Semicircular cavity resonator
A semicircular-cavity resonator is shown in Figure. The wave function of the TEnpq mode in the semicircular resonator can be written
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 TMnpq mode in the semicircular-cavity resonator can be written
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:
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.