LAMINATED TRANSMISSION LINES. I 885 



desirable to carry out simultaneously as complete a theoretical treat- 

 ment of Clogston-type transmission lines as possible. Clogston's original 

 paper brought out the fundamental ideas by analysis of idealized trans- 

 mission lines bounded by infinite parallel planes. The ])resent paper con- 

 siderably e.xtentls the theoretical analysis of pai'allel-plane systems, and 

 also treats laminated transmission lines l)ounded by coaxial circular 

 cylinders, which are of course the structures of practical engineering 

 interest. 



Part I of this paper deals with both plane and coaxial lines having 

 laminated conductors and ha\'ing the space between the conductoi'S filled 

 with a suitable main dielectric, which may so far as the theory is con- 

 cerned also be a nonconducting magnetic material. Structures of this 

 type are called "Clogston 1" transmission lines. Although in principle 

 the total space may be divided between the main dielectric and the 

 laminated stacks in any desired ratio, we suppose in Part I that the 

 width of the main dielectric is several times the total thickness of the 

 laminations. When this is true, the principal mode fields in the main 

 dielectric are almost identical to the fields of the transverse electro- 

 magnetic (TEM) mode between pei'fectly conducting planes or cylinders. 

 The phase velocity is controlled by the properties of the main dielectric, 

 while the attenuation constant is determined by the surface impedances 

 of the laminated boundaries (and the dissipation, if any, in the main 

 dielectric). The calculation of the surface impedance of a laminated plane 

 or cylindrical stack is reduced, using the generalized impedance concept 

 de\'eloped by Schelkunoff, to the calculation of the input impedance of a 

 chain of transducers with known impedance elements, the chain also 

 being terminated in a kno^\^l impedance. We are thus able to employ the 

 language and the I'esults of one-dimensional transmission theory to solve 

 our three-dimensional field problem. 



In the remaining sections of Part I we introduce various simplifying 

 appi'oximations and special assumptions into the general equations in 

 order to obtain simple and explicit results. We first calculate the propa- 

 gation constant and the field components of the principal mode under 

 the assumption that the individual conducting laminae are extremely 

 thin compared to the skin depth at the operating frequency, and show 

 that the attenuation constant is substantially independent of frequency 

 so long as this assumption is valid. We then give formulas for the reduc- 

 tion of the effective skin dejith in the stacks and the consec^uent increase 

 of attenuation with frequency when the laminae are of finite thickness. 

 Xext we investigate the efTect of varying the phase velocity of the line 

 away from the optimum value given by Clogston ; and in the last section 



