simulation of switching converters

Time

0s 1ms 2ms 3ms 4ms 5ms 6ms 7ms 8ms 9ms 10msV(out) AVG (V(out))

0V

20V

40VV(error) AVG (V(error))

-20V

0V

20VV(control) AVG (V(control))

0V

10V

20V

SEL>>

AVG (V(out))

V(out)

V(error)

AVG (V(error))

V(control)

AVG(V(control))

Chapter 9

Simulation

of

Switching Converters

Power switching converters Simulation of switching converters 2

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


PSpice Simulations using .CIR

An Ideal Open-Loop Buck Converter

LO

10mH

CO

RV

PWM

+

-

1 2

0

100µF 5O

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

.TRAN 50US 20MS

.OPTION ITL5=0

.PROBE

.END




Time

0s 5ms 10ms 15ms 20msV1(RL) I(C0) I(L0)

-4.0

0

4.0

8.0

I(C0)

I(L0)

V1(RL)




Time

0s 5ms 10ms 15ms 20ms 25ms 30ms 35ms 40ms 45ms 50ms

I(C0) I(L0) V(2)

-2.0

0

2.0

4.0

6.0

I(CO)

I(LO)

V(2)

L = 50 mH




L = 5 mH




Time

0s 5ms 10ms 15ms 20ms

V(2) I(LO) I(CO)

-2

0

2

4

6

8

10

V(2)

I(LO)

I(CO)

L = 1.25 mH




Time

0s 5ms 10ms 15ms 20ms

V(2) I(LO) I(CO)

-2.0

0

2.0

4.0

6.0

8.0

I(CO)

I(LO)

V(2)

L = 10 mH

and

C = 500 uF




Time

0s 5ms 10ms 15ms 20msV(2) I(LO) I(CO)

-5

0

5

10

I(CO)

I(LO)

V(2)L = 1.25 mH

and

C = 500 uF



S

Ron

N

N

N

+c

+N

-

-c

Voltage-controlled switch

S<name> N+ N- NC+ NC- SNAME

.MODEL SNAME VSWITCH (RON=0.01 ROFF=1E+7 VON=0.7 VOFF=0)



Current-controlled switch

Ron

W

N-

+N

NV

W<name> N+ N- VN WNAME

.MODEL WNAME ISWITCH (RON=0.01 ROFF=1E+7 ION=0.1 IOFF=0)



Buck Converter with an Ideal Switch

CO100uf

LO

10mH

1

S1

VPWM

DFW

0

VS 10V R5ohms

2

RSX

3

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

DFW 0 2 D1

L0 2 3 10M

C0 3 0 100U

RL 3 0 5

.MODEL SX VSWITCH (RON=0.01 ROFF=1E+7 VON=1 VOFF=0)

.MODEL D1 D

.TRAN 0.05MS 20MS

.PROBE

.END




Time


0

2.0

4.0

6.0

-1.0

I(CO)

I(LO)

V(3)




Time

15.0ms 15.5ms 16.0ms 16.5ms 17.0ms 17.5ms 18.0ms

V(3) 20* I(CO)

0

5.0

-3.0

I(CO)*20

V(3)



L0 2 3 100U IC=1

C0 3 0 IC=5

.TRAN 2NS 200NS UIC

Using Initial Conditions IC

Time


0

2.0

4.0

6.0

-1.0

I(CO)

I(LO)

V(3)


PSpice Simulations using

schematics entry

Boost converter

+-+-

S1

S VON = 1.0VVOFF = 0.0V

ROFF = 1e6RON = 1.0

pwm

Dbreak

D1

0

V2TD = 0

TF = 1nPW = 0.5mPER = 1m

V1 = 0

TR = 1n

V2 = 1 R1C1

V1

10Vdc

outL

1

10mH

20O+

-

100µF



schematics entry

Time

0s 5ms 10ms 15ms 20ms 25ms 30ms

V(out)

5V

10V

15V

20V

25V



schematics entry

Time

0s 5ms 10ms 15ms 20ms 25ms 30msI(L

1) I(C

1)

-2.0A

-1.0A

0A

1.0A

2.0A

3.0A

I(C1)

I(L1)


PSpice Simulations Using

Behavioral Modeling

ABM.OLB part library

Control system parts


PSpice-equivalent parts


Operators in ABM expressions


Functions in arithmetic

expressions


Examples of ABM blocks use

PARAMETERS:

