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
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
Hoz= amplitude of the magnetic field
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 :
Substitution of k2 = ω2με in equation (3), yields
It is interesting to note that the TM110 mode is dominant where 2a > d, and that the TE111 mode is dominant when d > 2a.