# Measurement of Dielectric Properties of Thin Materials for Radomes Using Waveguide Cavities
###### Abstract
They outline four prevalent methods: transmission/reflection line, open-ended coaxial probe, free-space, and resonant (cavity) [4]. Table 1, adapted from [4], summarizes the types of materials that would be most appropriate for each popular method of measurement. It also details which mode is assumed to perform these measurements. As dielectric property measurement is a long-standing topic, several recent works can provide some context for the different processes available for various types of materials [9, 10, 11, 12, 13]. Figure 1: TE and TM mode field orientations, where the E-field is depicted in blue and the H-field in red [6] (reproduced with permission from [PERSON], Lessons in Electric Circuits; 2021). We focused on the application of radomes, which, in our area of interest, require thin, flexible, inelastic materials. Also called'skin' materials, as their thickness can be down to the micrometer, these materials include a variety of types, including flexible fabrics [2,4]. There exist some permittivity measurement methods specific to testing skin materials. As with all permittivity measuring methods, they also depend upon the frequency range required for operation. Figure 2 summarizes prevalent methods of permittivity measurement across the EM spectrum [2]. This figure shows how a few measurement methods can be used across a majority of the frequency spectrum, such as capacitors, open coax probes, and transmission lines. On the other hand, most other methods can be used at various narrow bands at the higher end of the spectrum. Traditionally, thin films are measured with a capacitor setup. This requires a miniature microwave probe, where a thin dielectric film is deposited on a metal layer and then a top electrode layer. This allows for a one-port reflection measurement to be taken. The reflection coefficient is then measured from the incident waves and converted to impedance, from which the loss tangent can then be extracted [14]. However, in [14], the authors acknowledge that this does not create a perfect plate capacitance. Therefore, further complex calculations are required to account for the various losses across the multi-layered plates [14]. Our initial motivation for this research was to create a material database detailing relevant characteristics for use as radome covers, specifically for large phased arrays working around 1 to 6 GHz. Therefore, our research intended to begin at 1 GHz and increase in frequency as measurement methods became available to our lab. As such, according to Figure 2, a type of resonator would be the best method for this frequency area of interest. \begin{table}
\begin{tabular}{c c c} \hline
**Measurement Method** & **Material Types** & **Assumed Mode** \\ \hline Transmission/reflection line & Coaxial line, waveguides & Fundamental \\ Open-ended coaxial probe & Liquids, biological specimen, & TEM, TE \\  & semi-solids & \\ Resonant cavity & High temperatures, large/flat solids, & \\  & gas, hot liquids & TM, TE \\ Free-space & Rod-shaped solids, waveguides, liquids & TEM \\ \hline \end{tabular}
\end{table} 
Table 1: Summary of popular permittivity measurement methods with the types of material that can be measured and the modes that are assumed [4]. Figure 2: Permittivity measurement methods most appropriate for various bands of the frequency spectrum [2]. Dielectric resonators are used to hold a sample within a simple cavity so an electric field can be applied to it. Identifying the correct mode and measuring the resonant frequency and Q-factor before and after the sample is placed within the resonator allows the calculation of the permittivity to be completed. Q-factors are the frequency-to-bandwidth ratios of the cavity for the mode in question [15]. This type of resonator measurement is present in previous research, such as [2, 16, 17]. However, although these resonators are generally simple shapes, like cylinders, they are still specific devices created for permittivity measurement.