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Vg=28 Vo=15 Ro=3" L" y3 T0 {( m, Q! ~
H=5/15 分壓: A# Y p9 R1 H/ R9 f4 c& o
Vref=5
b' z: G! v0 }: m% VRM . _/ t( v& i ^/ i& w/ Q" ^& @
s = tf('s');( W- e8 ?' T; t$ s, g# K9 J& Y
% Input voltage Vin
2 C. B ^7 d$ \Vin=28
" F. m( M2 _4 f8 \1 g% Output voltage Vo
4 m" S- X& j" E" G$ T B: ^% nVo=15
# E G) \0 p$ x ?& e% LOAD R0 l$ H: G1 w0 |
RL=3: o* h/ q0 \/ ]4 ?0 P
% PWM operating frequency Fsw
( a1 ], j8 T3 J% NFsw=100e3
) A( x* y [5 J$ q' l% PWM operating period Ts
4 g& `! a& p5 @( Y5 HTs=1/Fsw
& B( E- J% l! e# ^. u. n% duty cycle D' ?4 j9 q# o) ?+ m/ @9 \
D=Vo/Vin
- O- r z$ t5 Q% Inductance L
- Y. K& m7 p: a2 u SL=50e-6, q+ i. O6 ~. P5 q
% Output capacitance
7 ?5 r- ~( A' g7 CCo=500e-6
- W P7 E& f9 z4 i5 a%power stage Gvd , u7 @2 s$ j1 v9 ]! [% 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)
. D; H9 G4 G; u! a9 n6 NGvd=(Vin*RL)/((s^2*L*Co*RL)+s*L+RL)+ D# p; c( u6 C& f
figure(1)* Y. P8 \# i1 e4 }, j8 K
margin(Gvd): L8 q* F% h# D9 U) y8 `% B
F0=1/(2*pi*sqrt(L*Co))
1 z }8 R; X# V%Fesr=1/(2*pi*Co*rc)/ s4 _4 ?: s( a: T
Fc=Fsw/20$ l2 h8 P' c! o) S1 e( n! i
% 分壓比
4 ?- F$ J! V* c) x2 r! I, rH=1/3
- L. p3 C, i; Y9 P% C8 h2 J! f3 J; u) P% PWM Vm
) U, i; Z3 r, U5 eVm=4! E# l5 u& i- O6 ?1 C) G4 X5 Q' l3 [% Y
% uncompensation loop gain Tu04 p0 T! p2 _9 y: [* d
Tu0=H*Vin/Vm
9 E8 o+ U4 W8 F( @% 補償zero Fz
8 w! x0 j4 e; ?* i. g* e/ AFz=Fc*sqrt((1-sin (52*(pi/180)))/(1+sin (52*(pi/180))))6 G. ?( O( U9 E# ?! p3 n
% 補償pole Fp
. P4 \9 j$ B A& [0 E/ [! XFp=Fc*sqrt((1+sin (52*(pi/180)))/(1-sin (52*(pi/180))))7 }0 u0 [" c4 h; _
Wz=2*pi*Fz
: E! z( e' r. W- zR1=2e3
( k1 @2 d" @) N8 Y1 B8 w) V: lC1=1/(R1*Wz)
; }0 [( B7 g1 u/ M6 r, _4 V3 }Wp=2*pi*Fp
% s a( r# }6 U$ V; I6 IR3=R1/(Wp*R1*C1-1)
8 Y m( e9 N" I d% compensation gain Gc07 @! m: u) ]' c! f7 x
Gc0=(((Fc/F0)^2)/Tu0)*sqrt(Fz/Fp)
; @4 O1 L! i. r t6 i4 ~$ S3 Q9 `R2=Gc0*(R1+R3); m+ m" [& c2 a
% OPA gain:A;OPA open loop gain:A0 ; dominant pole ; compensator close feedback gain:Gcl
. d* p! ]. D/ s. g' q- sA0=1
. D! }( ?* z, J Rp=10e3*2*pi
0 H# w! a+ _6 f* O5 K2 H5 BA=A0*p/(s+p)3 |( k6 V: W" d
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)))
( |9 q5 |/ r7 d7 qfigure(2)
4 G& S- ^- u( _8 {) cbode(Gc,A)( r* {' H$ Q' d/ o% L0 D3 M
% total loop gain T
/ r q8 z4 [. j3 Q4 iT=Tu0*Gc0*(1+s/Wz)*RL/((1+s/Wp)*((s^2*L*Co*RL)+s*L+RL))
+ v5 r# g2 L; R o2 L1 D% total colse loop gain Gcl
2 {- O. K) N* H PGcl=(Gc*(1/Vm)*Gvd)/(1+Gc*(1/Vm)*Gvd*H)
, f" l" k! |5 e, ]5 r$ Y6 [3 Ifigure(3)' F8 j& l4 t0 _' {5 a4 E
bode(Gvd,Gcl,Gc,A,T) |
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