# A Novel SIW Leaky-Wave Antenna for Continuous Beam Scanning from Backward to Forward
## 2 Antenna Design
The width and length of the discontinuity are assumed to be Wc = 1.4 mm and Lc = 1.1 mm, respectively. ANSYS Electronics Desktop is used for numerical simulation. The S-parameters are used in Equations (3) and (4) to calculate the  
Figure 1:0 Decomposition of rectangular-shaped H-plane discontinuity. Figure 1:1 Equivalent circuit: (a) H-plane step; (b) short waveguide section; (c) rectangular-shaped H-plane discontinuity. Figure 1:2 \(\Pi\)-network equivalent circuit for waveguide with rectangular shaped H-plane discontinuity. series and shunt impedance values in the equivalent circuit. The real and imaginary parts of the series and shunt impedance in \(\pi\)-network equivalent circuit are shown in Figure 1:3 It can easily be seen that the real part of the Zsh and the series impedance of Zs are smaller than the imaginary part of Zsh. The rectangular-shaped H-plane discontinuity can be modeled using shunt inductance, as shown in Figure 1:4  
Figure 10 shows the variation in the shunt reactance regarding the thickness and width of the discontinuity. Results confirm that the inductive effect of the proposed discontinuity is varied by thickness and width, which can be used for tunning in the impedance matching process. According to the presented circuit equivalent for the longitude slot and rectangular-shaped H-plane discontinuity, our proposed unit cell can be equivalently modeled with shunt susceptance, as shown in Figure 1:5 The imaginary parts of the shunt susceptance for the longitude slot, rectangular-shaped H-plane discontinuity, and proposed unit cell are shown in Figure 1:6 Results confirm that the rectangular-shaped H-plane compensates for the capacitive effect of the longitudinal slot. The combination of the longitude slot and rectangular-shaped H-plane discontinuity act as an open circuit and provides proper impedance matching in the proposed unit cell. Figure 1:7 Real and imaginary parts of the series and shunt impedance in \(\pi\)-network equivalent circuit. Figure 1:8 Variation in shunt reactance regarding width and length of discontinuity. Figure 1:9 Approximated model consists of shunt admittance for rectangular-shaped H-plane discontinuity. ### Unit Cell in Ideal Waveguide  
In this section, the performance of the proposed unit cell is investigated for realization in the SIW technology. In order to investigate the OSB suppression, the circuit equivalent and dispersion analysis must be performed for the unit cell. The width of the equivalent substrate-integrated waveguide corresponding to the ideal waveguide is obtained as follows:  
Figure 4.0  
The dimensions of the unit cell in the SIW technology, which is used in an array configuration, are presented in Figure 4.1  
The schematic of the longitude slot, rectangular-shaped h-plane discontinuity, and the proposed unit cell in the SIW technology are shown in Figure 4.2 The imaginary part of the shunt admittance in the circuit equivalent for mentioned unit cells is presented in Figure 4.3 It can easily be seen that the effective nature of the longitude slot is compensated by rectangular discontinuity, and the impedance matching is provided in the proposed unit cell. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value (mm)** & **Parameter** & **Value (mm)** \\ \hline W & 6.9 & Lc & 1.15 \\ Lofs & 2 & Wc & 1.15 \\ \(R_{d}\) & 0.3 & Ls & 5.2 \\ \(S\) & 1.2 & Ws & 0.4 \\ \(p\) & 12.8 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of SIW Periodic LWA. Figure 11: T-network circuit equivalent for proposed unit cell consisting of longitude slot and rectangular-shaped H-plane discontinuity. Figure 12: Imaginary part of shunt admittance for longitude slot, rectangular-shaped H-plane discontinuity, and proposed unit cell. In order to investigate the OSB suppression, a dispersion analysis must be performed in the following.