Abstract

The variational approach is used for solving the synthesis problem of plane rectangular array with waveguide excitation of its elements. The proposed functional includes three components that allow us to minimize the mean square deviation of the given and synthesized amplitude radiation patterns (RP), the value of the field amplitude in the given near zone regions, and the norm of excitation coefficients of the array elements. The mutual coupling of separate array radiators is taken into account solving the corresponding electrodynamic problem. The Hallen’s integral equation is used to determinate the current distribution in the array radiators. The optimal excitation coefficients of the radiators are determined minimizing the proposed functional, it is reduced to solving the nonlinear Euler integral equations system, since the amplitude radiation characteristics are the input data of the problem. The resulting system of nonlinear integral equations is solved efficiently by the method of successive approximations; the relaxation is its characteristic feature. The calculation results show that the developed approach can be used for arrays with different configurations, in particular with hexagonal placement of radiators.

中文翻译：

---

考虑辐射器相互耦合的平面波导阵列的合成

摘要

变分法用于解决平面矩形阵列单元的波导激励的综合问题。所提出的函数包括三个组件，它们使我们能够最小化给定和合成幅度辐射方向图 (RP) 的均方偏差、给定近区区域中的场幅度值以及阵列元素的激励系数范数. 考虑到单独阵列辐射器的相互耦合来解决相应的电动力学问题。哈伦积分方程用于确定阵列辐射器中的电流分布。辐射器的最佳激励系数被确定为最小化建议的函数，它被简化为求解非线性欧拉积分方程组，因为幅度辐射特性是问题的输入数据。通过逐次逼近的方法有效地求解非线性积分方程的结果系统；放松是它的特点。计算结果表明，所开发的方法可用于具有不同配置的阵列，特别是散热器的六边形布置。