On parallel resonant circuit ...

Quit[]

Parallel Resonant Circuit (function of delta)

ZOverZ0Parallel[beta_,Q0_,delta_]:=(beta/(1 + I Q0 delta))

Max value of the impedance = beta/Sqrt[2]

Manipulate[GraphicsGrid[{{Plot[Abs@ZOverZ0Parallel[beta,Q0,delta],{delta,-0.01,0.01},PlotRange-> {Automatic,{0,2}}],Plot[Arg@ZOverZ0Parallel[beta,Q0,delta],{delta,-0.001,0.001},PlotRange-> {Automatic,Automatic}]}}],{{beta,0.5},0,3},{{Q0,6000},2000, 8000}]

S11FromParallel[beta_,Q0_,delta_]:=((ZOverZ0Parallel[beta,Q0,delta] -1)/(ZOverZ0Parallel[beta,Q0,delta] +1))

Manipulate[Show[ParametricPlot[{Re@S11FromParallel[beta,Q0,delta],Im@S11FromParallel[beta,Q0,delta]},{delta,-0.01,0.01},Axes-> None,PlotStyle->{RGBColor[0,1,0]}],SChart,PlotRange->{Automatic,Automatic}],{{beta,0.5},0,5},{{Q0,6000},4000, 8000}]

Smith Chart Frame

SmithR[r_, t_] := { (Cos[t] + r)/(1 + r), Sin[t]/(1 + r) }

(* Parametrize the reactive x=X/Zo contours *)
SmithX[x_, t_] := { Cos[t]/x +1, (Sin[t] + 1)/x }
LineThichkness=0.005;
unitcircle = PolarPlot[1, {phi, 0, 2Pi}, 
		PlotStyle->{Thickness[LineThichkness]}, 		DisplayFunction->Identity];
	r1 = ParametricPlot[Evaluate[SmithR[1/2, t]], {t, 0, 2Pi},
		PlotStyle->{Thickness[LineThichkness]}, PlotLabel -> "R = 0.5",
		DisplayFunction->Identity];
	r2 = ParametricPlot[Evaluate[SmithR[1, t]], {t, 0, 2Pi},
		PlotStyle->{Thickness[LineThichkness]}, PlotLabel -> "R = 1.0",
		DisplayFunction->Identity];
	r3 = ParametricPlot[Evaluate[SmithR[2, t]], {t, 0, 2Pi},
		PlotStyle->{Thickness[LineThichkness]}, PlotLabel -> "R = 2.0",
		DisplayFunction->Identity];
	x1 = ParametricPlot[Evaluate[SmithX[2,t]], {t, 3Pi/2, 51Pi/64},
		PlotStyle->{Thickness[LineThichkness]},
		DisplayFunction->Identity];
	x2 = ParametricPlot[Evaluate[SmithX[1,t]], {t, 3Pi/2, Pi},
		PlotStyle->{Thickness[LineThichkness]},
		DisplayFunction->Identity];
	x3 = ParametricPlot[Evaluate[SmithX[1/2,t]], {t, 3Pi/2, 617Pi/512},
		PlotStyle->{Thickness[LineThichkness]},
		DisplayFunction->Identity];
	x4 = ParametricPlot[Evaluate[SmithX[-2,t]], {t, 13Pi/64, -Pi/2},
		PlotStyle->{Thickness[LineThichkness]},
		DisplayFunction->Identity];
	x5 = ParametricPlot[Evaluate[SmithX[-1,t]], {t, 0, -Pi/2},
		PlotStyle->{Thickness[LineThichkness]},
		DisplayFunction->Identity];
	x6 = ParametricPlot[Evaluate[SmithX[-1/2,t]], {t, -105Pi/512, -Pi/2},
		PlotStyle->{Thickness[LineThichkness]},
		DisplayFunction->Identity];

SChart=Show[unitcircle, r1, r2, r3, x1, x2, x3, x4, x5, x6,
		Graphics[{ Thickness[LineThichkness], Line[{ {-1,0}, {1,0} }] }],
		Axes->None,
		AspectRatio->Automatic,
		DisplayFunction->Identity];

