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

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• 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!