Voltage Mode Control of Buck Converter
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Transcript of Voltage Mode Control of Buck Converter
A
PROJECT REPORT ON
“VOLTAGE MODE CONTROL OF BUCK CONVERTER”
PROJECT ASSOCIATES
Anusha A. N Arpan Chatterjee
(4NM09EE008) (4NM09EE009)
Ashutosh Kumar Manish Kumar
(4NM09EE010) (4NM09EE031)
Under the guidance of
Mr. Suryanarayana K.
Assistant Professor, Dept. of Electrical and Electronics Engineering
NMAMIT, Nitte
Project Report submitted to NMAM Institute of Technology, Nitte An Autonomous Institution affiliated to VTU Belgaum, in partial fulfilment for the award
of Bachelor of engineering in Electrical and Electronics Engineering
DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING
PDFaid.com#1 pdf solutions
NMAM INSTITUTE OF TECHNOLOGY
(An Autonomous Institution affiliated to VTU, Belgaum) (NBA Accredited, ISO 9001:2008 Certified)
Nitte – 574110, Karkala, Udupi District, Karnataka, India
Department of Electrical and Electronics Engineering
CERTIFICATE
Certified that the project work entitled Voltage Mode Control of Buck Converter is a bonafide
work carried out by Anusha A.N (4NM09EE008), Arpan Chatterjee (4NM09EE009),
Ashutosh Kumar (4NM09EE010) and Manish Kumar (4NM09EE031) in partial fulfillment
for the award of Degree of Bachelor of Engineering in Electrical and Electronics Engineering
of the Visvesvaraya Technological University, Belgaum during the year 2012-2013. It is
certified that all corrections / suggestions indicated for Internal Assessment have been
incorporated in the report deposited in the departmental library. The project report has been
approved as it satisfies the academic requirements in respect of project work prescribed for the
Bachelor of Engineering Degree.
Signature of Guide Signature of HOD Signature of Principal
Semester End Viva Voce Examination
Name of the Examiners Signature with Date
1. _______________________________ ________________________________
2. _______________________________ ________________________________
i
ABSTRACT
The objective of this project is to design and develop a buck converter circuit using
PID Compensator to get a stable output of 5V, 5A from an input of 12V.
The Buck-converter converts an input voltage into a lower output voltage, it is also
called step-down converter. The buck converter is designed in continuous current
conduction mode. To get the regulated output voltage, compensation mechanism
using voltage mode control is used. This project involves simulation, design and
hardware construction of voltage mode control of buck converter using PID
compensator. The simulation of the circuit is done using Orcade (PSpice). MATLab
is used to study stability analysis of the closed loop system and to get the desired
phase and gain margin. The PID compensator is designed by modifying the open
loop buck converter circuit obtained from the simulation in Orcade (PSpice). The
error signal is compared with a saw-tooth ramp voltage and desired PWM signal.
The compensator and PWM scheme is implemented using NXP LPC1768.
ii
ACKNOWLEDGEMENT
We would like to take the opportunity to appreciate the help and support rendered to
us by Mr. Suryanarayana K., Assistant Professor, Dept. of E&E in completing this
project successfully under his guidance and for helping us procure some of the
components required for this project.
We also thank Mr. Pradeep Kumar, Assistant Professor, Dept. of E&E, for his
valuable suggestions and help rendered to us.
We are grateful to our principal Dr. Niranjan N. Chiplunkar and Prof. K. Vasudev
Shettigar, HOD, Dept. of E&E for extending encouragement and providing adequate
facilities in carrying out this project.
We are grateful to all the teaching and non-teaching staff of the Dept. of E&E, and
friends who have helped us through the course of this project.
Nitte
April 2013
PROJECT ASSOCIATES:
Anusha A.N (4NM09EE008)
Arpan Chatterjee (4NM09EE009)
Ashutosh Kumar (4NM09EE010)
Manish Kumar (4NM09EE031)
iii
TABLE OF CONTENTS
CHAPTERS TITLE PAGE NO.
ABSTRACT i
ACKNOWLEDGEMENT ii
TABLE OF CONTENTS iii
LIST OF FIGURES v
LIST OF TABLES vii
1 INTRODUCTION 1
1.1 Project Background 1
1.2 Project Objective 3
1.3 Project Scope 3
2 BUCK CONVERTER DESIGN AND OPERATION 5
2.1 Operation of Buck Converter 5
2.2 Calculation of L and C 8
2.3 Converter Power Stage Calculation 9
2.3.1 Calculation of Unknown Parameters 10
2.3.2 Calculation for Inductance 10
2.3.3 Calculation for Capacitance 11
2.3.4 Buck Converter Diode Selection 11
2.3.5 Buck Converter MOSFET Selection 11
2.3.6 Buck Converter Efficiency 12
3 COMPENSATOR DESIGN AND TRANSFER FUNCTION 13
3.1 Introduction 13
3.2 Buck Converter in Voltage Mode Control 14
4 HARDWARE DESIGN AND SIMULATION 24
4.1 Pulse Width Modulation 24
4.2 Buck Converter Simulations 24
4.3 NXP LPC1768 Microcontrollers 32
iv
4.3.1 Overview 32
4.3.2 Features 33
4.3.3 Tools and Software 33
4.3.4 Technical References 34
4.3.5 Hardware Overview 35
4.3.6 Major Functional Block 36
4.3.7 Memory 36
4.3.8 Implementation 37
5 CONCLUSION AND FUTURE PROSPECTS 38
5.1 Conclusion 38
5.2 Future Prospects 38
REFERENCES 39
APPENDIX- DATA SHEETS 40
v
LIST OF FIGURES
FIGURE NO. TITLE PAGE NO.
1.1 Basic Buck Converter 1
1.2 Voltage Mode Control 2
2.1 Buck Converter 5
2.2 When switch is closed 5
2.3 When switch is open 5
2.4 Voltage and current
waveform of buck
converter
6
3.1 Voltage mode control of
buck converter
14
3.2 Block diagram of Buck
converter
14
3.3 Type III Compensator 17
3.4 open loop control to
output transfer function
19
3.5 bode diagram 20
3.6 bode diagram 20
3.7 bode diagram 21
3.8 closed loop bode
diagram
21
3.9 Output impedance bode
diagram
22
3.10 Closed loop bode
diagram
22
4.1 PWM Control 23
4.2 Simulation of open loop
buck converter in PSpice
24
4.3 Inductor Current and
Output Voltage Waveform
24
4.4 Inductor Current 25
vi
Waveform
4.5 Output Voltage Waveform 25
4.6 Inductor Current
Waveform after Zoom area
25
4.7 Output Current Waveform 25
4.8 Inductor Voltage
Waveform
26
4.9 Gate Pulse for the
MOSFET
26
4.10 Voltage across Diode 26
4.11 Current across Diode 27
4.12 Output Power Waveform 27
4.3.1 NXP LPC1768 28
4.3.2 Block Diagram of NXP
LPC1768
31
4.3.3 Pin Diagram of NXP
LPC1768
32
vii
LIST OF TABLES
TABLE NO. TITLE PAGE
1.1 DESIGN SPECIFICATION
OF BUCK CONVERTER
4
2.1 INDUCTOR AND
CAPACITOR VALUE
(CALCULATED)
11
2.2 ESTIMATED SYSTEM
LOSS
12
3.1 COMPENSATION
COMPONENTS VALUE
19
VOLTAGE MODE CONTROL OF BUCK CONVERTER
Department of Electrical & Electronics Engineering, NMAMIT, NITTE 1
CHAPTER 1: INTRODUCTION
This chapter describes the project background, objectives, and the scope. In the
project background, a brief description of the buck converter and the voltage-mode
controller as well as the objective and the scope of the project are studied.
1.1 Project Background
Direct current to direct current (DC-DC) converters in power electronics circuits are
those which convert direct current (DC) voltage input from one level to another. DC-
DC converters are also known as switching converters, switching power supplies or
switches. DC-DC converters are important in portable devices such as cellular
phones and laptops [1].
Figure 1.1: Basic Buck Converter
The Figure shows a simple buck converter which accepts a dc input and uses pulse-
width modulation (PWM) of switching frequency to control the output of a power
MOSFET. A diode together with an inductor and a capacitor produces the regulated
dc output. Buck or step down converters produce an average output voltage lower
than the input source voltage.
The buck converter is the most widely used dc-dc converter topology in power
management and microprocessor voltage-regulator (VRM) applications. These
applications require fast load and line transient responses and high efficiency over a
wide range of load current. They can convert a voltage source into a lower regulated
voltage source. For example within a computer system, voltage needs to be stepped
VOLTAGE MODE CONTROL OF BUCK CONVERTER
Department of Electrical & Electronics Engineering, NMAMIT, NITTE 2
down and a lower voltage needs to be maintained. For this purpose the Buck
Converter can be used. Furthermore buck converters provide longer battery life for
mobile systems that spend most of their time in “stand-by”. Buck regulators are often
used as switch-mode power supplies for baseband digital core and the RF power
amplifier.
