Stored energies in electric and magnetic current densities for small antennas

TL;DR

This paper extends the analysis of antenna Q and D/Q bounds to include both electric and magnetic currents in small antennas, providing analytical and numerical insights into optimal shapes and current distributions.

Contribution

It introduces a method to evaluate antenna Q bounds considering combined electric and magnetic currents, extending previous electric-only models.

Findings

Antenna Q relates to the largest eigenvalue of combined polarizability tensors.

The bounds depend on antenna shape and are validated through numerical examples.

The method yields families of optimal current distributions for minimal Q.

Abstract

Electric and magnetic currents are essential to describe electromagnetic stored energy, as well as the associated quantities of antenna Q and the partial directivity to antenna Q-ratio, D/Q, for general structures. The upper bound of previous D/Q-results for antennas modeled by electric currents is accurate enough to be predictive, this motivates us here to extend the analysis to include magnetic currents. In the present paper we investigate antenna Q bounds and D/Q-bounds for the combination of electric- and magnetic-currents, in the limit of electrically small antennas. This investigation is both analytical and numerical, and we illustrate how the bounds depend on the shape of the antenna. We show that the antenna Q can be associated with the largest eigenvalue of certain combinations of the electric and magnetic polarizability tensors. The results are a fully compatible extension of the electric only currents, which come as a special case. The here proposed method for antenna Q provides the minimum Q-value, and it also yields families of minimizers for optimal electric and magnetic currents that can lend insight into the antenna design.