Smith Chart

Author

Eric W. Weisstein
August 27, 2026

This notebook downloaded from https://mathworld.wolfram.com/notebooks/ControlTheory/SmithChart.nb.

For more information, see Eric's MathWorld entry https://mathworld.wolfram.com/SmithChart.html.

©2026 Wolfram Research, Inc. except for portions noted otherwise

Figure

Module[{resistanceColor,reactanceColor,neutralColor,resistanceLevels,reactanceLevels,resistanceLabels,reactanceLabels,gamma,reactanceCurve},resistanceColor=RGBColor[0.08,0.45,0.78];reactanceColor=RGBColor[0.9,0.38,0.12];neutralColor=LightDarkSwitched[Black,White];resistanceLevels={(1/5),(1/2),1,2,5};reactanceLevels={-5,-2,-1,-(1/2),-(1/5),(1/5),(1/2),1,2,5};resistanceLabels={(1/5),(1/2),2,5};reactanceLabels={-2,-1,-(1/2),(1/2),1,2};gamma[z_]:=ReIm[((z-1)/(z+1))];reactanceCurve[x_]:=Append[gamma/@(Subdivide[0.,40.,320]+I x),{1.,0.}];Graphics[{Directive[resistanceColor],(Circle[{((#1)/(1+#1)),0},(1/(1+#1))]&)/@resistanceLevels,Directive[reactanceColor],(Line[reactanceCurve[#1]]&)/@reactanceLevels,Directive[neutralColor,Thickness[Small]],Circle[],Line[{{-1,0},{1,0}}],Table[Inset[Style[Row[{Style["r",Italic]," == ",r}],11,resistanceColor],{((r-1)/(r+1)),0.045},{Center,Bottom}],{r,resistanceLabels}],Table[Inset[Style[Row[{Style["x",Italic]," == ",If[x>0,"+",""],x}],11,reactanceColor],0.86 gamma[I x]],{x,reactanceLabels}],Directive[neutralColor,PointSize[0.018]],Point[{{-1,0},{0,0},{1,0}}],Inset[Style["short",neutralColor],{-0.88,-0.12}],Inset[Style["matched",neutralColor],{0,-0.12}],Inset[Style["open",neutralColor],{0.88,-0.12}]},BaseStyle->{FontFamily->"Times",12}]
]