Suppose we want to use a device with low voltage level and if devices such as
laptop or charger is directly connected to the rectified supplied from the socket at
home, the device might not function properly or it might be broken due to over
current or overvoltage. Therefore to avoid unnecessary damage to the equipment’s
and devices, we would need to convert the voltage level to suitable voltage level for
the equipment’s to function properly. In this project, the configuration of DC-DC
converter chosen for study was buck configuration. Buck converter converts the DC
supply voltage to a lower DC output voltage level. The buck converter targeted is
suitable for low power application due to the low voltage and current level at the
output (25 watts).
Figure 1.2: Voltage Mode Control
The control method chosen to maintain the output voltage from the buck converter is
voltage-mode control and is shown in figure 1.2. Voltage mode has a single voltage
feedback path with pulse width modulation performed by comparing the voltage error
signal with a constant ramp waveform. The difference between both the voltages will
drive the control element to adjust the output voltage to a desired voltage level. This
is called as output voltage regulation. Voltage regulation is very important in
electronic circuit to ensure that the load or the connected device can operate
properly and to avoid damage to the equipment from overvoltage and over current.
VOLTAGE MODE CONTROL OF BUCK CONVERTER
Department of Electrical & Electronics Engineering, NMAMIT, NITTE 3
1.2 Project Objective
The main objective of this project is to design a buck converter to convert the input
DC voltage to lower DC output voltage level for low power applications to solve the
problem of voltage regulation and high power loss of the linear regulator circuit.
Basically we design a buck converter circuit using PID Controller to get a stable
output of 5V, 5A from an input of 12V. The converter uses switching scheme which
operates the switches such as MOSFET in cut-off and saturation region to reduce
power loss across the MOSFET. The output voltage level is then regulated by the
voltage-mode control circuit to a desired output voltage level as shown in the design
specification in the table 1.1 below. The design specification is based on low power
applications such as laptop battery charger, hand phone charger etc. The circuit is
simulated by using PSpice software to obtain the desired power stage response.
1.3 Project Scope
The scope of this project is:
I. Study the operation of buck converter.
II. Study the operation of voltage-mode control circuit.
III. Simulation of buck converter frequency response using PSpice software.
IV. Designing the buck converter power stage circuit.
V. Designing the controller and compensator circuit.
VI. Testing and calibration of the completed buck converter to confirm the actual
response with the theoretical predictions.
VOLTAGE MODE CONTROL OF BUCK CONVERTER
Department of Electrical & Electronics Engineering, NMAMIT, NITTE 4
Table 1.1: Design specification of buck converter power stage
Topology Buck Converter
Inductance (L) 100 µF
Frequency ( ) 10 kHz
Critical inductance ( ) 49.64 μH
Output voltage ( ) 5 V
Output current ( ) 5 A
Output voltage ripple (∆V) 45 mV
Output current ripple (∆I) 1.5 A
Equivalent series resistance (ESR)
DC input voltage (Vin) 12 V
Switch selection IRF520 metal-oxide-semiconductor field-
effect transistor (MOSFET)
VOLTAGE MODE CONTROL OF BUCK CONVERTER
Department of Electrical & Electronics Engineering, NMAMIT, NITTE 5
CHAPTER 2: BUCK CONVERTER OPERATION AND
DESIGN
2.1 Operation of Buck Converter
The operation of the buck converter is simple, with an inductor and two switches
(usually a MOSFET and a diode) that control the inductor. It alternates between
connecting the inductor to source voltage to store energy in the inductor and
discharging the inductor into the load.
Figure 2.1: Buck Converter
Figure 2.1 shows the circuit diagram of a Buck-converter. The MOSFET M1 operates
as the switch, which is turned on and off by a pulse width modulated (PWM) control
voltage VPWM. The ratio of the on time (ton) when the switch is closed to the entire
switching period (Tsw) is defined as the duty cycle ⁄ .
................................................................. (2.1)
Figure 2.2: When the switch is closed Figure 2.3: When the switch is open
VOLTAGE MODE CONTROL OF BUCK CONVERTER
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The equivalent circuit in Figure 2.2 is valid when the switch is closed. The diode is
reverse biased, and the input voltage supplies energy to the inductor, capacitor and
the load. When the switch is open as shown in Figure 2.3 the diode conducts and the
capacitor supplies energy to the load, and the inductor current flows through the
capacitor and the diode. The output voltage is controlled by varying the duty cycle. In
steady state, the ratio of output voltage to the input voltage is “D”, given by Vout/ Vin.
Vcont
Tsw
ton t
V1
Vout=V1
t
VL
(Vin-Vout)
-Vout t
IL
ILmax ∆IL
ILoad=IL
ILmin t
Figure 2.4: Voltages and Currents Waveform of the Buck Converter
VOLTAGE MODE CONTROL OF BUCK CONVERTER
Department of Electrical & Electronics Engineering, NMAMIT, NITTE 7
In the figure 2.4 the analysis is assumed that the conducting voltage drop of the
MOSFET and the diode is zero. During the on-time of the MOSFET voltage V1 is
equal to Vin. When the transistor switches off (blocking phase), the inductor L
continues to drive the current through the load in parallel with C and the diode,
consequently the voltage V1 becomes zero. The voltage V1 stays at zero during the
off-time of the transistor provided that the current IL does not reduce to zero. This
mode of operation is called continuous mode. In this mode V1 is a voltage which
changes between Vin and zero, corresponding to the duty cycle of Vcont.
The low-pass filter formed by L and C, produces an average value of V1 i.e. Vout =
V1, therefore for continuous mode
............................................ (2.2)
For the continuous mode the output voltage is a function of the duty cycle and the
input voltage, and it is independent of the load. The inductor current IL has triangular
shape and its average value is determined by the load. The peak-to-peak current
ripple ∆IL is dependent on L and can be calculated as:
V = Ldi/dt → ∆i = V∆t/L → ∆IL = (Vin-Vout)ton/L = Vout(Tsw-ton)/L
For
and a switching frequency Fsw, it follows that for the continuous
mode:
The current ripple ∆IL is independent of the load.
The average of the current IL is equal to the output current Iout.
At low load current, in case that the current IL becomes zero in every
switching cycle. This mode is called discontinuous mode and for this mode, these
calculations are not valid.
VOLTAGE MODE CONTROL OF BUCK CONVERTER
Department of Electrical & Electronics Engineering, NMAMIT, NITTE 8
2.2 Calculation of L and C:
To ensure the continuous current mode of conduction, the selected value of
inductance should be greater than the critical value of the inductor Lc which acts as a
boundary condition for continuous and discontinuous current mode of operations.
The critical value of inductance is given by,
( )
........................................ (2.3)
The inductor value must be chosen by considering the fact that the magnitude of the
ripple current in the output capacitor as well as the load current is determined by the
appropriate inductor value. Hence, normally a ripple current of 10% to 20% of the
average output current is assumed for the design to achieve good performance of
the converter [7]. The value of inductor is determined by,
( ) ( ⁄ ) ............................ (2.4)
The capacitor value is determined by assuming the output voltage ripple as 1% to
2% of the output voltage. The capacitor value is determined by,
........................................................................ (2.5)
To calculate the value of L , a realistic value of ∆IL has to be selected.
If ∆IL is selected at a very low value, the value of L has to be relatively high and this
would require a very heavy and expensive inductor. If ∆IL is selected at a very high
level, the switch-off current of the MOSFET would be very high which would result in
high losses in the MOSFET. A good and usual compromise between these effects is:
............................................................ (2.6)
For L it follows:
( ) ( ⁄ ) ( ⁄ ).............................. (2.7)
The maximum value of the inductor current is:
.................................................. (2.8)
VOLTAGE MODE CONTROL OF BUCK CONVERTER
Department of Electrical & Electronics Engineering, NMAMIT, NITTE 9
Assuming that the inductor ripple current is small compared to its dc current the RMS
value of the current flowing through the inductor is given by:
√
........................................................ (2.9)
The capacitor C is chosen usually for a cut-off frequency of the LC-low-pass filter,
which is approximately 100 to 1000 times lower than the switching frequency. An
exact calculation of the capacitor depends on its maximum rating of the AC current
and its equivalent series resistance ESR both can be verified from the relevant data
sheet. The current ripple ∆IL causes a voltage ripple ∆Vat the output capacitor C. For
normal switching frequencies, this voltage ripple is determined by the equivalent
series resistance ESR.
The output voltage ripple is given by:
....................................................................... (2.10)
2.3 Converter Power Stage Calculation
For a Buck converter, we will calculate the required inductor and output capacitor
specifications. We will then determine the input capacitor, diode, and MOSFET
characteristics. With the selected components, we will calculate the system
efficiency.
The conventional buck converters are designed for the following specifications:
Input Voltage, V
Output Voltage,
Load Current,
Switching Frequency,
VOLTAGE MODE CONTROL OF BUCK CONVERTER
Department of Electrical & Electronics Engineering, NMAMIT, NITTE 10
2.3.1 Calculations of Unknown Parameters
Output resistance,
=5/5= 1Ohms
Using equation (2.2), Duty Ratio, D =0.416
Peak-Peak ripple current is limited to 30% of load current,
Using equation (2.6),
Switching period, ⁄ =100μs
Switch ON time, ton=D/Fsw= 0.416/10k= 41.6μs
2.3.2 Calculation for Inductance
Critical value of inductor:
Using equation (2.3), μH
Inductor value (30% ripple current)
Using equation (2.7), L=194μH
Let us choose value of inductor= 100μH
Inductor peak current (30% ripple current):
Using equation (2.8),
Inductor RMS current:
Using equation (2.9),
The power dissipated due to copper losses is:
0.75 Watt
VOLTAGE MODE CONTROL OF BUCK CONVERTER
Department of Electrical & Electronics Engineering, NMAMIT, NITTE 11
2.3.3 Calculation for Capacitance
Using equation (2.10), Ripple voltage ΔV= 45mV
Using equation (2.5), Capacitance C = 417μF
Let us choose value of capacitor as 470μF.
