wang juan lin yihua dec 25th,2010 discussion of resonant cavity and the simulation by software...
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Wang Juan Lin YihuaDec 25th,2010
Discussion of resonant cavity and the
simulation by software COMSOL
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
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
’
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
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
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
• TE (0,1,1) Mode:
II. Practical simulation 8
93 10 110
22 0.3
cHz
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
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
• TE (2,1,1) Mode:
Section: y=0a=2, b=1
893 10
1.5 102
0.33
cHz
II. Practical simulation
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
������������������������������������������
• The power flow in TE (2,1,1) Mode:
II. Practical simulation
Problem 1
1. When simulating electrical density in COMSOL:
The power density in the pipe is 2~3 ranges larger than that in the resonant cavity:
Key point
Solution
There exists a “power hole” in the process of simulating electrical density:
Problem 2
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?
Solution
1. How to smooth the edges to avoid the occurrence of sub sources?
Solution
2.How to “break” the symmetry of the wave source to avoid the same phase position?
• The result:
Solution
• 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
Thanks!
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