A short way of solving advanced problems in electromagnetic fields and other linear systems

Author

Rumsey, V.H.

Author_Institution

University of California, Berkeley, CA, USA

Volume

11

Issue

1

fYear

1963

fDate

1/1/1963 12:00:00 AM

Firstpage

73

Lastpage

86

Abstract

A linear system is characterized in the abstract by a source vector $a$ , a response vector $\\alpha$ and a system matrix $R$ , connected by $\\alpha = Ra$ . Specific interpretations for $a , \\alpha$ and $R$ are given for electromagnetic fields, the scalar product $a \\dot Rb$ being the reaction. The advantages of this method are illustrated by application to various problems. Mode expansions are defined by the eigenvector equation $Rm = C_{m}m$ , $C_{m}$ being the eigenvalue and $m$ the mode source. This means the mode is generated by a combination of electric and magnetic sources which, apart from the constant multiplier $C_{m}$ , are everywhere equal to the electric and magnetic fields, respectively. Such mode expansions are applied to typical waveguide problems. Waveguide theory is set up in terms of unit voltage and unit current mode sources, $v$ and $i$ , where $v \\dot v = 1 = i \\dot i$ . Then the definitions of waveguide current and voltage coincide with those for circuit theory, e.g., the mode current at cross section $P$ is the reaction on a unit voltage source placed at $P$ . The method also greatly simplifies scattering and antenna problems, such as the pattern of a monopole antenna which is immersed in a layer of gyrotropic plasma.

Keywords

Electromagnetic analysis; Linear systems; Eigenvalues and eigenfunctions; Electromagnetic fields; Electromagnetic waveguides; Equations; Linear systems; Magnetic fields; Transmission line matrix methods; Vectors; Voltage; Waveguide theory;

fLanguage

English

Journal_Title

Antennas and Propagation, IEEE Transactions on

Publisher

ieee

ISSN

0018-926X

Type

jour

DOI

10.1109/TAP.1963.1137982

Filename

1137982