The estimated power dissipation in the capacitor is:
Table 2.1: Inductor and Capacitor Value (calculated)
2.3.4 Buck Converter Diode Selection
Estimate Diode Current:
( )
Power Dissipation: VF·ID = 1.168 Watt
We have selected schottky diode 1N5826 of 15A, 20-40 volts. Forward voltage drop
for selected diode is 0.47V at peak current of 15A. Maximum diode reverse voltage
is 20V.
2.3.5 Buck Converter MOSFET Selection
( )
( ⁄ ) ( ) (
) = 0.717 Watt
= 0.925 Watt
VOLTAGE MODE CONTROL OF BUCK CONVERTER
Department of Electrical & Electronics Engineering, NMAMIT, NITTE 12
2.3.6 Buck Converter Efficiency
Output Power =25 Watt
Efficiency = 25/(25+2.9105) = 89.57 %
Table 2.2: Estimated System Loss
Components Value Units
Output power 25 Watt
MOSFET loss 0.925 Watt
Diode loss 1.168 Watt
Inductor loss 0.75 Watt
Capacitor loss 0.0675 Watt
Total loss 2.9105 Watt
Efficiency 89.57 %
This Buck converter design example has a calculated efficiency of 89.57%.If the
diode forward voltage drop could be lowered, the converter’s efficiency could be
raised. This buck converter design example is called an Asynchronous Buck
converter because the diode commutation (switching) is independent of the
MOSFET switching.
VOLTAGE MODE CONTROL OF BUCK CONVERTER
Department of Electrical & Electronics Engineering, NMAMIT, NITTE 13
CHAPTER 3: COMPENSATOR DESIGN AND TRANSFER
FUNCTION
3.1 Introduction
The easiest way to obtain a digital controller is first to design an analog compensator
and transpose it in the digital domain using the bilinear transformation. The
disadvantages of such a method are the mathematical calculus needed to obtain the
values of the passive components for the compensator and the fact that if the
designer decides to change the hardware, the calculus must be reevaluated.
In this chapter, a type III analog controller with its time domain transfer function and
frequency response is given. The analog compensator was designed without any
adjustments only by placing the position of the poles and zeros by a first
approximation based on the buck converters passive components. The type III digital
controller is obtained from the transfer function of an analog type III controller
transposed into digital domain using the bilinear transformation.
After mathematical calculations, the z-coefficients for the linear difference equation
needed to implement the compensator in a microcontroller are obtained. These
coefficients are dependent only on the pole-zero placements. The pole-zero
placements are obtained from calculation similar to the analog design using only the
given values of the converter parameters.
The advantage of this digital compensator is that the user does not need to calculate
anything if he wants to close the loop for a converter, the only data needed to be
transferred to the controller are the parameters of the converter. The control mode
used in this project is voltage mode control. The models are first simulated and the
results are compared and then the experimental results are presented.
VOLTAGE MODE CONTROL OF BUCK CONVERTER
Department of Electrical & Electronics Engineering, NMAMIT, NITTE 14
3.2 Buck Converter in Analog Voltage Mode Control
Figure 3.1: Voltage mode control of buck converter
In figure 3.1, a buck converter in voltage mode control is given. In voltage mode
control an external signal is compared with the control signal obtained for generating
the duty cycle needed to have the wanted output voltage. The output voltage Vout is
monitored and subtracted from the reference value Vref and an error signal Vcomp
results. This error signal is then used for the resulting control signal. The control
signal is then compared with the external ramp voltage Vramp and a pulse width
modulated signal is sent to the drivers of the MOSFET so that converter can react in
such a way so as to reduce the output error [2], [3], [4], [5].
Figure 3.2: Block diagram of buck converter
VOLTAGE MODE CONTROL OF BUCK CONVERTER
Department of Electrical & Electronics Engineering, NMAMIT, NITTE 15
The transfer function of power stage can be calculated as ratio of the output voltage
to duty cycle and given as:
( ) ( )
( )…………………………………………………………..… (3.1)
( ) ( )
( ) [ ( ) ] ( )
…… (3.2)
The “(s)” indicates that the transfer function varies as a function of the frequency.
The transfer function of the PWM modulator is ⁄ , where is the peak to
peak voltage of modulator. For simplification, we can combine the transfer function of
the PWM modulator and the buck converter power stage as:
( ) ( )
…………………………………... (3.3)
Therefore, G(s) is usually referred to as the transfer function of the power stage. The
roots of the polynomial in the denominator of (3.2) are called the poles of the transfer
function of the power stage. Similarly the roots of the numerator of (3.2) are the
zeros of the transfer function of the power stage. The transfer function of the power
stage is a second order system with a double pole at the resonance frequency (of
the LC filter) and a zero produced by the ESR of the capacitor.
Line to output transfer function is given as:
( )
( )
………...……………. (3.4)
Open loop transfer function:
( ) (
)(
)(
)
(
)(
)(
)
….… (3.5)
The pole located at cancels the zero located at FESR and the pole at Fp2 is located
well above crossover frequency.
Output impedance is given as:
( ) ( )
( )............................................................... (3.6)
VOLTAGE MODE CONTROL OF BUCK CONVERTER
Department of Electrical & Electronics Engineering, NMAMIT, NITTE 16
The parameter ⁄ is the inductor zero frequency and ( ) .
Closed loop output impedance is given as:
( ) ( )
( )....................................................................... (3.7)
The closed loop line to output TF:
( ) ( )
( )…………………….…..………………………. (3.8)
The open loop control to output voltage TF in Laplace domain is given by equation
(3.2)
( )
……………………………………...……. (3.9)
Frequency of double poles:
√ [ ( )⁄
( )⁄]
√ ………..……………… (3.10)
Frequency of zeros:
……………………………………….. (3.11)
PWM modulator gain is inversely proportional to the peak to peak ramp voltage
and given by:
( )
( )
………………………………………………………… (3.12)
The compensator transfer function from output voltage to COMP node is given as:
( ) (
)(
)
(
)(
)……………………………………. (3.13)
……………………………………………………… (3.14)
VOLTAGE MODE CONTROL OF BUCK CONVERTER
Department of Electrical & Electronics Engineering, NMAMIT, NITTE 17
Figure 3.3: Type III compensator
The type III compensator produces two zeros and three poles. One pole is located at
the origin to realize high DC gain and the relevant components values are given as:
Loop gain crossover frequency:
………………………………………………… ….. (3.15)
The loop gain crossover frequency is usually selected between ⁄ to
⁄ of the
switching frequency. It is the zero crossover frequency defined as frequency when
loop gain is unity.
Since
………………………………….. (3.16)
So type III-B compensator is suitable for this project. The poles and zeros of the
compensator will be placed as follows:
……………………………………………….. (3.17)
The type III compensator has 3 poles and 2 zeros.
√
……………………………………..……. (3.18)
√
……………………………….………… (3.19)
VOLTAGE MODE CONTROL OF BUCK CONVERTER
Department of Electrical & Electronics Engineering, NMAMIT, NITTE 18
is usually chosen as and this is about the maximum phase-lead obtained from
a lead compensator. The other zero of the compensator is chosen using the
following formula:
………………………………………….. (3.20)
………………………………….... (3.21)
…………………………………….…. (3.22)
……………………..……….. (3.23)
(
)
………………………………….…. (3.24)
……………………………………... (3.25)
…………………………………….. (3.26)
Considering = 2.2 nF and using equation from (3.15) to (3.26), we got the
following compensator value as shown in table below.
VOLTAGE MODE CONTROL OF BUCK CONVERTER
Department of Electrical & Electronics Engineering, NMAMIT, NITTE 19
Table 3.1: Compensation components values
Figure 3.4: Open loop control to Output transfer function
Components Value Units
Rc1 33 kΩ
Rc2 7.5 kΩ
Cc1 32 µF
Cc2 947 pF
Cc3 2.2 nF
RFB1 475 kΩ
RFB2 475 kΩ
VOLTAGE MODE CONTROL OF BUCK CONVERTER
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Figure 3.5: Bode diagram
Figure 3.6: Bode diagram
VOLTAGE MODE CONTROL OF BUCK CONVERTER
Department of Electrical & Electronics Engineering, NMAMIT, NITTE 21
Figure 3.7: Bode Diagram
Figure 3.8: Closed Loop Bode Diagram
VOLTAGE MODE CONTROL OF BUCK CONVERTER
Department of Electrical & Electronics Engineering, NMAMIT, NITTE 22
Figure 3.9: Output impedance Bode Diagram
Figure 3.10: Closed loop output impedance Bode Plot
VOLTAGE MODE CONTROL OF BUCK CONVERTER
Department of Electrical & Electronics Engineering, NMAMIT, NITTE 23
// Matlab program clc; clear all; num=[1.69*10^-4 12]; den=[4.7*10^-8 2.17*10^-4 1]; t=0.0001; fs=1/t; [b,a]=bilinear(num,den,fs) x0=1; x1=0; x2=0; y1=0; y2=0; y0 = zeros(40,1); for i=1:40 y0(i) = -a(2)*y1-a(3)*y2 + b*[x0;x1;x2]; y2 = y1; y1 = y0(i); x2=x1;x1=x0;x0=1; end subplot(211); stem(y0); y = filter(b,a,[1;zeros(39,1)]); subplot(212); stem(y);
Figure 3.11: Bode plot
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CHAPTER 4: HARDWARE DESIGN AND SIMULATION
4.1 Pulse Width Modulation
Figure 4.1: PWM control
Pulse Width modulation is a way to control the switch as shown in Figure 4.1 above.
