# Development of a Wideband Slotted Antenna Array with Low Profile and Low Sidelobe
## 2 Design of the Antenna Array
### Basic 2 \(\times\) 2-Slot Subarray  
Figure 2a presents a typical 2 \(\times\) 2 radiating unit of the double-layer full-corporate-feed hollow-waveguide slotted antenna array [22]. According to the exploded perspective view of the primary 2 \(\times\) 2-element subarray, the basic radiating unit consists of four radiation slots, an air-filled cavity, a plate with  
Figure 1: Overall configuration of the proposed waveguide-based multi-layered slotted cavity antenna array, which consists of four parallel copper plates: the radiation slot layer (“Layer1”), the cavity layer (“Layer2”), the coupling aperture layer (“Layer3”), and the feeding layer (“Layer4”). Figure 2: Configuration of (**a**) the primary and (**b**) the improved 2 \(\times\) 2-slot subarrays, and the top views to show the detailed dimension relationship of the improved subarray (**c**) among “Layer1”, “Layer2”, and “Layer3” and (**d**) between “Layer3” and “Layer4”. a narrow coupling slot, and a part of the feeding network. Each layer is made of the same metal copper and has same sectional area (i.e., the same \(w^{\prime}\) and \(l^{\prime}\)). To achieve good impedance matching, the designed thickness of each layer varies. As shown in Figure 2a, to optimize the radiation pattern, the four radiation slots in the primary subarray are evenly and symmetrically distributed in \"Layer1\". In order to minimize the grating lobes, the space between the slots (\(d^{\prime}\)) is designed less than one free-space wavelength. The back cavity designed in \"Layer2\" has four large metal walls, which are designed to suppress unwanted higher modes. The coupling aperture is placed at the center of the \"Layer3\", and to realize a strong excitation in the cavity, it has an offset from the center axis of the waveguide in \"Layer4\", as illustrated in Figure 2a. Considering that the atmospheric propagation loss at lower frequencies of the K-band is smaller, the center frequency of the antenna herein designed focuses on 20 GHz. It should be noted that the back cavity plays an important role in efficiently transmitting power from the coupling layer into the radiation slot layer. Thus, in order to optimize the radiation performance and to reduce the final profile, the back cavity is herein further improved by introducing the \(TE_{220}\) mode, leading to an improved subarray as shown in Figure 2b. Figure 3 presents the \(E\)-field distribution of the \(TE_{220}\) mode of the rectangular waveguide cavity in Figure 2b. It can be observed that there are four positions where the \(E\)-field has the maximum value, as denoted by \"+\" and \"-\" in Figure 3 to show the 180 deg phase difference of the \(TE_{220}\) mode. The four red-dashed rectangles represent the designed 2 \(\times\) 2 radiation slots of \"Layer 1\". It can be noted that the distances between the four slots are particularly designed, so that the radiated waves at the four slots are in phase. When the antenna works, the proposed cavity in \"Layer2\" performs as a resonance circuit. The relationship between the desired resonance frequency \(f_{TE_{220}}\) and the cavity dimensions can be described by [2]:  
\[f_{TE_{220}}=\frac{c}{2}\sqrt{\frac{4}{l_{c}^{2}}+\frac{4}{w_{c}^{2}}} \tag{1}\]  
where \(c\) represents the speed of light in free space, while \(l_{c}\) and \(w_{c}\) are the dimensions of the cavity in \"Layer2\" as shown in Figure 2b. The cavity is filled with air, and it is designed to excite the \(TE_{220}\) mode at the center of the operating frequency (i.e., 20 GHz). Hence, \(l_{c}\) and \(w_{c}\) can be readily obtained by using Equation (1). To reduce the grating lobe, the distance between the radiation slots is designed less than one wavelength and the width of the radiation slot is designed less than one-quarter wavelength. Hence, the length \(l\) and the width \(w\) of the improved subarray are both 1.41\(\lambda_{0}\), where \(\lambda_{0}\) is the free-space wavelength at the design frequency of 20 GHz. The dimensions of the proposed radiation unit in Figure 2b are listed in Table 1 in detail.