天线方向系数的一类计算逼近方法

天线的方向系数是天线的核心性能指标之一,准确计算方向系数是高性能天线应用的核心要求.本文基于平面近场测试理论、实测数据和快速傅里叶变换算法,系统阐述基于近场测试来数值计算天线方向系数的原理,并进行深入的误差分析.本文选择一种方向图函数和方向系数已知的被测天线,来检验所讨论的误差评估方案.评估分两步实现,第一步,针对这一天线,采用标准的近场测试配置,仿真模拟出(相当于实际测量出)一套平面近场数据.第二步,基于这套近场数据,利用数值积分计算出天线方向系数.本文使用或提出了四种数值算法,分析了提出的后三种算法本身的误差来源,并开发出程序搜索方案,确定出后两种算法的最小误差界.随后,利用这四种数值算法分别得出天线的方向系数.结果表明,计算所得的近场方向系数都比真实方向系数大,但误差不超过0.6 d B.这一结果对实际应用中正确评估基于近场测试的天线方向系数准确性有重要参考价值.

A class of approximate computation method for antenna directivity

Directivity is one of the core performance parameters for an antenna, and its accurate computation and measurement have been receiving attention in the past decades. While quite a number of computational methods for antenna directivity are developed, a comprehensive comparison among these methods, including their advantages and disadvantages, has not yet been reported. In the literature, most of these methods can be roughly classified as two categories, i.e. numerical methods and analytical methods. The numerical methods include those simplified numerical methods for accessing the radiation pattern. For example, some methods assume that the radiation pattern is only elevation-angle dependent, and an approximate truncation of the integral interval is often employed. The analytical methods are developed, where the electromagnetic radiation intensity and the total radiation power for a specific antenna are derived analytically. Nevertheless, so far there have been less efforts dedicated to developing general computational methods based on the antenna’s planar near-field theory and associated computational schemes, although indeed quite a few of advanced mathematical approaches have been used to obtain the accurate directivity, including the series expansion based on the spherical wave scheme and the Fourier expansion scheme. In spite of these efforts, one can see that a general accurate numerical scheme for the antenna directivity is still urgently required. As an important supplement to these efforts, this paper adopts or proposes four numerical integration methods regarding planar near-field measurement of the antennas under test. Based on the planar near-field theory, microwave near-field data, and fast Fourier transform(FFT), this paper discusses the numerical integration-based algorithm schemes based on the simulated(or measured) near-field data and relevant numerical uncertainty estimation. Specifically, an antenna with accurate directivity is chosen for illustrating the accuracy assessment. First, a set of near-field data under the well-established probing condition is simulated and then used as an input for subsequent numerical calculation of the antenna directivity value. Four different numerical integration methods are employed and their possible numerical errors are discussed. Consequently, the antenna directivity values are obtained respectively from the four different numerical methods. It is revealed that the numerically evaluated directivity values from the near-field data are roughly at most 0.6 d B larger than the accurate value. This work represents a substantial step toward a reliable estimation of the antenna directivity from the near-field data of an antenna.