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

The temperature coefficient of resonant frequency (τ_f) of a microwave resonator is determined by three materials parameters according to the following equation: τ_f=−(½ τ_ε + ½ τ_μ + α_L), where α_L, τ_ε, and τ_μ 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(Zn_1/3Ta_2/3)O₃, 0.8 at.% Ni-doped Ba(Zn_1/3Ta_2/3)O₃, and Ba(Ni_1/3Ta_2/3)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, τ_f.