The control signal is compared to a repetitive reference waveform at the desired
frequency. The switch control signal changes according to the output of the
comparison. The switch signal can be viewed as a pulse train with two states: on and
off. The Pulse Width Modulation is the method where the width of the on-part and
off-part of the switch signal are modulated to get the desired behaviour. In other
words, the method decides for how long the switch will be turned on [1].
4.2 Buck Converter Simulations
The buck converter power stage shown in Figure 4.2 is simulated using PSpice
software to obtain the output voltage and current response. The pulse-width
generator equivalent generates the pulse-width modulation to control the N-channel
MOSFET to either switch it on or off. TFis the time for the pulse to fall to zero and TR
is the time for the pulse to riseto+20 V value. PW is the time for positive pulse-width,
PER is the period for one complete cycle, Duty cycle is the positive duty cycle and
switching frequency is the desired switching frequency for the MOSFET. The
components value of the power stage is selected to be the same with the selected
values in Table 2.1. Load is selected to be 1 ohm and the input voltage is set to 12
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V. The current probe and voltage probe is used to measure the voltage and current
at the inductor and the load respectively.
From the waveform shown in the figure (4.2) to (4.3), it is clear that the converter is
operating in the continuous conduction mode.
The output voltage equals 4.3399 V and output current is 4.3550 A. The output
power is 19.107 W. The related waveforms obtained from the simulation are shown
as below.
Figure 4.2: Simulation of open loop buck converter in PSpice
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Figure 4.3: Inductor current and output voltage waveform
Figure 4.4: Inductor Current Waveform
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Figure 4.5: Output Voltage Waveform
Figure 4.6: Inductor current waveform after zoom area
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Figure 4.7: Output Current Waveform
Figure 4.8: Inductor Voltage Waveform
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Figure 4.9: Gate Pulses for the MOSFET
Figure 4.10: Voltage across diode
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Figure 4.11: Current across Diode
Figure 4.12: Output Power Waveform
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Figure 4.13: Buck converter
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4.3 NXP LPC1768 Microcontroller
4.3.1 Overview
The mbed Microcontrollers are a series of ARM microcontroller development boards
designed for rapid prototyping. The mbed NXP LPC1768 Microcontroller in particular
is designed for prototyping all sorts of devices, especially those including Ethernet,
USB, and the flexibility of lots of peripheral interfaces and FLASH memory. It is
packaged as a small DIP form-factor for prototyping with through-hole PCBs, strip
board and breadboard, and includes a built-in USB FLASH programmer.
Figure 4.3.1: NXP LPC1768
It is based on the NXP LPC1768, with a 32-bit ARM Cortex-M3 core running at
96MHz. It includes 512KB FLASH, 32KB RAM and lots of interfaces including built-in
Ethernet, USB Host and Device, CAN, SPI, I2C, ADC, DAC, PWM and other I/O
interfaces. The pin out above shows the commonly used interfaces and their
locations. Note that all the numbered pins (p5-p30) can also be used as digital in and
digital out interfaces.
The mbed Microcontrollers provide experienced embedded developers a powerful
and productive platform for building proof-of-concepts. For developers new to 32-bit
microcontrollers, mbed provides an accessible prototyping solution to get projects
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built with the backing of libraries, resources and support shared in the mbed
community.
4.3.2 Features
A. NXP LPC1768 MCU
I. High performance ARM® Cortex™-M3 Core
II. 96MHz, 32KB RAM, 512KB FLASH
III. Ethernet, USB Host/Device, 2xSPI, 2xI2C, 3xUART, CAN, 6xPWM,
6xADC, GPIO
B. Prototyping form-factor
I. 40-pin 0.1" pitch DIP package, 54x26mm
II. 5V USB or 4.5-9V supply
III. Built-in USB drag 'n' drop FLASH programmer
C. mbed.org Developer Website
I. Lightweight Online Compiler
II. High level C/C++ SDK
III. Cookbook of published libraries and projects
4.3.3 Tools and Software
The mbed Microcontrollers are all supported by the mbed.org developer website,
including a lightweight Online Compiler for instant access to your working
environment on Windows, Linux or Mac OS X.
Also included is a C/C++ SDK for productive high-level programming of peripherals.
Combined with the wealth of libraries and code examples being published by the
mbed community, the platform provides a productive environment for getting things
done.
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The mbed NXP LPC1768 is one of a range of mbed microcontroller packaged as a
small 40-pin DIP, 0.1-inch pitch form-factor making it convenient for prototyping with
solder less breadboard, strip board, and through-hole PCBs. It includes a built-in
USB programming interface that is as simple as using a USB Flash Drive.
4.3.4 Technical references
Power
I. Powered by USB or 4.5v - 9.0v applied to VIN
II. Less than 200mA (100mA with Ethernet disabled)
III. Real-time clock battery backup input VB
IV. 1.8v - 3.3v Keeps Real-time clock running
V. Requires 27uA, can be supplied by a coin cell
VI. 3.3v regulated output on VOUT to power peripherals
VII. 5.0v from USB available on VU (only available when USB is connected!)
VIII. Current limited to 500mA
IX. Digital IO pins are 3.3v, 4mA each, 400mA max total
Pins
I. Vin - External Power supply to the board
4.5v-9v, 100mA + external circuits powered through the Microcontroller
II. Vb - Battery backup input for Real Time Clock
1.8v-3.3v, 30uA
III. nR - Active-low reset pin with identical functionality to the reset button.
IV. Pull up resistor is on the board, so it can be driven with an open collector
V. IF+/- - Reserved for testing
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The microcontroller I/O is all 3.3v logic, but 5v tolerant. A digital pin can drive 40mA,
up to a total of 400mA.
Figure 4.3.2: Block diagram of NXP LPC1768
4.3.5 Hardware Overview
The board used is Keil MCB1700. It uses the NXP LPC 1768 processor, consisting
of an ARM core (specifically, the Cortex M3), 512 KB of flash memory and 64 KB of
SRAM. The board is connected to the host computer using USB cable. It provides
power to the MCB1700. The board itself is relatively simple, and aside from the LPC
1768 itself there are only a few support circuits (mostly RS-232 level converters,
Ethernet transceivers, audio amplifiers and so on). The board provides a USB port,
two serial (COM) ports, two CAN ports, an Ethernet connector, a micro SD card slot,
a potentiometer, a speaker and a set of LEDs and buttons. It also provides a full-
colour LCD display. Pin diagram of NXP LPC1768 is shown in the figure below:
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Figure 4.3.3: Pin diagram of NXP LPC1768
4.3.6 Major Functional Block
The LPC 1768 is a “system on a chip” that combines SRAM and a multichannel ADC
onto a single IC.A phase-locked loop or phase lock loop (PLL) is a control
system that generates an output signal whose phase is related to the phase of an
input "reference" signal. It is an electronic circuit consisting of a variable
frequency oscillator and a phase detector. The signal from the phase detector is
used to control the oscillator in a feedback loop. The 32-bit peripheral power control
register is referenced from C as LPC_SC->PCONP.LPC_SC is a general system-
control register block, and PCONP refers to Power CONTROL for Peripherals.
4.3.7 Memory
There are four different blocks of memory on the LPC 1768. There is a block of 512
KB of flash memory, located at the bottom of the address space, which is used for
storing your code and data. There is an 8 KB boot ROM, which is hard-coded and
unchangeable. There is a block of 32 KB of static RAM for use by the application (it’s
also possible to use this space for code, as an alternative to using the flash
memory). And finally, there are two banks of 16 KB of static RAM that are shared
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with peripheral devices. All the peripherals are memory-mapped, so they are
accessible directly from C.
4.3.8 Implementation
The compensator and PWM scheme is implemented here. The error signal is
compared with a saw-tooth ramp voltage and desired PWM signal. The board can
withstand a maximum voltage of 3.3V. The pins used here are as follows:Ground,
USB(Universal Serial Bus) cable to supply the power to the board through laptop, P21
is used as the output pin which is connected to the 6th pin the driver UC3715 and P15 is
used as the ADC pin where respective pulses are generated for the PWM(Pulse
Width Modulator) which in turn is connected to the 10k Potentiometer.
