ClearAll["Global '*"]; NN = 11;
tmax = 6.0;
fN = 1.0;
Rs = 50.0;
Resc_impair = Table[Rc[k] = 0.0, {k, 1, NN, 2}];
Resc_pair = Table[Rc[k] = 0.0, {k, 2, NN, 2}];
Rc[NN] = 1100.0;
Resl_impair = Table[Rl[k] = 0.0, {k, 1, NN, 2}];
Resl_pair = Table[Rl[k] = 0.0, {k, 1, NN, 2}];
Rl[NN] = 200.0;
t0 = 0.0; ts = 1.7 + t0; tflat = 300.0; tfall = 1.7; tc = ts + tflat;
td = tc + tfall; a0 = -10.0*10^3; {ts, tflat, tfall, td - tc}
Vs[t_] := Which[t <= t0, 0, t > t0 && t <= ts, a0 *(t - t0)/ts - t0,
t > ts && t <= tc, a0, t > t0 && t <= td, a0*((-t + td)/(td - tc)),
t > td, 0]
TabVs = Table[{t, Vs[t]/1000}, {t, 0, tmax, 0.01}];
VoltVs = ListPlot[TabVs, PlotRange -> All,
PlotStyle -> {AbsoluteThickness[1.4], RGBColor[0, 0, 1],
Thickness[0.008]}, FrameLabel -> {"Time(ns)", "Voltage(kV)"},
Joined -> True, GridLines -> {Automatic, Automatic},
FrameTicks -> {Automatic, Automatic}, Frame -> True,
LabelStyle -> Directive[Black, 17]]
np = 256; tfourier = 1000;
pulse = Table[Vs[t]/1000, {t, 0, tfourier, 0.05}];
datafin = Table[{f/(1.2), Abs[Fourier[pulse]][[f]]}, {f, 1, 60, 1}];
pVs = ListPlot[datafin, PlotRange -> {{0, 50}, All},
PlotStyle -> {AbsoluteThickness[1.8], RGBColor[0, 1, 0],
Thickness[0.008]}, FrameLabel -> {"Frequence(Mhz)", "Voltage(V)"},
Joined -> True, GridLines -> {Automatic, Automatic},
FrameTicks -> {Automatic, Automatic}, Frame -> True,
LabelStyle -> Directive[Black, 17]]
NIntegrate[Vs[t]/1000, {t, 0, 200}]
(*non linear capacitor*)
m = 1.08; V0 = 0.7; Cs0 = 0.000095;
p = (1.0 + 1*V[k][t]/V0)^m
Cv[k_][t_] := which[V[k][t] > -V0, Cs0/p, V[k][t] <= -V0, 10.0]
Cv[k_][t_] := Cs0/p
Ca[Va_] := Cs0/(1.0 + 1*Va/V0)^m
Cv[NN][t] := 10000000.0;
Plot[{Ca[Va]}, {Va, 0, 15}, AxesLabel -> {"Va", "Ca"},
PlotRange -> {0, Cs0}, PlotStyle -> {Thickness[.01], Red},
TicksStyle -> Directive["Black", 14],
AxesStyle -> {{Thick, Black}, {Thick, Black}},
AxesLabel -> {Style["t", Black, Italic, 30],
Style["x,Vin", Black, Italic, 30]}, Frame -> False,
PlotRange -> All]
(*non linear inductance*)
L0 = 465; La = 4.65; Is = 3.76;
Ls[k_][t_] := (L0 - La)*(Sech[i[k][t]/Is]^2) + La
La1[Ia_] := (L0 - La)*(Sech[(Ia/Is)]^2) + La
Plot[{La1[Ia]}, {Ia, 0, 100}, AxesLabel -> {"Ia", "La1"},
PlotRange -> {0, L0*1.2}, PlotStyle -> {Thickness[.01], Orange},
TicksStyle -> Directive["Black", 14],
AxesStyle -> {{Thick, Black}, {Thick, Black}},
