Cavity Resonator - In One Page

A cavity resonator is an enclosed volume with dimensions similar or larger than the operating wavelength of the electromagnetic wave. The enclosure surface is typically a highly conducting material and the enclosed volume is either free-space (air) or dielectric medium. The enclosure material, geometry and dielectric determine the resonator characteristics.

Shape

The cavity may or may not have a regular shape. Ordered structures are easy to analyze, design and manufacture. Rectangular, cylindrical and spherical cavities are examples of regular structures where distribution of electric and magnetic fields follow textbook patterns.

Analysis

Cavity resonance frequency is obtained as a solution to Maxwell’s equations by applying boundary conditions at the walls. The solution yields multiple modes similar to waveguides: different field patterns and resonant frequencies that are a function of cavity dimensions and dielectric property. The equations are solved in a coordinate system appropriate to the cavity geometry and axis of symmetry; it ‘simplifies’ the equations, solution derivation, result interpretation and analysis. [Caution: The equations become elegant. The mathematics is quite involved!] The symmetrical structure of the cavity may create degenerate modes that leads to identical resonant frequency for different modes.

Resonant Frequency

The resonant frequency of a rectangular cavity is based on its three orthogonal dimensions, that of a circular cavity on its length and radius dimensions, and of a spherical cavity on its radial dimension. The regular geometry ensures polarization stability in rectangular cavity, but circular and spherical cavities are susceptible to polarization drift and need intervention in the form of surface irregularities. Regular structures also generate harmonics and degenerate modes that interfere with the target resonant frequency; practical designs may have odd geometry to reduce and eliminate unwanted frequencies and modes.

Losses

An ideal cavity is lossless and will theoretically sustain oscillations for infinitely long time. A real cavity exhibits damped oscillations due to conduction loss at walls, coupling loss, radiation loss through apertures, and dielectric loss within the volume; the electromagnetic power loss needs to be replenished to sustain resonance in the cavity.

Excitation

A cavity resonator is excited with a small wire or loop inserted into its volume through an aperture in the cavity wall. The excitation probe and coupling mechanisms need to be factored during design and analysis. Frequency tuning elements may be required to compensate for aberrations introduced by feed-probes and coupling ports.

Applications

Resonant cavity applications include filters, oscillators, transmitters, particle accelerators, and so on.