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From Reflection Coefficient to LoadImpedance (Smith Chart)

• Reflection coefficient in phasor form

Ljir

L

L ejZZ

ZZ θ|| 0000

00 Γ=Γ+Γ=

+−

=Γ

The load reflectioncoefficient is identified inthe complex domain

0Γ

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Normalized impedance

ir

irinin j

j

d

djxrzZdZ

Γ−Γ−Γ+Γ+

=Γ−Γ+

=+==1

1

)(1

)(1/)( 0

irdjj jeed L Γ+Γ=Γ=Γ − βθ 2

0 ||)(

22

22

)1(

1

ir

irrΓ+Γ−

Γ−Γ−=

22)1(

2

ir

ixΓ+Γ−

Γ=

Real part of normalizedimpedance

Imaginary part ofnormalized impedance

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Inversion of complex reflection coefficient(constant normalized resistance)

222 )1

1()

1(

+=Γ+

+−Γ

rr

rir

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Inversion of complex reflection coefficient(constant normalized reactance)

222 )1

()1

()1(xxir =−Γ+−Γ

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Combined display: Smith Chart