Matrix methods in transmission-line and impedance calculations

In the course of radio research carried out at McGill University few years ago, the author had occasion to employ a variety of matrix devices in transmission-line and impedance calculations. Since these are not available in a connected exposition, it has been suggested that useful purpose would be served by bringing them together so as make them readily accessible in connected form. The methods are applicable, not merely to the principal wave on a two-conductor transmission line, but also to all plane-wave processes, in wave guides in space, which are amenable to representation by means of transmission lines. Furthermore, matrices of higher orders can be used the same way to deal with problems of multiple transmission. The use matrices in this connection is not new; 1, 2, 3 the object of the present paper is to specialize both methods and notation for practical purposes the basis of experience in using them. The paper also includes some new results. In particular, attention directed to formulae by which the input impedance may be calculated for a large number of loosely-coupled loads such as occur when long array is fed from a transmission line or wave guide (Section 9). Secondly, the simple conceptions of series- and shunt-loading are generalized in Section 8 in a manner appropriate to the loading waves; in this connection, it is unnecessary to use equivalent circuits, which sometimes hinder rather than assist effective representation. All of the methods indicated here have been found to be useful practice: they should therefore recommend themselves to electrical engineers and physicists.