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Vg=28 Vo=15 Ro=3% \) I7 N8 _: C2 d& F
H=5/15 分壓
% L& ?7 V/ t9 CVref=5
$ h8 I% {* O+ K" X# t% VRM d4 W1 U# T1 D
s = tf('s');" p' ~9 \8 e0 u( q) l- u
% Input voltage Vin
4 r% a4 U. X- i7 XVin=28
6 {$ A! j! g! ^: V/ B% Output voltage Vo
% s8 p: L7 z# h. S5 X' D0 N; |Vo=15) Q0 J$ p& x, S! T! V$ R3 ]; H
% LOAD R0 O7 A/ a- v) a5 W h
RL=3
* t( `) g+ N" \( I: J9 c: d& z5 ~% PWM operating frequency Fsw4 @: g, `1 H3 G% ~" \* m& l
Fsw=100e3
; p/ i6 T# F) O6 G5 m: v, f% PWM operating period Ts- P# X0 C2 l' p: L3 R, X1 ?
Ts=1/Fsw) \+ R+ Z" K) Q4 G
% duty cycle D
; [- O" l* y8 x! A( _* O/ Q0 FD=Vo/Vin
! E" {7 x9 t L q! [% Inductance L% Z- o' m0 a' E- D
L=50e-6) O+ a6 z( G$ H( ?
% Output capacitance+ A! I' o/ g+ I
Co=500e-6$ Q# w8 f" Q7 }2 w% p! v* X
%power stage Gvd
; l$ i6 O% ]$ z& X) R% m) d%Gvd=(Vin*((s*Co*RL*rc)+RL))/((s^2*L*Co*(RL+rc))+(s*(L+(Co*rc*rL)+Co*RL*(rc+rL)))+RL+rL)/ O+ K7 C, A* P9 g5 ?" n' {& D5 L4 N
Gvd=(Vin*RL)/((s^2*L*Co*RL)+s*L+RL)
" x0 [# G% S# @- m* H' P& ~- L# qfigure(1)
7 c$ W) }0 {2 X& Nmargin(Gvd) P Y6 q# ~+ ]9 a! S
F0=1/(2*pi*sqrt(L*Co))
8 G/ W6 z$ H, j) k" Z/ r; E%Fesr=1/(2*pi*Co*rc)1 q+ k2 B* \' y& ?
Fc=Fsw/20
! e. h _0 D4 T+ P, J7 u6 K% 分壓比/ a; t4 w5 A. Q
H=1/3! m* K4 A( h. ]& W k, P" z
% PWM Vm
- O2 U: q! F$ C: U- uVm=4
4 e# n2 e, b4 V7 t% }% uncompensation loop gain Tu01 L8 b- M. C( \6 G
Tu0=H*Vin/Vm- H/ [) h4 g/ w8 B$ |* T+ C1 X. s5 ^
% 補償zero Fz
. N. ?/ g, P0 gFz=Fc*sqrt((1-sin (52*(pi/180)))/(1+sin (52*(pi/180))))
e% `+ y$ S1 D; G* I6 T% 補償pole Fp
5 j; K1 G* Q) TFp=Fc*sqrt((1+sin (52*(pi/180)))/(1-sin (52*(pi/180))))
8 ?6 j& r- G. I/ s0 vWz=2*pi*Fz
$ R* z6 B. s2 u$ ? N" P/ v8 cR1=2e34 ]9 R8 {7 S: g/ ?0 M% c# q" V
C1=1/(R1*Wz)
' }& y' z2 s5 J9 j# f) sWp=2*pi*Fp) b E% y/ r6 {7 i' M. v8 @1 }1 O
R3=R1/(Wp*R1*C1-1); z9 \" A2 d3 H( x8 M' @' `
% compensation gain Gc0
# H7 o! U" D/ p+ p$ g+ ` {Gc0=(((Fc/F0)^2)/Tu0)*sqrt(Fz/Fp)
' o: E5 O; c6 g' t) l$ WR2=Gc0*(R1+R3)1 e8 B" [$ C F4 E# U
% OPA gain:A;OPA open loop gain:A0 ; dominant pole ; compensator close feedback gain:Gcl / p4 z" h( O+ c2 W4 H4 `! V
A0=1
, l, p2 b1 J: mp=10e3*2*pi
# a7 R$ i% O; h% d: p; D; o4 K& q1 [( BA=A0*p/(s+p)' M; }# [ k% p% f4 Q
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)))
3 w7 v7 c2 a+ o# v8 B/ f6 Hfigure(2)5 D/ m9 a* f9 C D
bode(Gc,A)
+ j e. \/ L1 f; \: t% total loop gain T
# w" q m' {) }- Q, s; Y z: J; TT=Tu0*Gc0*(1+s/Wz)*RL/((1+s/Wp)*((s^2*L*Co*RL)+s*L+RL)), U8 Z/ Q! h. Z$ \9 _
% total colse loop gain Gcl! M0 {8 D$ p1 `2 S
Gcl=(Gc*(1/Vm)*Gvd)/(1+Gc*(1/Vm)*Gvd*H)" f, z+ W9 @. u0 \5 g0 W: O! r) u
figure(3)) {) T6 c! n% G2 n
bode(Gvd,Gcl,Gc,A,T) |
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