LAMINATED TUAXSMISSION LINES. II 



1145 



cable ill wiiich mo = m, eo = e, and with the dimensions a = 0.0846, 

 Pi = 0.4156, and pi = 0.8316, these proportions iiaving been found 

 optimum, as discussed below, for a cable without magnetic loading in 

 wiiich the total thickness of both stacks is arbitrarily chosen equal to 

 \h. Fig. 14(b) shows the helds of a complete Clogston 2 with no inner 

 core, the scale being chosen so that the total one-way current is the 

 same in both cases. The attenuation constant of the first cable is 1.234 

 times that of the second one. Fig. 14 may be compared with Fig. 13 

 for the plane geometry, whence it should be possible to visualize ap- 

 proximately the fields of the principal mode in other coaxial structures 

 representing various stages of the transition between the extreme Clog- 

 ston 1 and the complete Clogston 2 cable. 



Now let us consider a Clogston line with infinitesimally thin laminae, 

 having fixed external dimensions and containing only materials with 

 given electrical constants. We may pose two questions: (1) Supposing 

 that for some practical I'eason the total available thickness of laminated 

 material is also fixed, how should this material be divided between the 

 two stacks to minimize the attenuation constant of the line? (2) Assum- 

 ing that the total thickness of laminations in the line is at our disposal, 

 what is the optimum amount of laminated material from the standpoint 

 of minimizing the attenuation, and how should this material be distrib- 

 uted in the optimum case? 



For plane transmission lines the first question is trivial; the stacks 

 should always be of equal thickness. In a coaxial cable, if the filling 

 ratio (si + S2)/6 is gi\'en, the proportions of the cable are completely 

 determined when we specify, for example, the relative radius a/6 of the 

 core and the relative thickness Si/(si + S2) of the inner stack. The opti- 



, f F 



Hc^ = 



H OR E 



H OR E 



Fig. 14 — Fields of principal mode in partially and completely filled coaxial 

 Clogston lines with mo = M, eo = «. 



