Chapter 9

Transcript Chapter 9

20V AVG(V(control)) 10V SEL>> 0V V(control) V(control) 20V AVG (V(error)) 0V V(error) AVG (V(control)) -20V 40V V(error) AVG (V(error)) V(out) 20V AVG (V(out)) 0V 0s V(out) 1ms 2ms AVG (V(out)) 3ms 4ms 5ms Time 6ms 7ms 8ms 9ms 10ms

Chapter 9

Simulation of Switching Converters

Overview

   PSpice  

PSpice Simulations using .CIR

PSpice Simulations using schematics entry

    

PSpice Simulations Using Behavioral Modeling PSpice simulations using vendor models Small-signal analysis of switching converters Creating capture symbols for PSpice simulation Solving convergence problems

Matlab Simulink Power switching converters Simulation of switching converters 2

PSpice Simulations using .CIR

An Ideal Open-Loop Buck Converter

Open-loop buck converter simulation * SWITCHING FREQUENCY = 1 KHZ ; DUTY CYCLE = 50% VPWM 1 0 PULSE(0 10 0 1US 1US 0.5MS 1MS) * PULSE PWM SOURCE: PULSED VOLTAGE = 10 V, RISE TIME = 1 US, * FALL TIME = 1 US, PULSE WIDTH = 500 US, PERIOD = 1 MS.

L0 1 2 10M C0 2 0 100U RL 2 0 5 1 L O 10mH 2 .TRAN 50US 20MS .OPTION ITL5=0 .PROBE

V PWM + C O 100 µF .END

0 Power switching converters Simulation of switching converters R 5O 3

PSpice Simulations using .CIR

An Ideal Open-Loop Buck Converter

8.0

V1(RL) 4.0

0 I(L0) I(C0) -4.0

0s V1(RL) I(C0) 5ms I(L0) Power switching converters 10ms Time Simulation of switching converters 15ms 20ms 4

PSpice Simulations using .CIR

L = 50 mH

An Ideal Open-Loop Buck Converter

6.0

V(2) 4.0

2.0

I(LO) I(CO) 0 Power switching converters -2.0

0s I(C0) 5ms I(L0) 10ms V(2) 15ms 20ms 25ms Time Simulation of switching converters 30ms 35ms 40ms 45ms 50ms 5

PSpice Simulations using .CIR

An Ideal Open-Loop Buck Converter

L = 5 mH Power switching converters Simulation of switching converters 6

PSpice Simulations using .CIR

An Ideal Open-Loop Buck Converter

10 L = 1.25 mH 8 V(2) 6 4 I(LO) 2 0 Power switching converters -2 0s V(2) I(LO) I(CO) 5ms I(CO) 10ms Time Simulation of switching converters 15ms 7 20ms

PSpice Simulations using .CIR

An Ideal Open-Loop Buck Converter

8.0

V(2) 6.0

L = 10 mH and C = 500 uF 4.0

2.0

I(LO) I(CO) 0 -2.0

0s V(2) I(LO) I(CO) 5ms 10ms Time 15ms Power switching converters Simulation of switching converters 8 20ms

PSpice Simulations using .CIR

An Ideal Open-Loop Buck Converter

10 L = 1.25 mH and C = 500 uF Power switching converters 5 V(2) I(LO) 0 I(CO) -5 0s V(2) I(LO) I(CO) 5ms Simulation of switching converters 10ms Time 15ms 9 20ms

PSpice Simulations using .CIR

N + Voltage-controlled switch N c + R on S N c N S N+ N- NC+ NC- SNAME .MODEL SNAME VSWITCH (RON=0.01 ROFF=1E+7 VON=0.7 VOFF=0) Power switching converters Simulation of switching converters 10

PSpice Simulations using .CIR

N + Current-controlled switch R on V N W N W N+ N- VN WNAME .MODEL WNAME ISWITCH (RON=0.01 ROFF=1E+7 ION=0.1 IOFF=0) Power switching converters Simulation of switching converters 11

PSpice Simulations using .CIR

Buck Converter with an Ideal Switch

OPEN-LOOP BUCK CONVERTER WITH AN IDEAL SWITCH * SWITCHING FREQUENCY = 1 KHZ ; DUTY CYCLE = 50% VS 1 0 10.0

VPWM 100 101 PULSE(0 1 0 1US 1US 500US 1MS) S1 1 2 100 101 SX RSX 100 0 10G 1 S1 DFW 0 2 D1 L0 2 3 10M C0 3 0 100U RL 3 0 5 VS 10V RSX VPWM 2 DFW LO 10mH 0 .MODEL SX VSWITCH (RON=0.01 ROFF=1E+7 VON=1 VOFF=0) .MODEL D1 D .TRAN 0.05MS 20MS .PROBE