PI = 3.141592654freq = 1k

3*sin (2*PI*freq*TIME)

sine

ABM and PARAM



control

3*V (sine)

Node voltages can be accessed from ABM blocks



rmssine

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))



control

pwm

0

If (V(%IN1) > V(%IN2),1,0)

V4

triangular

TD = 0

TF = 1uPW = 1nPER = 2u

V1 = -10

TR = 1u

V2 = 10

PWM modulator



Sin (2*PI*100k*ABS(V(%IN)) * TIME)

VCOtriangular

VCO implementation with ABM1


PSpice Simulations Using Control

Blocks

control

0

pwmtriangular

V4

TD = 0

TF = 0.5mPW = 1nPER = 1m

V1 = -10

TR = 0.5m

V2 = 10

100k10

0

PWM modulator with control blocks



Blocks

0

OpAmp

V4

1Vac

0Vdc

50

50 + sIN OUT

PARAMETERS:

Vcc

= +12

VEE

= 0

0

0

Vcc

VEE

In-

0

In+

R2

10Meg

100k

R1

10Meg

Model of an operational amplifier



Blocks

Frequency

10mHz 1.0Hz 100Hz 10KHz 1.0MHz 100MHz1.0mHz

P(V(OPAMP))

-100d

-50d

0dDB(V(OPAMP))

-50

0

50

100

SEL>>

Open loop frequency response



Blocks

V4

1Vac

0Vdc

R3

10k

OpAmp

0

R2

10Meg

R1

10Meg

0

In-

R4

1k

50

50 + sIN OUT

In+

0

PARAMETERS:

Vcc

= +12

VEE

= 0

100k

Vcc

VEE

0

Closed loop amplifier



Blocks

Frequency

10mHz 1.0Hz 100Hz 10KHz 1.0MHz 100MHz1.0mHz

P(V(OPAMP))

-100d

-50d

0d

SEL>>

DB(V(OPAMP))-50

0

50

Closed loop frequency response


Voltage –mode PWM boost

converter

Error amplifier

3

C1

0

0

1Meg

1Meg+s

pwm_out

If (V(%IN1) > V (%IN2),1,0)control

5

Dbreak

D1

12

-12V

ref

out

saw

V1

10Vdc

+-

+

-

S1

S VON = 1.0VVOFF = 0.0V

ROFF = 1e6RON = 0.05

error

R2

1

pwm

sense

V4TD = 0

TF = 1nPW = 1nPER = 1m

V1 = 0

TR = 999u

V2 = 10

PWM

modulator

R1

0

L1

10mH

-++-

E1

E

GAIN = 0.25

20100µF

+

-


Voltage –mode PWM boost

converter

Time

0s 1ms 2ms 3ms 4ms 5ms 6ms 7ms 8ms 9ms 10msV(out) AVG (V(out))

0V

20V

40VV(error) AVG (V(error))

-20V

0V

20VV(control) AVG (V(control))

0V

10V

20V

SEL>>

AVG (V(out))

V(out)

V(error)

AVG (V(error))

V(control)

AVG(V(control))


PSpice simulations using vendor

models

TL084

+

-

V+

V-

D1

MUR420

sense

L1

10mHIC = 0

R7

1

0

0

pwm_out

-15

saw

R6

100

+15

Vref

out

+15

R3

100k

R5

3k

R4

1k

V4TD = 0


V1 = 0

TR = 999u

V2 = 10

pwm

R2

300k

R8

300

PWM modulator

5

control

V1

10Vdc

Error amplifier

C1

100uF

LM311

+

-GV

+V

-

B/S B

R1

20

0

X2

MTP15N05E/MC ESR

10m

-15

+

-

.TRAN 0 30m 0 0.1u

.OPTIONS STEPGMIN

.OPTIONS ABSTOL= 10p

.OPTIONS ITL1= 400

.OPTIONS ITL4= 500

.OPTIONS RELTOL= 0.01

.OPTIONS VNTOL= 10u


PSpice simulations using vendor

models

Time

0s 5ms 10ms 15ms 20ms 25ms 30msV(out)

0V

10V

20V

SEL>>

V(control)4.8V

5.0V

5.2VI(L

1)

