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Wang Juan Lin YihuaDec 25th,2010
Discussion of resonant cavity and the
simulation by software COMSOL
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Content• 1.Theoretical deduction of TM wave
function
• 2.Practical simulation of TE & TM wave in resonant cavity by COMSOL
• 3.Some interesting questions in the process of simulation
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I. Theoretical deduction
0 0 02 2cos sin cos sing gik z ik zg g
xc c
k km m n m m nE i E x y e i E x y e
a k a b a k a b
’
0 0 02 2sin cos sin cosg gik z ik zg g
yc c
k kn m n n m nE i E x y e i E x y e
b k a b b k a b
’
0 0 0sin sin sin sing gik z ik z
z
m n m nE E x y e E x y e
a b a b
’
00 0 02
sin cos sin cosg gik z ik z
xc
kn m n m nB i E x y e E x y e
b ck a b a b
’
00 0 02
cos sin cos sing gik z ik z
yc
km m n m nB i E x y e E x y e
a ck a b a b
’
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00 0zxz a
E
According to:
0 02cos sin 0g gik z ik zg
c
km m ni x y E e E ea k a b
’
0 0E E ’
02cos sin 0g gik d ik dg
c
km m ni x y E e ea k a b
, ( 0 1,2,3 )g g
pk d p k p
d
, ……
Z=0:
Z=d:
I. Theoretical deduction
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022 cos sin sing iwt
xc
k m m n pE E x y z e
k a a b d
022 sin cos sing iwt
yc
k n m n pE E x y z e
k b a b d
02 sin sin cos iwtz
m n pE E x y z e
a b d
002
2 sin cos cos iwtx
c
k n m n pB i E x y z e
ck b a b d
002
2 cos sin cos iwty
c
k m m n nB i E x y z e
ck a a b d
0zB
I. Theoretical deduction
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I. Theoretical deduction
Resonance frequency:
In a cubical resonant cavity:
Define:Discussion of degree of degeneracy:
1. , the degree of degeneracy is 1;
2. , the degree of
degeneracy is 3;
3. , the
degree of degeneracy is 6;
2 2 2
2 2 2
m n pc
a b d
2 2 2
2 2 22 /
m n p
a b d
2 2 2cm n p
a
2 2 22 /a m n p
2 2 2m n p X
2 2 2
3
Xm n p
2 2 2,m n A p B 2 ,A B X A B
2 2 2, ,m A n B p C ,A B C A B C X
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• TE (0,1,1) Mode:
II. Practical simulation 8
93 10 110
22 0.3
cHz
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002
E 2 B sin sin iwtx
c
cky z e
k a a a
Section: z=0a=0, b=1
Section: y=0a=0, c=1
Section: x=0b=1, c=1
II. Practical simulation
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Section: y=0a=0, c=1
g02
2 B sin cos iwty
c
kB i y z e
k a a a
II. Practical simulation
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• TE (2,1,1) Mode:
Section: y=0a=2, b=1
893 10
1.5 102
0.33
cHz
II. Practical simulation
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II. Practical simulation
• Calculating the power flow:
x0 0
i1 1
B= Re(E ) 0 0
0 Re( ) Re( )
p
y z
j k
S E
B B
������������������������������������������
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• The power flow in TE (2,1,1) Mode:
II. Practical simulation
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Problem 1
1. When simulating electrical density in COMSOL:
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The power density in the pipe is 2~3 ranges larger than that in the resonant cavity:
Key point
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Solution
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There exists a “power hole” in the process of simulating electrical density:
Problem 2
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Key point
The sub sources interfered the inner distribution of electric density!Then the challenge comes:
1. How to smooth the edges to avoid the occurrence of sub sources?
2.How to “break” the symmetry of the wave source to avoid the same phase position?
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Solution
1. How to smooth the edges to avoid the occurrence of sub sources?
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Solution
2.How to “break” the symmetry of the wave source to avoid the same phase position?
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• The result:
Solution
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• Having known how to take advantage of simulation software to test the theoretical result;
• Try to think hard to find ways to eliminate all the problems when putting the model into practice!
Conclusion
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Thanks!