diodes with a shared anode In typical operation the base-emitter junction is forward biased and the basendashcollector junction is reverse biased
NPN BJT with forward-biased EndashB junction and reverse-biased BndashC junctioncopy Wikipedia
The first transistor
copy Bell Labs
Transistor ndash cont
Transistor as an amplifier
A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated
The relations between currents in BJT copy radartutorialeu
Transistor ndash cont
The most often used amplifier circuits
highmediumlowBandwidth4
00001800Phase Shift between input and output signals
3
lt 1highhighCurrent gain2
highlt 1highVoltage gain1
COMMON BASE
COMMON COLLECTOR
COMMON EMITTER
AMPLIFIER
Nr
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
The first transistor
copy Bell Labs
Transistor ndash cont
Transistor as an amplifier
A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated
The relations between currents in BJT copy radartutorialeu
Transistor ndash cont
The most often used amplifier circuits
highmediumlowBandwidth4
00001800Phase Shift between input and output signals
3
lt 1highhighCurrent gain2
highlt 1highVoltage gain1
COMMON BASE
COMMON COLLECTOR
COMMON EMITTER
AMPLIFIER
Nr
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Transistor ndash cont
Transistor as an amplifier
A voltage or current applied to one pair of the transistors terminals changes the current flowing through another pair of terminals Because the controlled (output) power can be much more than the controlling (input) power the transistor provides amplification of a signal In most cases the input signalchanges the base current and this way the much higher current flowing throughthe collector is modulated
The relations between currents in BJT copy radartutorialeu
Transistor ndash cont
The most often used amplifier circuits
highmediumlowBandwidth4
00001800Phase Shift between input and output signals
3
lt 1highhighCurrent gain2
highlt 1highVoltage gain1
COMMON BASE
COMMON COLLECTOR
COMMON EMITTER
AMPLIFIER
Nr
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Transistor ndash cont
The most often used amplifier circuits
highmediumlowBandwidth4
00001800Phase Shift between input and output signals
3
lt 1highhighCurrent gain2
highlt 1highVoltage gain1
COMMON BASE
COMMON COLLECTOR
COMMON EMITTER
AMPLIFIER
Nr
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Transistors ndash cont
If transistor is in an active mode then the following formula is true
IC = hFEmiddot IB = β middot IB
Where β coefficient is called the common-emitter current gain
The value of β is usually between 50 and 300
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Transistors ndash cont
Current-voltage characteristics of a BJT
The DC emitter and collector currents in active mode can be
described by a following equation
For ICgtgt IC0
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Transistors ndash cont
The input I-V characteristic The relation between ICand IB
The relation between βand IC
Please note that β is not constant and it remains a function of Ic
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Transistors ndash cont
Safe Operating Area (SOA) of a BJT
copy MOSPEC
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Transistors ndash cont
BJT ndash typical values of parameters copy ONsemi
a)Low power ndash BC548 b)high power ndash TIP122
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
BJT as a switch
a) An incandescent light bulb driver b) An electromagnetic relay driver
(the diode protects BJT againstvoltage spikes)
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Common collector amplifier
+Ucc
R
The output voltage
UE = UB ndash 06V
Input impedance = high outputimpedance = low voltageamplification lt1
A simple application ndashZener-diode based DC voltage regulator
Uout=Uz ndash 06V
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Small signal amplifiers
+Ucc
RER2
R1C1
C2
C1 and C2 capacitors define the bandwidth of the amplifier For C1 = 05microF C2 = 33 microF we obtain minimal frequency 20Hz andmaximal freq = 20 kHz
A small-signal common collector amplifier
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Small signal amplifiers
A common ndash emitter AC signal amplifier
+Ucc
RER2
R1C1
RC
C2
Parameters
UCC = 20V
R1 = 110kΩ R2 = 10kΩ
C1 = 01microF C2 = 1microF
RC = 10kΩ RE = 1kΩ
Voltage gain
kU = UOUTUIN = -RCRE
Here kU=-100001000 [VV] = -10 [VV]
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Operational amplifier
An ideal operational amplifier assumptions
copy Texas
Instruments
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Operational amplifier ndash cont
The basic circuits
copy National Semiconductor
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Operational amplifier ndash cont
copy National Semiconductor
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont
Operational amplifier ndash cont
A hardware implementation of mathematical operations copy National Semicond
Operational amplifier ndash cont
Operational amplifer ndash cont