Dielectric frequency-temperature compensation of high quality sapphire dielectric resonators

We show that it is possible to obtain frequency-temperature compensation in a sapphire dielectric resonator using a dielectric with opposite permittivity-temperature coefficient. The compensating dielectric should have low loss and a temperature-frequency dependence of opposite sign to sapphire. For example, monocrystalline strontium titanate and rutile fulfil these requirements. We show that by using this technique it is feasible to construct a microwave resonator with zero frequency-temperature dependence and a curvature of order 0.1 ppm/K ². From the ratio of filling factors and the dielectric loss tangent we calculated that Q-factors of order 10⁷ at 80 K and 10⁵ near room temperature are possible, with good quality compensation materials. With a sapphire-SrTiO₃ composite structure we obtained frequency-temperature compensation with a Q-factor of about 50,000 below 150 K. The low Q-factor achieved was due to the losses in the compensating dielectric. Another problem was due to the excess spurious modes that exist due to the high permittivity of the compensating dielectric. This can cause the temperature dependence to markedly degrade the curvature of compensation. Ways of countering this problem are discussed