New Bounds on Spherical Antenna Bandwidth and Directivity: Updates to the Chu-Harrington Limits

TL;DR

This paper revises fundamental limits on spherical antenna bandwidth and directivity by developing a new energy and Q definition, leading to improved bounds that surpass previous Harrington and Chu limits.

Contribution

It introduces a new self-consistent theory for spherical antenna limits, including a precise cutoff frequency and an enhanced directivity-bandwidth bound.

Findings

New spherical mode Q definition based on energy delineation

Derived a precise cutoff frequency for spherical waveguides

Achieved higher directivity and bandwidth bounds by exciting all spherical harmonics

Abstract

The Chu circuit model provides the basis for analyzing the minimum radiation quality factor, Q, of a given spherical mode. However, examples of electrically large spherical radiators readily demonstrate that this Q limit has limitations in predicting bandwidth. Spherical mode radiation is reexamined and an equivalent 1D transmission line model is derived that exactly models the fields. This model leads to a precise cutoff frequency of the spherical waveguide, which provides a clear boundary between propagating and evanescent fields. A new delineation of 'stored' and 'radiated' electromagnetic energy is postulated, which leads to a new definition of spherical mode Q. Next, attention is turned to the Harrington bound on the directivity-bandwidth tradeoff of an antenna with an arbitrary size. Harrington derived the maximum directivity for a specified number of spherical harmonics such that the Q is not 'large'. Here, the method of Lagrange multipliers is used to quantify the maximum directivity for a given bandwidth. It is shown that optimally exciting all spherical harmonics (including n>ka) enables both larger directivity and bandwidth than Harrington's previous limit. While Chu and Harrington's analyses are generally good approximations for most situations, the new self-consistent theory that defines fundamental antenna limits leads to updated results.