.END

Power switching converters Simulation of switching converters 3 CO 100uf R 5ohms 12

PSpice Simulations using .CIR

Buck Converter with an Ideal Switch

6.0

V(3) 4.0

2.0

I(LO) I(CO) 0 -1.0

0s V(3) I(LO) I(CO) 5ms Power switching converters 10ms Time Simulation of switching converters 15ms 20ms 13

PSpice Simulations using .CIR

5.0

Buck Converter with an Ideal Switch

V(3) I(CO)*20 0 -3.0

15.0ms

V(3) 15.5ms

20* I(CO) Power switching converters 16.0ms

16.5ms

Time 17.0ms

Simulation of switching converters 17.5ms

18.0ms

PSpice Simulations using .CIR

Using Initial Conditions IC 6.0

V(3) 4.0

2.0

0 L0 2 3 100U IC=1 C0 3 0 IC=5 .TRAN 2NS 200NS UIC -1.0

0s V(3) I(LO) I(CO) 5ms Power switching converters Simulation of switching converters I(LO) I(CO) 10ms Time 15ms 20ms 15

PSpice Simulations using schematics entry

Boost converter

V 1 + 10V dc L 1 10mH V1 = 0 V2 = 1 TD = 0 TR = 1n TF = 1n PW = 0.5m

PER = 1m V 2 pwm S 1 + + S D 1 D break VOFF = 0.0V

VON = 1.0V

ROFF = 1e6 RON = 1.0

0 out C 1 100 µF R1 20 O Power switching converters Simulation of switching converters 16

PSpice Simulations using schematics entry

25V 20V 15V 10V 5V 0s V(out) 5ms Power switching converters 10ms 15ms Time Simulation of switching converters 20ms 25ms 30ms 17

PSpice Simulations using schematics entry

3.0A

I(L 1 ) 2.0A

1.0A

0A -1.0A

-2.0A

0s I(L 1 ) 5ms I(C 1 ) I(C 1 ) 10ms 15ms Time Simulation of switching converters 20ms Power switching converters 25ms 30ms 18

PSpice Simulations Using Behavioral Modeling

 ABM.OLB part library  Control system parts Power switching converters Simulation of switching converters 19

Control system parts

Power switching converters Simulation of switching converters 20

Control system parts

Power switching converters Simulation of switching converters 21

Control system parts

Power switching converters Simulation of switching converters 22

Control system parts

Power switching converters Simulation of switching converters 23

Control system parts

Power switching converters Simulation of switching converters 24

PSpice-equivalent parts

Power switching converters Simulation of switching converters 25

PSpice-equivalent parts

Power switching converters Simulation of switching converters 26

Operators in ABM expressions

Power switching converters Simulation of switching converters 27

Operators in ABM expressions

Power switching converters Simulation of switching converters 28

Functions in arithmetic expressions

Power switching converters Simulation of switching converters 29

Functions in arithmetic expressions

Power switching converters Simulation of switching converters 30

Examples of ABM blocks use

PARAMETERS: PI = 3.141592654

freq = 1k 3*sin (2*PI*freq*TIME) sine Power switching converters ABM and PARAM Simulation of switching converters 31

Examples of ABM blocks use

3*V (sine) control Node voltages can be accessed from ABM blocks Power switching converters Simulation of switching converters 32

Examples of ABM blocks use

sine rms If (TIME<=0,0,SQRT(SDT(PWR(V(%IN),2))/TIME)) RMS meter If(argument,then,else) If (TIME<=0, 0, SQRT(SDT(PWR(V(%IN),2))/TIME)) Power switching converters Simulation of switching converters 33

Examples of ABM blocks use

Power switching converters V1 = -10 V2 = 10 TD = 0 TR = 1u TF = 1u PW = 1n PER = 2u control triangular If (V(%IN1) > V(%IN2),1,0) pwm 0 V 4 PWM modulator Simulation of switching converters 34

Examples of ABM blocks use

Sin (2*PI*100k*ABS(V(%IN)) * TIME) triangular VCO Power switching converters VCO implementation with ABM1 Simulation of switching converters 35

PSpice Simulations Using Control Blocks

control triangular V1 = -10 V2 = 10 TD = 0 TR = 0.5m

TF = 0.5m

PW = 1n PER = 1m 0 V 4 100k 10 0 pwm Power switching converters PWM modulator with control blocks Simulation of switching converters 36

PSpice Simulations Using Control Blocks

In 0 In+ 1V ac 0V dc 0 V 4 R 0 2 10Meg R 1 10Meg PARAMETERS: V cc = +12 V EE = 0 100k IN 50 50 + s OUT {V cc } {V EE } 0 OpAmp Power switching converters Model of an operational amplifier Simulation of switching converters 37

