the “pwm switch” in mode transitioning spice...

ON Semiconductor

The “PWM Switch” in mode transitioning SPICE models

PCIM Germany 2005

Christophe Basso - Application Manager

November 2001 Christophe Basso – PCIM 2005www.onsemi.com

2

The The ““PWM SwitchPWM Switch”” in mode transitioning SPICE modelsin mode transitioning SPICE models

Agenda

Why average simulations?What techniques already exist?The PWM Switch conceptThe voltage-mode caseThe current-mode caseChecking averaged model’s validityConclusion


3


Unveil open-loop ac response for stabilization purposesHelps to assess impact of stray elements variations on stabilityCan predict transient response with large-signal modelsSimulation time is quick as frequency component fades away

Why average simulations?


4


What techniques already exist?StateState--Space AveragingSpace Averaging (SSA)Introduced by Slobodan Ćuk in the 80’Long and painful processFails to predict sub-harmonic oscillations

uL

xLdt

dx 1211+−=

2.

1112 xCoutRload

xCoutdt

dx−=

211 xLdt

dx−=

2.

1112 xCoutRload

xCoutdt

dx−=

VoutL

C R

x1

x2u1

VoutL

C R

x1

x2

offon

Apply smoothing process Linearize

Pfffff!


5


What techniques already exist?The GSIMGSIM conceptIntroduced by Sam Ben-Yaakov in the 90’Easy to derive but not fully invariant (dual inductors converters?)Fully auto-toggling mode modelsFails to predict sub-harmonic oscillations

b c

Lf

on off

V(a

,b)

V(a

,c)

Fsw

a

Vin C R

Ib Ic

Ia

a

b

c

Lf

on

off

V(a,b)

V(a,c)

Fsw


6


What techniques already exist?The CoPECCoPEC modelIntroduced by the Colorado Power Electronic Center in the 90’Easy to derive and fully invariantFully auto-toggling mode modelsFails to predict sub-harmonic oscillations

i1(t)

i12(t)

v1(t) v2(t)

Q1 D1

d(t)

i1(t)

v1(t) v2(t)

i12(t)

D':D

i1(t)

i12(t)

v1(t) v2(t)

Q1 D1

d1(t)

i1(t)

v1(t) v2(t)

i12(t)

Re(d1) I2

I2=(Re x i1^2) / v2

CCM DCM


7


What techniques already exist?The RidleyRidley modelsIntroduced by Raymond Ridley from VPEC in the 90’Use z-transform methodNo auto-toggling mode modelsCan only work in acCan predict sub-harmonic oscillations in CCM

1

Rload3

5

Resr100m

Cout220uF

2

VgAC = 0

Vout

4

DutyV2AC = 1

3

Vin Vout

Gnd Ctrl

AC model

DRS = 20mFS = 50kVOUT = 5RL = 3VIN = 11X1RI = 0.33L = 37.5u

0

0

0

0.458 0


8


What techniques already exist?The PWM SwitchPWM SwitchIntroduced by Vatché Vorpérian in the mid-80’Easy to derive and fully invariantNo auto-toggling mode modelsCan predict sub-harmonic oscillations in CCMDCM model was never published!

ca

p

d

d'

Ia(t) Ic(t)

Vap(t) Vcp(t)

a c

PWM switch p

d

d'

Vin

L

C R Vout


9


The PWM Switch concept

Vin

L

C R Voutac

PW

M s

witc

hp

d

d'

Linear network

Linear network

off

on

diode + transistor = guilty for non-linearity!What do you plead?


10


The PWM Switch concept

1

4

2

Q1

5

Rb_upper1Meg

Rb_lower100k

Vg

Vout

8

3

7

h11 Beta.Ib

Rc10k

Re150

Ce1nF

ReqRb_upper//Rb_lower

b c

e

ib ic

ie

VinRc10k

Re150

Ce1nF

Vin

Vout

Ve

Remember the bipolarsEbers-Moll model…

Replace Q1 by its small-signal model


11


An invariant association

a c

PWM switch p

d

d'

Vin

L

C R Vout

Vin

L

C R Voutac

PW

M s

witc

hp

d

d'

Vin

LC R Vout

ac

PWM

sw

itch

p

d

d'

ca

p

d

d'