0A

2.0A

4.0A


Vorperian models for PSpice


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


Small-signal analysis of switching

converters

R20

0

U7

VMSSCCM

D = 0.5IC = -1.84

RD = 1e-6

RE = 10mRM = 1e-6

RMPHITE = 10

RSW = 10mVAP = -17.6

1

3

2

4

A

C

P

VC

Rs1

300k

out

Rs

1

Resr

10m

V1

10Vdc

0

L1

10mHIC = 0

Rs2

100k

sense

V4

1Vac

0Vdc

Cout

100uFIC = 0

+

-

Small-signal AC analysis



converters

Time

0s 5ms 10ms 15ms 20ms 25ms 30msV(OUT)

0V

10V

20V

SEL>>

I(L1)

0A

1.0A

2.0A

3.0A



converters

Frequency

1.0Hz 10Hz 100Hz 1.0KHz 10KHz 100KHz 1.0MHz

P(V(OUT))

-300d

-200d

-100d

-0dDB(V(OUT))

-80

-40

0

40

SEL>>

Open-loop transfer function



converters

U7

VMSSCCM

D = 0.5IC = -1.84

RD = 1e-6

RE = 10mRM = 1e-6

RMPHITE = 10

RSW = 10mVAP = -17.6

1

3

2

4

A

C

P

VC

Rs2

100k

Resr

10m

0V

4

1Vac

10Vdc

L1

10mHIC = 0

Rs

1

R

20 sense

out

Cout

100uFIC = 0

Rs1

300k

0

Input impedance



converters

Frequency


DB(V(V4:+)/I(V4))

0

20

40

60

80

100

Input impedance



converters

Output impedance

sense0

U7

VMSSCCM

D = 0.5IC = -1.84

RD = 1e-6

RE = 10mRM = 1e-6

RMPHITE = 10

RSW = 10mVAP = -17.6

1

3

2

4

A

C

P

VC

L1

10mHIC = 0

Resr

10m

0

out

Rs2

100k

V4

1Vac

10Vdc

R

20

Rs

1

V5

10Vdc

Rs1

300kC

out

100uFIC = 0

+

-



converters

Output impedance

Frequency


DB(V(V4:+)/I(V4))

-40

-20

0

20

40



converters

L1

10mHIC = 0

Rs

1

Rs1

300k

U7

VMSSCCM

D = 0.5IC = -1.84

RD = 1e-6

RE = 10mRM = 1e-6

RMPHITE = 10

RSW = 10mVAP = -17.6

1

3

2

4

A

C

P

VC

Rs2

100k

V1

10Vdc

sense

0

0

V4

TD = 20m

TF = 1nPW = 50mPER = 50m

V1 = 1.2

TR = 1n

V2 = 1.5

Cout

100uFIC = 0

Resr

10m

R

20

out

+

-

Small-signal transient analysis



converters

Small-signal transient analysis

Time

0s 5ms 10ms 15ms 20ms 25ms 30ms

I(L1)

0A

1.0A

2.0A

3.0AV(OUT)

0V

10V

20V

25V

SEL>>


Averaged-inductor model for a

voltage-mode boost converter

C1

100uIC = 0

V1

10

R2

20

R1

10m

0.5

out

U7 BOOSTVM

Rs = 1

FS = 1k

L = 10m

DON

IN OUT

GND

R3

1

0

+

-


Output voltage obtained with the

averaged-inductor model

Time

0s 5ms 10ms 15ms 20ms 25ms 30msV(OUT)

0V

5V

10V

15V

20V

25V

30V


Measuring the loop gain

0

V1

1Vac

0Vdc

R

20

0

0

Vf

0

Rs

1

-++-

E1

E

GAIN = 0.25

Vg

10Vdc

Cout

100uFIC = 0

Resr

10m

U7VMSSCCM

D = 0.5IC = -1.84

RD = 1e-6

RE = 10mRM = 1e-6

RMPHITE = 10

RSW = 10mVAP = -17.6

1

3

2

4

A

C

P

VC

L1

10mHIC = 0 out

0

+

-


Measuring the loop gain

Frequency

1.0mHz 10mHz 100mHz 1.0Hz 10Hz 100Hz 1.0KHz 10KHz 100KHz 1.0MHz 10MHzP(V(VF))

-360

-270

-180

-90

0

90

SEL>>

(100.000,-163.029)

DB(V(VF))-80

-40

0

20(100.000,-1.2488)


