A novel formula for the quality factor calculation for the multiphase microwave dielectric ceramic mixtures

Microwave dielectric ceramics are pillar materials in the microwave applications, for example, resonators. However, because most ceramics possess non-zero temperature coefficients, two or more ceramics, with temperature coefficient of opposite signs, are always mixed as a multiple phase system to obtain a zero temperature coefficient ceramic. While the dielectric constant can be calculated by the Maxwell-Wagner based formula, the quality factor (Q) is usually hard to be precisely calculated by the conventional method. In this paper, basing on the classical dispersion theory, we derive a new formula for the Q calculation for the ceramic mixtures. The deviation between the calculated and reported Q, of several typical ceramic systems, is around ±5%, for the example of two phases ceramic mixtures.