Ia(t) Ic(t)

Vap(t) Vcp(t)

Buck

BoostBuck-boost


12


Observe waveforms and averageaverage themca

p

d

d'

Ia(t) Ic(t)

Vap(t) Vcp(t)Vin

L

C RVout

0

1( ) ( ) ( )sw

sw sw

T

a a a c cT Tsw

I t I I t dt d I t dIT

= = = =∫0

1( ) ( ) ( )sw

sw sw

T

cp cp cp ap apT Tsw

V t V V t dt d V t dVT

= = = =∫


13


PWM Switch model in CCM: a 1:D transformer!

ca

p

Ia(t) Ic(t)

V=d.V(a,p)

p

I=d.Ic

ca

p

Ia(t) Ic(t)

1 dVap Vcp

Large-signal (non-linear) model


14


Use it immediately, SPICESPICE linearizes it for you!

L

d

100uH

Vbias0.4AC = 1

C1100u

R110

Vout

Vin10

a

cp10.0 10.0

16.7

0.400

Always verify the dc operating point!


15


The original CCM/DCM PWM Switch models

CCM: common « passive »

a

c

pd1 d2

d3

a c

p

d 1-d

DCM: common « common »

Looks likeauto-toggling

is impossible…

( )apv t ( )cpv t

( )cpv t( )acv t


16


Deriving the DCM PWM Switch in common « passive »

ca

p

d1

d2

Ia(t) Ic(t)

Vap(t) Vcp(t)Vin

L

C RVout

d3

IaIpeak

Vap

Ipeak

Ic

VcpVap

Vcp

d1Tsw d2Tsw d3Tsw

t

t

t

t

IaIpeak

Vap

Ipeak

Ic

VcpVap

Vcp

d1Tsw d2Tsw d3Tsw

t

t

t

t

1

2peak

a

I dI =

( )1 2 1 2

2 2 2peak peak peak

c

I d I d I d dI

+= + =

( ) ( )1 2 1 2

1 1

22

ac a

d d d dII Id d

+ += =

1

2peak

a

I dI =

( )1 2 1 2

2 2 2peak peak peak

c

I d I d I d dI

+= + =

( ) ( )1 2 1 2

1 1

22

ac a

d d d dII Id d

+ += =


17


An auto-toggling version: clamp the equation!

ca

p

Ia(t) Ic(t)

1 NVap Vcp

N=d1/(d1+d2)

12 1

1 1

2 ² 2c ac sw sw c

ac sw ac

I L V d T LF Id dV d T d V−

= = −Model input

Clamp d2:d2 CCM = 1- d1

d2 DCM = 1- d1- d3

d2 < d2 CCMmodel is in DCM!


18


In voltage mode, add the PWM modulator gain

3

V410

4

L175u

17d

a c

PWM switch VM p

X4PWMCCMVM

GAI

N

XPWMGAINK = 0.5

5.0

10.0

5.00

0.500 1PWM

peak

KV

=


19


Testing the auto-toggling modelVout

2

Cout100uIC = 0

Resr70m3

V410

4 17

L175u vout

vout

5

7

RupperRupper

Rlower10k

8

6

X2AMPSIMPVHIGH = 1.9

V22.5

Verr

13

R3R3

C3C3

14

R2R2

C1C1

C2C2

d

a c

PWM switch VM p

X10PWMVM2L = 75uFs = 100k

R520m 4.99

4.99

10.0

4.99

0.499

2.50

2.50

5.00

0.329

GA

IN XPWMGAINK = 0.5

19

XstepPSW1

Vstep

Vout

16

Cout100uIC =

Resr70m

10

V410

1 4

L175uIC =

7

X2PSW1

D2N = 0.01

R420m

vout

+-

36

X8COMPAR

VsawTran Generators = PULSE

13

RupperRupper

Rlower10k

8

X1AMPSIMPVHIGH = 1.9

V22.5

Verr

18

R3R3

C3C3

19

R2R2

C1C1

C2C2

vout

20

XstepPSW1 Vstep

Averaged model Cycle-by-cycle


20


Comparing results with a stepload…

4.60

4.80

5.00

5.20

5.40

,

9.75m 11.2m 12.7m 14.2m 15.7mtime in seconds

300m

500m

700m

900m

1.10

Cycle-by-cycle

Averaged model

Cycle-by-cycle

Averaged model

Output voltage

Error voltage I can’t believethis result…


21


Current-mode PWM switchSame approach as before:

observe and average waveformsget the equivalent representationperturb for small-signal analysis