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CHAPTER 5: CONCLUSION AND FUTURE PROSPECTS
5.1 Conclusion
Designing a voltage-mode controlled buck converter is very challenging. The most
difficult part is determining the compensation network and manipulating the poles
and zeros to build a robust and balanced system. The PWM is a relatively simple
concept, but a real world design of this block would be troublesome. Design and
simulation of the circuit is done using Orcade (PSpice). PID controller has been
designed and the system operates in closed loop. In other words, feedback stabilizes
the system. Phase margin and gain margin has been obtained and stability analysis
of the closed loop system has been studied using MATLAB. The PID compensator
is designed by modifying the open loop buck converter circuit obtained from the
simulation in Orcade (PSpice). The error signal is compared with a saw-tooth ramp
voltage and desired PWM signal. The compensator and PWM scheme is
implemented using microcontroller NXP LPC1768 using the software Keil µVision4.
Improvement in the transient response of the converters through the use of a
feedback path with proper compensation has been achieved.
5.2 Future prospects
Technology is still improving over the years. There are many types of configuration
for buck converter control available in the market. For instance, there are
synchronous buck converter, peak-current control buck converter and etc.
Thus, this project could be expanded by implementing peak-current mode control or
synchronous buck configuration into the voltage-mode control buck converter for
improvement in the controlling of the output voltage. By improving the control method
for the buck converter, the complexity of the design will arise, thus it will need more
research to be done in the future for such improvement.
Finally, even after such improvement, there will be more research that could be done
to improve the efficiency and reliability of the converter.
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REFERENCES
[1] Mohan, Ned, Undeland, T.M., and Robbins, P. W., “Power Electronics-
Converters Applications and Design”, Second Edition, John Wiley and Sons.
[2] Voltage-mode control and compensation Intricacies for buck regulators by
Timothy Hegarty, National Semiconductor - June 30, 2008.
[3] Application Note AN-1162- Compensator Design Procedure for Buck Converter
with Voltage Mode Error Amplifier By Amir M. Rahimi, Parviz Parto, and
PeymanAsadi.
[4] International Journal of Computer and Electrical Engineering Vol. 3, No. 2, April,
2011 On Modelling and Simulation of Closed loop controlled buck converter for solar
installation by A. Kalirasu and S.S.Dash.
[5] AN1452 using the MCP19035 on Synchronous buck converter design tool by
SergiuOprea, Microchip technology inc.
[6] Rashid, M.H., “Power Electronics- Circuits, Devices and Applications”, Third
Edition, Pearson.
[7] SMPS Buck Converter Design Example Web-Seminar, Microchip Technologies.
APPENDIX – DATA SHEETS
UC1714/5UC2714/5UC3714/5
FEATURES• Single Input (PWM and TTL
Compatible)
• High Current Power FET Driver, 1.0ASource/2A Sink
• Auxiliary Output FET Driver, 0.5ASource/1A Sink
• Time Delays Between Power andAuxiliary Outputs IndependentlyProgrammable from 50ns to 500ns
• Time Delay or True Zero-VoltageOperation Independently Configurablefor Each Output
• Switching Frequency to 1MHz
• Typical 50ns Propagation Delays
• ENBL Pin Activates 220µA SleepMode
• Power Output is Active Low in SleepMode
• Synchronous Rectifier Driver
DESCRIPTIONThese two families of high speed drivers are designed to provide drivewaveforms for complementary switches. Complementary switch configura-tions are commonly used in synchronous rectification circuits and activeclamp/reset circuits, which can provide zero voltage switching. In order tofacilitate the soft switching transitions, independently programmable delaysbetween the two output waveforms are provided on these drivers. The de-lay pins also have true zero voltage sensing capability which allows imme-diate activation of the corresponding switch when zero voltage is applied.These devices require a PWM-type input to operate and can be interfacedwith commonly available PWM controllers.
In the UC1714 series, the AUX output is inverted to allow driving ap-channel MOSFET. In the UC1715 series, the two outputs are configuredin a true complementary fashion.
6
5
7
8
INPUT
T1
T2
ENBL
SQ
R
TIMER
VREF
SQ
R
TIMER
VREF
50ns –500ns
50ns –500ns
5V
ENBL
VCC
3V
GND
BIAS
1.4V
ENABLE
UC1714ONLY
4 AUX
2 PWR
1 VCC
LOGICGATES
TIMERREF
3 GND
BLOCK DIAGRAM
Complementary Switch FET Drivers
SLUS170A - FEBRUARY 1999 - REVISED JANUARY 2002
UDG-99028Note: Pin numbers refer to J, N and D packages.
applicationINFOavailable
2
UC1714/5UC2714/5UC3714/5
ABSOLUTE MAXIMUM RATINGSSupply Voltage VCC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20VPower Driver IOH
continuous . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . −200mApeak. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . −1A
Power Driver IOLcontinuous . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400mApeak. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2A
Auxiliary Driver IOHcontinuous . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . −100mApeak . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . −500mA
Auxiliary Driver IOLcontinuous . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200mApeak. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1A
Input Voltage Range (INPUT, ENBL) . . . . . . . . . . −0.3V to 20VStorage Temperature Range . . . . . . . . . . . . . . −65°C to 150°COperating Junction Temperature (Note 1) . . . . . . . . . . . . 150°CLead Temperature (Soldering 10 seconds) . . . . . . . . . . . 300°C
Note 1: Unless otherwise indicated, voltages are referenced toground and currents are positive into, negative out of, the speci-fied terminals.Note 2: Consult Packaging Section of databook for thermal limi-tations and specifications of packages.
CONNECTION DIAGRAMS
DIL-8, SOIC-8 (Top View)J or N, D Packages
ELECTRICAL CHARACTERISTICS: Unless otherwise stated, VCC = 15V, ENBL ≥ 2V, RT1 = 100kΩ from T1 to GND,RT2 = 100kΩ from T2 to GND, and −55°C < TA < 125°C for the UC1714/5, −40°C < TA < 85°C for the UC2714/5, and 0°C < TA <70°C for the UC3714/5, TA = TJ.
PARAMETER TEST CONDITIONS MIN TYP MAX UNITS
Overall
VCC 7 20 V
ICC, nominal ENBL = 2.0V 18 24 mA
ICC, sleep mode ENBL = 0.8V 200 300 µA
Power Driver (PWR)
Pre Turn-on PWR Output, Low VCC = 0V, IOUT = 10mA, ENBL 0.8V 0.3 1.6 V
PWR Output Low, Sat. (VPWR) INPUT = 0.8V, IOUT = 40mA 0.3 0.8 V
INPUT = 0.8V, IOUT = 400mA 2.1 2.8 V
PWR Output High, Sat. (VCC − VPWR) INPUT = 2.0V, IOUT = −20mA 2.1 3 V
INPUT = 2.0V, IOUT = −200mA 2.3 3 V
Rise Time CL = 2200pF 30 60 ns
Fall Time CL = 2200pF 25 60 ns
T1 Delay, AUX to PWR INPUT rising edge, RT1 = 10kΩ (Note 4) 20 35 80 ns
T1 Delay, AUX to PWR INPUT rising edge, RT1 = 100kΩ (Note 4) 350 500 700 ns
PWR Prop Delay INPUT falling edge, 50% (Note 3) 35 100 ns
SOIC-16 (Top View)DP Package
3
UC1714/5UC2714/5UC3714/5
ELECTRICAL CHARACTERISTICS: Unless otherwise stated, VCC = 15V, ENBL ≥ 2V, RT1 = 100kΩ from T1 to GND,RT2 = 100kΩ from T2 to GND, and −55°C < TA < 125°C for the UC1714/5, −40°C < TA < 85°C for the UC2714/5, and 0°C < TA <70°C for the UC3714/5, TA = TJ.
PARAMETER TEST CONDITIONS MIN TYP MAX UNITS
Auxiliary Driver (AUX)
AUX Output Low, Sat (VAUX) VIN = 2.0V, IOUT = 20mA 0.3 0.8 V
VIN = 2.0V, IOUT = 200mA 1.8 2.6 V
AUX Output High, Sat (VCC – VAUX) VIN = 0.8V, IOUT = -10mA 2.1 3.0 V
VIN = 0.8V, IOUT = -100mA 2.3 3.0 V
Rise Time CL = 1000pF 45 60 ns
Fall Time CL = 1000pF 30 60 ns
T2 Delay, PWR to AUX INPUT falling edge, RT2 = 10kΩ (Note 4) 20 50 80 ns
T2 Delay, PWR to AUX INPUT falling edge, RT2 = 100kΩ (Note 4) 250 350 550 ns
AUX Prop Delay INPUT rising edge, 50% (Note 3) 35 80 ns
Enable (ENBL)
Input Threshold 0.8 1.2 2.0 V
Input Current, IIH ENBL = 15V 1 10 µA
Input Current, IIL ENBL = 0V −1 −10 µA
T1
Current Limit T1 = 0V −1.6 −2 mA
Nominal Voltage at T1 2.7 3 3.3 V
Minimum T1 Delay T1 = 2.5V, (Note 4) 40 70 ns
T2
Current Limit T2 = 0V −1.2 −2 mA
Nominal Voltage at T2 2.7 3 3.3 V
Minumum T2 Delay T2 = 2.5V, (Note 4) 50 100 ns
Input (INPUT)
Input Threshold 0.8 1.4 2.0 V
Input Current, IIH INPUT = 15V 1 10 µA
Input Current, IIL INPUT = 0V −5 −20 µA
Note 3: Propagation delay times are measured from the 50% point of the input signal to the 10% point of the output signal’s transi-tion with no load on outputs.
