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Department of Electrical and
Computer Engineering
ECSE 352 Electromagnetic Waves and Optics
4.4 Wave equations in parallel plate
waveguides
References: Section 14.4
@AGK
4.41
Learning outcomes
After taking this class you should be able to:
• Explain how to find the field solutions for a
general waveguide configuration
elate the cut
ff frequency to the field solutions
•
Relate the cutoff frequency to the field solutions
• Sketch the E and H fields for TE and TM modes in
planar waveguides
• Calculate the impedance for TE and TM modes
• Explain what is meant by a mode
ECSE 352 4.42
Parallel plate waveguides
perfectly reflecting surface
x
d
λ
k
k
x
k
z
κ
m
θ
m
RE
•
roject 
ctor onto z and x axes
z
222
kk
+
β
m
=k
z
VIEW
Project
k
vector onto z and x axes
•D
e
f
i
n
e
zx
kkk
=+
cos
mx
m
κθ
==
22
mm
k
=−
lectric field:
sin
mz
m
βθ
Phase constant
n
m
j
z
E
e
π
−
⎛⎞
⎟
ECSE 352 4.43
•
Electric field:
0
sin
y
EE
d
=
⎜⎟
⎝⎠
Cut
Cutoff frequency and wavelength
off frequency and wavelength
• Cutoff frequency:
cm
mc
nd
ω
=
2
1
cm
m
n
c
– Phase constant is only real for
ω>ω
c
•
Cutoff wavelength:
–
hase constant is only real for
<λ
2
nd
m
λ
=
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−
=
cm
m
n
1
2
Phase constant is only real for
λ<λ
c
d
z
−
⎞
TE mode:
ECSE 352 4.44
m=1
m=2
m=3
2
m
d
=
m
d
=
0
sin
m
jz
y
e
d
=
3
/
2
d
m
=
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View Full DocumentGeneral field solution
• We derived the equation for the Efield for a TE
mode in a parallel plate waveguide by considering
wave interference
•
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 Spring '08
 Davis

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