Frequency compensation

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

PID compensation 1 11 1

1( ) 90 2 tan 2 tancomp

z p

f ff

f f

22

1 11 10 1 10 10( ) 20 (2 ) 40 1 40 1comp

z p

f fM f Log f Log Log

f f

1 1

11

90 2 tan

tan2

comp

p

z

z

f

fff

f

2

2 11 10 1 10 1 10( ) 20 (2 ) 40 1 40 1comp z

p

fM f Log f Log f Log

f


PID compensation

1p

3 3

1 = f

2 CR

2

1 2

p

2 1 2

( + )C C = f

2 C CR

1z

2 1

1 = f

2 CR

2z

1 3 3

1 = f

2 ( + )CR R

21

1

R = K

R

2 1 32

1 3

( + )R R R = K

R R

3 1 23

2 1 2

C CR = .C

+ C CR

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


Boost switching converter with

PID compensator

-15

pwmR

s

1

+15

saw

Cout

100uFIC = 20

L1

10mHIC = 4

C1

5.0014e-005

R2

518.3291

V110V

dc

0

R1

10k

0

-15

sense

R6

100

V3

-15

out

5

+15

LM311

+

-G

V+

V-

B/S B

Rs3

1k

0

0

D1

MUR420

+15

C3

2.5483e-006

Error amplifier

R

20

R4

10meg

Vref

V4TD = 0


V1 = 0

TR = 999u

V2 = 10

Rs2

3k

TL084

+

-

V+

V-

ESR

10m

R8

300

R3

173.0498

V2`15

control

VX2

MTP15N05E/MC

PWM

modulator

C2

1.1461e-006

-15

pwm_out

+

-


Simulation results with a PID

compensator

Time

0s 5ms 10ms 15ms 20ms 25ms 30msV(out)

0V

20V

40VV(control)

5.0V

7.5V

10.0V

SEL>>

I(L1)

4.0A

4.5A

5.0A


PI compensation

0 Cout

200uFIC = 0

0

EAO

0

10

-10

L1

10mHIC = 0

Vg

10Vdc

Rs

1out

100k

Resr

10m

0

10

10 + s

error

R

20

Vf

0

R1

1k

V1

1Vac

0Vdc

Vf

C1

500n

U7VMSSCCM

D = 0.5IC = -1.84

RD = 1e-6

RE = 10mRM = 1e-6

RMPHITE = 10

RSW = 10mVAP = -17.6

1

3

2

4

A

C

P

VC

0

-++-

E1

E

GAIN = 0.25

R2

10k

+

-

Small-signal model of the boost converter with PI

compensation

1 1

1 2

1sC RTF

sC R


PI compensation

Frequency

1.0mHz 10mHz 100mHz 1.0Hz 10Hz 100Hz 1.0KHz 10KHz 100KHz 1.0MHz

P(V(VF)) P(V(EAO))

-360

-270

-180

-90

0

90

180

DB(V(VF)) DB(V(EAO))-200

-100

0

SEL>>

Compensated loop gain

Uncompensated loop gain

Compensated loop gain

Uncompensated loop gain

100


PI compensation using ABM

blocks

0

saw

Resr

10m

0

51

1 + s

out

Dbreak

D1

10

-10

R2

10k

R1

1k

R3

100k

if( V(%IN1) < V(%IN2),1,0)

13

2

V2TD = 0

TF = 0.05uPW = 0.05uPER = 100u

V1 = 0

TR = 99.9u

V2 = 10

C1

500n

C2

1n

+-

+

-

S1

S

VON = 1.0VVOFF = 0.0V

Cout

100uIC = 20

Rs

0.1

ref

0

0

R

20gate

100k

L1

10mHIC = 1.8

1 2

V1

10Vdc

pwm

control

0.25

+

-


Simulation results of the PI

compensation using ABM blocks

Time

0s 5ms 10ms 15ms 20ms 25ms 30msV(CONTROL)

0V

5V

10VV(OUT)

0V

10V

20V

30V

SEL>>

I(L1)

