Method of Mode Matching in Time Domain

Abstract

A new method is presented for analysis of transient electromagnetic fields in regular structures with abrupt discontinuities. The method is based on mode expansion of the fields in the Time Domain. The modes propagate independently in the regular parts of the structure and are coupled at the discontinuity. The main idea consists in solving 1D FDTD equations for each independent mode channel in the regular waveguides and using mode-matching at the junction cross-section in order to relate the mode amplitudes in all the channels at the same time instant via imposing boundary conditions. As examples the problems of pulse signal diffraction at a step discontinuity in a parallel-plate waveguide, diffraction at a junction of circular and coaxial waveguides, and pulse radiation of a bi-conical antenna are considered. The latter problem is treated as a junction of two conical lines (one of which is the free space) that are regular in spherical coordinates.

Mode expansions in time domain

“…Another interesting time domain calculation technique for waveguide diffraction problem has been designed by uniting 1D FDTD schemes for independent mode channels with mode matching technique for coupling at the obstacle (like iris or junction) [11].…”

“…This approach also enabled us to consider radiation by TEM-horn like antennas (like biconical) as diffraction at junction of conical line with free space [11].…”

“…Surely the references list below is far from completeness because of limited space; more references can be found in the latest papers by the author [10][11][12].…”

Axially Symmetric Transient Electromagnetic Fields in a Radially Inhomogeneous Biconical Transmission Line

“…Further, the electromagnetic properties and characteristics of the biconical antenna have been investigated in [5,6,8]. In papers [9,10] a problem of transient TEM wave excitation and diffraction in the biconical antenna has been solved in the time domain using an approach based on mode matching incorporated into the finite difference time stepping scheme for the mode channels. The problems of electromagnetic waves excitation in complex structures of slotted cones have been solved rigorously in [11,12].…”

“…Also METD is developed for studying the transient electromagnetic processes in conical transmission lines [40][41][42][43][44]. In order to use METD for solving electromagnetic pulse diffraction problems on a junction of two regular transmission lines, Mode Matching Time Domain Method was developed [9,10].…”