Short note: Microwave cavity resonators

A cavity resonator is a closed metallic enclosure (a section of waveguide shorted at both ends, or a circular/re-entrant cavity) that stores electromagnetic energy at certain resonant frequencies, like an LC tank circuit at microwave frequencies. Lumped L and C are unusable at microwave frequencies because of radiation and skin-effect losses, so cavities are used instead.

     +---------------------+
     |                     |  b
     |   standing wave     |
     +---------------------+
     <-------- d ---------->
   rectangular cavity a × b × d
   coupled by probe, loop or iris

Resonant frequency (rectangular cavity, TEmnp or TMmnp):

 f_r = (c/2) √((m/a)² + (n/b)² + (p/d)²)

The cavity length must be a whole number of half guide wavelengths: d = p·λg/2. For a circular cavity (TE011, TM010) the resonant frequency depends on the Bessel roots. Example: an a = 2.286 cm, b = 1.016 cm, d = 2 cm cavity in TE101 resonates at (3×10⁸/2)√((1/0.02286)² + (1/0.02)²) ≈ 9.96 GHz.

Quality factor:

• Q = 2π × (energy stored)/(energy lost per cycle) = ω0·W/P
• Unloaded Q (wall loss only) is very high, 10³–10⁴ (higher than lumped circuits); loaded Q includes the external circuit: 1/QL = 1/Q0 + 1/Qext.

Types: rectangular, cylindrical (circular), re-entrant (used in klystrons), coaxial and dielectric resonators.

Coupling methods: probe (electric), loop (magnetic) and aperture/iris coupling.

Tuning: a plunger changes d, or a screw/dielectric rod perturbs the field.

Applications: klystron and magnetron tuned circuits, cavity wavemeters (frequency measurement), filters, stable oscillators, and measurement of dielectric constant (cavity perturbation).