ECE604
Homework 10
Out:
Tuesday, April 13, 2004 (Session 25)
Due:
Tuesday, April 20 (Session 27)
[Students with tape delays:
due according to session number]
Problem numbers are from the text by Ramo, Whinnery and Van Duzer (3
P
rd
P
edition, 1994).
1.
8.7a
2)
8.7g
3)
8.8d
4)
Start with the gaussian function f(t) given by Eq. 8.16(13). Using this in Eq. 8.16(10),
show that the envleope broadens with z as given by Eq. 8.16(14).
Hint:
Use the
following Fourier transform identity:
(
)
(
)
1/ 2
2
j
t
2
exp
t
e
dt
exp
/ 4
− ω
π
⎛
⎞
−Γ
=
−ω
Γ
⎜
⎟
Γ
⎝
⎠
∫
5)
10.3d
Hint:
Review section 6.4 and note equivalence between
σ
and
′′
ωε
.
6)
10.4a
7)
A simple airfilled transmission line resonantor may be constructed by shorting both ends
of a transmission line, as pictured below left, for ideal (lossless) resonator.
The ideal resonator supports resonant modes such that m halfwavelengths fit within the
resonator, i.e.,
m
L
2
λ
=
, where m is a positive integer.
a)
What is the frequency of the m
th
resonance?
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 Spring '08
 Staff
 Electromagnet, Resonator, Baseband transmission, Acoustic resonance, Waveguide

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