SmithChartSheet 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 =……
