w=1 E=10*exp(j*0) L=1 R1=1 R2=1

C=2

Zlc=(j*w*L*(-j*1/(w*C)))/(j*w*L-j*1/(w*C))

Uc=(E/(R2+Zlc))*Zlc

Il=Uc/(j*w*L)

Uc0=abs(Uc)*2^(1/2)*sin(angle(Uc))

Il0=abs(Il)*2^(1/2)*sin(angle(Il))

X0=[Il0;Uc0]

Ucu=(E/(R1+R2+Zlc))*Zlc

Ilu=Ucu/(j*w*L)

Ucu0=abs(Ucu)*2^(1/2)*sin(angle(Ucu))

Ilu0=abs(Ilu)*2^(1/2)*sin(angle(Ilu))

Xu0=[Ilu0;Ucu0]

Xp0=X0-Xu0

A=[0 1/L;-1/C -1/(C*(R1+R2))]

s=eig(A)

LAMBDA=[s(1) 0;0 s(2)]

S=[1 1;s(1) s(2)]

Sodwr=S^(-1)

t=0:0.1:20

ucu=abs(Ucu)*2^(1/2)*sin(w*t+angle(Ucu))

ilu=abs(Ilu)*2^(1/2)*sin(w*t+angle(Ilu))

Xu=[ucu;ilu]

Ucp1=(1/(s(1)-s(2)))*exp(real(s(1))*t)

Ucp2=(-2*j*sin(imag(s(1))*t)*0.5*Xp0(1))-2*j*sin(imag(s(1))*t)*0.25*Xp0(2)

Ucp3=(s(1)-s(2))*Xp0(2)*cos(imag(s(1))*t)-(s(1)+s(2))*Xp0(2)*j*sin(imag(s(1))*t)

Ucp=(Ucp3+Ucp2).*Ucp1

plot(t,ucu,'w')

hold on

pause

plot(t,Ucp,'r')

hold on

pause

plot(t,Ucp+ucu,'g')

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