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03/04/2013 PHY 712 Spring 2013 -- Lecture 21 1
PHY 712 Electrodynamics11-11:50 AM MWF Olin 107
Plan for Lecture 22:
Continue reading Chap. 8
A. Examples of waveguides
B. TEM, TE, TM modes
C. Resonant cavities
03/04/2013 PHY 712 Spring 2013 -- Lecture 21 2
03/04/2013 PHY 712 Spring 2013 -- Lecture 21 3
Reminders: Topic choice for “computational project” due
Friday 3/8/2013 (via email or written on paper) Outstanding homework due before 3/13/2013
(when mid term grades are due) Exam 2 will be available after 3/13/2013 and is
due 3/25/3013
03/04/2013 PHY 712 Spring 2013 -- Lecture 21 4
03/04/2013 PHY 712 Spring 2013 -- Lecture 21 5
Boundary values for ideal conductor
k̂H0
At the boundary of an ideal conductor, the Eand H fields decay in the direction normal to the interface.
Waveguide terminology• TEM: transverse electric and magnetic (both E and H
fields are perpendicular to wave propagation direction)• TM: transverse magnetic (H field is perpendicular to
wave propagation direction)• TE: transverse electric (E field is perpendicular to wave
propagation direction)
tit
eet tii
,ˆ2
1,
,
:conductor theInside/ˆ
0/ˆ
rHkrE
HrH rkrk
03/04/2013 PHY 712 Spring 2013 -- Lecture 21 6
Wave guides
Coaxial cableTEM modes
Top view:
a
b
ez
00
for :mediuminsideequationssMaxwell'
BEBEBE
εiωi
ba
(following problem 8.2 in Jackson’s text)
Inside medium, e assumed to be real
03/04/2013 PHY 712 Spring 2013 -- Lecture 21 7
Electromagnetic waves in a coaxial cable -- continued
ˆcosˆsinˆˆsinˆcosˆ
ˆ
ˆ
for solution Example
0
0
yxφyxρ
φB
ρE
tiikz
tiikz
eaB
eaE
baTop view:
a
b
e
zBES ˆ22
1
:),(with mediumcablethin vector wiPoynting22
0*
e
e
aBavg
e
e
00
:Find
BE
k
03/04/2013 PHY 712 Spring 2013 -- Lecture 21 8
Electromagnetic waves in a coaxial cable -- continuedTop view:
a
b
e
abaB
ddavg
b
a
lnˆ
:materialcablein power averagedTime22
02
0 e
zS
03/04/2013 PHY 712 Spring 2013 -- Lecture 21 9
Analysis of rectangular waveguide
Boundary conditions at surface of waveguide:Etangential=0, Bnormal=0
z x
y
Cross section view b a
03/04/2013 PHY 712 Spring 2013 -- Lecture 21 10
Analysis of rectangular waveguide
z x
y
tiikz
zyx
tiikzzyx
eyxEyxEyxE
eyxByxByxB
zyxE
zyxB
ˆ,ˆ,ˆ,
ˆ,ˆ,ˆ,
2222
bn
amk e
03/04/2013 PHY 712 Spring 2013 -- Lecture 21 11
Solution for m=n=1
byn
axmamByxiE
byn
axmbnByxiE
byn
axmByxB
bn
amy
bn
amx
z
cossin/,
sincos/,
coscos,
220
220
0
yxBz ,
yxiEx , yxiEy ,
03/04/2013 PHY 712 Spring 2013 -- Lecture 21 12
Resonant cavity
z x
y
dzbyax
000
dpk
kzyxBkzyxBzyxBkzyxEkzyxEzyxE
ezyxEzyxEzyxE
ezyxBzyxBzyxB
iii
iii
tizyx
tizyx
cos,or sin,,,cos,or sin,,,:generalIn
ˆ,,ˆ,,ˆ,,
ˆ,,ˆ,,ˆ,,
zyxE
zyxB
03/04/2013 PHY 712 Spring 2013 -- Lecture 21 13
Resonant cavity
z x
y
dzbyax
000
2222
222
22
1dp
bn
am
bn
am
dpk
e
e
