Energy radiated by the switching of currents in a system of conductors

The calculation of transient electromagnetic fields becomes more important in the future because of the increasing demands on system design under EMC-constraints. The switching of currents in a system of conductors is especially crucial because a transient wave is stimulated in the nonconducting environment which can be responsible for the default of electronic systems. The total energy which is radiated by the transient wave can be calculated by integrating the poynting vector over an appropriate closed surface and over the time interval between the switching moment and infinity. It can be a first criterion to evaluate the system behaviour. Unfortunately the calculation of the transient wave is rather complicated even for an elementary system. The calculation of the total energy radiated by a switching process can be simplified by applying the principle of conservation of energy. As a consequence only the energy which is dissipated in the conducting space during the transient current distribution after the moment of switching has to be calculated. The applicability is shown for two characteristic examples. In the first one a permeable and conducting hollow sphere is exposed to the transient field of a current of arbitrary time dependence flowing in a loop of arbitrary shape. In the second example a continuous current flowing in a homogeneous two wire loop in parallel with a solid conductor of rectangular cross section is switched off. At the moment of switching a part of the energy of the nonconducting space is transferred by a guided wave. The remaining energy can be calculated from the current sheet which is excited on the conductors surface at the moment of switching. This part of energy is dissipated in the material during the following transient current distribution.