In[1]:= ClearAll["Global '*"];
NN = 11;
tmax = 6.0;
fN = 1.0;
Rs = 50.0;
Rescimpair = Table[Rc[k] = 0.0, {k, 1, NN, 2}];
Rescpair = Table[Rc[k] = 0.0, {k, 2, NN, 2}];
Rc[NN] = 1100.0;
Reslimpair = Table[Rl[k] = 0.0, {k, 1, NN, 2}];
Reslpair = Table[Rl[k] = 0.0, {k, 2, 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}, {t, 0., tmax}];
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}, {t, 0., tmax}];
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, 1, 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]
Out[13]= {1.7, 300., 1.7, 1.7}
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Out[23]= (1. + 1.42857 V[k][t])^1.08
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AspectRatio->0.6180339887498948,
Axes->{True, True},
AxesLabel->{None, None},
AxesOrigin->{0, 0},
DisplayFunction->Identity,
Frame->{{True, True}, {True, True}},
FrameLabel->{{
FormBox["\"Voltage(kV)\"", TraditionalForm], None}, {
FormBox["\"Time(ns)\"", TraditionalForm], None}},
FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
GridLines->{Automatic, Automatic},
GridLinesStyle->Directive[
GrayLevel[0.5, 0.4]],
LabelStyle->Directive[
GrayLevel[0], 17],
Method->{"OptimizePlotMarkers" -> True, "OptimizePlotMarkers" -> True,
"CoordinatesToolOptions" -> {"DisplayFunction" -> ({
Identity[
Part[#, 1]],
Identity[
Part[#, 2]]}& ), "CopiedValueFunction" -> ({
Identity[
Part[#, 1]],
Identity[
Part[#, 2]]}& )}},
PlotRange->{{0, 6.}, {-10., 0}},
PlotRangeClipping->True,
PlotRangePadding->{{
Scaled[0.02],
Scaled[0.02]}, {
Scaled[0.05],
Scaled[0.02]}},
Ticks->{Automatic, Automatic}]\)
