Frequency dependence measurement of complex permittivity for C-, A- and R-plane sapphire substrates from 30 to 50GHz band

A sapphire is expected as a good substrate for a low loss millimeter wave circuit such as a superconductor filter, because a good YBCO film can be manufactured on the substrate. In order to design millimeter wave circuits, it is necessary to obtain the accurate complex permittivity. However, there are few reports for sapphire substrates in millimeter wave region. In this paper, the measured complex permittivity values of C-, A-, and R-plane sapphire substrates are presented using the cutoff circular waveguide method in the frequency range of 30–50GHz. Moreover the measured results are discussed with the crystal structure.