
102 Microwave Engineering
3.3.7.3 Variation of Z
z
,
υ
and
λ
with Frequency
The variation of characteristic impedances (for TM and TE waves) with fre-
quency is given by Equations 3.26 and 3.28. The other parameters, namely,
operating frequency (f), cutoff frequency (f
c
), velocity (
υ
), velocity at cutoff
(
υ
c
), operating wavelength (
λ
) and cutoff wavelength (
λ
c
) are related and will
be as discussed below. These relations are obtained in view of Equations 3.22
and the general relations, for example,
υ
= f
λ
,
υ
=
ω
/
β
and
λ
= 2
π
/
β
obtained
in Chapter 2.
υ
= f
λ
=
ω
/
β
=
υ
0
/√{1 − (
ω
c
/
ω
)
2
} =
υ
0
/√{1 − (f
c
/f)
2
} (3.29a)
λ
=
λ
g
= 2
π
/
β
= 1/[f√(
μ
/
ε
)√{1 −