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ECE 222B, Winter 2010
Homework Set 6, Due March 11th
1. Assume that you are given a dielectric covered ground plane as shown in
Figure 830 of Balanis. Assume that the height of the dielectric covering
is
h
, the dielectric permittivity is
²
d
, and the permeability
μ
is ther same
for both the dielectric and the vacuum regions. We wish to examine the
propagation properties of the ideal
TM
z
0
mode; that is, the mode with a
zerofrequency cutoﬀ and vector potential
A
z
(
y,z
) =
A
d
sin(
β
yd
y
)exp(
jβ
z
z
)
for
y < h
, and
A
z
(
y,z
) =
A
0
exp(

αy
)exp(
jβ
z
z
)
for
y > h
, and where
A
d
and
A
0
are constants.
(a) Since
β
yd
→
0 and
α
→
0 as
ω
→
0, use a small argument expansion
in frequency to demonstrate that
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