AxesLabel -> {Style["t", Black, Italic, 30],
Style["x,Vin", Black, Italic, 30]}, Frame -> False,
PlotRange -> All]
Ls[NN][t] := 1.0*10^-8
Ls[k_][t_] := 280.0
(*Equation for the First Section*)
eqi = Table[{-i[k]'[t] +
Vs[t]/Ls[k][t] - (Rs/Ls[k][t])*
i[k][t] - (Rc[k]/Ls[k][t] )*(i[k][t] - i[k + 1][t]) - (V[k][
t])/Ls[k][t] - (Rl[k]/Ls[k][t] )*(i[k][t]) ==
0, -V[k]'[t] + (i[k][t] - i[k + 1][t])/Cv[k][t] == 0}, {k, 1, 1}];
(*Equation for the intermediate Section*)
eqs = Table[{-i[k]'[
t] + (Rc[k - 1]/Ls[k][t]) *(i[k - 1][t] -
i[k][t]) + (V[k - 1][t])/
Ls[k][t] - (Rc[k]/Ls[k][t] )*(i[k][t] - i[k + 1][t]) - (V[k][
t])/Ls[k][t] - (Rl[k]/Ls[k][t] )*(i[k][t]) ==
0, -V[k]'[t] + (i[k][t] - i[k + 1][t])/Cv[k][t] == 0}, {k, 2,
NN - 1}];
eqpartial = Join[eqi, eqs, eqf];
eqfinal = Flatten[eqpartial];
(*Equation for the finale Section*)
eqf = Table[{-i[k]'[
t] + (Rc[k - 1]/Ls[k][t] )*(i[k - 1][t] -
i[k][t]) + (V[k - 1][t])/
Ls[k][t] - (Rc[k]/Ls[k][t] )*(i[k][t] ) - (V[k][t])/
Ls[k][t] - (Rl[k]/Ls[k][t] )*(i[k][t]) ==
0, -V[k]'[t] + (i[k][t])/Cv[k][t] == 0}, {k, NN, NN}];
eqpartial = Join[eqi, eqs, eqf];
eqfinal = Flatten[eqpartial];
initial1 = Flatten[Table[{i[k][0] == 0., V[k][0] == 0.}, {k, 1, NN}]];
Vlist = Flatten[Table[{V[k][t], i[k][t]}, {k, 1, NN}]];
sol = NDSolve[Join[eqfinal, initial1], Vlist, {t, 0., tmax},
MaxSteps -> Infinity];
sol1 = Flatten[sol];
inputiv =
Table[{i[k][t] = i[k][t] /. sol1, V[k][t] = V[k][t] /. sol1}, {k, 1,
NN}];
outiv = Flatten[inputiv];
V[0][t_] := Vs[t] - Rs*i[1][t];
Vfp = Table[
V[k][t_] = Rc[k]*(i[k][t] - i[k + 1][t]) + V[k][t], {k, 1, NN - 1}];
V[NN][t_] := Rc[NN]*(i[NN][t]) + V[NN][t]
Pload[t_] := V[NN][t] i[NN][t]
Pint[t_] := Vs[t] i[1][t]
VoltFim =
ListPlot[outiv, PlotRange -> All,
PlotStyle -> {AbsoluteThickness[1.4], RGBColor[0, 0, 1],
Thickness[0.008]}, FrameLabel -> {"Time(ns)", "Voltage(kV)"},
Joined -> True, GridLines -> {Automatic, Automatic},
FrameTicks -> {Automatic, Automatic}, Frame -> True,
LabelStyle -> Directive[Black, 17]]
Show[VoltVs, VoltFim]
Error:NDSolve::nlnum: The function value {-0.00174035,-1. (1.68378*10^-10-1.66057*10^-17 Rl[2]),0.,0.,0.,0.,0.,0.,0.,0.,<<12>>} is not a list of numbers with dimensions {22} at {t,i[1][t],i[2][t],i[3][t],i[4][t],i[5][t],i[6][t],i[7][t],i[8][t],i[9][t],<<17>>} = {0.0000828415,-1.0813*10^-7,-4.64959*10^-15,0.,0.,0.,0.,0.,0.,0.,<<17>>}.