PSpice Simulations Using Control Blocks

100 50 0 SEL>> -50 0d DB(V(OPAMP)) -50d -100d 1.0mHz

10mHz P(V(OPAMP)) 1.0Hz

1.0MHz

100MHz 100Hz 10KHz Frequency Open loop frequency response Power switching converters Simulation of switching converters 38

PSpice Simulations Using Control Blocks

R 3 10k Power switching converters 1V ac 0V dc In R 4 1k 0 In+ 0 V 4 R 2 10Meg 0 R 10Meg 0 1 PARAMETERS: V cc = +12 V EE = 0 100k IN {V cc } 50 50 + s OUT {V EE } Closed loop amplifier Simulation of switching converters OpAmp 39

PSpice Simulations Using Control Blocks

50 0 -50 0d DB(V(OPAMP)) -50d SEL>> -100d 1.0mHz

10mHz P(V(OPAMP)) 1.0Hz

100Hz Frequency 10KHz 1.0MHz

100MHz Power switching converters Closed loop frequency response Simulation of switching converters 40

Voltage – mode PWM boost converter R 2 1 V 1 + 10V dc 0 L 1 10mH pwm S 1 + + S D 1 D break VOFF = 0.0V

VON = 1.0V

ROFF = 1e6 RON = 0.05

If (V(%IN1) > V (%IN2),1,0) pwm_out PWM modulator control saw V1 = 0 V2 = 10 TD = 0 TR = 999u TF = 1n PW = 1n PER = 1m 0 V 4 out C 1 100 µF R 1 20 E 1 + + GAIN = 0.25

sense E 0 error 12 -12 1Meg 1Meg+s Error amplifier 3 Power switching converters Simulation of switching converters 5 V ref 41

Voltage – mode PWM boost converter 20V AVG(V(control)) 10V SEL>> 0V V(control) V(control) 20V AVG (V(error)) 0V V(error) AVG (V(control)) -20V 40V V(error) AVG (V(error)) V(out) 20V AVG (V(out)) 0V 0s V(out) 1ms 2ms AVG (V(out)) 3ms Power switching converters 4ms 5ms 6ms Time Simulation of switching converters 7ms 8ms 9ms 10ms 42

PSpice simulations using vendor models

10V dc + V 1 R 7 1 L 1 pwm 10mH IC = 0 R 6 X 2 100 MTP15N05E/MC D 1 MUR420 out C 1 100uF ESR 10m R 1 20 R 2 300k R 3 100k 0 +15 R 5 -15 3k R 8 300 .TRAN 0 30m 0 0.1u .OPTIONS STEPGMIN .OPTIONS ABSTOL= 10p .OPTIONS ITL1= 400 pwm_out .OPTIONS ITL4= 500 .OPTIONS RELTOL= 0.01

.OPTIONS VNTOL= 10u B/S LM311 + G 0 -15 PWM modulator control saw V1 = 0 V2 = 10 TD = 0 TR = 999u TF = 1n PW = 1n PER = 1m 0 V 4 TL084 +15 sense R 4 1k + 5 V ref Error amplifier Power switching converters Simulation of switching converters 43

PSpice simulations using vendor models

4.0A

2.0A

0A 5.2V

I(L 1 ) 5.0V

4.8V

20V V(control) 10V SEL>> 0V 0s V(out) 5ms Power switching converters 10ms 15ms Time Simulation of switching converters 20ms 25ms 30ms 44

Vorperian models for PSpice

Power switching converters Simulation of switching converters 45

Vorperian models for PSpice

Power switching converters Simulation of switching converters 46

Vorperian models for PSpice

Power switching converters Simulation of switching converters 47

Vorperian models for PSpice

**** VMSSCCM **** * Small signal continuous conduction voltage mode model * Params: RMPHITE --> External ramp height * D --> Duty cycle * Ic --> Current flowing from terminal C * Vap --> Voltage across terminal A P * Rsw --> Switch on resistance * Rd --> diode on resistance * Rm --> which models the base storage effects * Re --> models ripple across esr of cap * Pins control voltage - * common -------- | * passive----- | | * active -- | | | .subckt VMSSCCM A P C VC Params: RMPHITE=2 D=0.4 IC=1 VAP=20 + Rsw=1e-6 Rd=1e-6 Re=1e-6 Rm=1e-6 efm 4 0 value ={v(Vc)/rmphite} e2 A 6 value={v(0,4)*Vap/d} g1 A P value={v(4)*IC} gxfr 6 P VALUE={I(vms)*D} exfr 9 P VALUE={V(6,P)*D} vms 9 8 0 rd 8 C {d*rd+(1-d)*rsw+d*(1-d)*re+rm} rope 4 0 1g rgnd 0 P 1g .ends Power switching converters Simulation of switching converters 48

