Stored Electromagnetic Energy and Antenna Q

TL;DR

This paper explores the decomposition of electromagnetic energy into stored and radiated parts, compares different definitions of stored energy, and evaluates their impact on antenna Q and bandwidth estimates.

Contribution

It demonstrates that stored energy defined as the difference between energy density and far field energy aligns with Vandenbosch's expressions and clarifies cases with negative stored energy.

Findings

Stored energy matches Vandenbosch's expressions in many cases.

Differentiated impedance yields lower stored energy estimates in some cases.

Bandwidth and Q are inversely related, depending on bandwidth type and reflection coefficient threshold.

Abstract

Decomposition of the electromagnetic energy into its stored and radiated parts is instrumental in the evaluation of antenna Q and the corresponding fundamental limitations on antennas. This decomposition is not unique and there are several proposals in the literature. Here, it is shown that stored energy defined from the difference between the energy density and the far field energy equals the new energy expressions proposed by Vandenbosch for many cases. This also explains the observed cases with negative stored energy and suggests a possible remedy to them. The results are compared with the classical explicit expressions for spherical regions where the results only differ by ka that is interpreted as the far-field energy in the interior of the sphere. Numerical results of the Q-factors for dipole, loop, and inverted L-antennas are also compared with estimates from circuit models and differentiation of the impedance. The results indicate that the stored energy in the field agrees with the stored energy in the Brune synthesized circuit models whereas the differentiated impedance gives a lower value for some cases. The corresponding results for the bandwidth suggest that the inverse proportionality between bandwidth and Q depends on the relative bandwidth or equivalent the threshold of the reflection coefficient. The Q from the differentiated impedance and stored energy are most useful for relative narrow and wide bandwidths, respectively.