Nonuniformities in Laminated Transmission Lines

The remainder of this paper is divided into seven parts. Section II contains an outline of the notation used and then a discussion of a new formula for the losses in a parallel-plane laminated transmission line* due to irregularities in the laminations. The section concludes with an outline of a procedure for calculating losses in a given line due to known irregularities. Section I I I shows the derivation of the formula by the application of a perturbation procedure to a differential equation derived by Morgan. 3 ! The procedure leads to an expansion of the attenuation in a * The fundamental notions about laminated conductors, often called "Clogston conductors" or "Clogston lines", are given in a paper by Clogston. 1 F u r t h e r details and embodiments are also shown in U. S. Patents 2,769,147 (A. M. Clogston and H. S. Black),2,769,148 (A. M. Clogston), 2,769,149 (J. (i. Kreer) and 2,769,150 (H. S. Black and S. 1'. Morgan). Experimental results were described in a report by Black, Mallinckrodt and Morgan. 2 The most thorough mathematical treatment published to date is an exhaustive and detailed analysis by Morgan. 3 Vaage 4 has reduced some of the results to terms more familiar to transmission engineers. King and Morgan 5 give a lucid retrospective glance over the whole subject, and present a series of charts and formulas which enable one easily to make quantitative estimates of transmission parameters of interest. This paper is probably the easiest place to start a study of laminated conductors, and provides more than enough background for reading the present paper.