Analytical Solution for Characteristic Modal Power Distribution and Truncation Limit for Spherical Wave Expansion of Antenna Radiation Pattern

Abstract

_—In this paper the Spherical Wave Expansion (SWE) is used to represent an antenna radiation pattern. An analytical expression for the characteristic modal distribution of power radiated by an arbitrary antenna is derived from the assumption of equal average amplitude for each mode over the surface of the minimum sphere enclosing the antenna. The relative power error of a truncated expansion is obtained from the derived modal power distribution. The result offers a convenient way to determine an appropriate truncation limit of the modes in a SWE as a function of the desired accuracy and antenna size. This method is more accurate than the formulas given previously in the literature. Moreover, it allows one to choose the accuracy of the resulting field, contrary to the earlier formulas. The derived truncation limit is compared with expressions given previously in the literature and with analytically and numerically determined radiation pattern examples. The modal power distributions are also compared with the calculated examples.