Microwave cavity

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Two microwave cavities (left) from 1955, each attached by waveguide to a reflex klystron (right) a vacuum tube used to generate microwaves. The cavities serve as resonators (tank circuits) to determine the frequency of the oscillators

A microwave cavity or radio frequency (RF) cavity is a special type of resonator, consisting of a closed (or largely closed) metal structure that confines electromagnetic fields in the microwave region of the spectrum. The structure is either hollow or filled with dielectric material. The microwaves bounce back and forth between the walls of the cavity. At the cavity's resonant frequencies they reinforce to form standing waves in the cavity. Therefore, the cavity functions similarly to an organ pipe or sound box in a musical instrument, oscillating preferentially at a series of frequencies, its resonant frequencies. Thus it can act as a bandpass filter, allowing microwaves of a particular frequency to pass while blocking microwaves at nearby frequencies.

A microwave cavity acts similarly to a resonant circuit with extremely low loss at its frequency of operation, resulting in quality factors (Q factors) up to the order of 106, compared to 102 for circuits made with separate inductors and capacitors at the same frequency. They are used in place of resonant circuits at microwave frequencies, since at these frequencies discrete resonant circuits cannot be built because the values of inductance and capacitance needed are too low. They are used in oscillators and transmitters to create microwave signals, and as filters to separate a signal at a given frequency from other signals, in equipment such as radar equipment, microwave relay stations, satellite communications, and microwave ovens.

RF cavities can also manipulate charged particles passing through them by application of acceleration voltage and are thus used in particle accelerators and microwave vacuum tubes such as klystrons and magnetrons.

Theory of operation

The inside of a cavity from a Russian military radar transmitter, with the cover removed. Parts:
(1) A setscrew trimmer capacitor used to adjust the frequency
(2) The top of the GS13-1 triode vacuum tube which generates the microwaves
(3) A wire coupling loop from which the output power is taken



Quality factor

The quality factor of a cavity can be decomposed into three parts, representing different power loss mechanisms.

  • , resulting from the power loss in the walls which have finite conductivity[clarification needed]






  • , resulting from the power loss in the lossy dielectric material filling the cavity.






  • , resulting from power loss through unclosed surfaces (holes) of the cavity geometry.







where k is the wavenumber, is the intrinsic impedance of the dielectric, is the surface resistivity of the cavity walls, and are relative permeability and permittivity respectively and is the loss tangent of the dielectric.

Cavity geometry

Rectangular cavity

Rectangular cavity

Resonance frequencies of a rectangular microwave cavity for any or resonant mode can be found by imposing boundary conditions on electromagnetic field expressions. This frequency is given by[1]






where is the wavenumber, with , , being the mode numbers and , , being the corresponding dimensions; c is the speed of light in vacuum; and and are relative permeability and permittivity of the cavity filling respectively.

Cylindrical cavity

Cylindrical cavity

The field solutions of a cylindrical cavity of length and radius follow from the solutions of a cylindrical waveguide with additional electric boundary conditions at the position of the enclosing plates. The resonance frequencies are different for TE and TM modes.

TM modes
TE modes

Here, denotes the -th zero of the -th Bessel function, and denotes the -th zero of the derivative of the -th Bessel function.

Comparison to LC circuits

LC circuit equivalent for microwave resonant cavity

















where V is the cavity volume, is the mode wavenumber and and are permittivity and permeability respectively.


Losses in LC resonant circuits

An absorption wavemeter. It consists of an adjustable cavity calibrated in frequency. When the resonant frequency of the cavity reaches the frequency of the applied microwaves it absorbs energy, causing a dip in the output power. Then the frequency can be read off the scale.




Losses in cavity resonators


Some satellite resonators are silver-plated and covered with a gold flash layer. The current then mostly flows in the high-conductivity silver layer, while the gold flash layer protects the silver layer from oxidizing.


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