Digital Signal Processing Reference
In-Depth Information
Region A
Region B
x
Incident wave
z
y
Transmitted wave
Reflected wave
Figure 2-25
Incident electromagnetic wave propagating in dielectric region
A
and
impinging on dielectric region
B
, showing that a portion of the wave is reflected back in
the
−
z
-direction and a portion is transmitted in the
+
z
-direction.
2.7.2 Plane Wave Incident on a Lossless Dielectric
In Section 2.7.1 we considered the special case where a propagating electromag-
netic plane wave was incident on a plane boundary where the second medium
was a perfect conductor. Now we consider the more general case where the sec-
ond medium is a lossless dielectric. When a plane wave impinges on an area
with a different dielectric, a portion of the wave is reflected and a portion of the
wave in transmitted into the new medium, where it continues to propagate, as
shown in Figure 2-25.
If we assume that the incident fields are represented by phasors, we can sep-
arate the total plane wave into three parts:
1. Incident wave:
E
i
(z)
=
a
x
E
i
e
−
jβ
A
z
1
H
i
(z)
=
a
y
η
A
E
i
e
−
jβ
A
z
2. Reflected wave:
E
r
(z)
=
a
x
E
r
e
+
jβ
A
z
H
r
(z)
=−
a
y
1
η
A
E
r
e
+
jβ
A
z
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