prof. david r. jackson ece dept. spring 2014 notes 19 ece 6341 1
TRANSCRIPT
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Prof. David R. JacksonECE Dept.
Spring 2014
Notes 19
ECE 6341
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Cylindrical Surface Waves
TMz SW:
0
21 1
20
cos ( )cos( )
cos ( )
z n z
zz n
A n H k k z
A A n H k e
TMk k
2 2 2 21 1 0 0zk k k k k
dipole
y
x
r 1
0Source
z = 0
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Cylindrical Surface Waves (cont.)
TEz SW:
0
21 1
20
sin ( )sin( )
sin ( )
z n z
zz n
F n H k k z
F B n H k e
TEk k
2 2 2 21 1 0 0zk k k k k
dipole
y
x
r 1
0Source
z = 0
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Cylindrical Surface Waves (cont.)
0
21 0 1
20 0
( ) cos( )
( )
z z
zz
A H k k z
A A H k e
VED: TMz only
TMk k
2 21 1
2 20 0
zk k k
k k
dipole
y
x
r 1
0VED
z = 0
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Cylindrical Surface Waves (cont.)
0
21 0 1
20 0
( )sin( )
( )
z z
zz
F H k k z
F B H k e
TEk k
2 21 1
2 20 0
zk k k
k k
VMD: TEz only
dipole
y
x
r 1
0VMD
z = 0
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Cylindrical Surface Waves (cont.)
HED: TMz+TEz
TMz SW:
0
21 1 1
20 1
cos ( )cos( )
cos ( )
TMz z
zTMz
A H k k z
A A H k e
TEz SW:
0
21 1 1
20 1
sin ( )sin( )
sin ( )
TEz z
zTEz
F H k k z
F B H k e
1n
2 2 2 21 1 0 0zk k k k k
dipole
y
x
r 1
0HED
z = 0
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Cylindrical Surface Waves (cont.)
Consider a TMz surface wave that varies in a region as zjk ze
1
1
zz
z
z
Ajk
E jAH
k
0 TM zk
Z
21
1
z
z
AE
j z
AH
(Similarly for TEz)
0TE
z
Zk
Hence
Note: The characteristic impedance is independent of the azimuthal index n
and the radial distance .
(We could also examine E and H.)
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Cylindrical Surface Waves (cont.)
Hence the same TRE is found as in the case of a 1D SW, with
1
2 2 2 2zk k k
cyl 1Dxk k
instead of
1
2 2 2 2z xk k k
Hence
(Here x is the direction of propagation for a 1D SW.)