|
Vg=28 Vo=15 Ro=3
/ x3 a" {& i' m1 D0 w4 mH=5/15 分壓( @- O% Y+ |( d L% ?5 }5 X
Vref=5
% x2 x/ N2 ?2 J' ^0 \8 z4 ~% VRM
& F& w( `3 z B$ Rs = tf('s');, s7 V2 z6 U# f P; G1 B
% Input voltage Vin
7 K7 s' }$ k' t; o/ h9 N) [Vin=28
' Y' E2 x1 {* ?* F% Output voltage Vo8 z( A A- B% k. u+ J: N; e
Vo=15
6 z) }# H' O7 f0 P+ K! g; L( X% LOAD R0 ^1 k5 ` n9 D/ L
RL=3: i* m, w6 X5 `1 W4 @
% PWM operating frequency Fsw; S9 r' F2 _& C4 L
Fsw=100e3
9 K' S6 k0 u( I, l$ C/ H4 w; f% x% PWM operating period Ts1 K) Q. ^$ N3 L/ ?9 E$ ^
Ts=1/Fsw6 f4 P+ D2 P5 K# `
% duty cycle D& t; `! r. X4 o$ ?" ?
D=Vo/Vin
$ v+ d3 M% R2 U0 H' X% Inductance L6 R# F$ z% y% R
L=50e-66 d; x- y" R# g: O6 L
% Output capacitance
1 V( J+ d3 Q# V7 ~Co=500e-6$ j- c! t( p4 b+ k+ H, y
%power stage Gvd
# Y: j# o" p$ O" t+ 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)7 M) Q- n+ b, J: M G1 u
Gvd=(Vin*RL)/((s^2*L*Co*RL)+s*L+RL)+ U. i$ R v0 S, p
figure(1)
( F0 D9 Y+ Q6 N% K: O+ ^margin(Gvd)* F3 s: S' ^/ R( M, _7 @
F0=1/(2*pi*sqrt(L*Co)). t4 d6 `0 l3 U4 @) A! {/ Y! Z. z! |
%Fesr=1/(2*pi*Co*rc)4 @- f9 \1 Y2 N# B1 ^, S
Fc=Fsw/20
: T3 K! j( x* t6 |% 分壓比- k& A5 V' L9 `0 Z' D5 g5 ]
H=1/3( A+ W& T& X% d0 N- M$ B
% PWM Vm
! O; n. y- E( j2 |2 ]Vm=45 n$ `$ N' \- E
% uncompensation loop gain Tu00 k8 _) K& D3 I E7 Z9 e
Tu0=H*Vin/Vm& e2 p9 {6 X9 r
% 補償zero Fz - t* K- O F7 n+ H" N# l
Fz=Fc*sqrt((1-sin (52*(pi/180)))/(1+sin (52*(pi/180))))
4 i& G) ?1 s) B, G. X% 補償pole Fp 3 z$ q) j1 `0 @# u+ N E6 G
Fp=Fc*sqrt((1+sin (52*(pi/180)))/(1-sin (52*(pi/180))))2 u7 m% G5 \" w c9 J. k% h
Wz=2*pi*Fz+ U E8 x% g: v4 A, f$ K
R1=2e38 E [/ N) d: t. J( f F v! o
C1=1/(R1*Wz)) l& N2 Z7 z7 ^' r0 @1 I0 G; D
Wp=2*pi*Fp
: o) m6 u* {6 yR3=R1/(Wp*R1*C1-1)( D% x7 q E* {
% compensation gain Gc0
% i% [, u) C# F8 }( U' s# g" {1 SGc0=(((Fc/F0)^2)/Tu0)*sqrt(Fz/Fp)
1 o4 Z. F" t& M: yR2=Gc0*(R1+R3)
7 }; G' I6 A" l% OPA gain:A;OPA open loop gain:A0 ; dominant pole ; compensator close feedback gain:Gcl ) ?* {/ m6 k; U' x2 Y+ t
A0=1
" Q3 O2 c2 |- M- B5 Sp=10e3*2*pi
: }, J7 f( {+ aA=A0*p/(s+p)
3 Z/ F z. h9 @$ t% T" CGc=(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)))
/ X( n" C# l$ C' Cfigure(2)
4 {% ]: K" ^1 z& ?$ U) q8 B" fbode(Gc,A)+ v" ?$ r) E2 w9 @6 w) X, U
% total loop gain T
4 T. Q* O; I- Q# l3 x% p& tT=Tu0*Gc0*(1+s/Wz)*RL/((1+s/Wp)*((s^2*L*Co*RL)+s*L+RL))* v) V/ f: v4 ?% Q" t
% total colse loop gain Gcl" s, t1 T9 i2 I: {# ]
Gcl=(Gc*(1/Vm)*Gvd)/(1+Gc*(1/Vm)*Gvd*H)
" s4 \ c9 w7 q7 i3 P$ Q+ X9 ^figure(3)
6 A) n% v Z3 v% {" J& y+ Wbode(Gvd,Gcl,Gc,A,T) |
|