Recoverable Energy of Dissipative Electromagnetic Systems

TL;DR

This paper clarifies the concept of recoverable energy in electromagnetic systems, relating it to stored energy and fractional bandwidth, and provides closed-form calculations for lumped and radiating systems.

Contribution

It introduces a well-defined recoverable energy concept, links it to fractional bandwidth, and derives closed-form expressions using rational function approximation.

Findings

Recoverable energy can be calculated in closed form for various systems.

A relationship between recoverable energy and fractional bandwidth is established.

Lumped circuits demonstrate the link between recoverable and stored energy.

Abstract

Ambiguities in the definition of stored energy within distributed or radiating electromagnetic systems motivate the discussion of the well-defined concept of recoverable energy. This concept is commonly overlooked by the community and the purpose of this communication is to recall its existence and to discuss its relationship to fractional bandwidth. Using a rational function approximation of a system's input impedance, the recoverable energy of lumped and radiating systems is calculated in closed form and is related to stored energy and fractional bandwidth. Lumped circuits are also used to demonstrate the relationship between recoverable energy and the energy stored within equivalent circuits produced by the minimum phase-shift Darlington's synthesis procedure.