Note 4: T1 delay is defined from the 50% point of the transition edge of AUX to the 10% of the rising edge of PWR. T2 delay is de-fined from the 90% of the falling edge of PWR to the 50% point of the transition edge of AUX.
PIN DESCRIPTIONSAUX: The AUX switches immediately at INPUT’s risingedge but waits through the T2 delay after INPUT’s fallingedge before switching. AUX is capable of sourcing 0.5Aand sinking 1.0A of drive current. See the Time Relation-ships diagram below for the difference between theUC1714 and UC1715 for INPUT, MAIN, and AUX. Duringsleep mode, AUX is inactive with a high impedance.
ENBL: The ENBL input switches at TTL logic levels (ap-proximately 1.2V), and its input range is from 0V to 20V.
The ENBL input will place the device into sleep modewhen it is a logical low. The current into VCC during thesleep mode is typically 220µA.
GND: This is the reference pin for all input voltages andthe return point for all device currents. It carries the fullpeak sinking current from the outputs. Any tendency forthe outputs to ring below GND voltage must be dampedor clamped such that GND remains the most negativepotential.
4
UC1714/5UC2714/5UC3714/5
INPUT: The input switches at TTL logic levels (approxi-mately 1.4V) but the allowable range is from 0V to 20V,allowing direct connection to most common IC PWM con-troller outputs. The rising edge immediately switches theAUX output, and initiates a timing delay, T1, beforeswitching on the PWR output. Similarly, the INPUT fallingedge immediately turns off the PWR output and initiatesa timing delay, T2, before switching the AUX output.
It should be noted that if the input signal comes from acontroller with FET drive capability, this signal providesanother option. INPUT and PWR provide a delay only atthe leading edge while INPUT and AUX provide the delayat the trailing edge.
PWR: The PWR output waits for the T1 delay after theINPUT’s rising edge before switching on, but switches offimmediately at INPUT’s falling edge (neglecting propaga-tion delays). This output is capable of sourcing 1A andsinking 2A of peak gate drive current. PWR output in-cludes a passive, self-biased circuit which holds this pinactive low, when ENBL ≥ 0.8V regardless of VCC’s volt-age.
T1: A resistor to ground programs the time delay be-tween AUX switch turn-off and PWR turn-on.
T2: This pin functions in the same way as T1 but controlsthe time delay between PWR turn-off and activation ofthe AUX switch.
T1, T2: The resistor on each of these pins sets thecharging current on internal timing capacitors to provideindependent time control. The nominal voltage level ateach pin is 3V and the current is internally limited to1mA. The total delay from INPUT to each output includesa propagation delay in addition to the programmabletimer but since the propagation delays are approximatelyequal, the relative time delay between the two outputscan be assumed to be solely a function of the pro-grammed delays. The relationship of the time delay vs.RT is shown in the Typical Characteristics curves.
Either or both pins can alternatively be used for voltagesensing in lieu of delay programming. This is done bypulling the timer pins below their nominal voltage levelwhich immediately activates the timer output.
VCC: The VCC input range is from 7V to 20V. This pinshould be bypassed with a capacitor to GND consistentwith peak load current demands.
PIN DESCRIPTIONS (cont.)
PROPAGATIONDELAYS
INPUT
PWR OUTPUT
T1 DELAY T2 DELAY
UC1714 AUX OUTPUT
UC1715 AUX OUTPUT
TYPICAL CHARACTERISTICS
Time relationships. (Notes 3, 4)UDG-99027
0
100
200
300
400
500
0 10 20 30 40 50 60 70 80 90 100RT (kW)
DE
LAY
(ns)
T1 vs RT1 T2 vs RT2
T1 Delay, T2 Delay vs. RT
5
UC1714/5UC2714/5UC3714/5
15
16
17
18
0 10 20 30 40 50 60 70 80 90 100
RT (kΩ)
Icc
(mA
)
ICC vs RT with Opposite RT = 50k
0
100
200
300
400
500
600
-75 -50 -25 0 25 50 75 100 125
Temperature (°C)
De
adba
ndD
ela
y(n
s)
RT1 = 100k
RT1 = 50k
RT1 = 10kRT1 < 6k
T1 Deadband vs. Temperature AUX to PWR
Figure 1. Typical application with timed delays.
TYPICAL APPLICATIONS
UDG-94011
Figure 2. Using the timer input forzero-voltage sensing.
UDG-94012
0
100
200
300
400
500
600
-75 -50 -25 0 25 50 75 100 125
Temperature (°C)
De
adba
ndD
ela
y(n
s)
RT2 = 100k
RT2 = 50k
RT2 = 10kRT2 < 6k
T2 Deadband vs. Temperature PWR to AUX
16
17
18
19
20
21
0 100 200 300 400 500 600 700 800 9001000
Switching Frequency (kHz)
Icc
(m
A)
TYPICAL CHARACTERISTICS (cont.)
ICC vs Switching Frequency with No Load and 50%Duty Cycle RT1 = RT2 = 50k
6
UC1714/5UC2714/5UC3714/5
Figure 5. Synchronous rectifier application with a charge pump to drive the high-side n-channel buck switch.VIN is limited to 10V as VCC will rise to approximately 2VIN.
UDG-94014-1
Figure 4. Using the UC1715 as a complementary synchronous rectifier switch driver with n-channel FETs
UDG-94015-2
Figure 3. Self-actuated sleep mode with the absence of an input PWM signal. Wake up occurs with the firstpulse while turn-off is determined by the (RTO CTO) time constant.
TYPICAL APPLICATIONS (cont.)
UDG-94013
7
UC1714/5UC2714/5UC3714/5
Figure 7. Using an N-channel active reset switch with a floating drive command.
UDG-94017-1
Figure 6. Typical forward converter topology with active reset provided by the UC1714 driving an N-channelswitch (Q1) and a P-channel auxilliary switch (Q2).
TYPICAL APPLICATIONS (cont.)
UDG-94016-1
IMPORTANT NOTICE
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Mailing Address:
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Copyright 2002, Texas Instruments Incorporated
This datasheet has been download from:
www.datasheetcatalog.com
Datasheets for electronics components.
©2002 Fairchild Semiconductor Corporation IRF520 Rev. B
IRF520
9.2A, 100V, 0.270 Ohm, N-Channel Power MOSFET
This N-Channel enhancement mode silicon gate power field effect transistor is an advanced power MOSFET designed, tested, and guaranteed to withstand a specified level of energy in the breakdown avalanche mode of operation. All of these power MOSFETs are designed for applications such as switching regulators, switching convertors, motor drivers, relay drivers, and drivers for high power bipolar switching transistors requiring high speed and low gate drive power. These types can be operated directly from integrated circuits.
Formerly developmental type TA09594.
Features
• 9.2A, 100V
• r
DS(ON)
= 0.270
Ω
• SOA is Power Dissipation Limited
• Single Pulse Avalanche Energy Rated
• Nanosecond Switching Speeds
• Linear Transfer Characteristics
• High Input Impedance
• Related Literature- TB334 “Guidelines for Soldering Surface Mount
Components to PC Boards”
Symbol
Packaging
JEDEC TO-220AB
Ordering Information
PART NUMBER PACKAGE BRAND
IRF520 TO-220AB IRF520
NOTE: When ordering, use the entire part number.G
D
S
SOURCE
DRAIN (FLANGE)
DRAINGATE
Data Sheet January 2002
©2002 Fairchild Semiconductor Corporation IRF520 Rev. B
Absolute Maximum Ratings
T
C
= 25
o
C, Unless Otherwise Specified
IRF520 UNITS
Drain to Source Breakdown Voltage (Note 1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .V
DS
100 V
Drain to Gate Voltage (R
GS
= 20k
Ω)
(Note 1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V
DGR
100 V
Continuous Drain Current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I
D
T
C
= 100
o
C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I
D
9.26.5
AA
Pulsed Drain Current (Note 3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I
DM
37 A
Gate to Source Voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .V
GS
±
20 V
Maximum Power Dissipation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .P
D
60 W
Dissipation Derating Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.4 W/
o
C
Single Pulse Avalanche Energy Rating (Note 4) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .E
AS
36 mJ
Operating and Storage Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T
J,
T
STG
-55 to 175
o
C
Maximum Temperature for SolderingLeads at 0.063in (1.6mm) from Case for 10s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T
L
Package Body for 10s, See Techbrief 334 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T
pkg
300260
o
C
o
C
CAUTION: Stresses above those listed in “Absolute Maximum Ratings” may cause permanent damage to the device. This is a stress only rating and operation of thedevice at these or any other conditions above those indicated in the operational sections of this specification is not implied.
NOTE:
1. T
J
= 25
o
C to 150
o
C.
