Synthesis of planar continuous current sources (planar CCSs) with arbitrary shapes is developed for the generation of specified radiation patterns by method of moments (MoM) and method of least squares (MLS). First, an integral equation is expressed, which relates planar CCS current distribution to its radiation pattern. Second, the planar CCS region is divided into several segments and its current distribution is expressed in terms of the pulse expansion functions to discretise the integral equation. Third, the resulting discretised integral equation is converted to a linear equations system by MoM and MLS. Fourth, the resulting linear equations system is solved to determine unknown coefficients of planar CCS current distribution. To evaluate and compare the efficacy of proposed methods, two parameters of synthesis error (SE) and superdirectivity ratio (SR) are used. It is shown that the number of segments should be properly determined to achieve specified SE and SR. If resulting radiation pattern does not meet design goal, a perturbation procedure is applied to current distribution in order to improve the characteristics of radiation patterns of the planar CCS, such as side-lobe level and pattern ripple. Several examples are given to validate the efficacy of the proposed methods.

中文翻译：

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通过矩量和最小二乘法合成具有任意形状的平面连续电流源，以生成所需的辐射图

通过矩量法（MoM）和最小二乘法（MLS），开发出具有任意形状的平面连续电流源（平面CCS）的合成方法，以生成指定的辐射图。首先，表达一个积分方程，它将平面CCS电流分布与其辐射方向图联系起来。其次，将平面CCS区域划分为几个部分，并根据脉冲扩展函数表达其电流分布，以离散积分方程。第三，将得到的离散积分方程通过MoM和MLS转换为线性方程组。第四，求解所得的线性方程组以确定平面CCS电流分布的未知系数。为了评估和比较建议方法的功效，使用了综合误差（SE）和超指向比（SR）两个参数。结果表明，应适当确定段数以实现指定的SE和SR。如果最终的辐射方向图不符合设计目标，则对电流分布应用微扰程序，以改善平面CCS辐射方向图的特性，例如旁瓣电平和方向图纹波。给出了几个例子来验证所提出方法的有效性。例如旁瓣电平和模式波纹。给出了几个例子来验证所提出方法的有效性。例如旁瓣电平和模式波纹。给出了几个例子来验证所提出方法的有效性。