## 4 Experimental Results and Discussion
The routine considers several values for LC permittivity and loss tangent, and keeps the device dimensions invariant. As a result, the software protocol gives rise to a preliminary estimation of the dielectric properties of the LC. Therefore, the extreme values of permittivities, \(\varepsilon_{\mathrm{r\perp}}\) and \(\varepsilon_{\mathrm{rl}}\), and LC loss tangent, tan \(\delta_{\mathrm{\perp}}\) and tan \(\delta_{\mathrm{l}}\) are inferred. As it is shown in Figure 8, a fairly good agreement between the measured filter frequency response (when no voltage is applied) and the simulated response (with \(\varepsilon_{\mathrm{r}}=2.62\) and tan \(\delta=0.05\)) is achieved. In the same way, the measured frequency response by applying the saturation voltage value (\(15~{}\mathrm{V_{rms}}\)) and the simulation response, considering \(\varepsilon_{\mathrm{r}}=3.06\) and tan \(\delta=0.02\), are also in reasonable agreement (Figure 9). Therefore, in a preliminary estimation, it can be inferred that the dielectric properties for the used LC at \(5\) GHz are the shown in Table 5. \begin{table}
\begin{tabular}{c c c c c c} \hline
**LC Drive** & **LC Dielectric** & **Central** & **Bandwidth** & **Relative** & **Return Loss** \\
**Voltage** & **Constant (\(\varepsilon\))** & **Frequency (\(f_{\mathrm{c}}\))** & **(BW)** & **Bandwidth (BW/\(f_{\mathrm{c}}\))** & **(RL)** \\ \hline \(0~{}\mathrm{V_{rms}}\) & \(\varepsilon_{\mathrm{r\perp}}\) & 5.045 GHz & 636 MHz & 0.126 & 5.4 dB \\ \(15~{}\mathrm{V_{rms}}\) & \(\varepsilon_{\mathrm{rl}}\) & 4.688 GHz & 568 MHz & 0.122 & 4.9 dB \\ \hline \end{tabular}
\end{table} 
Table 4: Summary of the experimental measurements of the spectral response for the new LC bandpass filter. Figure 8: Comparison between the measured frequency response when no voltage is applied and the simulated considering when \(\varepsilon_{\mathrm{r}}=2.62\) and tan \(\delta=0.05\). Let us note that LC loss tangent estimated values are high. This may be the reason why the filter exhibits high insertion loss, as it is shown in Figure 5.  
With these estimated values, a comparison between the microstrip conventional square patch and the new patch, supposing the cavity filled with LC, can be obtained in simulation for the extreme values of LC permittivity and loss tangent. Figure 10 shows the frequency response of both structures considering \(\varepsilon_{\mathrm{r\perp}}=2.62\) and tan \(\delta_{\perp}=0.05\). In Table 6, the performances of the new square patch structure and the conventional one are summarized. A filter bandwidth narrowing of 14.7% and a pass-band return loss increase of 1.5 dB, which means an increase of 30.6%, are achieved by using the new patch. In the same way, Figure 11 and Table 7 present a comparison between both structures when \(\varepsilon_{\mathrm{r\perp}}=3.06\) and tan \(\delta_{\mathrm{l}}=0.02\) are considered, obtaining a filter narrowing of 17.8% and a pass-band return loss improvement of 1.9 dB, which means an improvement of 38.8%. \begin{table}
\begin{tabular}{c c c c} \hline
**Structure** & **Central Frequency (\(f_{\mathrm{c}}\))** & **Bandwidth (BW)** & **Return Loss (RL)** \\ \hline With a conventional patch & 5.037 GHz & 737 MHz & 3.4 dB \\ With a new patch & 5.039 GHz & 629 MHz & 4.9 dB \\ \hline \end{tabular}
\end{table} 
Table 6: Comparison between the performance of both dual-mode filters considering \(\varepsilon_{\mathrm{r\perp}}=2.62\) and tan \(\delta_{\perp}=0.05\). Figure 9: Comparison between the measured frequency response when 15 V\({}_{\mathrm{rms}}\) are applied and the simulated considering when \(\varepsilon_{\mathrm{r}}=3.06\) and tan \(\delta=0.02\).