Trasmission Line effect on the Parallel Circuit

ZOverZ0ParallelXX[beta_,Q0_,ratio_]:=(beta/(1 + I Q0 (ratio -1/ratio)))

S11FromParallelXX[beta_,Q0_,ratio_]:=((ZOverZ0ParallelXX[beta,Q0,ratio] -1)/(ZOverZ0ParallelXX[beta,Q0,ratio] +1))

TraslatedParallelZZ[AttenuationLengthOverLambda_,LineLengthOverLambda_,beta_,Q0_,ratio_]:=(ZOverZ0ParallelXX[beta,Q0,ratio]-I Tan[(ratio+I /(2 Pi AttenuationLengthOverLambda)) 2 Pi LineLengthOverLambda])/(1-I ZOverZ0ParallelXX[beta,Q0,ratio] Tan[(ratio+I /(2 Pi AttenuationLengthOverLambda)) 2 Pi LineLengthOverLambda])

S11FromParallelTraslated[AttenuationLengthOverLambda_,LineLengthOverLambda_,beta_,Q0_,ratio_]:=((TraslatedParallelZZ[AttenuationLengthOverLambda,LineLengthOverLambda,beta,Q0,ratio] -1)/(TraslatedParallelZZ[AttenuationLengthOverLambda,LineLengthOverLambda,beta,Q0,ratio] +1))

N[S11FromParallelTraslated[100,100,0.7,12000,1.1]];

Manipulate[GraphicsGrid[{{Plot[Abs@ZOverZ0ParallelXX[beta,Q0,ratio],{ratio,0.99,1.01},PlotStyle->{Thickness[0.01]},PlotRange-> {{0.99,1.01},{0,1.1 beta/Sqrt[2]}}],Plot[Arg@ZOverZ0ParallelXX[beta,Q0,ratio],{ratio,0.999,1.001},PlotStyle->{Thickness[0.01]},PlotRange-> {Automatic,Automatic}]}}],{{beta,0.5},0,3},{{Q0,6000},2000, 8000}]

Manipulate[GraphicsGrid[{{Plot[Abs@S11FromParallelTraslated[AttenuationLengthOverLambda,LineLengthOverLambda,beta,Q0,ratio],{ratio,0.999,1.001},PlotRange-> {Automatic,{0,1}},PlotStyle->{Thickness[0.015]}],Plot[Arg@S11FromParallelTraslated[AttenuationLengthOverLambda,LineLengthOverLambda,beta,Q0,ratio],{ratio,0.999,1.001},PlotStyle->{Thickness[0.015]},PlotRange-> {Automatic,Automatic}]}}],{{beta,0.5},0,3},{{Q0,6000},2000, 11000},{{AttenuationLengthOverLambda,10},1,300},{{LineLengthOverLambda,0.5},0,2}]

Manipulate[Show[ParametricPlot[{Re@S11FromParallelTraslated[AttenuationLengthOverLambda,LineLengthOverLambda,beta,Q0,ratio],Im@S11FromParallelTraslated[AttenuationLengthOverLambda,LineLengthOverLambda,beta,Q0,ratio]},{ratio,0.8,0.99},Axes-> None,PlotStyle->{RGBColor[0,0,1],Thickness[0.015]}],ParametricPlot[{Re@S11FromParallelTraslated[AttenuationLengthOverLambda,LineLengthOverLambda,beta,Q0,ratio],Im@S11FromParallelTraslated[AttenuationLengthOverLambda,LineLengthOverLambda,beta,Q0,ratio]},{ratio,0.99,1.01},Axes-> None,PlotStyle->{RGBColor[0,1,0],Thickness[0.015]}],ParametricPlot[{Re@S11FromParallelTraslated[AttenuationLengthOverLambda,LineLengthOverLambda,beta,Q0,ratio],Im@S11FromParallelTraslated[AttenuationLengthOverLambda,LineLengthOverLambda,beta,Q0,ratio]},{ratio,1.01,1.2},Axes-> None,PlotStyle->{RGBColor[1,0,0],Thickness[0.015]}],SChart,PlotRange->{Automatic,Automatic}],{{beta,0.7},0,2},{{Q0,6000},4000, 11000},{{AttenuationLengthOverLambda,10},1,300},{{LineLengthOverLambda,0.5},0,2}]