**Subject :**Microwave Engineering

## Circular Cavity Resonator

A circular-cavity resonator is a circular waveguide with two ends closed by a metal wall (see Figure). The wave function in the circular resonator should satisfy Maxwell's equations, subject to the same boundary conditions described for a rectangular-cavity resonator. It is merely necessary to choose the harmonic functions in z to satisfy the boundary conditions at the remaining two end walls. These can be achieved if

**Figure : Coordinates of circular resonator
**

........(1)

where n = 0, 1, 2, 3, is the number of the periodicity in the Φ direction

p = 1, 2, 3, 4, is the number of zeros of the field in the radial direction

q = 1, 2, 3, 4, is the number of half-waves in the axial direction

Jn = Bessell's function of the first kind

H_{oz}= amplitude of the magnetic field

and ,

....(2)

where,.

n = 0,1,2,3,

P = 1, 2, 3, 4, .

q = 0, 1, 2, 3, .

Eoz = amplitude of the electric field

The separation equations for TE and TM modes are given by :

....(3)

Substitution of k^{2} = ω^{2}με in equation (3), yields

It is interesting to note that the TM_{110} mode is dominant where 2a > d, and that the TE_{111} mode is dominant when d __>__ 2a.