CCM DCM


22


CCM operation, current expression

1

2

3

'( )( ) ( ) ( )

2

(1 )2

f swc i c sw e

c sw e swc cp

i i

S d t TI t R V t d t T S

V T S TI d V dR R L

= − −

= − − −

1 2

3

ca

p

Ia(t) Ic(t)

I=Vc/Ri

p

I=d.Ic I=Iu Cs

'( )( ) ( ) ( )

2

(1 )2

f swc i c sw e

c sw e swc cp

i i

S d t TI t R V t d t T S

V T S TI d V dR R L

= − −

= − − −

1 2

3

ca

p

Ia(t) Ic(t)

I=Vc/Ri

p

I=d.Ic I=Iu Cs


23


DCM operation, current expression1c sw e

peaki

V d T SIR

− ×=

12

c sw ec sw f

i

V d T SI d T SR

α−= −

( )1 2 1 2

2 2 2peak peak peak

c

I d I d I d dI

+= + =

ca

p

Ia(t) Ic(t)

I=Vc/Ri

p

I=(d1/(d1+d2)).Ic I=Iu

1 1 22

( , ) 12

d Tsw Se d dV c pI d TswRi L

µ × × +⎛ ⎞= + × × × −⎜ ⎟⎝ ⎠


24


The PWM SwitchPWM Switch, the final encapsulation

Vout

16

Cout220uF

Resr70m

V425

1 4

L175u

vout

9

d

a c

PWM switch CM p

duty-cycle2

X1PWMDCMCM

duty_cycle

R420m

10

X5PSW1

V2

6

R710k

R810k

7

8

X4AMPSIMP

V62.5

vout

Y4

L41p

11

C31p

V7AC = 1

12

R120k

C110n

C2470p

Vout

16

Cout220uFIC = 4.6

Resr70m

V425

1 4

L175uIC = 250m

voutR41

12

X2PSW1

2

V1

10+-

614

13

X3COMPAR

17

R3470

C1x100p

B1Voltage

V(4,vout)

D11n5818

18

R710k

R810k

19

X4AMPSIMP

V62.5

vout

Verr

24

R120k

C110n

C2470p

20

X5PSW1

V2

S

R

Q

Q

A buck: averaged model vs cycle-by-cycle


25


Good matching between both models

Error voltage

Output voltage

It can’t be, he is cheating!


26


Testing the ac response

2

Vin126

1 4

X1xXFMRRATIO = -0.1

D1MBR140P

6

L12.2uH

Rs10m

Rload149

R17300m

C210uF

15

R4100m

C1470uF

5

R151.5k

10

16

out1

14

LoL1kH

12

CoL1kF

VstimAC = 1

out2

13

X3TL431

Rlow1k

Rupp3.9k

out2

Cf100nF

7

R5100m

C5470uF

out1

Vout

vcac

PW

M s

witc

h C

Mp

duty

-cyc

le

3

18

PWMCMX1L = 1.8mFs = 66kRi = 1.5

dc

L31.8m

11

V34.8

R78k

VFB

126

-127

12.7

12.2 12.2 12.2

12.212.2

10.6

9.88

0.6490.649

0

2.50

12.2

0

0.649

0.408

4.80

A dcm current-mode flyback


27


10 100 1K 10K 100K

0

Y = 20dB/div Y = 45°/div

Phase Gain

BW = 600Hz

Simulation Measurement

Ac simulation results of the flyback converter


28


If the load increases…

-20.0

0

20.0

40.0

60.0

vdbf

b in

db(

volts

)pl

ot1

1

10 100 1k 10k 100kfrequency in hertz

60.0

100

140

180

220

ph_v

fb in

deg

rees

Plo

t2

2

CCM operation

Sub-harmonic oscillations!

