## 5 Conclusions  
With increasing interest in the W-band, there is a growing focus on parabolic reflector antennas, which are known for efficiently inducing high-gain radiation characteristics. Furthermore, parabolic antennas with defocus-fed configurations have diverse applications, including monopulse tracking, multi-beam formation using multiple feeds, and shared-aperture antennas for multi-band operation. This paper presents a simple method for analyzing the radiation characteristics of defocus-fed parabolic antennas. The derivation of the presented method involves discretely dividing the parabolic surface, accounting for the feeder's influence at each division point, and employing an electric field analysis using array theory. Additionally, to simplify the method, only scalar functions, not vector fields, were considered. Through applying the presented method to ensure the performance of the radiation characteristic analysis of defocus-fed parabolic reflector antennas, it was confirmed that the maximum division intervals criterion \(\left(g_{\psi},\ g_{\phi}\right)\) is 0.5\(\lambda\), according to the parabolic reflector surface division procedure. To validate the analysis performance of the presented method, which applies this maximum criterion for the division intervals, a comparison was conducted with the analysis results from GRASP and CST. These are representative analysis tools for various defocus-fed parabolic antenna configurations. It was observed that there were differences of only 0.99 dB (compared with GRASP) and 1.14 dB (compared with CST) within the region of primary interest (near the main beam). Consequently, it was confirmed that the presented method in this paper can efficiently analyze the radiation characteristics of various defocus-fed parabolic reflector antennas. The presented method can thus be applied in various areas, such as communication link \begin{table}
\begin{tabular}{l c c c c c c c c} \hline  & \(\boldsymbol{\theta}\)**-Cut** & **Directivity Difference** & \multicolumn{3}{c}{**HPBW Difference**} & \multicolumn{3}{c}{**Pattern Difference**} \\  & \(\boldsymbol{\phi}\) & **with with** & **with with** & **with** & **with** & **with** & **Region** \\  & **GRASP** & **CST** & **GRASP** & **CST** & **GRASP** & **CST** & **GRASP** & **CST** & \\ \hline Case \#1 & 00\({}^{\circ}\) & 0.71 dB & 1.38 dB & 0\({}^{\circ}\) & 0.89 dB & 1.05 dB & \(-2.7^{\circ}\)\(\leqslant\theta\leq 2.7^{\circ}\) \\ Case \#2 & 00\({}^{\circ}\) & 1.32 dB & 0.64 dB & 0\({}^{\circ}\) & 0\({}^{\circ}\) & 1.98 dB & 1.08 dB & \(-1.3^{\circ}\)\(\leqslant\theta\leq 1.3^{\circ}\) \\ Case \#3 & 00\({}^{\circ}\) & 1.13 dB & 0.01 dB & 0.4\({}^{\circ}\) & 0.1\({}^{\circ}\) & 1.45 dB & 0.93 dB & \(-5.3^{\circ}\)\(\leqslant\theta\leq 5.3^{\circ}\) \\ Case \#4 & 00\({}^{\circ}\) & 0.65 dB & 0.94 dB & 0\({}^{\circ}\) & 0\({}^{\circ}\) & 0.59 dB & 0.77 dB & \(-2.0^{\circ}\)\(\leqslant\theta\leq 2.0^{\circ}\) \\ Case \#5 & 00\({}^{\circ}\) & 0.69 dB & 1.35 dB & 0.1\({}^{\circ}\) & 0\({}^{\circ}\) & 1.08 dB & 0.97 dB & \(-10.1^{\circ}\)\(\leqslant\theta\leq-1.8^{\circ}\) \\ Case \#6 & 90\({}^{\circ}\) & 0.65 dB & 1.31 dB & 0.1\({}^{\circ}\) & 0.1\({}^{\circ}\) & 1.11 dB & 1.66 dB & \(-12.8^{\circ}\)\(\leqslant\theta\leq-4^{\circ}\) \\ Case \#7 & 00\({}^{\circ}\) & 0.62 dB & 0.97 dB & 0\({}^{\circ}\) & 0\({}^{\circ}\) & 0.65 dB & 0.85 dB & \(-6.1^{\circ}\)\(\leqslant\theta\leq 6.1^{\circ}\) \\ Case \#8 & 00\({}^{\circ}\) & 0.41 dB & 0.41 dB & 0\({}^{\circ}\) & 0\({}^{\circ}\) & 0.74 dB & 1.07 dB & \(-4.6^{\circ}\)\(\leqslant\theta\leq 4.6^{\circ}\) \\ Case \#9 & 00\({}^{\circ}\) & 0.71 dB & 1.16 dB & 0\({}^{\circ}\) & 0\({}^{\circ}\) & 0.72 dB & 1.28 dB & \(-2.8^{\circ}\)\(\leqslant\theta\leq 2.8^{\circ}\) \\ Case \#10 & 00\({}^{\circ}\) & 0.8 dB & 0.19 dB & 0.4\({}^{\circ}\) & 0.5\({}^{\circ}\) & 0.78 dB & 1.74 dB & \(-2.3^{\circ}\)\(\leqslant\theta\leq 11.4^{\circ}\) \\ \hline \end{tabular}
\end{table} 
Table 3: Quantitative comparison of simulation results.