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smithchart_Part1

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SmithChartPart1Sheet 1 of 13

Smith Chart Tutorial Part1 To begin with we start with the definition of VSWR, which is the ratio of the reflected voltage over the incident voltage. The Reflection coefficient Γ is simply the complex (ie has phase) version of VSWR:Define voltage standing wave ratio (VSWR)

Vmax V1 + V2 = Vmin V1 V2 Voltage reflection coefficient Γ - Complex

V1e+j. .l

β

V2e-j. .l

β

T.L

ZL

L
Γ = V2 e V = 2 e j 2 β .l + j .β .l V1 V1 e V2 V1
j . β .l

At the load Γ (l = 0) ; Γ =

but this may be complex number if there is an instantaneous phase change which we’ll call (φ) on reflection.

V2

V 2 V 2 j = e ..... (a) L = 0 V1 V1

Phase Diagram

V1 θ

Sheet 2 of 13

At L > 0 Γ(L) = Γ( 0 )e j .φ =

V2 V1

e j (φ 2 βl )

For a lossless line V1 & V2 do not vary with L ∴ Γ is constant =
smithchart_Part1
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