
205Smith Chart
the phasor Γ(d). As r and x are the normalised values giving z(d) (= r + jx), the
actual Z(d) can be obtained on multiplying z(d) by Z
0
.
6.8.2 Evaluation of Γ(d) and Z(d) for Given Z
R
, Z
0
and d
Let Z
R
= 25 + j100 Ω, Z
0
= 50 Ω and d = 0.18
λ
. In view of the relation Γ(d) = Γ
R
exp(−j2
β
d) = Γ
R
, the magnitude of the reection coefcient is constant along a
lossless transmission line terminated by a specied load. Thus, on a complex
plane, a circle with the centre at the origin and radius |Γ
R
| can represent all
possible reection coefcients found along the transmission line. Using this
constant |Γ
R
| circle on the Smith chart, the values ...