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Vg=28 Vo=15 Ro=3
+ }$ L# ]$ b& z( k, MH=5/15 分壓
/ Q; B8 F2 a! P: Z7 l/ p7 v7 c0 ~Vref=5% X; X. j* X+ A7 Q, b0 i
% VRM 6 [1 \' K7 k' W- j, e1 W
s = tf('s');9 B4 M. [* ]6 {+ M" l. Z. G
% Input voltage Vin
+ q9 h+ }$ b7 Q/ p7 AVin=28& b: U) c0 ^/ t: R0 b) i* Q
% Output voltage Vo. K( d0 j! l. G8 }* e5 @9 y$ a
Vo=15- k5 o) G# c7 E) F3 _3 J) s' r2 t
% LOAD R- Z u4 M0 s8 h6 U
RL=3
^7 I" p+ b# B. r* f/ Y6 O q% PWM operating frequency Fsw
- L# b8 \6 d1 n% zFsw=100e3
9 _( f2 y2 S) C5 G: t- u% PWM operating period Ts
5 R& ~+ x$ K: `: BTs=1/Fsw
) D0 j( j7 q- T, x& }- s- b& `% duty cycle D1 q- W0 d Z& F5 \5 |( s
D=Vo/Vin
$ Q) U/ ^. o+ N0 r T% Inductance L y% h0 t: p S
L=50e-6
" d) p4 K1 f1 x; w% Output capacitance/ H) U9 u5 M" O) [) g3 j
Co=500e-61 \' d+ I$ ?6 ^, ?% [
%power stage Gvd
( Q, @- f+ C* S9 h9 e9 q I4 a$ `%Gvd=(Vin*((s*Co*RL*rc)+RL))/((s^2*L*Co*(RL+rc))+(s*(L+(Co*rc*rL)+Co*RL*(rc+rL)))+RL+rL). h/ i1 w+ X" |
Gvd=(Vin*RL)/((s^2*L*Co*RL)+s*L+RL)
/ }4 C1 E+ ? v+ ^: K% sfigure(1)
/ N9 P0 N _: O0 {margin(Gvd)
; u7 e7 u& D2 |; [# c( k3 f5 j: W8 UF0=1/(2*pi*sqrt(L*Co)): K2 V9 a; n3 Z! H2 s$ m+ Z
%Fesr=1/(2*pi*Co*rc)& }# ?; X) o8 r, O
Fc=Fsw/20* ~5 l- c$ ^% j; J: @( k9 S7 \% X
% 分壓比! h+ R, i$ D9 B4 O& b8 O& |
H=1/3
3 Q' |- h( H) X% V7 O3 V4 x# p% PWM Vm
- ?6 D, r) q% X4 EVm=4
' \5 v( j# C% g1 x% uncompensation loop gain Tu0# `6 f1 y" d! L4 {& T9 M0 b" d9 W
Tu0=H*Vin/Vm, E3 \# h2 ]$ d6 R& u8 V5 f% p
% 補償zero Fz I `& ]9 F0 ~
Fz=Fc*sqrt((1-sin (52*(pi/180)))/(1+sin (52*(pi/180))))" W! x8 C } ?* \( X2 e2 M1 o
% 補償pole Fp
) s! {) B4 k0 v, FFp=Fc*sqrt((1+sin (52*(pi/180)))/(1-sin (52*(pi/180))))! M- \2 Z7 E' f8 K% _9 B' O+ F
Wz=2*pi*Fz) s+ s" W/ r% [. v# E+ w4 K6 Q
R1=2e3
' A# i. H' h. S5 K! u& gC1=1/(R1*Wz) [8 `/ F) e+ C+ n" Q6 @
Wp=2*pi*Fp' @% J7 P E: V- p; J, Z8 P
R3=R1/(Wp*R1*C1-1)) t: `+ X" k2 X" J. k, U
% compensation gain Gc0& ~7 l) n$ R) w! e/ z5 u
Gc0=(((Fc/F0)^2)/Tu0)*sqrt(Fz/Fp)
3 R6 t {) V+ @/ N. `0 VR2=Gc0*(R1+R3)
1 d3 g1 v$ w# e9 F! M- ~% OPA gain:A;OPA open loop gain:A0 ; dominant pole ; compensator close feedback gain:Gcl
, c! |9 G4 i1 c! MA0=1" Z, |0 R s3 T8 @* @- h
p=10e3*2*pi+ ]3 j" ?1 y J( n, A
A=A0*p/(s+p)
2 }2 [8 M: d! y1 l9 N3 q+ v% \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)))
/ y* F; x1 H4 H/ W" Vfigure(2)
- o& U/ V B8 s( ? xbode(Gc,A)
# [0 p' m, z+ A6 W2 y" K% total loop gain T
" p7 s/ |7 T7 `# i. S4 GT=Tu0*Gc0*(1+s/Wz)*RL/((1+s/Wp)*((s^2*L*Co*RL)+s*L+RL))5 N! d* i$ Z/ [# q
% total colse loop gain Gcl
X& g7 ? i1 a# d9 C. aGcl=(Gc*(1/Vm)*Gvd)/(1+Gc*(1/Vm)*Gvd*H)
$ d; f8 V6 T5 d: Qfigure(3)2 O( W) V8 w6 d, z0 l" n9 T6 k# T
bode(Gvd,Gcl,Gc,A,T) |
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