0A

2.0A

4.0A


PI compensation using vendor

models

R3

10

0

R1

1k

-15

+15

V110V

dc

V2

TD = 0

TF = 0.05uPW = 0.05uPER = 100u

V1 = 0

TR = 99.9u

V2 = 10

-15

Cout

100uIC = 20

0

ref

0

0

gate

out

X1

MTP15N05E/MC

R

20

0

Rs

0.1

V3

+15Vdc

C1

500nLM311

+

-G

V+

V-

B/S BR

6

1k

TL084

+

-

V+

V-

5

0

L1

10mHIC = 1.8

1 2

R5

3k

0

R2

10k

saw

-15

Resr

10m

control

+15

pwm

V4

-15Vdc

D2

MUR420

R4

300

+15

+

-


Simulation results of the PI

compensation using vendor

models

Time

0s 2ms 4ms 6ms 8ms 10ms 12ms 14ms 16ms 18ms 20ms

V(CONTROL)

0V

5V

10V

SEL>>

V(OUT)0V

20V

40VI(L

1)

0A

2.0A

4.0A


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


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


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


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


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


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


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


Bias point (DC) convergence

Checking circuit topology and connectivity

Modeling of circuit components

PSpice options are checked to ensure that

they are properly defined


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


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


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


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


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


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


Transient convergence

The circuit topology and connectivity should

first be checked

Followed by the PSpice options


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



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



connectivity

Increase the rise/fall times of the PULSE

sources

Ensure that there is no unreasonably large

capacitor or inductor


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


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


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

1 2

2

2

0 0

1 1( )

( )1

o z z

d

s s

s sv sK

s sd s

Q

2(1 )

sd

VK

D

1

1z

ESR

sR C

2

2

(1 )( || ) ind

z ESR

RDs R R R

L L

0

(1 )1 ind e

ESR

R r D D

R RLC

||e ESRr R R

0

(1 ) 1

( )ind e

ESR

QR r D

L C R R



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))));



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:

-5.317e-008 s^2 - 0.05648 s + 82.32

4.913e-006 s^2 + 0.01343 s + 1sysTF



Matlab

The location of the poles can be

found using

poles = roots(DEN)

and the frequency response can be

plotted using

bode(sysTF)

Bode Diagram

Frequency (rad/sec)

Ph

ase

(de

g)

Ma

gn

itu

de

(dB

)

-40

-20

0

20

40

101

102

103

104

105

106

107

-270

-225

-180

-135

-90

-45

0



Matlab The small signal transient step response can be plotted using

Figure % this command opens a new figure window

step(sysTF) Step Response

Time (sec)

Am

plitu

de

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08-10

0

10

20

30

40

50

60

70

80

90



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



Matlab ^

^ ^ ^1

^

2

10

1 10 0

sVDxL

x u dL L

xC RC

A=[ 0 -1/L

1/cap -1/(Rload*cap)]

B1=[ 1/L

0]; %during Ton

B2=[ 0

0]; %during Toff

B=B1*D+B2*(1-D)

C=[0 1];



Matlab

OLpoles = eig(A)

sysOL=ss(A,B,C,0)

step(sysOL)

Time (sec.)

Am

plitu

de

Step Response

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

x 10-3

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

From: U (1)

To

:Y

(1)



Matlab

gamma=[ Vs/L

0];

closed-loop poles:

P=1e3*[-0.3298 + 0.10i -0.3298 - 0.10i]';

Bf= gamma*(D/Vref);

F=place(A,Bf ,P)



Simulink

-5.317e-8 s^2 - 0.05648 s + 82.32

4.913e-6 s^2 + 0.01343 s + 1sysTF

[NUM,DEN] = TFDATA(sysTF,’v’)

-5.317e-8s -0.0565s+82.322

4.913e-6s +0.0134s+1.02

Transfer Fcn

time

To Workspace1

output

To Workspace

Step Scope

Clock

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05-10

0

10

20

30

40

50

60

70

80

90

Time (s)

Ou

tpu

t



Simulink

sysZPK = zpk(sysTF)

-0.010821 (s+1.064e006) (s-1455)

(s+2657) (s+76.6)sysZPK

zeroes: [-1.0638e+006 +1455]

poles: [-2657 -76.6]

gain: [-0.010821]

-0.010821(s+1.0638e+006)(s-1455)

(s+2657)(s+76.6)

Zero-Pole

time

To Workspace1

output

To Workspace

Step Scope

Clock



Simulink

0 752

10638 2660

214.82 0 '

0 1 '

0

A

B

C

D

time

To Workspace1

output

To Workspace

Step

x' = Ax+Bu

y = Cx+Du

State-Space

Scope

Clock

simulation of switching converters

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