# Measurement of Dielectric Properties of Thin Materials for Radomes Using Waveguide Cavities
## 3 Results  
### Simulated Results  
To confirm the accuracy of the simplified equations found in the literature, simulations of a waveguide cavity were performed in CST Studio Suite [24]. To begin this modeling, the cavity size had to be chosen. Due to the waveguide cavities available to us, a WR650 cavity and a WR137 cavity were chosen, with a length of 105 mm and 127 mm, respectively. A WR650 waveguide has a recommended frequency band of 1.15 to 1.72 GHz and a width and height of 165.1 mm and 82.55 mm, respectively [28]. A WR137 waveguide has a recommended frequency band of 5.85 to 8.20 GHz and a width and height of 34.85 mm and 15.8 mm, respectively [29]. By using Equation (2), many mode frequencies were calculated (\(p\) = 1, 2,..., 10) for the WR650 and WR137 cavities and then sorted by frequency (see Tables 4 and 5 [30,31]). This allowed for an easier identification of the correct modes in both simulations and measurements, as mode overlap and degeneracy can occur when multiple modes are excited at similar or the same frequencies. This is observed with the frequencies displayed in Tables 4 and 5, where there are multiple modes around 6 GHz for the WR650 cavity and 22 GHz for the WR137 cavity. Next, the most appropriate diameter for the iris in the shims was determined. The smaller the iris, the weaker the coupling and the higher the Q-factor. The larger the iris, the higher the transmission coefficient, and hence the signal to noise on the measurement of center frequency and Q. The diameter of the iris was chosen to ensure that the Q-factor dropped significantly when the material sample was added to the cavity. Previous experience within our group was used to help determine that a radius of 6.1 mm (7.4% of the narrow wall), and thus a diameter of 12.2 mm, would work best for the WR650 cavity. For the WR137 cavity, a shim iris diameter of 7.2 mm was chosen. These diameters were then used in the simulation model in CST Studio Suite [24]. The s-parameters were checked to ensure the model performed as expected, with clear resonant peaks and no discontinuities. To check the accuracy of Equations (3)-(5), multiple models of a WR650 cavity were simulated in CST with loss tangents of 0.1, 0.05, 0.01, 0.005, and 0.001 and permittivity values of 1.5, 2.2, and 2.9 corresponding to the range of values we were interested in for skin materials in radome applications. The S21 data from these \begin{table}
\begin{tabular}{l c c c c c} \hline \hline \multirow{2}{*}{**Material**} & \multicolumn{4}{c}{**Features**} \\ \cline{2-6}  & **Flame-** & **Waterproof** & **Windproof** & **Abrasion** & **Inelastic** \\ \hline PTFE Fabric * & & & & & \\ Dyneema * & & & & & \\ Polyester & & & & & \\ Ecopak & & & & & \\ Etaproof & & & & & \\ Cordura & & & & & \\ N-Shell & & & & & \\
3-LL & & & & & \\
2-LL & & & & & \\ \hline \hline \end{tabular}  
* Reference materials that have been used as radomes in previous projects.  
\end{table} 
Table 3: Features of the fabrics to assess their applicability as radomes [25, 26, 27]. numerous simulations were then processed in the same way as the experimental data to assist in determining whether these simplified equations were accurate and reliable. The results obtained from these simulations are displayed in Table 6 for the WR650 cavity and in Table 7 for the WR137 cavity. \begin{table}
\begin{tabular}{c c|c c|c c|c c} \hline \hline  & \multicolumn{6}{c}{**WR650 (Length = 105 mm)**} \\ \hline \multirow{2}{*}{**Mode**}  
In Table 6, by comparing the simulated permittivity (\(\epsilon_{r-sim}\)) and loss tangent (\((\tan\delta)_{sim}\)) values to the calculated permittivity (\(\epsilon_{r}\)) and loss tangent (\(\tan\delta\)) values, we case see that there is little error between the two. Even for the lower loss tangent values, we see quite good agreement between the simulated and calculated values. By calculating the percentage error, we can further confirm this agreement. The results in Table 5 show that we obtained a permittivity error of less than 1% and a loss tangent error of less than 24%.