Software for calculating permittivity of resonators: HakCol & ErCalc

The HakCol and ErCale programmes are designed to quickly and accurately calculate the relative permittivity of microwave dielectric resonators. The HakCol programme assumes a simple Hakki-Coleman style parallel-plate dielectric-post geometry resonating in the Te ₀₁₁ mode, which is typically used to measure low-loss samples. The only inputs required are the cylindrical geometry of the resonator (diameter and thickness) and the resonant frequency. The ErCalc programme instead assumes a Te ₀₁₈ mode microwave shielded resonator in a cavity, in which case the required inputs also include the geometry of the test cavity and the dielectric constants of the surroundings. The latter technique is generally intended for very precise complex permittivity measurements of bulk low-loss cylindrical resonators. Some existing algorithms use a curve-fit to estimate the ratio of Bessel functions and modified Bessel functions in the isotropic resonator equation, leading to a small but measurable error. The chief advantage of the HakCol and ErCalc programmes is that all of the various Bessel functions are numerically calculated individually for an improved accuracy. The use of both programmes will be discussed, their algorithms analysed, and their outputs compared to alternative software currently available.