The dual-mode frequency-locked technique for the characterisation of the temperature coefficient of permittivity of ainsotropic materials

In this work we present a new method for obtaining accurate characterization of the temperature coefficient of permittivity (TCP) of an anisotropic crystal, which we call the dual-mode frequency-locked technique. The technique requires precise simultaneous frequency measurements of two orthogonally polarized modes as a function of temperature. This was achieved by configuring a sapphire resonator as a pound-locked dual-mode oscillator and measuring the frequencies with a frequency counter, while simultaneously recording the temperature with a platinum thermometer. From the two data files of frequency versus temperature, and knowledge of the electric and dimensional filling factors (obtained from finite element analysis), it was possible to calculate the integrals of the TCP without resorting to polynomial fits. This resulted in a precise model of the components of the TCP between 50 and 77 K for sapphire. The model is accurate enough to predict, within a few kelvin, the frequency turnover temperatures of the difference frequency of a dual-mode oscillator.