An Approximation Mathematical Formula of Pattern Analysis for Distorted Reflector Antennas considering Surface Normal Vector Variation

Abstract

An approximation mathematical formula to compute the distorted radiation pattern for reflector antennas is presented. In this approximation formula, besides the phase error caused by the structural deformation being added in the far field integral, the surface normal vector variation is also taken into consideration. The formula is derived by expanding the surface normal vector into a first-order Taylor series and the phase error into a second-order Taylor series. By assembling the integrals including the contributions of both surface normal vector variation and phase error, the far field electrical vector expressed as a function of structural nodal displacements is further obtained in a matrix form. Simulation results of a distorted reflector show the application of this formula.

A review of full-path electromechanical coupling modeling and compensation for reflector antennas

“…Zhang等人 [50] 基于机电耦合设计研究 了变形反射面辐射图的近似分析方法, 该方法采用形 函数插值确定积分点变形, 进而建立了节点信息和辐 射图之间的函数关系, 通过回忆存储的数据和结构有 限元信息, 实现变形反射面辐射图的快速计算. 之后, Zhang等人 [51] 又研究了考虑表面法向量变化的变形反 射面天线方向图分析的近似数学公式, 通过将曲面法 向量展开为一阶泰勒级数, 将相位误差展开为二阶泰 勒级数, 完善了变形反射面方向图快速计算的过程.…”