This paper demonstrates a novel form of substrate integrated waveguide SIW antenna array based on Fourier Series Equations. An optimized SIW power divider feeds the proposed structure where a micro-strip transition is used for impedance matching at 50 Ohm. The proposed antenna is traveling wave antenna type, in conventional methods the curve of antenna is of a linear or exponential form. In our method, we used the FSE to modify the contour of the antenna. The method is based on optimization of the Fourier series coefficients in order to maximize the gain for φ = π/2 and θ = π/2. The results of the return loss, the field’s distribution, the radiation pattern and the realized gain were analysed. Furthermore, the antenna is designed in HFSS and CST with a comparison between them. The simulated return loss was compared with experimental measurements. The return loss of the proposed 1 × 4 antenna array is less than −10 dB at 5.5–6.8 GHz with an average gain about of 6 dBi and a peak gain about of 7.2 dBi. The proposed 1 × 4 antenna array is optimized with HFSS and designed using FR4 substrate, and considered in C-band for centimeters waves applications.

中文翻译：

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使用用于 C 波段应用的傅里叶级数方程优化 SIW 对映 Vivaldi 天线阵列

本文展示了一种基于傅里叶级数方程的新型基板集成波导 SIW 天线阵列。优化的 SIW 功率分配器为建议的结构供电，其中微带过渡用于 50 欧姆的阻抗匹配。所提出的天线是行波天线类型，在传统方法中，天线的曲线是线性或指数形式。在我们的方法中，我们使用 FSE 来修改天线的轮廓。该方法基于傅里叶级数系数​​的优化，以使增益最大化φ=π/2和θ=π/2。分析了回波损耗、场分布、辐射方向图和实现增益的结果。此外，天线采用 HFSS 和 CST 设计，并进行了比较。将模拟回波损耗与实验测量值进行比较。所提出的 1 × 4 天线阵列的回波损耗在 5.5-6.8 GHz 时小于 -10 dB，平均增益约为 6 dBi，峰值增益约为 7.2 dBi。所提出的 1 × 4 天线阵列使用 HFSS 进行了优化，并使用 FR4 基板进行设计，并考虑在 C 波段用于厘米波应用。