Properties of Modal Quality Factors

TL;DR

This paper rigorously investigates the properties of modal quality factors derived from spherical wave functions in antenna theory, providing new mathematical properties and power series expansions that are broadly applicable.

Contribution

It offers a rigorous proof of longstanding open problems regarding modal quality factors and introduces new properties and power series expansions related to spherical Bessel functions.

Findings

New properties of modal quality factors established

Power series expansions for these factors derived

Results applicable to spherical Bessel functions and antenna analysis

Abstract

Spherical wave functions play an important role in the theoretical study of antenna. When they are used to investigate the stored energy outside the circumscribing sphere of the antenna, two different types of modal quality factors appear which exhibit some interesting properties. These properties can be easily demonstrated by numerical tabulations but have never proved rigorously and have remained unsolved for many years. An attempt is made in this paper to try to solve these longstanding problems. New properties and new power series expansions for the modal quality factors have been obtained, which essentially belong to the spherical Bessel functions and therefore are universally applicable.