Computation of Farfield Radiation Patterns by Use of a General Integral Solution to the Time-Dependent Scalar Wave Equation

Abstract

The computation of farfield radiation patterns by use of a general integral solution to the time-dependent scalar wave equation is considered. The use of this theorem in this connection appears to offer advantages that may have been overlooked. In particular, the general theorem is capable of interpretation in terms of an analogous network of linear systems whose inputs are the nearfield measured pressures and whose summed output is the desired farfield pressure. Moreover. the general theorem is valid for signals that are general functions of the time, including noise signals, as well as for signals having only a single frequency component. It may accordingly be applied to a much wider class of signals than the Helmholtz formula or the Green's formula, which have been used as the basis for most farfield computations in the past. The network interpretation of the general theorem is discussed in some detail and the forms of the network response function for both a plane and a spheroidal surface of measurement are given.