phase

gain


29


Testing on a multi-output forward

parametersRsense=0.35Vout=28L1=130uL2=130uN1=0.5N2=0.215

Rupper=(Vout-2.5)/250ufc=5kpm=50Gfc=8.84pfc=-66

G=10^(-Gfc/20)boost=pm-(pfc)-90pi=3.14159K=tan((boost/2+45)*pi/180)C2=1/(2*pi*fc*G*k*Rupper)C1=C2*(K^2-1)R2=k/(2*pi*fc*C1)

Vout1

6

Cout148u

Resr1245m

11 3

L1L1

13

RupperRupper

Rlower10k

18

V32.5

19

Verrx

R970m

20

R2R2

C1C1

C2C2

X4AMPSIMP

vc

a c

PWM switch CM p

duty-cycle

10 8

1

X5PWMCM2L = L1/N1^2+L2/N2^2Fs = 200kRi = RsenseSe = 0

X6XFMRRATIO = N1V6

160

dc

9 Vout2

2

Cout2100u

Resr2100m

4 5

L2L2

R2x70m

Rload26

X1XFMRRATIO = N2

vout

vout

LoL1kH

7

CoL1kF

Rload17

V1AC = 1

X7XFMRRATIO = N1/N2

28.0

28.0

28.3 28.3

2.50

2.500.861

0.861

160 56.6

0.861

0.356

12.0

12.0

12.2 12.2

0

Coupled inductances

28 V

12 V

A multi-output forward


30


Output voltage bang on the 28 V output…

27.2

27.6

28.0

28.4

28.8

vout

, vou

t1 in

vol

tsPl

ot1

13


11.7

11.9

12.1

12.3

12.5

vout

2#a

in v

olts

11.6

11.8

12.0

12.2

12.4

vout

2 in

vol

tsPl

ot2

24

A forward converter

Inductances arecoupled…

28 V

12 V

Cycle-by-cycleAveraged


31


Output voltage bang on the 28 V output…

A forward converter

Inductances areun-coupled…

27.2

27.6

28.0

28.4

28.8

vout

, vou

t1 in

vol

tspl

ot1

14


11.2

11.6

12.0

12.4

12.8

vout

2, v

out2

#a in

vol

tsP

lot2

23

28 V

12 V

Cycle-by-cycleAveraged


32


Instability in the buck DCM current-mode

1 10 100 1k 10k 100k 1Megfrequency in hertz

-80.0

-40.0

0

40.0

80.0vd

bout

, vdb

out#

1, v

dbou

t#2

in d

b(vo

lts)

-180

-90.0

0

90.0

180

vpho

ut, v

phou

t#1,

vph

out#

2 in

deg

rees

Plo

t1

1

2

3

4

5

6

Phase Vin = 7 V Rload = 100 Ω

Phase Vin = 7.5 V Rload = 50 Ω

Gain Vin = 7.5 V Rload = 50 Ω

Phase Vin = 10 V Rload = 50 Ω

Gain Vin = 7 V Rload = 100 Ω

Gain Vin = 10 V Rload = 50 Ω

Vin = 7V M = 0.71 Vin = 7.5V M = 0.66 Vin = 10V M = 0.5

The DCM buckshows instability

as M > 0.66without ramp

> 20 dB increase

Phase jumps to –180°


33


Instability in the buck DCM current-mode

Adding 0.086 x Soff

cures the problem

1 10 100 1k 10k 100k 1Megfrequency in hertz

-180

-90.0

0

90.0

180

vpho

ut, v

phou

t#2

in d

egre

es

-40.0

-20.0

0

20.0

40.0

vdbo

ut, v

dbou

t#2

in d

b(vo

lts)

Plot

1

1

2

3

4

Phase Vin = 7 V Rload = 100 Ω No ramp

Phase Vin = 7 V Rload = 100 Ω Sa = 12.28 kV/s

Gain Vin = 7 V Rload = 100 Ω No ramp

Gain Vin = 7 V Rload = 100 Ω Sa = 12.28 kV/s


34


The conclusion

The CM PWM Switch DCM was derivedTwo auto-toggling models developedGood matching of average vs realityModels also exist in BCM (PFC simulations)Exist in both IsSpice and PSpice

the “pwm switch” in mode transitioning spice...

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