Measurements of Complex Permittivity at Millimeter-Wave Frequencies With an End-Loaded Cavity Resonator

Abstract

A novel cavity resonator method is proposed for measuring the complex permittivity of a dielectric plate in the millimeter-wave region. In this method, the dielectric plate is loaded at the end of the cavity resonator. The relative permittivity $\varepsilon'$ and loss tangent ${\rm tan}\delta$ are determined from measured resonant frequency and unloaded $Q$ of the ${\rm TE}_{011}$ mode. This structure prevents excessive lowering of the resonant frequency due to the placement of the dielectric plate sample in the cavity. The suppression of spurious modes and the design of the cavity resonator are discussed. The values of $\varepsilon'$ and ${\rm tan}\delta$ were measured in the millimeter-wave range for low-temperature co-fired ceramic (LTCC), Al $_{2}$O$_{3}$ , and sapphire plates. The temperature dependence of the complex permittivity of the LTCC plate was measured at 34 GHz. The measurement accuracies are estimated to be within 0.6% for $\varepsilon'$ , and within 10% for ${\rm tan} \delta$ of 10$^{-3}$ .