# A Wide-Angle Scanning Leaky-Wave Antenna Based on a Composite Right/Left-Handed Transmission Line
## 2 Operation Principle and Scheme of the Proposed LWA
### Proposed LWA Configuration  
Figure 1a shows the scheme of the proposed LWA, which is a varactor-loaded CPWG structure. The CPWG is composed of a central conductor strip and bilateral strips, which are connected to the ground by metalized vias. The CPWG can restrain back radiation and avoid surface wave leakage. The top view of each unit cell is displayed in Figure 1b. A symmetrical topology is used to equalize the impedance of two ports. Two series varactors with opposite polarity are loaded at the center strip of each unit cell. One end of each varactor is connected to the grounded strip, which is used to apply a negative DC bias voltage. The other end of each varactor is connected to the central conductor strip, which is used to apply a positive DC bias voltage. The barrier capacitance of the varactor varies with the reverse voltage. As the reverse voltage increases, the capacitance decreases. Skyworks SMV2020-079L varactors were used in this study. Based on their manual specifications, these varactors have a variable capacitance range of 0.35 pF-3.20 pF. The applied DC bias voltage varied from 20 V to  
0 V. As shown in Figure 1a, 100 nH chip inductors were loaded between the central conductor strip and the positive bias voltage line to isolate the AC signal. On the two ends of the LWA, there are two pF chip capacitors with 0603 packages that isolate the DC signal. Thus, for an LWA with \(N\) unit cells, a total of \(2N\) varactors, \(N+1\) chip inductors, and two chip capacitors are employed. The antenna structure is supported on the substrate of F4B-2 (\(\varepsilon\)r = 2.65), with a thickness of 3 mm. Table 1 shows the dimensions of the unit cell structure. The radiation structure and the DC bias network of the varactors are very simple; all varactors can easily acquire the same voltage simultaneously.  
To predict the performance of the proposed LWA and better guide future work, an equivalent circuit model of each unit cell was established and is shown in Figure 2. The varactors and the metalized vias serve as left-handed capacitors \(C_{L,VAR}\) and left-handed inductors \(L_{L}\), respectively, while the TL itself provides the right-handed capacitance \(C_{R}\) and the right-handed inductance \(L_{R}\). Based on this equivalent circuit model, the phase constant of the fundamental mode in the CRLH TL can be derived as:  
\[\beta\ =\ \frac{1}{p}\cos^{-1}(1+\frac{ZY}{2}) \tag{4}\]  
\[Z\ =\ j(\omega L_{R}-\frac{1}{\omega C_{L,VAR}}) \tag{5}\]  
\[Y\ =\ j(\omega C_{R}-\frac{1}{\omega L_{L}}). \tag{6}\]  
The Bloch impedance can be extracted from the \(S\)-parameters of the unit cell by (7):  
\[Z_{B}\ =\ \frac{2 jZ_{0}S_{21}\sin(\beta p)}{(1-S_{11})(1-S_{22})-S_{21}S_{12}}. \tag{7}\]  
Using Equations (4)-(6), the dispersion curves of the CRLH TL can be obtained, and the \(Z_{B}\) in Equation (7) can be used to optimize the impedance of the unit cell in the LWA.  
Figure 1: Scheme of the proposed leaky-wave antenna (LWA). (**a**) Structure of the LWA; (**b**) Top view of the unit cell.