**Subject :**Microwave Engineering

## Semicircular cavity resonator

A semicircular-cavity resonator is shown in Figure. The wave function of the TE_{npq} mode in the semicircular resonator can be written

.....(1)

where n = 0, 1, 2, 3, .

p = 1, 2, 3,4, .

q = 1, 2, 3, 4, .

a = radius of the semicircular-cavity resonator

d = length of the resonator

**Figure : Semicircular cavity resonator
**

The wave function of the TM_{npq} mode in the semicircular-cavity resonator can be written

....(2)

where n = 1, 2, 3, 4, .

p = 1, 2, 3, 4, .

q = 0, 1, 2, 3, .

With the separation equations given in below

the equations of resonant frequency for TE and TM modes in a semicircular-cavity resonator are the same as in the circular-cavity resonator. They are repeated as follows:

......(3)

......(4)

However, the values of the subscripts n, p, and q differ from those for the circularcavity resonator. Also, it must be emphasized that the TElll mode is dominant if d > a and that the TMllo mode is dominant if d < a.