Small-signal analysis of switching converters

10V dc + V 1 R s 1 L 1 10mH IC = 0 0 1 A 1V 0V ac dc U7 P 2 VMSSCCM D = 0.5

IC = -1.84

RMPHITE = 10 RD = 1e-6 RM = 1e-6 RE = 10m V 4 RSW = 10m VAP = -17.6

0 Small-signal AC analysis out C out 100uF IC = 0 R esr 10m R 20 R s1 300k R s2 100k sense Power switching converters Simulation of switching converters 49

Small-signal analysis of switching converters

3.0A

2.0A

1.0A

0A 20V I(L 1 ) 10V SEL>> 0V 0s V(OUT) 5ms Power switching converters 10ms 15ms Time Simulation of switching converters 20ms 25ms 30ms 50

Small-signal analysis of switching converters

Open-loop transfer function 40 0 -40 SEL>> -80 -0d DB(V(OUT)) -100d -200d -300d 1.0Hz

P(V(OUT)) 10Hz Power switching converters 100Hz 1.0KHz

Frequency Simulation of switching converters 10KHz 100KHz 1.0MHz

Small-signal analysis of switching converters

1V ac 10V dc V 4 R s 1 L 1 10mH IC = 0 0 1 A U7 VMSSCCM P 2 D = 0.5

IC = -1.84

RMPHITE = 10 RD = 1e-6 RM = 1e-6 RE = 10m RSW = 10m VAP = -17.6

Input impedance

Power switching converters Simulation of switching converters out C out 100uF IC = 0 R esr 10m R 20 R s1 300k R s2 100k sense 52

Small-signal analysis of switching converters

100 80 60 40 20 0 1.0Hz

10Hz DB(V(V4:+)/I(V4)) 100KHz 1.0MHz

100Hz 1.0KHz

Frequency

Input impedance

10KHz Simulation of switching converters Power switching converters 53

Small-signal analysis of switching converters

10V dc + V 5 R s 1 L 1 10mH IC = 0 0 1 A U7 VMSSCCM P 2 D = 0.5

IC = -1.84

RMPHITE = 10 RD = 1e-6 RM = 1e-6 RE = 10m RSW = 10m VAP = -17.6

Output impedance

out C out 100uF IC = 0 R esr 10m R 20 R s1 300k sense 1V ac 10V dc R s2 100k V 4 Power switching converters Simulation of switching converters 54

Small-signal analysis of switching converters

40 20 0 -20 -40 1.0Hz

10Hz DB(V(V4:+)/I(V4)) Power switching converters 100Hz 1.0KHz

Frequency

Output impedance

10KHz Simulation of switching converters 100KHz 1.0MHz

Small-signal analysis of switching converters

10V dc + V 1 R s 1 L 1 10mH IC = 0 0 V1 = 1.2

V2 = 1.5

TD = 20m TR = 1n TF = 1n PW = 50m PER = 50m 1 A P 2 U7 VMSSCCM V 4 D = 0.5

IC = -1.84

RMPHITE = 10 RD = 1e-6 RM = 1e-6 RE = 10m RSW = 10m VAP = -17.6

0 out C out 100uF IC = 0 R esr 10m R 20 R s1 300k R s2 100k sense

Small-signal transient analysis

Power switching converters Simulation of switching converters 56

Small-signal analysis of switching converters

25V 20V 10V SEL>> 0V 3.0A

V(OUT) 2.0A

1.0A

0A 0s I(L 1 ) Power switching converters 5ms 10ms 15ms 20ms Time

Small-signal transient analysis

Simulation of switching converters 25ms 30ms 57

Averaged-inductor model for a voltage-mode boost converter

R 3 1 0.5

U7 BOOSTVM IN DON OUT GND Rs = 1 FS = 1k L = 10m V 1 + 10 out R 1 10m C 1 100u IC = 0 0 Power switching converters Simulation of switching converters R 2 20 58

Output voltage obtained with the averaged-inductor model

30V 25V 20V 15V 10V 5V 0V 0s V(OUT) Power switching converters 5ms 10ms 15ms Time Simulation of switching converters 20ms 25ms 30ms 59

Measuring the loop gain

10V dc + V g R s 1 L 1 10mH IC = 0 0 1 A 1V 0V ac dc 0 P 2 U7 VMSSCCM V 1 D = 0.5

