Switch-Mode Power Converters: Design and Analysis

Appendix E: MATLAB Listing, Converter Simulation

N1=19;

N2=12;

Lm=1150*N1^2*10^-9;

rw=0.1;

Ron=0.2;

Roff=10^7;

L1=102*10^-6;

rL1=0.005;

Vg=28;

L2=385*10^-6;

rL2=0.077;

RL=5;

fs=125*10^3;

T=1/fs;

C9=100*10^-6;

rc1=0.01;

VD=0.5;

Vref=2.5;

A=10^5;

R35=9.76*10^3;

R70=11.11*10^3;

kf=R35/(R35+R70);

Rp=(rc1*RL)/(rc1+RL);

k=RL/(rc1+RL);

R12=2*10^3;

R45=24.3*10^3;

C37=560*10^-12;

C29=2200*10^-12;

R43=10*10^3;

Vbe=0.7;

R20=5.11*10^3;

R33=2.94*10^3;

hfe=150;

R19=5.11*10^3;

R31=6.65*10^3;

R39=33.2*10^3;

C39=560*10^-12;

C7=60*10^-6;

rc2=2.61;

C8=60*10^-6;

Rx=50*10^6;

Du=0.328;

a11=-(rL1+Rp)/L1-((rw + Ron)*(N2/N1)^2)/L1;

a12=-k/L1;

a18=N2/(L1*N1);

a19=-N2*(rw+Ron)/(L1*N1);

a21=Rp/(rc1*C9);

a22=(k-1)/(rc1*C9);

a31=-(A*kf*Rp)/((1+A)*R12*C37);

a32=-(A*kf*k)/((1+A)*R12*C37);

a33=-A/((1+A)*R45*C37)-1/(R45*C29);

a34=(A/((1+A)*C37))*(1/R12+1/R45+(1+A)/Rx)+1/(R45*C29);

a41=(kf*Rp)/((1+A)*R12*C37);

a42=(kf*k)/((1+A)*R12*C37);

a43=1/((1+A)*R45*C37);

a44=-(1/((1+A)*C37))*(1/R12+1/R45+(1+A)/Rx);

Kb2=(A*R20)/(R20*R43+(1+hfe)*R33*(R20+R43));

a54=((hfe*R31*R19/(R31+R19))/((1+A)*R31*C39))*Kb2;

a55=(R19/((R19+R31)*R31)-1/R31-(1+A)/R39)/(1+A)*C39);

a66=-rL2/L2;

a68=-1/L2;

a77=-1/(rc2*C7);

a78=1/(rc2*C7);

a81=-N2/(N1*C8);

a86=1/C8;

a87=1/(rc2*C8);

a88=-a87;

a89=-a86;

a91=-N2*(rw+Ron)/(N1*Lm);

a98=1/Lm;

a99=-(rw+Ron)/Lm;

A1 = [ a11 a12 0 0 0 0 0 a18 a19; a21 a22 0 0 0 0 0 0 0; a31 a32 a33 a34 0 0 0 0 0;a41 a42 a43 a44 0 0 0 0 0;0 0 0 a54 a55 0 0 0 0;0 0 0 0 0 a66 0 a68 0;0 0 0 0 0 0 a77 a78 0;a81 0 0 0 0 a86 a87 a88 a89;a91 0 0 0 0 0 0 a98 a99];

b1=-VD/L1;

b3=-A^2*Vref/((1+A)*Rx*C37);

b4=A*Vref/((1+A)*Rx*C37);

Kb1=(-R43*(10-VD)+(R20+R43)*(10-Vbe)-A*R20*Vref)/(R20*R43+(1+hfe)*R33*(R20+R43));

b5=((hfe*R31*R19/(R31+R19))/((1+A)*R31*C39))*Kb1+(A*Vref)/((1+A)*R39*C39);

b6=Vg/L2;

B=[b1;0;b3;b4;b5;b6;0;0;0];

d11=-(rL1+Rp)/L1;

d99=-(rw+Roff)/Lm;

A2 = [ d1 1 a12 0 0 0 0 0 0 0; a21 a22 0 0 0 0 0 0 0; a31 a32 a33 a34 0 0 0 0 0;a41 a42 a43 a44 0 0 0 0 0;0 0 0 a54 a55 0 0 0 0;0 0 0 0 0 a66 0 a68 0;0 0 0 0 0 0 a77 a78 0;0 0 0 0 0 a86 a87 a88 a89;0 0 0 0 0 0 0 a98 d99];

A3=A1*Du*T;

A4=A2*(1-Du)*T;

I=eye(9,9);

X1=inv(I-expm(A4)*expm(A3))*(-expm(A4)*inv(A1)*(I-expm(A3))*B-inv(A2)*(I-expm(A4))*B)

X2=expm(A3)*X1-inv(A1)*(I-expm(A3))*B

Y1=[];

for t=0:T/100:Du*T;

Y1=[Y1 expm(A1*t)*X1-inv(A1)*(I-expm(A1*t))*B];

end

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