# A Novel SIW Leaky-Wave Antenna for Continuous Beam Scanning from Backward to Forward
## 2 Antenna Design
### Unit Cell in Ideal Waveguide  
As shown in Figure 1, the unit cell of the proposed LWA consists of a longitudinal slot and rectangular-shaped H-plane discontinuity. To perturb the surface current for radiation, the longitudinal slots are placed offset from the center and on top of the metallic plate of SIW. In this paper, the length of the slot and distance from the centerline were selected to provide a longitudinal slot with capacitive behavior. In [33], metallic via has been used to compensate for the capacitive effect of the longitudinal slot and provide impedance matching for OSB suppression. In a similar way to the cylindrical post, which is used in waveguide structures such as filters, the metallic via effectively behaves as an inductance. The rectangular-shaped H-plane discontinuity is another mechanism that can provide an inductive behavior in the waveguide [34; 35]. Iris is one of the application examples for the H-plane discontinuity, which is widely used in waveguide filters. It is possible that the rectangular-shaped H-plane discontinuity, which is realized by using metalized via in the SIW technology, is similar to the method presented in [33]. As presented earlier, in the proposed method, rectangular-shaped H-plane discontinuity is used. In contrast, the technique presented in [33] is based on similarities between metallic-via cylindrical posts in providing an inductive effect. For revealing this difference, the proposed design for the unit cell is verified with the ideal waveguide technology, and then the results are presented for the SIW structure. Consider an ideal waveguide with the longitude slot placed at the top plate, as shown in Figure 2. The waveguide is filled by the dielectric substrate with a relative permittivity  
Figure 1: Proposed SIW LWA: (**a**) array configuration; (**b**) unit cell. of \(\varepsilon\tau=3.55\) and tan\(\sigma=0.0027\). The height and width of the waveguide are W = 6.6 mm and h = 0.813 mm. All numerical simulations for the ideal waveguide are performed for the mentioned specifications. The numerical simulation is performed using the commercial EM software of ANSYS Electronics Desktop (HFSS V.15.0.2, Canonsburg, PA, USA) The length and width of the slot are Ls = 5.1 mm and Ws = 0.4 mm. The offset of the longitudinal slots from the centerline of the top plate is Lofs = 2 mm. The period of the unit cell must be considered to be \(p=11.9\) mm to provide the broadside frequency at 18 GHz based on Equations (1) and (2). The longitude slot is modeled with T-network, as shown in Figure 3[36]. The series and shunt normalized impedance in T-network is calculated by formulations presented in [36] and is shown in Figure 4.  
It can easily be seen that the series impedance and the real part of the shunt impedance are very small and can be neglected in the equivalent circuit. Therefore, the longitude slot can be modeled by shunt capacitance. As shown in Figure 5, the rectangular-shaped H-plane discontinuity can be decomposed to the two H-plane steps with a width of Wc and the waveguide section with a length of Lc and width of W-Wc. Figure 4: Normalized series and shunt impedance of T-network for longitude slot. Figure 3: T-Network model for longitude slot. Figure 2: Ideal waveguide with longitude slot. The H-plane step discontinuity can be modeled using shunt inductance [37]. The waveguide section is modeled using series impedance. The circuit equivalent of the rectangular-shaped H-plane discontinuity is represented based on \(\pi\)-networks, as shown in Figure 6. The series and shunt impedance values of the circuit equivalent are obtained as follows:  
\[Z_{S}=\frac{(1+S_{11})^{2}-(S_{21})^{2}}{2S_{21}} \tag{3}\]  
\[Z_{sh}=\frac{(1+S_{11})^{2}-(S_{21})^{2}}{(1-S_{21})^{2}-(S_{11})^{2}} \tag{4}\]  
The \(\Pi\)-network equivalent circuit for waveguide with rectangular shaped H-plane discontinuity is shown in Figure 7.  
The S-parameters of the rectangular-shaped H-plane discontinuity are calculated using numerical simulation.