IC = -1.84

RMPHITE = 10 RD = 1e-6 RM = 1e-6 RE = 10m RSW = 10m VAP = -17.6

0 out C out 100uF IC = 0 R esr 10m R 20 GAIN = 0.25

E1 + E -+ V f 0 0 Power switching converters Simulation of switching converters 60

Measuring the loop gain

20 0 (100.000,-1.2488) -40 -80 90 DB(V(VF)) 0 -90 -180 -270 SEL>> -360 1.0mHz

10mHz P(V(VF)) 100mHz Power switching converters (100.000,-163.029) 1.0Hz

10Hz 100Hz 1.0KHz

Frequency Simulation of switching converters 10KHz 100KHz 1.0MHz 10MHz 61

Frequency compensation

choose f1 = 100 Hz for a switching frequency of 1 kHz 

comp f

PID compensation

 1  

f f

   2 tan  1  

f f p

1  

M comp f



M comp f

f z f

1   20

Log

10 (2   tan       

comp

   20

Log

10 (2 

1 )  2 40  1

Log

10  

f f

           

1 )  40

Log

10  1  1   

f z

    2      40

Log

10    40

Log

10     1    Power switching converters Simulation of switching converters 1   

f f p

1   2   

f p

  2    62

PID compensation

f f f f 1 p

= 2



R 3 C 3 p

= ( C 2



1 + C R 2 2 C C ) 2 1 z

= 2



R 2 C 1 1 z

= R 1 + R 3 )C 3 K 1 = R 2 R 1 K 2 = 1 + R 3 3 R 3 R 2 C 3 = C 1 + C 2 2 .

)

Mag_comp_f1 = -7.0985

Ph_comp = 32 k1_db = -24.6094

k1 = 0.0588

k2_db = -5.0259

k2 = 0.5607

R2 = 588.2076

R3 = 269.7258

C1 = 5.0034e-005 C2 = 1.3496e-006 C3 = 2.8658e-006 Power switching converters Simulation of switching converters 63

Boost switching converter with PID compensator

10V dc + V 1 R s 1 L 1 10mH IC = 4 R 6 pwm X2 100 MTP15N05E/MC +15 0 `15 +15 V 2 -15 R 8 300 pwm_out -15 V 3 B/S + LM311 G 0 -15 PWM modulator control saw V1 = 0 V2 = 10 TD = 0 TR = 999u TF = 1n PW = 1n PER = 1m 0 V 4 0 Power switching converters D 1 V MUR420 out C out 100uF IC = 20 E SR 10m R 20 R s2 3k sense R C s3 2 1k R 4 10meg 1.1461e-006 R 2 518.3291

C 1 5.0014e-005 -15 173.0498

R 3 R 1 10k 2.5483e-006 C 3 Simulation of switching converters TL084 +15 + 5 V ref Error amplifier 64

Simulation results with a PID compensator

5.0A

4.5A

4.0A

10.0V

I(L 1 ) 7.5V

SEL>> 5.0V

40V V(control) 20V 0V 0s V(out) Power switching converters 5ms 10ms 15ms Time Simulation of switching converters 20ms 25ms 30ms 65

PI compensation

L 1 R s U7 VMSSCCM 1 10mH IC = 0 1 A P 2 D = 0.5

IC = -1.84

RMPHITE = 10 10V dc + V g 0 RD = 1e-6 RM = 1e-6 RE = 10m RSW = 10m VAP = -17.6

1V ac 0V dc V 1 0 0 R 1 C 1 500n 1k

 1  1

s C R

1 2 EAO 10 -10 10 10 + s error 100k Small-signal model of the boost converter with PI compensation Power switching converters Simulation of switching converters 10k R 2 0 out C out 200uF IC = 0 R esr 10m R 20 V f 0 GAIN = 0.25

E1 + E V f 0 66

PI compensation

100 Compensated loop gain 0 Uncompensated loop gain -100 SEL>> -200 DB(V(VF)) 180 90 0 -90 -180 -270 -360 1.0mHz

10mHz P(V(VF)) DB(V(EAO)) 100mHz P(V(EAO)) 1.0Hz

Power switching converters 10Hz 100Hz Frequency Compensated loop gain Uncompensated loop gain Simulation of switching converters 1.0KHz

10KHz 100KHz 1.0MHz

PI compensation using ABM blocks

10V dc + 0 V 1 R s 0.1

C 2 R 3 1n 1 L 1 2 pwm D 1 100k gate 10mH IC = 1.8

0 D break S 1 + S + VOFF = 0.0V

VON = 1.0V

if( V(%IN1) < V(%IN2),1,0) 3 2 control 1 saw out C out 100u IC = 20 R esr 10m R 20 0 R 1 1k C 1 500n 0.25

