Basic electronics

Optical interfaces:

Detect and control

Ohm’s lawCurrent = voltage / resistance• I = V / R• V = I x R

Definitions • Voltage = potential energy / unit charge, units = Volts• Current = charge flow rate, units = Amps• Resistance = friction, units = Ohms

Example• Voltage drop when current flows through resistor

• V1 - V2 = I R

IR

V1

V2

Schematics

• Symbols represent circuit elements• Lines are wires

+ Battery

Resistor

Ground

+VRI

Sample circuit

Ground voltagedefined = 0

Parallel and series resistorsSeries

• same current flows through all

Parallel

• save voltage across all

+

Note: these points are connected together

I

VR1

R2

Series circuitV = R1 I + R2 I = Reff IReff = R1 + R2

Parallel circuitI = V/R1 + V/R2 = V/Reff 1/Reff = 1/R1 + 1/R2

+V

R1R2I1 I2

I

Resistive voltage divider• Series resistor circuit• Reduce input voltage to desired level• Advantages:

– simple and accurate– complex circuit can use single voltage source

• Disadvantage: – dissipates power– easy to overload– need Rload << R2

New schematic symbol:external connection

+

Vin

R1

R2 I

IVout

Resistive dividerI = Vin/Reff = Vout/R2

Vout = Vin (R2 / (R1 + R2) )

Variable voltage divider

• Use potentiometer (= variable resistor)• Most common: constant output resistance

+

Vin Rvar

Rout I

IVout

Variable voltage dividerVout = Vin (Rout / (Rvar + Rout) )

New schematic symbol:potentiometer

Capacitors • Charge = voltage x capacitance• Q = C VDefinitions • Charge = integrated current flow , units = Coloumbs = Amp - seconds• I = dQ/dt• Capacitance = storage capacity, units = FaradsExample • Capacitor charging circuit• Time constant = RC =

Capacitor charging circuitV = VR + VC = R dQ/dt + Q/CdQ/dt + Q/RC = V/RQ = C V (1 - exp(-t/RC))Vout = Vin (1 - exp(-t/RC))

New schematic symbol:capacitor

+V R

C

IVout

Q

Vout

t

Vin

= RC

Capacitor charging curvetime constant = RC

AC circuits• Replace battery with sine (cosine) wave source• V = V0 cos(2 f t)Definitions • Frequency f = cosine wave frequency, units = Hertz Examples • Resistor response: I = (V0/R) cos(2 f t)• Capacitor response: Q = CV0 cos(2 f t)

– I = - 2 f CV0 sin(2 f t)– Current depends on frequency– negative sine wave replaces cosine wave – - 90 degree phase shift = lag

V0 cos(2 f t)

RI = (V0/R) cos(2 f t)

Resistive ac circuit

New schematic symbol:AC voltage source

V0 cos(2 f t)

CI =

- 2 f CV0 sin(2 f t)

Capacitive ac circuit• 90 degree phase lag

Simplified notation: ac-circuits• V = V0 cos(2 f t) = V0 [exp(2 j f t) + c.c.]/2

• Drop c.c. part and factor of 1/2

• V = V0 exp(2 j f t)

Revisit resistive and capacitive circuits

• Resistor response: I = (V0/R) exp(2 j f t) = V / R = V/ ZR

• Capacitor response: I = 2 j f CV0 exp(2 j f t) = (2 j f C) V = V/ ZC

Definition: Impedance, Z = effective resistance, units Ohms

• Capacitor impedance ZC = 1 / (2 jf C)

• Resistor impedance ZR = R

Impedance makes it look like Ohms law applies to capacitive circuits also

• Capacitor response I = V / ZC

Explore capacitor circuitsImpedance ZC = 1/ (2 jf C)

• Limit of low frequency f ~ 0– ZC --> infinity

– Capacitor is open circuit at low frequency

• Limit of low frequency f ~ infinity– ZC --> 0

– Capacitor is short circuit at low frequency

V0 cos(2 f t)

CI = V/ZC

Capacitive ac circuit

Revisit capacitor charging circuit

Replace C with impedance ZC

• Charging circuit looks like voltage divider

• Vout = Vin (ZC / (ZR + ZC) ) = Vin / (1 + 2 jf R C )

Low-pass filter

Crossover when f = 1 / 2 R C = 1 / 2 , is time constant

• lower frequencies Vout ~ Vin = pass band

• higher frequencies Vout ~ Vin / (2 jf R C ) = attenuated

Capacitor charging circuit= Low-pass filter

Vin = V0 cos(2 f t)

R

C

IVout

Ilog(Vout)

log(f )

logVin

f = 1 / 2

Low-pass filter response• time constant = RC =

Single-pole rolloff6 dB/octave= 10 dB/decade

knee

Inductors

Capacitor charging circuit= Low-pass filter

Vout

log(Vout)

log(f )

logVin

f = R / 2 jL

High-pass filter response

• Voltage = rate of voltage change x inductance• V = L dI/dtDefinitions • Inductance L = resistance to current change, units = HenrysImpedance of inductor: ZL = (2 jf L)• Low frequency = short circuit• High frequency = open circuitInductors rarely used

Vin = V0 cos(2 f t)

RL

I

INew schematic symbol:Inductor

Capacitor filters circuits• Can make both low and high pass filters

Low-pass filterVin = V0 cos(2 f t)

RC

IVout

I

High-pass filterVin = V0 cos(2 f t)

CR

IVout

I

log(Vout)

log(f )

logVin

f = 1 / 2

Gain response

log(Vout)

log(f )

logVin

f = 1 / 2

Gain response

knee

phase

log(f )

f = 1 / 2

Phase response

-90 degrees

phase

log(f )

f = 1 / 2

Phase response

-90 degrees

0 degrees 0 degrees

Summary of schematic symbols

+Battery Resistor

Ground

Externalconnection

Capacitor AC voltagesource

Inductor

Non-connecting wires -

+

Op amp

Potentiometer

Potentiometer2-inputs plus

center tap

Diode

Color code• Resistor values determined by color• Three main bands

– 1st = 1st digit– 2nd = 2nd digit– 3rd = # of trailing zeros

• Examples– red, brown, black– 2 1 no zeros = 21 Ohms– yellow, brown, green– 4 1 5 = 4.1 Mohm– purple, gray, orange– 7 8 3 = 78 kOhms

• Capacitors can have 3 numbers– use like three colors

Color

black

brown

red

orange

yellow

green

blue

violet

gray

white

Number

0

1

2

3

4

5

6

7

8

9