Network Analogs of Maxwell's Field Equations in One and Two Dimensions

Abstract

Network analogs are developed representing Maxwell's equations in the time domain for one and two spatial dimensions. Maxwell's equations are first cast into matrix form. Then the connection between these matrices and the branch node incidence matrix of the equivalent network is made. Next, the relationship between the field variables (electric and magnetic fields) and the across and through variables (currents and voltages) of the network is demonstrated, resulting in Ohm's law for electromagnetic fields in the time domain. Although not required for the derivation, the connected graphs (electrical circuits) of the network analogs are shown. Finally, the appropriate network analog is applied to the practical problem of determining the transient response of a dipole antenna to an incident electromagnetic field.