100k V1 = 0 V2 = 10 TD = 0 TR = 99.9u

TF = 0.05u

PW = 0.05u

PER = 100u 0 V 2 10 -10 1 1 + s Power switching converters Simulation of switching converters R 2 10k ref 5 68

Simulation results of the PI compensation using ABM blocks

4.0A

2.0A

0A 30V I(L 1 ) 20V 10V SEL>> 0V 10V V(OUT) 5V 0V 0s V(CONTROL) 5ms Power switching converters 10ms 15ms Time Simulation of switching converters 20ms 25ms 30ms 69

PI compensation using vendor models

D 2 R s 0.1

IC = 1.8

gate 1 L 1 10mH R 3 10 2 pwm X 1 MUR420 MTP15N05E/MC out C out 100u IC = 20 R esr 10m R 20 10V dc + V 1 R 5 3k R 6 1k 0 0 +15 0 +15 +15V dc R 4 300 B/S LM311 + G 0 V 3 -15V dc V 4 -15 -15 control saw V1 = 0 V2 = 10 TD = 0 TR = 99.9u

TF = 0.05u

PW = 0.05u

PER = 100u 0 V 2 R 1 1k C 1 -15 500n TL084 + +15 ref 0 0 5 R 2 10k Power switching converters Simulation of switching converters 70

Simulation results of the PI compensation using vendor models

4.0A

2.0A

0A 40V I(L 1 ) 20V 0V 10V V(OUT) 5V SEL>> 0V 0s 2ms V(CONTROL) 4ms Power switching converters 6ms 8ms 10ms Time 12ms Simulation of switching converters 14ms 16ms 18ms 20ms 71

PI compensation using vendor models

*Analysis directives: .TRAN 0 30m 0 10n SKIPBP .OPTIONS STEPGMIN .OPTIONS PREORDER .OPTIONS ABSTOL= 10.0p

.OPTIONS CHGTOL= 0.1p

.OPTIONS ITL2= 200 .OPTIONS ITL4= 400 .OPTIONS RELTOL= 0.01

.OPTIONS VNTOL= 10.0u

I/O ERROR -- Probe file size exceeds 2000000000 JOB ABORTED TOTAL JOB TIME 912.11

Power switching converters Simulation of switching converters 72

Creating capture symbols for PSpice simulation

•Vendors often provide PSpice models for their circuit components. They are normally provided in a text file with extension .LIB; if the file has a different extension, it should be changed to .LIB •Start the PSpice Model Editor and from the File menu, choose Create Parts •Browse to find the input model library (.LIB file) and click OK to start •This step creates an .OBL file with a schematic symbol linked to your model •To place the new part into the schematic, open Capture, and from the Place menu choose Part. Click Add library, then find and add the new “.OLB” file Power switching converters Simulation of switching converters 73

Solving convergence problems

 PSpice uses the Newton-Raphson algorithm to solve the nonlinear equations in these analyses  The algorithm is guaranteed to converge only if the analysis is started close to the solution  If the initial guess is far away from the solution, this may cause a convergence failure or even a false convergence  If the node voltages do not settle down within a certain number of iterations, an error message will be issued Power switching converters Simulation of switching converters 74

DC analysis error messages

 The DC Analysis calculates the small-signal bias points before starting the AC analysis or the initial transient solution for the transient analysis  Solutions to the DC analysis may fail to converge because of incorrect initial voltage guesses, model discontinuities, unstable or bistable operation, or unrealistic circuit impedances  When an error is found during the DC analysis, SPICE will then terminate the run because both the AC and transient analyses require an initial stable operating point in order to start Power switching converters Simulation of switching converters 75

DC analysis error messages

 No convergence in DC analysis  PIVTOL Error  Singular Matrix  Gmin/Source Stepping Failed  No Convergence in DC analysis at Step = xxx Power switching converters Simulation of switching converters 76

Transient analysis error messages  If the node voltages do not settle down, the time step is reduced and SPICE tries again to determine the node voltages  If the time step is reduced beyond a certain fraction of the total analysis time, the transient analysis will issue an error message “ Time step too small ” and the analysis will be halted  Transient analysis failures are usually due to model discontinuities or unrealistic circuit, source, or parasitic modeling Power switching converters Simulation of switching converters 77

Solutions to convergence problems

 There are two ways to solve convergence problems  the first only tries to fix the symptoms by adjusting the simulator options  while the other attacks the root cause of the convergence problems  Once the circuit is properly modeled, many of the modifications of the "options" parameters will no longer be required  It should be noted that solutions involving simulation options may simply mask the underlying circuit instabilities Power switching converters Simulation of switching converters 78

