Energy Stored by Radiating Systems

TL;DR

This paper explores the complex concept of stored electromagnetic energy in radiating systems, reviewing theoretical foundations, existing methods, and providing numerical comparisons to clarify the challenges and solutions in defining stored energy.

Contribution

It offers a comprehensive review of methods for defining stored energy in radiating systems, introducing the concept of unobservable energy and comparing techniques through numerical examples.

Findings

Existing methods have different strengths and limitations.

Equivalences between methods are identified under common assumptions.

Numerical comparisons highlight the relative accuracy of techniques.

Abstract

Though commonly used to calculate Q-factor and fractional bandwidth, the energy stored by radiating systems (antennas) is a subtle and challenging concept that has perplexed researchers for over half a century. Here, the obstacles in defining and calculating stored energy in general electromagnetic systems are presented from first principles as well as using demonstrative examples from electrostatics, circuits, and radiating systems. Along the way, the concept of unobservable energy is introduced to formalize such challenges. Existing methods of defining stored energy in radiating systems are then reviewed in a framework based on technical commonalities rather than chronological order. Equivalences between some methods under common assumptions are highlighted, along with the strengths, weaknesses, and unique applications of certain techniques. Numerical examples are provided to compare the relative margin between methods on several radiating structures.