Nonlinear variation of resonant frequency with temperature and temperature-dependent τf in Al2O3–TiO2 microwave dielectric composites

The temperature coefficient of resonant frequency (τf) is a key parameter for microwave dielectric ceramics, and it is usually regarded as a temperature-independent constant over a wide temperature range. However, the present theoretical prediction shows that the resonant frequency (f0) first increases then decreases with temperature, and τf decreases monotonously in Al2O3–TiO2 composite with small τf, which fits the experimental data very well. The nonlinear variation of f0 with temperature and temperature-dependent τf are attributed to the temperature-sensitive permittivity (εr) and τf of the constituting phases and also dependent on the dielectric mixing rule that the composite obeys. Such temperature-dependent dielectric behaviors are predicted to be common in microwave dielectric composites with small τf, and the negligence of them probably conceals the real large variation of f0 with temperature and seriously misleads the practical applications. Therefore, it is strongly suggested to understand the real temperature dependence of f0 and τf in microwave dielectric composites by measuring f0 at more temperatures with a smaller interval, so that the central frequency shift can be correctly evaluated for the resonator units and devices where the microwave dielectric composites are utilized. Furthermore, the nonlinear variation of f0 with temperature and temperature dependence of τf are expected to be suppressed by microstructural engineering and adopting more suitable constituting phases.