Bias point (DC) convergence

 Checking circuit topology and connectivity  Modeling of circuit components  PSpice options are checked to ensure that they are properly defined Power switching converters Simulation of switching converters 79

Checking circuit topology and connectivity

 Make sure that all of the circuit connections are valid  Check for incorrect node numbering or dangling nodes  Verify component polarity  Check for syntax mistakes  Make sure that the correct PSpice units (i.e. MEG for 1E6, not M, which means mili in simulations) are used Power switching converters Simulation of switching converters 80

 Make sure that there is a DC path from every node to ground  Make sure that there are at least two connections at every node  Make sure that capacitors and/or current sources are not connected in series  Make sure that no (groups of) nodes are isolated from ground by current sources and/or capacitors  Make sure that there are no loops of inductors and/or voltage sources only Power switching converters Simulation of switching converters 81

 Place the ground (node 0) somewhere in the circuit  Be careful when floating grounds (e.g., chassis ground) are used; a large resistor should be connected from the floating node to ground. All nodes will be reported as floating if "0 ground" is not used  Make sure that voltage/current generators use realistic values, and verify that the syntax is correct  Make sure that dependent source gains are correct, and that E/G element expressions are reasonable Power switching converters Simulation of switching converters 82

 Verify that division by zero or LOG(0) cannot occur  Voltages and currents in PSpice are limited to the range +/- 1e10  Avoid using digital components, unless really necessary  Initialize the digital nodes with valid digital values  Avoid situations where an ideal current source delivers current into a reverse-biased p-n junction without a shunt resistance Power switching converters Simulation of switching converters 83

Setting up the options for the analog simulation

        Increase ITL1 to 400 Use NODESETs to set node voltages to the nearest reasonable guess at their DC values Enable the GMIN stepping algorithm Set PREORDER in Simulation Profiles options Setting the value of ABSTOL to 1 µ PSpice does not always converge when relaxed tolerances are used Setting GMIN to a value between 1n and 10n will often solve convergence problems Setting GMIN to a value, which is greater than 10n, may cause convergence problems Power switching converters Simulation of switching converters 84

Transient convergence

 The transient analysis can fail to complete if the time step becomes too small  This can be due to either  (a) the Newton-Raphson iterations would not converge even for the smallest time step size  (b) something in the circuit is moving faster than can be accommodated by the minimum step size Power switching converters Simulation of switching converters 85

Transient convergence

 The circuit topology and connectivity should first be checked  Followed by the PSpice options Power switching converters Simulation of switching converters 86

Circuit topology and connectivity

 Avoid using digital components, unless really necessary  Initialize the nodes with valid digital value to ensure there are no ambiguous states  Use RC snubbers around diodes  Add Capacitance for all semiconductor junctions Power switching converters Simulation of switching converters 87

Circuit topology and connectivity

 Add realistic circuit and element parasitics  It is important that switching times be nonzero  It is recommended that all inductors have a parallel resistor  Look for waveforms that transition vertically (up or down) at the point during which the analysis halts Power switching converters Simulation of switching converters 88

Circuit topology and connectivity

 Increase the rise/fall times of the PULSE sources  Ensure that there is no unreasonably large capacitor or inductor Power switching converters Simulation of switching converters 89

PSpice options

 Set RELTOL=.01  Reduce the accuracy of ABSTOL/VNTOL if current/voltage levels allow it  ABSTOL and VNTOL should be set to about 8 orders of magnitude below the level of the maximum voltage and current  Increase ITL4, but no more than 100 Power switching converters Simulation of switching converters 90

PSpice options

 Skipping the bias point is not recommended  Any applicable .IC and IC= initial conditions statements should be added to assist in the initial stages of the transient analysis Power switching converters Simulation of switching converters 91

Switching converter simulation using Matlab

Working with transfer functions

Consider a buck converter designed to operate in the continuous conduction mode having the following parameters: R = 4Ω, L = 1.330 mH, C = 94 µf, Vs = 42 V, Va = 12 V



K d

  1  1 

s s z

1  1 

 0

Q s s z

2 

2  0 2  

s z

2  (1 

) 2

(



R ESR

Power switching converters 

R ind L K d

 (1 

V s D

) 2

s z

1  1

R ESR C

Simulation of switching converters  0  1

LC r e



R ESR

R R ind



R r D e



ESR



)



R ind

 0 

r e

(1 

) 

