Theory of Magnetic Transmission Lines

Abstract

This paper presents, for the first time, the frequencydomain theory of magnetic transmission lines, i.e., transmission lines where electromagnetic energy guidance is assured by means of two magnetic-flux carrying parallel magnetic wires, as opposed to the ordinary situation of two current carrying parallel electric wires (an electric transmission line). Propagation equations for the fundamental quasi-TEM mode are established and solved. Wave parameters are analyzed. A transmission matrix is described.

Formulation of Multiwire Magnetic Transmission-Line Theory

“…As mentioned in [14], it must be emphasized that in the x, y transverse plane, the magnetic field is a purely gradient field ∇ × H = 0 (with open field lines, beginning and ending on different wires), and that the electric displacement vector is a purely solenoidal field ∇ · D = 0 (with closed field lines, embracing one or several wires). In what follows the wire labeled 0 is taken as the reference magnetic wire (where the scalar magnetic potential is arbitrarily set to zero).…”

“…. u N , yielding the result in (2), where g ki are dimensionless real coefficients that only depend on the geometry of the MTL, and where each magnetic voltage [14,19] is defined in (3), the open integration path − → i0 belonging to the transverse plane. Note that in a transverse plane, where H is a gradient field, the concept of magnetic voltage is equivalent to magnetic scalar potential difference.…”

“…Moreover, the pul transverse inductance matrix L T of the MGTL is not to be confused with the familiar pul longitudinal inductance matrix L L of electric MTLs. Nonetheless, for ELTLs and MGTLs sharing the same geometry, matrices L T and L L are intimately correlated (see [14], about the role played by the geometrical factors g). The relationship between matrices L T and L L is given in (9a), where 1 is the identity matrix of rank N .…”

“…In addition to [14][15][16], references to MGTLs can only be found in patent [17] dated of 1968 aimed at transients suppression in a power transformer, and also in a recent patent [18] where future terahertz applications of MGTL are speculated. The theoretical background for two-wire homogeneous magnetic transmission-line analysis has been set in [14], considering the quasi TEM approach. An application of MGTL theory to the analysis of ideal transformers has been provided in [15].…”

“…The contribution of the present paper to advancing the state of the art on MGTL is the extension of the two-wire formalism in [14] to the most general case of multiwire inhomogeneous systems. The multiwire MTL theory is illustrated through numerical simulations concerning a three-wire system with three-fold symmetry, where two degenerate modes (odd and even modes) can be defined.…”