Cavity Resonator

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References

* De Broglie, L. V. Elektromagnitnye volny v volnovodakh i polykh rezonatorakh. Moscow, 1948. (Translated from French.)

* Vainshtein, L. A. Elektromagnitnye volny. Moscow, 1957………….(1)

* http://www.daenotes.com/electronics/microwave-radar/cavity-resonator#axzz28frY00SL…..……(2)

* http://www.dbdcom.co.uk/catalogue/filters/addinfo_cavity_resonators....(3)

Cavity resonators

What is the Cavity Resonator:
(1) A space totally enclosed by a metallic conductor and excited in such a way that it becomes a source of electromagnetic oscillations. Also known as cavity; microwave cavity; microwave resonance cavity; resonant cavity; resonant chamber; resonant element; rhumbatron; tuned cavity; waveguide resonator. an oscillatory system that operates at superhigh frequencies; it is the analog of an oscillatory circuit.

The cavity resonator has the form of a volume filled with a dielectric—air, in most cases. The volume is bounded by a conducting surface or by a space having differing electrical or magnetic properties. Hollow cavity resonators—cavities enclosed by metal walls—are most widely used. Generally speaking, the boundary surface of a cavity resonator can have an arbitrary shape. In practice, however, only a few very simple shapes are used because such shapes simplify the configuration of the electromagnetic field and the design and manufacture of resonators. These shapes include right circular cylinders, rectangular parallelepipeds, toroids, and spheres. It is convenient to regard some types of cavity resonators as sections of hollow or dielectric wave guides limited by two parallel planes.

The solution of the problem of the natural (or normal) modes of oscillation of the electromagnetic field in a cavity resonator reduces to the solution of Maxwell’s equations with appropriate boundary conditions. The process of storing electromagnetic energy in a cavity resonator can be clarified by the following example: if a plane wave is in some way excited between two parallel reflecting planes such that the wave propagation is perpendicular to the planes, then when the wave arrives at one of the planes, it will be totally reflected. Multiple reflection from the two planes produces waves that propagate in opposite directions and interfere with each other. If the distance between the planes is L = nλ/2, where λ is the wavelength and n is an integer, then the interference of the waves will produce a standing wave (Figure 1); the amplitude of this wave will increase rapidly if multiple reflections are present. Electromagnetic energy will be stored in the space between the planes. This effect is similar to the resonance effect in an oscillatory circuit.

Figure 1. Formation of standing wave in space between two parallel planes as a result of interference between direct wave and reflected wave

Normal oscillations can exist in a cavity resonator for an infinitely long time if there are no energy losses. However, in practice, energy losses in a cavity resonator are unavoidable. The alternating magnetic field induces electric currents on the inside walls of the resonator, which heat the walls and thus cause energy losses (conduction losses). Moreover, if there are apertures in the walls of the cavity and if these apertures intersect the lines of current, then an electromagnetic field will be generated outside the cavity, which causes energy losses by radiation. In addition, there are energy losses within the dielectric and losses caused by coupling with external circuits. The ratio of energy that is stored in a cavity resonator to the total losses in the resonator taken over one oscillation is called the figure of merit, or quality factor, or Q, of the cavity resonator. The higher the figure of merit, the better the quality of the resonator.

By analogy with wave guides, the oscillations that occur in a cavity resonator are classified in groups. In this classification, the grouping depends on...
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