UNIVERSITY OF CALIFORNIA
Santa Barbara
Department of Electrical and Computer Engineering
Problem Set No. 8
Issued:
November 21, 2007
Fall 2007
Due:
November 28, 2007
ECE 201A
1.
Metal
Air
Dielectric
Metal
The Microstrip transmission line shown in the Figure above is widely used in Monolithic
Microwave Integrated Circuits (MMICs).
The purpose of this problem is to show that such
structures cannot support TEM waves.
The problem also identifies the conditions for a TEM
mode to exist.
(a)
Prove that the electric field obeys the differential equation in a uniform dielectric medium.
∇
+
=
2
2
0
0
G
G
E
E
ω μ ε
(b)
In an axially uniform structure traveling waves that have the
z
dependence as
exp(
)
−
j z
β
exist.
Then the previous equation reduces to
∇
+
−
=
T
E
E
2
2
0
2
0
G
G
(
)
ω μ ε
β
where
∇
T
is the transverse component of the
∇
operator.
A TEM wave has no longitudinal
components of
E
and
H,
no field components in the direction of propagation.
Thus
E
and
H
are
purely transverse i.e.,
E
=
E
T
and
H
=
H
T
(c)
Prove that
∇
×
=
T
T
E
G
0
Therefore
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 Spring '09
 O
 uniform dielectric medium, TEM mode, eigenvalue equations

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