
67Fundamentals of Wave Propagation
Power input =
V
R
V
x
R
V
R
V Rl
Z
X
X
S
X
S
S
S
2
2
2 2
0
2
2
= = =sin
2
β
(2.94a)
Thus,
R
Z
Rl
x
X
=
2
0
2
2
sin β
(2.94b)
Thus input resistance varies as square of sine of angular distance from the
SC end.
2.29.2 Quarter-Wave Section as Impedance Transformer
Equation 2.81b for the particular case of a quarter-wave section, that is, for
ℓ =
λ
/4, thus
β
ℓ =
π
/2, cos
β
ℓ = 0, and sin
β
ℓ = 1, yields the relation Z Z Z
S R
=
0
2
,
which spells matching or impedance inversion, that is, if Z
R
= R + jX
L
,
Z
S
= R − jX
C
. If Z
S
and Z
R
are taken to be the normalised values (z
S
= Z
S
/Z
0
andz
R
= Z
R
/Z
0
) the equation Z Z
S R
= Z
0
2
transforms to Z
S
Z
R