Engineering Electromagnetics
BECE205L
Transmission Line Theory
Age of Telephones
Smith Chart
It is basically a
graphical indication of
the impedance of a
transmission line and
of the corresponding
reflection coefficient
as one moves along
the line.
We will first examine
how the Smith chart is
constructed and later
employ it in our
calculations
of
transmission
line
characteristics such as
Γin and Zin·
© Wikipedia
Real/Resistance Circles (Γr)
Imaginary/Reactance Circles (Γi)
Complex impedances (R + jX)
Smith chart
(Standard)
Impedance Mapping in Smith chart
𝑍𝐿 = 60 + 𝑗40
𝑍0 = 50
Step – 1: Calculate the normalized
load impedance
𝑍𝐿 60 + 𝑗40
𝑧𝐿 =
=
𝑍0
50
𝑧𝐿 = 1.2 + 𝑗0.8
r=1.2
Unit circle
𝑧𝐿 = 1.2 + 𝑗0.8
jx=j0.8
Input impedance for an
electrical length βl
Example-3
𝑍𝐿 60 + 𝑗40
𝑧𝐿 =
=
𝑍0
50
𝑧𝐿 = 1.2 + 𝑗0.8
r=1.2
jx=j0.8
Alternatively:
In Smith chart
Γ=z
56o
Radius of the smith chart
RSmith
Step-3: Find the guided wavelength and
find electrical length:
56o
120o
176o
2π λ 2π
β𝑙 =
=
= 120𝑜
λ 3
3
56 +120 = 176
SWR circles
Ex-1
Given:
Z0=70 Ω, s= 1.6 and θΓ=300o, l= 0.6 λ
Given:
Z0=70 Ω, s= 1.6 and θΓ=300o, l= 0.6 λ
In Smith chart
Γ=z
Γ × 𝑅𝑆𝑚𝑖𝑡ℎ
Radius of the smith chart
RSmith
Γ=z
Γ = 0.2307∠300𝑜
r=1.15
x=0.8