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Vg=28 Vo=15 Ro=3
& s7 J: P$ c4 x/ j% b; h- d4 LH=5/15 分壓
6 E4 V; S% y$ S! p$ r: {0 ]Vref=5/ ~! N: ^4 a0 ]3 H& @4 Z! y1 b
% VRM 7 ~- ^0 n4 p) @
s = tf('s');
7 D- H: R4 ^3 d" @% Input voltage Vin ( `! S. w% c- [ A5 T
Vin=28
9 j* U. s) ?- g1 c9 d+ [4 d6 n. z% Output voltage Vo+ G3 H+ u( t0 I/ t& m
Vo=15
8 G: P# k% i) y! N8 @% L% LOAD R+ G6 Z; m) C# o6 y! X! b
RL=38 s% x6 N, D- a; p$ k
% PWM operating frequency Fsw4 i, q' B3 t& [, f% |) t+ p
Fsw=100e3
8 h$ n I+ {: K, p9 c8 M% PWM operating period Ts% Z/ m1 s( ?3 m% I: [9 O r
Ts=1/Fsw
0 |$ O7 L7 Y7 v/ Q% duty cycle D
3 a- h( i: f: Z0 ND=Vo/Vin
4 l0 c8 `8 [1 f& F2 K: u% Inductance L
& L) O$ ^$ d9 L9 GL=50e-6, r, E% S: X1 Z9 |
% Output capacitance
7 A: |, V+ S1 |/ O$ p4 Y9 t9 VCo=500e-6
) q0 v8 `3 I! T9 D6 s, I1 w: N%power stage Gvd
" X T9 j7 S% h ~6 ?( P+ Z- h%Gvd=(Vin*((s*Co*RL*rc)+RL))/((s^2*L*Co*(RL+rc))+(s*(L+(Co*rc*rL)+Co*RL*(rc+rL)))+RL+rL); C: m: z9 Q' I. ~. {$ {1 ]* `* z
Gvd=(Vin*RL)/((s^2*L*Co*RL)+s*L+RL)9 Q7 ^7 s4 G3 c5 R" t) N
figure(1). _* H4 v# f r+ ~
margin(Gvd)
( L( @. b c: P& D$ [7 B" }F0=1/(2*pi*sqrt(L*Co))# p: k) A& Z$ W1 Q8 n) e/ }
%Fesr=1/(2*pi*Co*rc)
& l& E+ M) U; ^) E' ^, EFc=Fsw/20
( a# d1 A, t$ b1 `2 ]7 \" V% 分壓比1 b0 b5 T4 J) Y9 C
H=1/31 f4 g1 Q7 o1 q# Z* Q$ [
% PWM Vm
4 v) G! V! B8 jVm=40 z7 {" C) {( u8 s1 T: T
% uncompensation loop gain Tu0
" j b& l) W! A2 ^Tu0=H*Vin/Vm
& V. z0 N' Q9 s6 z% 補償zero Fz 9 P# c/ w5 j$ p) c
Fz=Fc*sqrt((1-sin (52*(pi/180)))/(1+sin (52*(pi/180))))4 v) j `8 D- f2 e8 ]
% 補償pole Fp , }2 n% R: d3 p2 |4 _
Fp=Fc*sqrt((1+sin (52*(pi/180)))/(1-sin (52*(pi/180))))2 F* n: n4 u( w" `' ?
Wz=2*pi*Fz
3 x% y) ^ \, J- l1 P% DR1=2e3
! r# { ~9 M+ Q" }3 {1 }C1=1/(R1*Wz)7 ]7 \5 {6 O/ }, a
Wp=2*pi*Fp
( |0 k' g( ~- iR3=R1/(Wp*R1*C1-1)
- C0 s, f4 w1 [; {% compensation gain Gc0
: E0 c5 ^% U+ S4 BGc0=(((Fc/F0)^2)/Tu0)*sqrt(Fz/Fp)
8 p; z5 D& J" v0 |( dR2=Gc0*(R1+R3)1 p2 a5 f+ D+ ]' T/ V5 \5 Y
% OPA gain:A;OPA open loop gain:A0 ; dominant pole ; compensator close feedback gain:Gcl
4 W/ }' e$ ^" P" V/ S) qA0=1
% l0 a) |5 \. F' up=10e3*2*pi7 C( b) @$ @4 }/ O& f& i
A=A0*p/(s+p)/ k' X$ a& J8 ^3 c- i6 {+ w; J9 f
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)))7 q: t. X# G) ?, x0 |9 P
figure(2)) J8 v3 w+ l9 e
bode(Gc,A)
! u y' U7 z+ q% total loop gain T4 n# N8 r4 Z7 N
T=Tu0*Gc0*(1+s/Wz)*RL/((1+s/Wp)*((s^2*L*Co*RL)+s*L+RL))% W( t% ^. A2 t" V0 K) Y
% total colse loop gain Gcl- c! H5 y3 z- R4 C" c! m" I5 L. d) V
Gcl=(Gc*(1/Vm)*Gvd)/(1+Gc*(1/Vm)*Gvd*H)
. P% D% k. ?- ]7 F- V3 c) Q- ~figure(3)
) y9 G! z/ }6 H/ K5 L* r. _bode(Gvd,Gcl,Gc,A,T) |
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