Numerical integration methods for antenna pattern calculations

A study of numerical integration methods suitable for antenna pattern calculations was conducted for the purpose of determining which method provides a given accuracy with the greatest economy. The accuracy for a given method depends on the number of points at which the integrand is calculated, while the cost for a given number of points depends on the complexity of the method. This paper discusses the general principles of numerical integration, and outlines four methods in detail. The results of applying these methods on a digital computer to a simple cosine distribution are presented and analyzed. The relation of these results to those obtained for a pattern integral having a nonlinear phase function is discussed. The Gaussian quadratures are shown to have, in general, the highest degree of precision and lowest cost, while Filon´s method is preferable when integrals having a linear phase function are calculated over a large range of pattern angle. The procedure for applying these methods to double numerical integration is outlined.