Odrediti napon na početku voda, u1(t)
clear variables
close all
syms tau s Zc Z1 Z2 U1 I1 U2 I2 Ug
Resavanje sistema jednacina
Braninove jednacine u s-domenu
jednBr = [U1 == Zc*I1 + Zc*I2*exp(-s*tau) + U2*exp(-s*tau),...
U2 == Zc*I2 + Zc*I1*exp(-s*tau) + U1*exp(-s*tau)]
jednBr = 
jednacine = [jednBr ,...
Ug == Z1*I1 + U1,...
U2 == -Z2*I2]
jednacine = 
res = solve(jednacine, [U1 I1 U2 I2])
res = struct with fields:
U1: (Ug*Zc^2 - Ug*Zc^2*exp(-2*s*tau) + Ug*Z2*Zc + Ug*Z2*Zc*exp(-2*s*tau))/(Z1*Z2 + Z1*Zc + Z2*Zc + Zc^2 - Zc^2*exp(-2*s*tau) - Z1*Z2*exp(-2*s*tau) + Z1*Zc*exp(-2*s*tau) + Z2*Zc*exp(-2*s*tau)) I1: (Ug*Z2 + Ug*Zc - Ug*Z2*exp(-2*s*tau) + Ug*Zc*exp(-2*s*tau))/(Z1*Z2 + Z1*Zc + Z2*Zc + Zc^2 - Zc^2*exp(-2*s*tau) - Z1*Z2*exp(-2*s*tau) + Z1*Zc*exp(-2*s*tau) + Z2*Zc*exp(-2*s*tau)) U2: (2*Ug*Z2*Zc*exp(-s*tau))/(Z1*Z2 + Z1*Zc + Z2*Zc + Zc^2 - Zc^2*exp(-2*s*tau) - Z1*Z2*exp(-2*s*tau) + Z1*Zc*exp(-2*s*tau) + Z2*Zc*exp(-2*s*tau)) I2: -(2*Ug*Zc*exp(-s*tau))/(Z1*Z2 + Z1*Zc + Z2*Zc + Zc^2 - Zc^2*exp(-2*s*tau) - Z1*Z2*exp(-2*s*tau) + Z1*Zc*exp(-2*s*tau) + Z2*Zc*exp(-2*s*tau))
Napon na pocetku voda, u1
res.U1
ans = 
syms C T t U
assume(T>0 & C>0 & Zc>0 & tau>0) % vazno za Laplasovu tranformaciju
Uh = laplace(U*(heaviside(t) - heaviside(t-T)), t, s)
Uh = 
U1_zam = simplify(subs(res.U1, [Z1, Z2, Ug],[Zc, 1/(s*C), Uh]))
U1_zam = 
u1_zam(t) = ilaplace(U1_zam , s, t)
u1_zam(t) = 
% u1_zam(t) = subs(u1(t), Ug, heaviside(t) - heaviside(t-tau))
vrednosti = vpa([Zc==50, tau==60e-9, C==200e-12, U==1, T==10e-9],4)
vrednosti = 
u1_zam_num(t) = simplify(subs(u1_zam(t), lhs([vrednosti]), rhs([vrednosti])))
u1_zam_num(t) = 
fplot(t, u1_zam_num, [0 200e-9])