Electrical Specifications
T
C
= 25
o
C, Unless Otherwise Specified
PARAMETER SYMBOL TEST CONDITIONS MIN TYP MAX UNITS
Drain to Source Breakdown Voltage BV
DSS
I
D
= 250
µ
A, V
GS
= 0V (Figure 10) 100 - - V
Gate to Threshold Voltage V
GS(TH)
V
GS
= V
DS
, I
D
= 250
µ
A 2.0 - 4.0 V
Zero Gate Voltage Drain Current I
DSS
V
DS
= 95V, V
GS
= 0V - - 250
µ
A
V
DS
= 0.8 x Rated BV
DSS
, V
GS
= 0V, T
J
= 150
o
C - - 1000
µ
A
On-State Drain Current (Note 2) I
D(ON)
V
DS
> I
D(ON)
x r
DS(ON)MAX
, V
GS
= 10V (Figure 7) 9.2 - - A
Gate to Source Leakage Current I
GSS
V
GS
=
±
20V - -
±
100 nA
Drain to Source On Resistance (Note 2) r
DS(ON)
I
D
= 5.6A, V
GS
= 10V (Figure 8, 9) - 0.25 0.27
Ω
Forward Transconductance (Note 2) gfs V
DS
≥
50V, I
D
= 5.6A (Figure 12) 2.7 4.1 - S
Turn-On Delay Time t
d(ON)
V
DD
= 50V, I
D
≈
9.2A, R
G
= 18
Ω
, R
L
= 5.5
Ω
MOSFET Switching Times are Essentially Independent of Operating Temperature
- 9 13 ns
Rise Time t
r
- 30 63 ns
Turn-Off Delay Time t
d(OFF)
- 18 70 ns
Fall Time t
f
- 20 59 ns
Total Gate Charge(Gate to Source + Gate to Drain)
Q
g(TOT)
V
GS
= 10V, I
D
= 9.2A, V
DS
= 0.8 x Rated BV
DSS
, I
g(REF)
= 1.5mA (Figure 14) Gate Charge is Essentially Independent of OperatingTemperature
- 10 30 nC
Gate to Source Charge Q
gs
- 2.5 - nC
Gate to Drain “Miller” Charge Q
gd
- 2.5 - nC
Input Capacitance C
ISS
V
DS
= 25V, V
GS
= 0V, f = 1MHz(Figure 11)
- 350 - pF
Output Capacitance C
OSS
- 130 - pF
Reverse Transfer Capacitance C
RSS
- 25 - pF
Internal Drain Inductance L
D
Measured From the Contact Screw On Tab To Center of Die
Modified MOSFET Symbol Showing the Internal Devices Inductances
- 3.5 - nH
Measured From the Drain Lead, 6mm (0.25in) From Package to Center of Die
- 4.5 - nH
Internal Source Inductance L
S
Measured From the Source Lead, 6mm (0.25in) From Header to Source Bonding Pad
- 7.5 - nH
Thermal Resistance Junction to Case R
θ
JC
- - 2.5
o
C/W
Thermal Resistance Junction to Ambient R
θ
JA
Free Air Operation - - 80
o
C/W
LD
LS
D
S
G
IRF520
©2002 Fairchild Semiconductor Corporation IRF520 Rev. B
Source to Drain Diode Specifications
PARAMETER SYMBOL TEST CONDITIONS MIN TYP MAX UNITS
Continuous Source to Drain Current I
SD
Modified MOSFET Symbol Showing the Integral Reverse P-N Junction Diode
- - 9.2 A
Pulse Source to Drain Current (Note 3) I
SDM
- - 37 A
Source to Drain Diode Voltage (Note 2) V
SD
T
J
= 25
o
C, I
SD
= 9.2A, V
GS
= 0V (Figure 13) - - 2.5 V
Reverse Recovery Time t
rr
T
J
= 25
o
C, I
SD
= 9.2A, dI
SD
/dt = 100A/
µ
s 5.5 100 240 ns
Reverse Recovered Charge Q
RR
T
J
= 25
o
C, I
SD
= 9.2A, dI
SD
/dt = 100A/
µ
s 0.17 0.5 1.1
µ
C
NOTES:
2. Pulse test: pulse width
≤
300
µ
s, duty cycle
≤
2%.
3. Repetitive rating: pulse width limited by Max junction temperature. See Transient Thermal Impedance curve (Figure 3).
4. V
DD
= 25V, starting T
J
= 25
o
C, L = 640mH, R
G
= 25
Ω,
peak I
AS
= 9.2A.
Typical Performance Curves
Unless Otherwise Specified
FIGURE 1. NORMALIZED POWER DISSIPATION vs CASE TEMPERATURE
FIGURE 2. MAXIMUM CONTINUOUS DRAIN CURRENT vs CASE TEMPERATURE
FIGURE 3. MAXIMUM TRANSIENT THERMAL IMPEDANCE
G
D
S
TC, CASE TEMPERATURE (oC)25 50 75 100 125 150 1750
PO
WE
R D
ISS
IPA
TIO
N M
ULT
IPL
IER
0
0.2
0.4
0.6
0.8
1.0
1.2
TC, CASE TEMPERATURE (oC)
50 75 100 17525
10
8
6
0
4
I D, D
RA
IN C
UR
RE
NT
(A
)
2
125 150
ZθJ
C, T
RA
NS
IEN
T 1
0.1
0.0110-210-5 10-4 10-3 0.1 1 10
t1, RECTANGULAR PULSE DURATION (s)
PDM
t1t2
10
NOTES:DUTY FACTOR: D = t1/t2PEAK TJ = PDM x ZθJC + TC
SINGLE PULSE
0.5
0.020.05
0.2
0.01
0.1
TH
ER
MA
L IM
PE
DA
NC
E (
oC
/W)
IRF520
©2002 Fairchild Semiconductor Corporation IRF520 Rev. B
FIGURE 4. FORWARD BIAS SAFE OPERATING AREA FIGURE 5. OUTPUT CHARACTERISTICS
FIGURE 6. SATURATION CHARACTERISTICS FIGURE 7. TRANSFER CHARACTERISTICS
FIGURE 8. DRAIN TO SOURCE ON RESISTANCE vs GATE VOLTAGE AND DRAIN CURRENT
FIGURE 9. NORMALIZED DRAIN TO SOURCE ONRESISTANCE vs JUNCTION TEMPERATURE
Typical Performance Curves Unless Otherwise Specified (Continued)
100
10
1
10001 10 1000.1
I D, D
RA
IN C
UR
RE
NT
(A
)
VDS, DRAIN TO SOURCE VOLTAGE (V)
TC = 25oCTJ = MAX RATEDSINGLE PULSE
10µs
100µs
1ms
10msOPERATION IN THISAREA IS LIMITEDBY rDS(ON)
10V
VDS, DRAIN TO SOURCE VOLTAGE (V)200 50
15
12
9
0
6
I D, D
RA
IN C
UR
RE
NT
(A
)
VGS = 7V
3
30
VGS = 6V
VGS = 8V PULSE DURATION = 80µs
10 40
VGS = 5V
VGS = 4V
DUTY CYCLE = 0.5% MAX
15
12
9
0
6
1 2 3 40 5
I D, D
RA
IN C
UR
RE
NT
(A
)
VDS, DRAIN TO SOURCE VOLTAGE (V)
3
VGS = 6V
VGS = 5V
VGS = 4V
VGS = 7V
VGS = 8V
VGS = 10VPULSE DURATION = 80µsDUTY CYCLE = 0.5% MAX
102
0.12 4 6 80
I D(O
N),
ON
-STA
TE
DR
AIN
CU
RR
EN
T (
A)
VGS, GATE TO SOURCE VOLTAGE (V)
1
10
10
175oC 25oC
VDS ≥ 50VPULSE DURATION = 80µsDUTY CYCLE = 0.5% MAX
ID, DRAIN CURRENT (A)16 320 40
2.5
2.0
1.5
0
1.0
r DS
(ON
), D
RA
IN T
O S
OU
RC
E O
N R
ES
ISTA
NC
E
PULSE DURATION = 80µs
8 24
0.5
VGS = 10V
VGS = 20V
DUTY CYCLE = 0.5% MAX
3.0
1.8
0.6
0 60-60
TJ, JUNCTION TEMPERATURE (oC)
NO
RM
AL
IZE
D O
N R
ES
ISTA
NC
E
2.4
1.2
0-40 -20 20 40 80 100 140120 160 180
ID = 9.2A, VGS = 10VPULSE DURATION = 80µsDUTY CYCLE = 0.5% MAX
IRF520
©2002 Fairchild Semiconductor Corporation IRF520 Rev. B
FIGURE 10. NORMALIZED DRAIN TO SOURCE BREAKDOWN VOLTAGE vs JUNCTION TEMPERATURE
FIGURE 11. CAPACITANCE vs DRAIN TO SOURCE VOLTAGE
FIGURE 12. TRANSCONDUCTANCE vs DRAIN CURRENT FIGURE 13. SOURCE TO DRAIN DIODE VOLTAGE
FIGURE 14. GATE TO SOURCE VOLTAGE vs GATE CHARGE
Typical Performance Curves Unless Otherwise Specified (Continued)
1.25
1.05
0.85
0 180
TJ, JUNCTION TEMPERATURE (oC)
NO
RM
AL
IZE
D D
RA
IN T
O S
OU
RC
E
1.15
0.95
0.75-60
BR
EA
KD
OW
N V
OLT
AG
E
60 120
ID = 250µA
VDS, DRAIN TO SOURCE VOLTAGE (V)
C, C
APA
CIT
AN
CE
(p
F)
1000
800
600
400
200
0
VGS = 0V, f = 1MHzCISS = CGS + CGDCRSS = CGDCOSS ≈ CDS + CGD
1 10 102
CISS
COSS
CRSS
ID, DRAIN CURRENT (A)3 6 9 120 15
5
4
3
0
2
gfs
, TR
AN
SC
ON
DU
CTA
NC
E (
S)
1
TJ = 175oC
TJ = 25oC
PULSE DURATION = 80µsVDS ≥ 50
DUTY CYCLE = 0.5% MAX
TJ = 175oC
I SD
, SO
UR
CE
TO
DR
AIN
CU
RR
EN
T (
A)
VSD, SOURCE TO DRAIN VOLTAGE (V)
100
