Efficient Procedure for the Calculation of Electric and Magnetic Energies in Vacuum

Abstract

New expressions are derived to calculate the reactive energy stored in the electromagnetic field surrounding an electromagnetic device. The resulting expressions are 1. very simple to interpret, 2. general, 3. rigorous in terms of the currents flowing on the device, and 4. fast since they involve integrals solely over the device generating the field. The new technique is very feasible to be used in cases where the electric and magnetic reactive energies are important in practice, for example in the case of resonators, or in the case of radiating structures. Used there, they allow to study in a rigorous way the effect of the shape of the device on the amount of reactive energy, and thus for example on the Q of the device. The implementation of the new expressions in numerical CAD tools is extremely simple and straight-forward. In this paper, the expressions are derived for sources in the homogeneous medium vacuum, but this is not a fundamental restriction.