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smith chart basics

This page covers smith chart basics and rules for impedance matching using smith chart. It mentions equations from which smith chart is derived.

Following are two equations which help draw constant resistance circles and constant reactance circles.

smith chart basics,fig1

Superimposing circles as drawn by above two equations over the complex polar form of normalized impedance Z plane on the unit circle yields smith chart.

Normalized resistance circle r range, 0<= r< +Infinite
Normalized reactance circle x range, -Infinite< x < +Infinite

smith chart basics,fig2
As shown in the figure, upper part of the smith chart maps inductive components,lower part maps capacitive components. Moreover left side origin is at impedance (Z) of zero(short circuit) and right side origin is at impedance of infinite value(open circuit). One rotation on smith chart is half of lambda.

smith chart basics,fig3
Figure helps map L and C components on the smith chart for impedance matching and for other calculations. If one add series L component on Z-chart(Impedance chart), need to move clockwise to that much of value. If one add series C component on Y-chart(Admittance chart), need to move anti-clockwise.

Remember that rotating reflection coefficient chart in the Z-smith chart by 180 degree results in Y-smith chart.

If one add Shunt L on Y-chart, need to move anti-clockwise, If one add Shunt C on Y-chart, need to move clockwise.

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