Analytical Design of Phase Variation-Based Dielectric Constant Sensors

A phase variation sensor is designed in this paper for dielectric constant measurements of solid dielectrics. The sensor is designed using a coplanar waveguide (CPW) transmission line terminated with a semi-lumped LC resonator. The inductance (L) of the resonator is made of a thin meandered wire, whereas the capacitance is realized as the edge capacitance between a rectangular patch and ground metallization. By placing dielectric slabs with different permittivities on top of capacitive patch, phase of the reflection coefficient $(S_{11})$ is modified, from which the dielectric constant of the material-under-test (MUT) is identified. A circuit-based analytical design procedure is developed for the sensor to optimize the sensing performance for an arbitrary operation frequency and dielectric constant range of the material-under-test (MUT). The design procedure is validated through EM and circuit model simulation as well as the measurement of a fabricated sensor prototype.