# A 3-D Metal-Printed Dual-Polarized Ridged Waveguide Slot Array Antenna for X-Band Applications
## 3 Antenna Design and Analysis Procedure  
### Compact Dual-Polarized Ridged Waveguide Array  
Dual-polarized slotted waveguide array antennas have high power capability and mechanical stability. The configuration of the array must be decided to determine the unit cell dimensions and structure to be used during the design process. To ensure the array performance, the requirements for the spacing between radiating elements in the waveguide of a resonant array must be met. As a result, the dimensions of the waveguide need to be selected appropriately in the operating frequency band and must meet the compactness of the design. In Figure 2, a comparison of three prototypes of air-filled waveguide structures is given, including a conventional rectangular waveguide together with two proposed compact RWGs for VP and HP. In Figure 2a, a conventional rectangular waveguide (WR-90) typically has an \(A\) broad wall dimension of \(0.75\lambda_{0}\) and a \(B\) narrow wall dimension of \(0.33\lambda_{0}\) at the highest frequency in the operation band. When two conventional rectangular waveguides are combined in the azimuth, they create a dual-polarized structure with a total size of approximately \(1.2\lambda_{0}\), including the wall thickness. In this case, the distance between the waveguides is more than one wavelength, and the grating lobes in the azimuth plane completely overlap the visible region at any scanning angle [17]. Therefore, it is difficult to produce effective radiation patterns in the HP using conventional rectangular waveguides so that the grating lobes are not visible. Since the distance between the waveguides is limited to less than one wavelength, ridge loading should be used to achieve the required guided wavelength without exceeding the waveguide width limit. Two RWGs for VP and HP are proposed for dual-polarized arrays to miniaturize the waveguide dimensions and reduce the distance between elements in the array. The RWG width is limited by two factors: The first is that the effective operating bandwidth of the RWG is defined as the frequency range between the two cutoff frequencies in the fundamental propagation mode (dominant mode and second mode). The second is the distance \(d_{x}\) of the adjacent linear arrays with respect to the radiation so that no grating lobes appear when the beam is scanned. When the polarization scans along the waveguide axis, the spacing between the slot elements for the linear resonant array inside the waveguide should be half the guide wavelength, which means that \(d_{y}=0.5\lambda_{g}\). To obtain uniformity between the beam squints in the VP and HP arrays, the guide wavelengths used in both polarizers must be the same. This forces the distance between the co-polarized waveguides to be equal when the scan polarization is perpendicular to the axis of the waveguide. Therefore, the optimal width for a pair of waveguides is \(d_{x}=d_{y}=0.5\lambda_{g}=0.725\lambda_{0}=22.2\) mm, and each RWG used for vertical and horizontal slots has a corresponding width of \(w_{hr}=w_{vr}=0.327\lambda_{0}=10.008\) mm, excluding wall thickness \(t=1\) mm. The dominant and second mode determines the effective bandwidth of the waveguide prototypes TE10 and TE20, respectively. Since these modes are unaffected by changes in the waveguide height, the size of the array can be decreased by reducing the height of the RWG. The choices of height are limited by the vertically polarized elements. The height is chosen to be neither too small to produce bandwidth problems for slot excitations nor too large to restrict the range of radiative emissions from vertically polarized slots. The height of the optimal RWG is \(h_{hr}=h_{\sigma}=0.25\lambda_{0}=7.66\) mm. As shown in Figure 2b, the wave propagation constant curves represent rectangular waveguides and two RWGs. By tuning the size of the ridge to match the width of the RWG, the cutoff frequencies of the operating modes change.