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Vg=28 Vo=15 Ro=33 t! g \2 X( u4 V: H
H=5/15 分壓
! Y/ G% R# L8 g4 o1 |3 N2 P) NVref=5
" @: V$ a) f1 u8 E5 ^) s5 c% VRM 6 c. q+ ]; x$ G; y
s = tf('s');+ X& l. h* N: O% d4 L1 S1 s& x" p, t
% Input voltage Vin " j* o+ m1 Q ]8 {% V+ e" U
Vin=28
7 p$ }4 {4 ~" t8 u$ H% Output voltage Vo
$ y* b6 C4 |1 Y7 ?; P0 a5 h9 XVo=15
; I+ y/ ]; l* G% LOAD R
2 H7 N2 z! o* h7 FRL=38 ]$ \3 F) Z5 E! o( ?
% PWM operating frequency Fsw3 w! ?! I. ]* W( ]5 X9 Q# n5 R; R
Fsw=100e3, m& A) t0 Y" Z7 E' R
% PWM operating period Ts
0 k' {6 V4 t* \. X: B# g$ o$ H% X- XTs=1/Fsw4 |0 B' K' o' |( g% I c/ t) I% c
% duty cycle D
2 ~' [% |4 ^: @- J7 ~% ID=Vo/Vin
: G: c8 f7 e' J3 ?6 C% Inductance L( b) B8 v# ~4 P3 l) t: Y
L=50e-68 ~ Z$ G- Q" t$ e8 e0 M# v
% Output capacitance2 L: s# r& m! T
Co=500e-6
# T- _1 Y$ C3 i0 S9 ?%power stage Gvd
1 p4 l% r; Y# O2 e%Gvd=(Vin*((s*Co*RL*rc)+RL))/((s^2*L*Co*(RL+rc))+(s*(L+(Co*rc*rL)+Co*RL*(rc+rL)))+RL+rL)8 _4 ]; t( u1 A
Gvd=(Vin*RL)/((s^2*L*Co*RL)+s*L+RL)
" S" o5 I+ b$ _0 Z; @figure(1)
6 R* I r1 v& j' \# z% f* pmargin(Gvd)
* a" |- w! ?: }6 lF0=1/(2*pi*sqrt(L*Co))! D. d& A4 R3 y! Y4 T- e
%Fesr=1/(2*pi*Co*rc)
! [5 z& I# N4 e$ e7 ]Fc=Fsw/20
# T) p+ d8 P/ `* U. L% 分壓比
( d' D X' Z2 J( V1 `4 uH=1/3$ g4 `8 N0 e' o& P& u
% PWM Vm8 P& c$ G* k, I" c
Vm=47 d" b _4 x9 F' b
% uncompensation loop gain Tu0$ z2 e0 O7 u& t; o" x
Tu0=H*Vin/Vm& ]6 h; W5 |& A% i4 N
% 補償zero Fz : m, j) k" O, l
Fz=Fc*sqrt((1-sin (52*(pi/180)))/(1+sin (52*(pi/180)))), s8 N" k& b$ q; s- [/ E' |
% 補償pole Fp % L( }0 t# r/ U2 d0 o
Fp=Fc*sqrt((1+sin (52*(pi/180)))/(1-sin (52*(pi/180))))
8 x7 V2 w6 ?/ n+ _Wz=2*pi*Fz4 S& G+ Z8 V4 I" I6 I
R1=2e3
# B! p4 d2 e$ G, `" ~% xC1=1/(R1*Wz)
, N4 u9 N2 ^* M" r' y7 U4 u- l5 fWp=2*pi*Fp! F9 r! m+ C$ J6 p e
R3=R1/(Wp*R1*C1-1)6 C: L% r4 E- E( z# c
% compensation gain Gc0# m2 R: j9 W; ?
Gc0=(((Fc/F0)^2)/Tu0)*sqrt(Fz/Fp)4 w! L) c9 z' ]# m1 S: g) u; L
R2=Gc0*(R1+R3)
- {7 i" d* _5 z- G& ~) B6 F7 b) }+ f% OPA gain:A;OPA open loop gain:A0 ; dominant pole ; compensator close feedback gain:Gcl ' n% o$ I8 y; y' l$ f
A0=1
( B( t- Q3 f! [( d: `p=10e3*2*pi! }4 f0 z/ ^6 Z
A=A0*p/(s+p)
6 E1 f B1 x. k' V$ O% w8 LGc=(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)))! D5 }: {8 X4 f0 ~6 w; Q
figure(2)
3 `( {! [7 @, s& Q5 Cbode(Gc,A)
$ Y) V- y& m) m: I& b- X) o7 f$ Z7 g% total loop gain T! K# U7 |) W$ y: p- g- ]! b" E! V
T=Tu0*Gc0*(1+s/Wz)*RL/((1+s/Wp)*((s^2*L*Co*RL)+s*L+RL))+ R7 T: A1 e! Z; l& P% r9 W
% total colse loop gain Gcl
, K) k8 T. F8 [5 FGcl=(Gc*(1/Vm)*Gvd)/(1+Gc*(1/Vm)*Gvd*H)6 C' V* C* [/ O8 i$ P% ?
figure(3)/ i8 E. y) H$ V
bode(Gvd,Gcl,Gc,A,T) |
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