Mathematical Theory of Laminated 

 Transmission Lines — Part II 



By SAMUEL P. MORGAN, JR. 



lliis part of the paper continues the analysis of the low-loss, broad-band, 

 laminated transniission lines proposed by A. M. Clogston, and deals 

 particularly with ''Clogston 2" lines, in which the entire propagation space 

 is filled with laminated material. 



TABLE OF CONTENTS 



Page 



VIII. Principal Mode in Clogston 2 Lines with Infinitesimally Thin Laminae 1121 

 IX. Partially Filled Clogston Lines. Optimum Proportions for Principal 



Mode _ 1133 



X. Higher Modes in Clogston Lines 1150 



XI. Effect of Finite Lamina Thickness. Frequency Dependence of Atten- 

 uation in Clogston 2 Lines 1163 



XII. Effect of Nonuniformity of Laminated Medium 1181 



XIII. Dielectric and Magnetic Losses in Clogston 2 Lines 1201 



Appendix II: Optimum Proportions for Heavily Loaded Clogston 



Cables 1203 



Appendix III: Power Dissipation in a Hollow Conducting Cylinder. 1204 



VIII. PRINCIPAL MODE IN CLOGSTON 2 LINES WITH INFINITESIMALLY 

 THIN LAMINAE 



In Part I* of this paper we have set up a general mathematical frame- 

 work for the analysis of Clogston-type laminated transmission lines 

 and have applied it to Clogston 1 lines having laminated conductors, 

 but with the total thickness of the laminations small compared to the 

 overall dimensions of the line, so that most of the forward power flow 

 takes place in the main dielectric. In Part II we shall consider Clogston 

 2 lines, which instead of containing a main dielectric have the propaga- 

 tion space entirely filled with laminations; and we shall also derive 

 results, in Sections IX and X, for the general laminated transmission 



* S. P. Morgan, Jr., Bell System Tech. J., 31, 883 (1952). Since the two parts of 

 the paper are very closely related, the sections, equations, figures, and footnotes 

 have been numbered consecutively throughout the whole paper. A table of 

 symbols appears at the end of Part I. 



1121 