ESR



) 92

Switching converter simulation using Matlab

% this is a comment % parameters R= 4; L = 1.330 e-3; Rind = 100 e-3; C = 94 e-6; Resr = 10 e-3 Vs = 42; Va = 12; D=Va/Vs; Kd= Vs/(1-D)^2; Sz1=1/(Resr*C); Req = R-(Resr*R/(Resr+R)); Sz2 = (1/L)*(1-D)^2* Req – Rind/L; Re=(Resr*R)/( Resr+R); Wo = (1/sqrt(L*C)) * sqrt((Rind+re*D*(1-D))/(Resr+R)); Q = Wo/(((Rind+re*(1-D))/L)+(1/(C*(Resr+R)))); Power switching converters Simulation of switching converters 93

Switching converter simulation using Matlab

% polynomials are entered in descending order of S.

n1=[1/Sz1 1] n2=[-1/Sz2 1] NUM=conv(n1,n2) % the convolution realizes the product of 2 polynomials % define denumerator DEN = [1/(Wo^2) 1/(Wo*Q) 1] % create TF variable sysTF = Kd * tf(NUM,DEN) which returns Transfer function:

sysTF

 -5.317e-008 s^2 - 0.05648 s + 82.32

4.913e-006 s^2 + 0.01343 s + 1 Power switching converters Simulation of switching converters 94

Switching converter simulation using Matlab

Bode Diagram The location of the poles can be found using poles = roots(DEN) and the frequency response can be plotted using bode(sysTF) 40 20 -20 0 -40 0 -45 -90 -135 -180 -225 -270 10 1 10 2 10 3 10 4 Frequency (rad/sec) 10 5 10 6 Power switching converters Simulation of switching converters 95 10 7

Switching converter simulation using Matlab

The small signal transient step response can be plotted using Figure % this command opens a new figure window step(sysTF) Step Response 90 80 70 60 50 40 30 20 10 0 -10 0 0.01

0.02

0.03

0.04

Time (sec) 0.05

Simulation of switching converters 0.06

0.07

0.08

Power switching converters 96

Switching converter simulation using Matlab

Working with matrices

Consider a buck converter designed to operate in the continuous conduction mode having the following parameters: R = 4Ω, L = 1.330 mH, C = 94 µf, Vs = 42 V, Va = 12 V.

% state-space averaged model of a Buck converter Rload= 4;% load resistance L= 1.330e-3; % inductance cap=94.e-6; % capacitance Ts=1.e-4; % switching period Vs=42; % input DC voltage Vref=12; % desired output voltage The average duty cycle is: D=Vref/(Vs); % ideal duty cycle Power switching converters Simulation of switching converters 97

Switching converter simulation using Matlab

 ^      0 1

 1

  



D L

^     

^ A=[ B1=[ 0 1/cap 1/L 0]; -1/L -1/(Rload*cap)] %during Ton B2=[ 0 0]; %during Toff B=B1*D+B2*(1-D) C=[0 1]; Power switching converters Simulation of switching converters 98

Switching converter simulation using Matlab

Step Response From: U (1) 0.35

OLpoles = eig(A) sysOL=ss(A,B,C,0) step(sysOL) 0.3

0.25

0.2

0.15

0.1

0.05

0 0 0.5

1 1.5

2 Time (sec.) 2.5

Simulation of switching converters 3 3.5

4 4.5

x 10 -3 99 Power switching converters

Switching converter simulation using Matlab

gamma=[ 0]; Vs/L closed-loop poles: P=1e3*[-0.3298 + 0.10i -0.3298 - 0.10i]'; Bf= gamma*(D/Vref); F=place(A,Bf ,P) Power switching converters Simulation of switching converters 100

Switching converter simulation using Simulink

Step

sysTF

[NUM,DEN] = TFDATA(sysTF,’v’) Clock  -5.317e-8 s^2 - 0.05648 s + 82.32

4.913e-6 s^2 + 0.01343 s + 1 Transfer Fcn time To Workspace1 Scope output To Workspace 90 80 70 60 50 40 30 20 10 0 -10 0 0.005

0.01

0.015

0.02

0.025

Time (s) 0.03

0.035

0.04

0.045

0.05

Power switching converters Simulation of switching converters 101

Switching converter simulation using Simulink

sysZPK = zpk(sysTF)

sysZPK

 -0.010821 (s+1.064e006) (s-1455) (s+2657) (s+76.6) zeroes: [-1.0638e+006 +1455] poles: [-2657 -76.6] gain: [-0.010821] Step Clock -0.010821(s+1.0638e+006)(s-1455) (s+2657)(s+76.6) Zero-Pole time To Workspace1 Scope output To Workspace 102 Power switching converters Simulation of switching converters

Switching converter simulation using Simulink

A B C

      0 10638 214.82

 0 752  2660   Step Clock x' = Ax+Bu y = Cx+Du State-Space time To Workspace1 Scope output To Workspace 103 Power switching converters Simulation of switching converters