# Radiation from a Cavity-Backed Circular Aperture Array Antenna Enclosed by an FSS Radome
## 3 Numerical Results and Measurement  
Before proceeding with the analysis of radiation pattern of the 3 \(\times\) 3 circular aperture array antenna enclosed by the multi-layer FSS radome as shown in Figure 3, it is important to check the accuracy of our mode matching formulation and to analyze the antenna properties in detail. Firstly, the number of modes used is \(\mathrm{m}=\pm 19\) (\(\phi\) direction) and \(\mathrm{n}=10\) (z direction). In order to ensure that the convergence was made, we tabulated the modal coefficients in the circular cavity in Table 2. From Table 2, we figured out that the contributing modes are \(\mathrm{TM}_{(-4)5}\), \(\mathrm{TM}_{02}\), \(\mathrm{TM}_{03}\), \(\mathrm{TM}_{04}\), \(\mathrm{TM}_{05}\), \(\mathrm{TM}_{06}\)  
Figure 2: Analysis procedure. In order to further validate our formulation, we conducted the experiment. Figure 6 shows the normalized radiation pattern of the \(3\times 3\) cavity-backed circular aperture array antenna at 10 GHz. The comparison between our computation result (blue solid line with circle) and measured data (red dotted line with plus) generally shows a good agreement. Meanwhile, because of a difficulty in predicting reflection and transmission coefficients of a curved FSS layer, we exploited reflection and transmission coefficients under an assumption that the FSS layer is locally flat. The discrepancy between two results at higher degrees above about 75 comes from the fact that we assumed an infinite conductor plane when modeling the antenna. We fabricated a tangent-ogive multi-layer FSS radome (see Figure 7a) and the unit cell of the cross-loop dipole FSS layer (see Figure 7b and reference [10]). The multi-layer FSS radome is a foam-core sandwich type FSS. To be specific, the innermost and outermost layer are E-glass/epoxy and the third layer is the FSS layer. The remaining layers consist of a foam. The initially fabricated planar FSS layer is cut to shape and size, and then the cut pieces are molded through thermal-forming between the foam layers. The tangent-ogive multi-layer radome is one of the typical radomes. In this paper, we designed and fabricated the FSS radome to validate our hybrid method. When the cut pieces of the FSS sheet were molded on the radome, boundary lines between the pieces can cause an  
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unavoidable defect of the FSS layer. In order to reduce effects of the defect, we chose a cross-loop dipole FSS because it is less vulnerable to the broken unit cell effect than others. In addition, the cross-loop dipole FSS has an excellent bandpass characteristic and is easy to fabricate while maintaining the unit cell of the FSS due to the rectangular configuration. This is why we chose the tangent-ogive multi-layer radome with the cross-loop dipole FSS. We also carefully fabricated the tip of the FSS radome to reduce the distortion of the transmitted wave. That is why we chose the tangent-ogive multi-layer radome with the cross-loop dipole FSS. We also carefully fabricated the tip of the FSS radome to reduce the distortion of the transmitted wave. Figure 8 illustrates measurement setup. We measured the radiation pattern of the cavity-backed circular aperture array antenna enclosed by the radome. Figure 9 illustrates the radiation patterns of the 3 \(\times\) 3 cavity-backed circular antenna with the designed FSS and dielectric radomes. These values are normalized to the maximum magnitude of the designed antenna without any radome. The dielectric radome is comprised of three layers; the innermost and outermost layer are E-glass/epoxy and the inserted layer between them is a foam. In other words, the second, third, and fourth layers are combined into one foam layer in Figure 1. As can be seen from Figure 9, the amount of the radiation field from the 3 \(\times\) 3 cavity-backed circular aperture array antenna with the FSS radome is smaller than that with the dielectric radome. At \(\theta=0^{\circ}\), we found out that there is a discrepancy between our theoretical results and measured data.