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Vg=28 Vo=15 Ro=3
* P, y: M5 q6 F/ |H=5/15 分壓
$ R4 S) Q4 o9 u+ d, Q- x$ c; lVref=5
/ J( t) z9 ?0 p& c5 K- Q! D1 t' m% VRM ! d1 j9 }5 v( Z% v
s = tf('s');
5 ]" K! P& J5 F% Input voltage Vin
% I/ x9 v F" Q* L6 oVin=289 l* `( M( O- ^2 q4 E- Z
% Output voltage Vo4 z& Z' j+ E1 Q
Vo=15
6 c) t1 i6 ?9 l* U) m% LOAD R: C( V5 G" x1 n* R) n8 e
RL=3
: B; C8 ~0 R, E3 i4 ?% PWM operating frequency Fsw
- G0 ?+ G$ g% N+ _$ c; v; BFsw=100e38 U7 _0 N X7 Z7 u0 H5 Z& x
% PWM operating period Ts" A. x- T3 h' G7 l6 d! l) \
Ts=1/Fsw
! @, c1 Q& l$ N# f2 b% duty cycle D, ]& y* A7 R2 m; }- }
D=Vo/Vin
4 @# z+ {6 n6 g% Inductance L/ ~7 r/ J0 k$ B* K* M
L=50e-6% ?1 D. K9 k# x- r2 f6 z
% Output capacitance
# R: }3 N& Q( F. ^3 s$ C) e9 Q' qCo=500e-6* q) g, k2 A' A& R% k
%power stage Gvd
( X, l* {! d7 h5 d: W%Gvd=(Vin*((s*Co*RL*rc)+RL))/((s^2*L*Co*(RL+rc))+(s*(L+(Co*rc*rL)+Co*RL*(rc+rL)))+RL+rL)+ N' c' X! V" S# \' w/ s, ~
Gvd=(Vin*RL)/((s^2*L*Co*RL)+s*L+RL)) `4 s4 W: v; V
figure(1)
9 R6 D' K! v# ]3 `: X, h' ?margin(Gvd)/ t4 H0 i, |* P* @* [
F0=1/(2*pi*sqrt(L*Co))
7 y" c3 J" R$ e* p. ^& x%Fesr=1/(2*pi*Co*rc)
. C8 w# s4 J& wFc=Fsw/20- {: m! T- h! G7 b% G9 h9 F) c
% 分壓比
* J4 C+ p+ t8 X5 Z) UH=1/3
8 `* ]3 f) p5 B A4 }/ `' p9 z% PWM Vm
2 ]/ L3 O. q# {9 jVm=4* b0 b! h9 [ D
% uncompensation loop gain Tu0/ _6 f8 g% z8 Q, F( w7 H8 M/ a4 K
Tu0=H*Vin/Vm6 j" Y" A$ m, p/ y/ Z# Z
% 補償zero Fz ! ^9 }8 j1 C2 q2 G% N1 W# p
Fz=Fc*sqrt((1-sin (52*(pi/180)))/(1+sin (52*(pi/180))))
/ ~$ y$ p; U6 R h& u( }6 y% 補償pole Fp
: F G# c Y9 j6 @/ Y" o# kFp=Fc*sqrt((1+sin (52*(pi/180)))/(1-sin (52*(pi/180))))- l" F- X; t5 d
Wz=2*pi*Fz6 `) d+ L0 z5 w. g
R1=2e3
+ z5 G" J0 B5 B* _C1=1/(R1*Wz)1 @) k$ A8 {3 r# t
Wp=2*pi*Fp
6 K( e ~' r% u% [) G* U) WR3=R1/(Wp*R1*C1-1)3 B/ V; k2 M, ~. w8 W4 S( y
% compensation gain Gc07 K9 T o& ?2 |
Gc0=(((Fc/F0)^2)/Tu0)*sqrt(Fz/Fp)
4 f" a. S7 h, LR2=Gc0*(R1+R3)
& ^ O. o- N. ^% T% OPA gain:A;OPA open loop gain:A0 ; dominant pole ; compensator close feedback gain:Gcl $ z$ S8 P% h* b0 N2 \
A0=1
" R5 d& M$ Q$ t( ^4 f& Ep=10e3*2*pi& O1 d$ {1 [; d8 M, A
A=A0*p/(s+p)+ h' i. q) Y+ m" R0 \+ ?' G: o
Gc=(A0*p*R2+s*A0*p*R1*R2*C1)/(s^2*(R1*R2*C1+C1*R1*R3)+s*(A0*p*R1*R3*C1+p*R1*R3*C1+p*R1*R2*C1+R1+R2+R3)+(A0*p*R1+A0*p*R3+p*(R1+R3+R2)))) [" m* E* u: u3 I
figure(2): |: m0 E# o0 f8 u3 J
bode(Gc,A)4 t: I; N+ h- P$ {
% total loop gain T- J) F: [- D; \; ^$ C0 O( g& W
T=Tu0*Gc0*(1+s/Wz)*RL/((1+s/Wp)*((s^2*L*Co*RL)+s*L+RL))
1 o( e' O8 l. W- u0 r, v4 p% total colse loop gain Gcl. `# O R/ I( d2 d
Gcl=(Gc*(1/Vm)*Gvd)/(1+Gc*(1/Vm)*Gvd*H): t0 }5 c d3 K' L1 ?
figure(3)
- r- n' {0 t! K2 k" {bode(Gvd,Gcl,Gc,A,T) |
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