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Vg=28 Vo=15 Ro=3
' e7 X$ D; G# p5 c1 X& I" uH=5/15 分壓
+ e9 S- }& E' E! e4 Y! E* Q2 zVref=5% O, K- b( O, F% s9 j) s' c
% VRM ' F) A3 q$ D+ G- I9 v9 P
s = tf('s');
4 V2 X$ W( C; N: s( p6 X6 f) _' b% Input voltage Vin
& w& h7 Y, h j( h' f TVin=28
3 J3 m- y$ k( ^. N$ i% Output voltage Vo
0 ]* r& q! l' ^% j5 qVo=15
1 w3 w& O# o2 t0 O% LOAD R
# F& n+ u2 M) y3 q, r+ f1 I7 T# |RL=3
+ ^# N6 v% S* k& r' w+ r% PWM operating frequency Fsw1 `' C/ q, x& b1 x- n8 |0 p5 W) x
Fsw=100e3
+ f. ^4 D6 {! v, Z! a+ p' m% PWM operating period Ts
. M) i: b5 c- V1 w6 h5 RTs=1/Fsw& j) I. M. o3 ?7 t2 c
% duty cycle D" q# I2 C' r) ^9 ]6 q
D=Vo/Vin
$ [6 p; L. T# K- U8 A7 C4 O! I% Inductance L
) [5 U) S; B6 W* {L=50e-64 n% a9 S. x+ X; X
% Output capacitance
, r- k9 N9 Q W- z6 \4 _9 W4 LCo=500e-61 }' k, a' a( G& k# F& E; W
%power stage Gvd 9 s Y# h# {& s& Y
%Gvd=(Vin*((s*Co*RL*rc)+RL))/((s^2*L*Co*(RL+rc))+(s*(L+(Co*rc*rL)+Co*RL*(rc+rL)))+RL+rL)
0 [9 ]2 D0 I* i. r) H7 dGvd=(Vin*RL)/((s^2*L*Co*RL)+s*L+RL)
6 ~7 k: @9 a: T. G8 D5 D) L+ Tfigure(1)
7 _" H7 K0 i; lmargin(Gvd)4 b1 ~1 q6 h% W# w. e
F0=1/(2*pi*sqrt(L*Co)): e R' A/ @1 v
%Fesr=1/(2*pi*Co*rc)
8 A1 K) {: i7 ~1 Q, OFc=Fsw/20% z0 e/ v, R$ y
% 分壓比
, n% h7 b8 u2 W; G+ _% C, l7 bH=1/3 r$ K- P9 {! d
% PWM Vm
. f) b9 A9 ^- H$ K# W. b6 k' XVm=4
5 l" n3 ], T4 {. Q" V% uncompensation loop gain Tu0
( ?( X( o" `6 u3 h4 y3 |. xTu0=H*Vin/Vm
" _: d' k% P% m, y: k- t% 補償zero Fz & [ r2 d% S5 i5 I! X4 P
Fz=Fc*sqrt((1-sin (52*(pi/180)))/(1+sin (52*(pi/180))))
! P$ U. k( f G5 b& T% 補償pole Fp `. @$ h: u1 L; Y/ p j3 N* r
Fp=Fc*sqrt((1+sin (52*(pi/180)))/(1-sin (52*(pi/180))))
3 S4 e" f' P- v. xWz=2*pi*Fz ^9 u( t5 {) O3 o# A% x, w! X9 r; A
R1=2e3
# a8 P8 U2 [% W6 h7 rC1=1/(R1*Wz)
9 T2 `" u5 [; s; [3 s! I$ BWp=2*pi*Fp" T9 P- e3 f D; o
R3=R1/(Wp*R1*C1-1)9 h1 \6 v! q& J o: s
% compensation gain Gc0
- `6 {+ N" s: a- p0 |$ g% PGc0=(((Fc/F0)^2)/Tu0)*sqrt(Fz/Fp)
; U9 d V, I+ i1 e5 g6 M8 lR2=Gc0*(R1+R3)/ N# N: {, w$ t I& L; R6 I8 o
% OPA gain:A;OPA open loop gain:A0 ; dominant pole ; compensator close feedback gain:Gcl ; @7 _( V+ Y/ q O2 T
A0=13 r: k' J- O: v; f3 }& g9 F
p=10e3*2*pi
5 @ J% D+ C) U S% x. k- k' J2 TA=A0*p/(s+p)
, B, b8 Y$ M, WGc=(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)))! I# a. |: M$ W- @. m
figure(2)
" a! P. R E/ kbode(Gc,A)9 t; `3 M" O. R$ f
% total loop gain T
5 _) z) v9 ]% T1 ^7 ?6 tT=Tu0*Gc0*(1+s/Wz)*RL/((1+s/Wp)*((s^2*L*Co*RL)+s*L+RL))
/ o7 I6 o/ D& t9 _% total colse loop gain Gcl, j% v6 L( x9 J9 h0 Q; |3 V
Gcl=(Gc*(1/Vm)*Gvd)/(1+Gc*(1/Vm)*Gvd*H)1 H4 l4 T- {) I& x. M
figure(3)4 c. m1 k& V1 i- V/ G) B( A+ J9 ]7 v
bode(Gvd,Gcl,Gc,A,T) |
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