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 1/3 Ta 2/3 )O 3 , 0.8 at.% Ni‐doped Ba(Zn 1/3 Ta 2/3 )O 3 , and Ba(Ni 1/3 Ta 2/3 )O 3 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 .