Stored Energies and Q-Factor Expressed in Material Derivatives

Stored energies of radiating systems have generated research interest for several decades due to their relationship with Q-factor and fractional bandwidth. In this letter, material derivatives are used to provide a new interpretation of widely used stored energy expressions. This provides a fundamental relationship between stored energies of radiating systems and their electromagnetic material properties. It is shown that electric stored energy is related to the electricmaterial parameter (permittivity) derivative. Similarly, magnetic stored energy is linked to the derivative of the permeability. Furthermore, as an extension, Cauchy-Riemann equations are used to relate stored energy to dissipation.