10
0.10 0.4 1.2 1.6 2.00.8
TJ = 25oC1
PULSE DURATION = 80µsDUTY CYCLE = 0.5% MAX
Qg, GATE CHARGE (nC)
3 6 9 120 15
20
8
0
VG
S, G
AT
E T
O S
OU
RC
E V
OLT
AG
E (
V)
4
ID = 9.2A
16
12
VDS = 20VVDS = 50VVDS = 80V
IRF520
©2002 Fairchild Semiconductor Corporation IRF520 Rev. B
Test Circuits and Waveforms
FIGURE 15. UNCLAMPED ENERGY TEST CIRCUIT FIGURE 16. UNCLAMPED ENERGY WAVEFORMS
FIGURE 17. SWITCHING TIME TEST CIRCUIT FIGURE 18. RESISTIVE SWITCHING WAVEFORMS
FIGURE 19. GATE CHARGE TEST CIRCUIT FIGURE 20. GATE CHARGE WAVEFORMS
tP
VGS
0.01Ω
L
IAS
+
-
VDS
VDDRG
DUT
VARY tP TO OBTAIN
REQUIRED PEAK IAS
0V
VDD
VDS
BVDSS
tP
IAS
tAV
0
VGS
RL
RG
DUT
+
-VDD
tON
td(ON)
tr
90%
10%
VDS90%
10%
tf
td(OFF)
tOFF
90%
50%50%
10%PULSE WIDTH
VGS
0
0
0.3µF
12VBATTERY 50kΩ
VDS
S
DUT
D
G
Ig(REF)0
(ISOLATEDVDS
0.2µF
CURRENTREGULATOR
ID CURRENTSAMPLING
IG CURRENTSAMPLING
SUPPLY)
RESISTOR RESISTOR
SAME TYPEAS DUT
Qg(TOT)
Qgd
Qgs
VDS
0
VGS
VDD
IG(REF)
0
IRF520
DISCLAIMER
FAIRCHILD SEMICONDUCTOR RESERVES THE RIGHT TO MAKE CHANGES WITHOUT FURTHERNOTICE TO ANY PRODUCTS HEREIN TO IMPROVE RELIABILITY, FUNCTION OR DESIGN. FAIRCHILDDOES NOT ASSUME ANY LIABILITY ARISING OUT OF THE APPLICATION OR USE OF ANY PRODUCTOR CIRCUIT DESCRIBED HEREIN; NEITHER DOES IT CONVEY ANY LICENSE UNDER ITS PATENTRIGHTS, NOR THE RIGHTS OF OTHERS.
TRADEMARKS
The following are registered and unregistered trademarks Fairchild Semiconductor owns or is authorized to use and isnot intended to be an exhaustive list of all such trademarks.
LIFE SUPPORT POLICY
FAIRCHILD’S PRODUCTS ARE NOT AUTHORIZED FOR USE AS CRITICAL COMPONENTS IN LIFE SUPPORTDEVICES OR SYSTEMS WITHOUT THE EXPRESS WRITTEN APPROVAL OF FAIRCHILD SEMICONDUCTOR CORPORATION.As used herein:1. Life support devices or systems are devices orsystems which, (a) are intended for surgical implant intothe body, or (b) support or sustain life, or (c) whosefailure to perform when properly used in accordancewith instructions for use provided in the labeling, can bereasonably expected to result in significant injury to theuser.
2. A critical component is any component of a lifesupport device or system whose failure to perform canbe reasonably expected to cause the failure of the lifesupport device or system, or to affect its safety oreffectiveness.
PRODUCT STATUS DEFINITIONS
Definition of Terms
Datasheet Identification Product Status Definition
Advance Information
Preliminary
No Identification Needed
Obsolete
This datasheet contains the design specifications forproduct development. Specifications may change inany manner without notice.
This datasheet contains preliminary data, andsupplementary data will be published at a later date.Fairchild Semiconductor reserves the right to makechanges at any time without notice in order to improvedesign.
This datasheet contains final specifications. FairchildSemiconductor reserves the right to make changes atany time without notice in order to improve design.
This datasheet contains specifications on a productthat has been discontinued by Fairchild semiconductor.The datasheet is printed for reference information only.
Formative orIn Design
First Production
Full Production
Not In Production
OPTOLOGIC™OPTOPLANAR™PACMAN™POP™Power247™PowerTrenchQFET™QS™QT Optoelectronics™Quiet Series™SILENT SWITCHER
FASTFASTr™FRFET™GlobalOptoisolator™GTO™HiSeC™ISOPLANAR™LittleFET™MicroFET™MicroPak™MICROWIRE™
Rev. H4
ACEx™Bottomless™CoolFET™CROSSVOLT™DenseTrench™DOME™EcoSPARK™E2CMOSTM
EnSignaTM
FACT™FACT Quiet Series™
SMART START™STAR*POWER™Stealth™SuperSOT™-3SuperSOT™-6SuperSOT™-8SyncFET™TinyLogic™TruTranslation™UHC™UltraFET
STAR*POWER is used under license
VCX™
This datasheet has been download from:
www.datasheetcatalog.com
Datasheets for electronics components.
Features High Surge Capability
Types up to 40V
Maximum Ratings Operating Temperature: -65 C to +150
Storage Temperature: -65 C to +175
Part NumberMaximumRecurrent
Peak ReverseVoltage
MaximumRMS Voltage
Maximum DCBlockingVoltage
Electrical Characteristics @ 25 Unless Otherwise SpecifiedAverage ForwardCurrent
IF(AV) 15A TC =100
Peak Forward SurgeCurrent
IFSM 500A 8.3ms , half sine
MaximumInstantaneousForward Voltage
VF
IRmA
TJ = 25
T = 25
V RRM
Maximum ThermalResistance,Junction To Case
R jc C/W
0.44V
IFM =15 A
DO-5DO-5
MM
NN
BB
CC
JJ
PP
FF
GG
DD
EEAA
KK
SCHOTTKY DIODES STUD TYPE 15 A
Notes:1.Standard Polarity:Stud is Cathode2.Reverse Polarity:Stud is Anode
1N5827(R)1N5826(R)
1N5828(R)
20V30V40V
14V21V28V
20V30V40V
mA 10
250
1.8
TJ = 125
0.47V 0.50V
; j
(1N5826) (1N5827) (1N5828)
15Amp Rectifier 20-40 Volts
1N5826(R) THRU1N5828(R)
DIMENSIONS
INCHES MM
DIM MIN MAX MIN MAX NOTE
A ¼ 1/4 -28 Threads Standard Polarity
B .669 .687 17.19 17.44
C ----- .794 ----- 20.16
D ----- 1.020 ----- 25.91
E .422 .453 10.72 11. 50
F .115 .200 2.93 5.08
G ----- .460 ----- 11.68
H . .
J ----- .375 ----- 9.52
K .156 ----- 3.96 -----
M ----- .667 ----- 16.94
N ----- .080 ----- 2.03
P .140 .175 3.56 4.45
--------------------
NOTE (1)
Pulse Test: Pulse Width 300 usec, Duty Cycle 2%
NOTE : (1) <
Voltage
Maximum InstantaneousReverse Current AtRated DC Blocking
NOTE (1)
Transys ElectronicsL I M I T E D
Ave
rage
For
wA
rd R
ectif
ied
Cur
rent
- A
mP
eres
Case Temperature -
Figure 2Forward Derating Curve
0 18030 60 90 1200
6
150
InS
tant
aneo
us
For
war
d C
urre
nt
- A
mpe
res
Instantaneous Forward Voltage - Volts
Figure 1Typical Forward Characteristics
Amps
Volts
1 10040
100
8
Figure Peak Forward Surge Current
Peak
Fo
rwar
d Su
rge
Curre
nt- A
mpe
res
Number Of Cycles At 60Hz - Cycles
Cycles
2 6 10 20 60 8040
Reverse Voltage - Volts
Figure 4Typical Reverse Characteristics
Volts
Amps
Am
ps
200
300
400
500
600
0 0.2 0.4 0.6 0.8 1.0 1.2
9
15
3
1N5826( R ) THRU 1N5828(R)
12
18
10
20
6.0
40
60
100
1.0
2.0
4.0
125 C
25 C
40
60
200
100
5010 20 30 40
.1
.2
.4
.6
1
2
4
6
10
20
400
600
.01
.02
.04
.06
0
Tj =125 C
TJ =25
TJ =75
Tj =150 C
1000
3
Single Phase, Half Wave60Hz Resistive or Inductive Load
Am
ps
m
I ns t
ant a
neou
s
Rev
ers e
Lea
kage
Cur
rent
- M
illm
pere
sA