Numerical analysis of the Yagi-Uda array

An important performance index of a Yagi-Uda array is the directivity. Many studies have been made on the subject of optimization for Yagi-Uda antenna arrays. Shen [1971] obtained an optimum design for a Yagi array under constraints on bandwidths directivity or the size of the array. It was shown that the array configuration is determined by any two of these three being specified. However, due to the nature of the approximation used in Shen's analysis, no information on the input impedance of the Yagi antenna is given. Recently, Cheng and Chen [1973] developed a method for the maximization of the forward directivity of a Yagi-Uda array by adjustment of the inter-element spacing. To what extent the bandwidth is affected when the dimensions of the array are adjusted for maximum directivity remains unanswered. In this study the work of Shen and of Chen and Cheng is extended. Namely, the behavior of the input impedance of the Yagi-Uda array is investigated as the operating frequency is varied. The effect on the bandwidth of a Yagi-Uda array when its gain is optimized by adjusting the spacing of the directors as proposed by Cheng and Chen is also investigated. The analysis makes use of King's three term theory, which converts an integral equation into a complex matrix equation, which is solved using a digital computer.