An application of a mode dielectric resonator is described for precise measurements of complex permittivity and the thermal effects on permittivity for isotropic dielectric materials. The Rayleigh-Ritz technique was employed to find a rigorous relationship between permittivity, resonant frequency, and the dimensions of the resonant structure, with relative computational accuracy of less than . The influence of conductor loss and its temperature dependence was taken into account in the dielectric loss tangent evaluation. Complex permittivities of several materials, including cross-linked polystyrene, polytetrafluoroethylene, and alumina, were measured in the temperature range of 300-400 K. Absolute uncertainties of relative permittivity measurements were estimated to be smaller than 0.2%, limited mainly by uncertainty in the sample dimensions. For properly chosen sample dimensions, materials with dielectric loss tangents in the range of to can be measured using the mode dielectric resonator.

Whispering gallery modes were used for very accurate permittivity and dielectric loss measurements of ultralow loss isotropic and uniaxially anisotropic single crystals. Several materials including sapphire, YAG, quartz, and SrLaAlO4 were measured. The total absolute uncertainty in the real part of permittivity tensor components was estimated to be ±0.1%, limited principally by the uncertainty in sample dimensions. Imaginary parts of permittivities were measured with uncertainties of about 10%, limited by the accuracy of Q-factor measurements of whispering gallery modes. It has been observed that, for most crystals, dielectric losses can be approximated by a power function of absolute temperature only in limited temperature ranges. At temperatures between 4-50 K, losses are often affected by impurities, which are always present in real crystals.

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Two techniques are evaluated for the accurate measurement of the microwave permittivity of polycrystalline yttrium iron garnet (YIG) at frequencies between 5.5 and 12.5 GHz: split post dielectric resonator (SPDR) and ferrite disc resonator (Courtney). Both techniques separate YIG permittivity from that of YIG permeability by applying a magnetic induction bias to the YIG sample under test. The SPDR method needs no special sample preparation in the case of YIG substrates, whereas the Courtney method requires the grinding of rods from bulk YIG. The Courtney measurements of the YIG real permittivity are found to be higher on average than SPDR measurements. Agreement between the two techniques improves with increasing magnetic induction bias.