Fundamental mechanisms responsible for the temperature coefficient of resonant frequency in microwave dielectric ceramics

The temperature coefficient of resonant frequency (τf) of a microwave resonator is determined by three materials parameters according to the following equation: τf=−(½ τε + ½ τμ + αL), where αL, τε, and τμ are defined as the linear temperature coefficients of the lattice constant, dielectric constant, and magnetic permeability, respectively. We have experimentally determined each of these parameters for Ba(Zn1/3Ta2/3)O3, 0.8 at.% Ni-doped Ba(Zn1/3Ta2/3)O3, and Ba(Ni1/3Ta2/3)O3 ceramics. These results, in combination with density functional theory calculations, have allowed us to develop a much improved understanding of the fundamental physical mechanisms responsible for the temperature coefficient of resonant frequency, τf