Mathematical Theory of Laminated 

 Transmission Lines — Part I 



By SAMUKL P. MOlU; AN, JR. 



.1 inatlu'niadcdl (inulysis is given of the low-losa, broad-bdnd, UuninaUd 

 transmission lines 'proposed by A. M. Clogston, including bulk idealized 

 parallel-plane lines and coaxial cables. Part I deals with ''Clogston i" 

 lines, which have laminated conductors with a dielectric, chosen to provide 

 the proper phase velocity for waves on the line, jilUng the space between the 

 conductors. Part II will treat lines having an arbitrary fraction of their 

 total volume filled with laminations and the rest with dielectric, and will be 

 concerned in particular with '"Clogston ^" lines, in which the entire propaga- 

 tion space is occupied by laminated material. 



The electromagnetic problem is first formulated in general terms, and then 

 specialized to yield detailed results. The major theoretical questions treated 

 include the determination of the propagation constants and the fields of the 

 principal mode and the higher modes in laminated transmission lines, the 

 choice of optimum proportions for these lines, the calculation of the fre- 

 quency dependence of attenuation due to the finite thickness of the laminae, 

 the increase in loss caused by improper phase velocity (dielectric mismatch) 

 in Clogston 1 lines and by nonuniformity of the laminated material in 

 Clogston 2 lines, and the effects of dielectric and magnetic dissipation. 



TABLE OF CONTENTS 



I. Introduction 884 



II. Wave Propagation Between Plane and Cylindrical Impedance Sheets. 887 



III. Surface Impedance of a Laminated Boundary 89G 



IV. Principal Mode in Clogston 1 Lines with Infinitesimally Thin Laminae 908 

 V. Effect of Finite Lamina Thickness. Frequency Dependence of Attenu- 

 ation in Clogston 1 Lines 921 



VL Effect of Dielectric Mismatch 931 



VII. Dielectric and Magnetic Losses in Clogston 1 Lines 940 



Appendix I : Bessel Function Expansions 944 



Table of Symbols 946 



883 



