Determining the Quality Factor of Dielectric Ceramic Mixtures with Dielectric Constants in the Microwave Frequency Range

Microwave dielectric ceramic materials are extensively utilized in microwave applications because of their high dielectric constants and quality factors. These applications also require ceramics of zero temperature coefficients at the resonant frequency (τ (f)), which can be realized through mixing a ceramic that one is interested in with another ceramic with −τ (f), or by performing the ionic substitution. With the mixing/ionic substitution, it is indispensable to compute the quality factors precisely. Previous study indicates that the quality factor depends on the grain size, porosity, internal strain, structure, phase evolution, and conductivity etc. Here we derive a quality factor formula based on the definition, which works very well for multiphase composites, single phase solid solutions, and equivalent ionic substituted single phase materials. Our formula calculation and fits to the previous experimental results demonstrate that the quality factor of the ceramic mixtures strongly depend on the dielectric constants and the dielectric constant variation index. Our results suggest that the impacts from grain size, porosity, and internal strain etc. can be summarized to the dielectric constant or dielectric constant variation index, which is of great importance for future design of high performance microwave dielectric ceramics.