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1
ECE604
Homework 12
Out:
Tuesday, April 12, 2005
Due:
Tuesday, April 19, 2005
Announcements:
•
Prof. Weiner will not
be available for office hours on Wednesday, April 13, 2005.
•
Final exam will be held Monday, May 2, 2005, 3:205:20pm, Room to be announced
Problems given by number are from the text by Ramo, Whinnery and Van Duzer (3
rd
edition,
1994).
1.
Consider the
m,n
TE
and
TM
modes of a metallic rectangular waveguide
()
m0
,
n0
≠≠
.
Show that for any specific values of m and n, the
m,n
TE
and
TM
modes are orthogonal (use same m,n for TE and TM mode).
More precisely show that
(
)
**
TM
(TE)
TE
(TM)
1
Pd
A
R
e
E
H
E
H
0
2
⎧⎫
⎡⎤
=×
+
×
=
∫
⎨⎬
⎢⎥
⎣⎦
⎩⎭
±±
Note:
It is sufficient to consider only the zcomponent of
P
 i.e., the component of
power along the waveguide direction.
2.
10.3d
Hint:
Review section 6.4 and note equivalence between
σ
and
′′
ωε
3.
10.4a
4.
10.4c
5.
In this problem we consider data transmission in two different metal waveguide
structures:
(I) the parallelplate waveguide and (II) the square waveguide.
Both
waveguides are taken to be airfilled and lossless.
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(a)
We wish to transmit information using a baseband transmission scheme.
Our data
rate is R (units of bits/second), and each bit has duration T = 1/R.
For each data bit
equal to ‘1’, we simply transmit a constant DC voltage during time T.
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