Energy Stored by Radiating Systems

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.

Control of a quantum emitter's bandwidth by managing its reactive power

“…The analysis of the reactive power [1,2] and related quantities such as the stored energy [3,4] plays a central role in the design of classical radiating systems and the identification of their fundamental limits. This aspect is particularly relevant for electrically small antennas, since the smaller the size of an emitter, the larger the impact of the reactive fields on its performance.…”

State‐space models and stored electromagnetic energy for antennas in dispersive and heterogeneous media

“…The energy expressions presented here are restricted to electrically small antennas where they are positive definite. The open question of defining and efficiently evaluating the stored energy for electrically large structures remains, as of yet, unsolved, see also [ Schab et al , ].…”

“…Because of its relation to the bandwidth the Q factor is an important parameter for antenna design. Thus, it has become imperative to define stored energy for antennas [ Chu , ; Yaghjian and Best , ; Volakis et al , ; Gustafsson et al , ; Capek et al , ; Schab et al , ]. However, this is not trivial as electromagnetic fields, current densities, and circuit models can give different interpretations of the stored energy, see Figure .…”

“…Stored energy is instrumental for antenna analysis in terms of the Q factor [ Collin and Rothschild , ; Yaghjian and Best , ; Gustafsson et al , , ; Volakis et al , ; Capek et al , ; Chu , ; Schab et al , ]. In Yaghjian [], Yaghjian et al [], and Hansen et al [] stored energy is considered for small antennas composed of dispersive or lossy media, embedded in free space.…”

On Localized Antenna Energy in Electromagnetic Radiation

“…Energy localization is now seen as a fundamental factor in electromagnetic therapy in general [6] and microwave hyperthermia in particular [7]. However, while looking into the electromagnetic energy in the near-field of antennas, the applied electromagnetics community mostly focuses the attention towards the "reactive energy" for antennas [8][9][10][11][12][13][14][15]. It should be noted here that near-field focusing is another classical antenna application where energy localization is essential [16][17][18], and the same is true for the closely related subject of wireless power transfer [19].…”