Equivalent Circuit of the Field Equations of Maxwell-I

TLDR

The paper considers a broad range of electromagnetic problems—including antenna radiation, waveguide and cavity propagation, eddy currents, and conductor stresses—where the field can be nonhomogeneous, nonisotropic, and segmented into uneven blocks. It aims to develop an equivalent circuit that represents Maxwell’s field equations for electromagnetic fields containing conductors and bound charges. The authors construct the circuit in all curvilinear orthogonal reference frames, using two‑dimensional transmission‑line networks of resistors, inductors, and capacitors, with dual networks that incorporate ideal transformers and impedance‑less conductors to capture three‑dimensional symmetry. The resulting circuit enables the study of both transient and sinusoidal field behavior with a network analyzer or numerical methods.

Abstract

An equivalent circuit is developed representing the field equations of Maxwell for an electromagnetic field containing conductors and bound charges. Both transient and sinusoidal field phenomena may now be studied by the network analyzer or by numerical and analytical circuit methods. Examples are radiation from antennas, propagation through wave guides and cavity resonators of arbitrary shapes, eddy currents in conductors, stresses in current-carrying structures, and other general problems in which moving charges either do not enter, or if they do, they may be replaced by equivalent dielectric constants, as in small signal waves on stationary or moving space charge. The circuits are developed for all curvilinear orthogonal reference frames to allow the solution, to any desired degree of accuracy, of special three-dimensional problems with axial and other symmetry by the use of only a two-dimensional network. The electromagnetic field may be nonhomogeneous, nonisotropic (of a special form), and may be divided into blocks of uneven length in different directions. The transient character of the circuit allows the variation of the frequency of the impressed quantities on the alternating-current network analyzer without varying the magnitude of the circuit impedances. One set of two-dimensional networks, the transmission-line type, requires only resistances, inductances, and capacitors, while its dual set requires also ideal transformers in series with the inductive coils. (In the transmission-line type of networks the dual ideal transformers consist of impedanceless conductors.) The three-dimensional network, being its own dual, requires both ideal transformers and impedanceless conductors.