# A Wide-Angle Scanning Leaky-Wave Antenna Based on a Composite Right/Left-Handed Transmission Line
## 3 LWA Design and Experiment Results  
### Simulated Results for the Unit Cell  
The electromagnetic full-wave analysis software Ansoft HFSS was used to simulate the proposed LWA. Firstly, the \(S_{11}\) of the unit cell with various series capacitances was simulated; the simulation's results indicate that the amplitude of \(S_{11}\) (\(|S_{11}|\)) in dB is less than \(-10\) dB when the capacitance varies from \(0.38\) pF to \(1.9\) pF at the frequency of \(3.0\)-\(4.0\) GHz. In practice, the capacitance variation is controlled by the loaded varactors with different DC bias voltages. Figure 3 shows the simulated \(|S_{11}|\) in dB when the capacitance \(C_{L,var}\) equals several selected values, i.e., \(0.6\) pF, \(1.0\) pF, and \(1.9\) pF. The\(|S_{11}|\) that corresponds to these capacitances at \(3.2\) GHz is \(-21.5\) dB, \(-20.7\) dB, and \(-14.8\) dB, respectively.  
The parameters of the equivalent circuit model in Figure 2 can be extracted from the S-parameters of the unit cell through the parametric fitting method. The extracted results are shown in Table 2. The dispersion diagram of the TL structure, which consists of infinite unit cells, was extracted based on Equations (4)-(6) and is shown in Figure 4. It can be deducted from Figure 4 that, with the increase of the capacitance values of the varactors, the dispersion curves are shifted down in a vertical direction. Based on this phenomenon, the scanning properties of the proposed LWA with large number of unit cells can be predicted. At the frequency of \(3.2\) GHz, positive, zero, and negative phase constants can be obtained with different varactor capacitance values. As a consequence, the continuous backward to forward beam-scanning can be achieved at \(3.2\) GHz.  
The Bloch impedance \(Z_{B}\) was calculated using Equation (7). The Bloch impedance \(Z_{B}\) with \(C_{L,var}=1.3\) pF is shown in Figure 5 as an example. Figure 5 shows that the real part of the extracted Bloch impedance is about \(50\Omega\), from \(2.8\) GHz to \(5.5\) GHz, and the real part tends to zero. According to other simulation results, the Bloch impedance of around \(50\)\(\Omega\) can also be obtained with other loaded capacitances in a wide bandwidth.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(\mathbf{G_{1}}\) & \(\mathbf{G_{2}}\) & \(\mathbf{G_{3}}\) & \(\mathbf{W_{f}}\) & \(\mathbf{S}\) & \(\mathbf{S_{vp}}\) \\ \hline \(20\) & \(31\) & \(15\) & \(4\) & \(0.6\) & \(4\) \\ \hline \(\mathbf{D}\) & \(\mathbf{gap}\) & \(\mathbf{l_{1}}\) & \(\mathbf{l_{2}}\) & \(\mathbf{l_{3}}\) & \\ \hline \(0.5\) & \(4.5\) & \(1.6\) & \(0.8\) & \(0.3\) & \\ \hline \end{tabular}
\end{table}
Table 1: Dimensions of the unit cell(unit:mm).  
Figure 2: Equivalent circuit model of the unit cell.  
Figure 4: Dispersion diagram of the unit cell with various capacitances of varactors.  
Figure 5: Extracted Bloch impedance of the unit cell with \(C_{L,\text{tur}}=1.3\) pF.  
Figure 3: \(|S_{11}|\) of the unit with different capacitance values.  
\begin{table}
\begin{tabular}{c c c c c} \hline  & **5 V** & **10 V** & **15 V** & **20 V** \\ \hline \(C_{L,\text{tur}}\)(pF) & 1.19 & 0.57 & 0.41 & 0.35 \\ \(L_{L}\)(nH) & 1.82 & 1.53 & 1.01 & 0.77 \\ \(C_{R}\)(pF) & \multicolumn{4}{c}{1.95} \\ \(L_{R}\)(nH) & \multicolumn{4}{c}{9.78} \\ \hline \end{tabular}
\end{table}
Table 2: Extracted equivalent circuit model parameters at 3.2 GHz.