clear all
syms R R1 R2 R3 R4 R5 R6 R7 R8 Rg1 Rg2 iul1 iul2 iul3 j1 j2 j3 jg1 jg2 ug1 ug2 v1 v10 v11 v2 v3 v4 v5 v6 v7 v8 v9
jednacine = unique([jg1 + (v1 - v5)/Rg1 == 0,...
v1 == ug1, jg2 + (v2 - v4)/Rg2 == 0,...
v2 == ug2, j3 + v3/R8 - (v11 - v3)/R7 == 0,...
-((v2 - v4)/Rg2) + iul2 == 0, -((v1 - v5)/Rg1) + iul1 == 0,...
j2 + (v6 - v10)/R4 - (v8 - v6)/R2 == 0, j1 + (v7 - v11)/R5 + (v7 - v9)/R3 == 0, ...
-iul2 - (v9 - v8)/R1 + (v8 - v6)/R2 == 0, -iul1 - (v7 - v9)/R3 + (v9 - v8)/R1 == 0,...
-((v6 - v10)/R4) + v10/R6 + iul3 == 0, -((v7 - v11)/R5) + (v11 - v3)/R7 - iul3 == 0,...
iul1 == 0, iul2 == 0, iul3 == 0, ...
v5 == v9, v4 == v8, v10 == v11])
jednacine = 
assume([Rg1 Rg2 R1 R2 R3 R4 R5 R6 R7 R8], 'positive')
promenljive = [v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, j1, j2, j3, iul1, iul2, iul3, jg1, jg2]
promenljive = 
odziv = solve(jednacine, promenljive)
odziv = struct with fields:
v1: ug1 v2: ug2 v3: -(R1*R4*R7*ug1 - R1*R5*R6*ug2 + R2*R5*R6*ug1 + R1*R6*R7*ug1 - R2*R5*R6*ug2 + R3*R4*R7*ug1 - R1*R6*R7*ug2 + R2*R6*R7*ug1 - R3*R4*R7*ug2 - R2*R6*R7*ug2 + R3*R6*R7*ug1 - R3*R6*R7*ug2)/(R1*R5*(R4 + R6)) v4: ug2 v5: ug1 v6: (R1*ug2 - R2*ug1 + R2*ug2)/R1 v7: (R1*ug1 + R3*ug1 - R3*ug2)/R1 v8: ug2 v9: ug1 v10: (R6*(R1*ug2 - R2*ug1 + R2*ug2))/(R1*(R4 + R6)) v11: (R6*(R1*ug2 - R2*ug1 + R2*ug2))/(R1*(R4 + R6)) j1: -(R1*R4*ug1 + R1*R6*ug1 + R3*R4*ug1 - R1*R6*ug2 + R2*R6*ug1 - R3*R4*ug2 - R2*R6*ug2 + R3*R6*ug1 + R4*R5*ug1 - R3*R6*ug2 - R4*R5*ug2 + R5*R6*ug1 - R5*R6*ug2)/(R1*R5*(R4 + R6)) j2: -(R1*ug2 - R2*ug1 + R2*ug2 - R4*ug1 + R4*ug2 - R6*ug1 + R6*ug2)/(R1*(R4 + R6)) j3: (R1*R4*R7*ug1 + R1*R4*R8*ug1 - R1*R5*R6*ug2 + R2*R5*R6*ug1 + R1*R6*R7*ug1 - R2*R5*R6*ug2 + R3*R4*R7*ug1 - R1*R6*R7*ug2 + R1*R6*R8*ug1 + R2*R6*R7*ug1 - R3*R4*R7*ug2 + R3*R4*R8*ug1 - R1*R6*R8*ug2 - R2*R6*R7*ug2 + R2*R6*R8*ug1 - R3*R4*R8*ug2 +… iul1: 0 iul2: 0 iul3: 0 jg1: 0 jg2: 0
zamena = [R2 == R, R3 == R, R4 == R, R5 == R, R6 == R, R7 == R]
zamena = 
odziv.v3
ans = 
subs(odziv.v3, lhs(zamena), rhs(zamena))
ans = 
v3Sol = simplify(subs(odziv.v3, lhs(zamena), rhs(zamena)))
v3Sol = 
syms T U t uR8(t) ug1(t) ug2(t)
assume(0 < U & 0 < T & 0 < t);
pobude = [ug1 == U * heaviside(t-T), ug2 == U * heaviside(t - 2*T)]
pobude(t) = 
subs(v3Sol, lhs(pobude), rhs(pobude))
ans = 
vrednosti = [U == sym(10), T == sym(1), R == sym(1000), R1 == sym(2000)]
vrednosti = 
uR8(t) = subs(subs(v3Sol, lhs(pobude), rhs(pobude)), lhs(vrednosti), rhs(vrednosti) )
uR8(t) = 
ug1(t) = subs(subs(ug1, lhs(pobude), rhs(pobude)), lhs(vrednosti), rhs(vrednosti))
ug1(t) = 
ug2(t) = subs(subs(ug2, lhs(pobude), rhs(pobude)), lhs(vrednosti), rhs(vrednosti))
ug2(t) = 
figure
fplot(ug1(t), [0.1, 3])
hold on
fplot(ug2(t), [0.1, 3])
fplot(uR8(t), [0.1, 3], '-*')
hold off
legend({'ug1', 'ug2', 'uR8'});
pg = subs(jg1*ug1 + jg2*ug2, odziv)
pg(t) = 
0