Completing the complex Poynting theorem: Conservation of reactive energy in reactive time

Abstract

The complex Poynting theorem is extended canonically to a time-scale domain $(t,s)$ by replacing the phasors of time-harmonic fields by the analytic signals $X(r,t+is)$ of fields $X(r,t)$ with general time dependence. The imaginary time $s>0$ is shown to play the role of a time resolution scale, and the extended Poynting theorem splits into two conservation laws: its real part gives the conservation in $t$ of the scale-averaged active energy at fixed $s$, and its imaginary part gives the conservation in $s$ of the scale-averaged reactive energy at fixed $t$. At coarse scales (large $s$, slow time), where the system reduces to the circuit level, this may have applications to the theory of electric power transmission and conditioning. At fine scales (small $s$, fast time) it describes reactive energy dynamics in radiating systems.

21 pages, no figures

References in corpus (2)

• Electromagnetic inertia, reactive energy, and energy flow velocity
• The Reactive Energy of Transient EM Fields

Cited by in corpus (1)

• Conservation of reactive electromagnetic energy in reactive time