# Measurement of Dielectric Properties of Thin Materials for Radomes Using Waveguide Cavities
## 3 Results
### Measured Results  
Once the appropriate data, such as frequencies and bandwidths, were extracted, Equations (6)-(11) were then used to calculate the permittivity and loss tangent of each material under test within the WR650 and WR137 cavities [30; 31; 33; 34]. These results are summarized in Table 8.  
The results for these two cavities initially tell us that reference radome materials had permittivity values of about 2.6 and 2.9 but very low loss tangents of less than 0.002 for lower frequencies and less than 0.02 at higher frequencies. This highlights the importance of knowing the permittivity and having a low loss for radome applications. These results also showcase the viability of three materials within the materials purchased for this experiment. N-Shell, 3-LL, and 2-LL demonstrate much lower permittivity values than the reference materials, with approximated permittivity of 1.4, 2, and 1.9, respectively.  
Figure 8: Examples of normalized simulated and experimental resonant peak of dominant TE\({}_{101}\) mode for WR650 cavity: (**a**) empty; (**b**) with only foam; (**c**) with foam and PTFE Fabric sample [30; 31; 34].  
The equivalent noise temperature added by these materials can be calculated using Equation (12).  
\[T_{n}=T_{phys}(1-L_{linear}), \tag{12}\]  
where \(T_{n}\) is the noise temperature in Kelvin, \(T_{phys}\) is the physical temperature of the room where the measurements were obtained, and _loss_ is the absorption losses of S\({}_{21}\). These losses were determined using the previously calculated properties of each material, including the permittivity (\(\epsilon_{r}\)), loss tangent (tan \(\delta\)), material thickness (\(d\)) in meters, and frequency (\(f\)) in gigahertz (Equations (13) and (14)) [21].  
\[L_{linear}=10^{(\frac{8.6840d}{10})}, \tag{13}\]  
\[\alpha=\pi f\sqrt{\mu_{0}\epsilon_{0}e_{r}}\text{tan}(\delta), \tag{14}\]  
where \(\mu_{0}\) is the dielectric constant (4\(\pi\)\(\times\) 10\({}^{-7}\) H/m), and \(\epsilon_{0}\) is the electric constant (8.854 \(\times\) 10\({}^{-12}\) F/m).  
Using Equations (12)-(14), we determined the following noise contributions due to the losses for each material, as shown in Table 8. We can observe noise temperature contributions of less than 0.4 K at 5.575 GHz and 0.1 K at 1.65 GHz. The fabric with the best results, other than the two reference materials, was N-Shell, with noise contributions of 0.0236 K at the lower frequency and only 0.1169 at the higher frequency. These results are quite promising for the investigated fabrics.  
We can also observe that there were some slight differences in measured values between the two cavities. This is unexpected and could be due to the various factors discussed in the following section, Section 3.4.  
Therefore, we can conclude that our results for these materials are accurate enough to determine which materials would be most suitable for further testing as a radome. We suggest that N-Shell would be the most appropriate due to its low permittivity of 1.4 and relatively low loss tangent of less than 0.01. It would also be worth further investigating 3-LL and 2-LL as they also displayed similarly low values for permittivity and loss tangent across the approximate 1 to 6 GHz range.