Air-Filled Rectangular Cavity Resonator Calculator

This page provides an air-filled rectangular cavity resonator calculator. It’s part of a larger collection of converters and calculators.

The calculator determines resonant frequency, unloaded quality factor, and half-power bandwidth.

This particular calculator is specifically designed for cavity resonators operating in the TE 101 mode. Therefore, m = 1, n = 0, and p = 1. It’s assumed to be air-filled, which means 1/√(με) = 3 x 10¹⁰.

EXAMPLE:

• INPUTS:
  • b = 3 cm
  • a = 5 cm
  • h = 10 cm
  • conductivity = 6.17E7
• OUTPUTS:
  • Resonant frequency (GHz) = 3.35
  • Unloaded Quality factor = 15580.7
  • Half power bandwidth = 215.272 KHz

Rectangular Cavity Resonator Equation

As we know, electromagnetic (EM) waves in a waveguide propagate freely along the z-direction. However, when the waveguide is closed by perfectly conducting walls, this propagation in the z-direction is halted. The reflected waves from these walls create standing waves.

These standing waves form a pattern along the direction of propagation. The transverse electric (E) field becomes zero at the walls and also at half-wavelength points along the guide.

If we place another perfectly conducting transverse wall at any of these null points, the field configurations remain unchanged. This creates a cavity. This cavity will have a length in multiples of λ_g/2.

This cavity will exhibit resonant properties at specific, well-defined frequencies. If the waveguide is rectangular, the resulting cavity is called a rectangular cavity.

The following equation (or formula) is used in the air-filled rectangular cavity resonator calculator: