## 4 Experimental Results and Discussion  
The device S-parameters are measured by using an Agilent 8703B network analyzer (Agilent Technologies, Santa Clara, CA, USA). A sinusoidal AC signal of 1 kHz is used as the voltage for \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 & 7.69 GHz & 1320 MHz & 4.3 dB \\ With a new patch & 7.665 GHz & 1050 MHz & 5.8 dB \\ \hline \end{tabular}
\end{table} 
Table 2: Comparison between the performances of both dual-mode filters. Figure 4: Manufactured LC bandpass filter. A filter central frequency tuning range of 357 MHz is achieved, which means a tuning relative range of 7.3%. Comparison between liquid crystal filters is not an easy task because multiple criteria, for comparing performance of the filters, are available: central frequency, filter bandwidth, number of poles, topology, _etc_. However, not at all comparable between them. Tunable bandpass filters of Table 3 share some characteristics that are comparable between them, independently of the specific structure, configuration and dimensions. Therefore, the new filter we have proposed, with a compact and non-complex structure, has similar performance, in terms of relative tuning range, than filters with the same number of poles [13,14]. But, the performance could be improved even further if high dielectric anisotropy liquid crystals were used [15]. Of course, by increasing the number of poles of the filter [3], leads to higher performance but also to higher filter complexity. The filter bandwidth gets narrower as an increasing voltage is applied, while the relative bandwidth, defined as the ratio between the bandwidth and the central frequency, remains constant. The pass-band return loss of the filter slightly gets worse as an increasing voltage is applied. Table 4 shows a summary of the measurements. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**LC-based filter**} & **Centroal** & **Relative** & **Number** & **Comments** \\  & **Frequency (\(f_{0}\))** & **Tuning Range** & **of Poles** & **Merck BL037 as used LC \\ \hline \multirow{2}{*}{Presented work} & \multirow{2}{*}{5 GHz} & \multirow{2}{*}{7.3\%} & \multirow{2}{*}{2} & Dual-mode filter structure. Merck \\  & & & & MDA-98-1602 as used LC \\ \multirow{2}{*}{[PERSON] _et al_. [3]} & \multirow{2}{*}{20 GHz} & \multirow{2}{*}{10\%} & \multirow{2}{*}{3} & 3-pole microstrip filter. A highly \\  & & & & anisotropic LC is used \\ \multirow{2}{*}{[PERSON] _et al_. [13]} & \multirow{2}{*}{5 GHz} & \multirow{2}{*}{6\%} & \multirow{2}{*}{2} & DBR filter structure. \\  & & & & Merck BL037 as used LC \\ \multirow{2}{*}{[PERSON] _et al_. [14]} & \multirow{2}{*}{5 GHz} & \multirow{2}{*}{4.8\%} & \multirow{2}{*}{2} & 2-pole DBR structure. \\  & & & & Merck LC K15 is used \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Filter performance compared to other LC-based bandpass filters. Figure 7: Tunability of the filter central frequency as a function of the LC driving voltage. The variation of the frequency as a function of the applied voltage shown in Figure 7 suggests that the LC director \(\mathrm{\SIUnitSymbolMicro h}\), which is the vector that represents the local average orientation of LC molecules in the LC bulk, has an average tilt angle which changes as voltage is applied. For low values of voltage, tilt angle is close to \(0^{\circ}\), while it is nearby \(90^{\circ}\) for high values of voltage. This average tilt angle presents a quasi-linear dependence for intermediate values of the applied voltage, while it tends to saturation for extreme values. A complementary analysis of the spectral response performance, comparing the simulations and the measurements, has been carried out this time for the filter filled with the LC. Due to LC features are initially unknown at microwave frequencies, an iterative process is programed for fitting both experimental and simulated responses.