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To build the highest frequency stable microwave oscillators, high-Q sapphire dielectric resonators must have the temperature coefficient of permittivity annulled. This is achieved by fixing thin slabs of low loss crystalline rutile to the ends of the sapphire cylinder. Rigorous finite element analysis has been applied to this resonator. This has allowed optimization of the structure with respect to designability of the annulment temperature and the amount of spurious modes present.