Electromagnetic characterization of dielectric pills in the microwave frequency range by resonance methods

Piotr Czekała

supervisor: Bartłomiej Salski

In the proposed research we aim at constructing measurement equipment dedicated to characterization of dielectric samples, which in microwave frequency band have shape of small cylindrical discs (pills). Knowledge of the electromagnetic properties of these materials is of importance for industry and academia working on 5G technologies. The measurement set-up for characterization of these materials will be based on Fabry-Perot open resonator (FPOR), which offers high quality factor (`Q>10^5`), easy access to the cavity and allows measurements at many frequencies in range 20-50 GHz. Measured resonance frequency shift caused be placing sample with unknown permittivity (ε) inside the FPOR is subsequently compared with data based calculated using a mathematical model of FPOR and as a result of that comparation ε can be determined.

Proposed model divides resonator into three non-resonant sections (as shown in Figure 1) and describe each section by it’s scattering parameters. In case of mirrors scattering parameters may be computed using near-field scattering equations, while in case of sample mode matching technique has been used. Resonance frequencies of the structure may be found be searching for zeros of the characteristic equation:

`det(\bar{\bar{\I}}-\bar{\bar{\Gamma_M}}(f)\bar{\bar{\Gamma_R}}(f)) = 0`

Where `f` is frequency, `I` unit matrix, `\bar{\bar{I}}` multimodal reflection coefficient matrix. `\bar{\bar{\Gamma_M}}` describes left mirror section while `\bar{\bar{\Gamma_R}}` sample and right mirror. Both `\bar{\bar{\Gamma_M}}` and `\bar{\bar{\Gamma_R}}` are computed at left sample’s boundary.