706 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1953 



Part II — Derivation and Evaluation of Formulas 



In this part of the paper, approximate formulas for the counter- 

 parts of the usual primary constants used in transmission line computa- 

 tions are derived for Clogston I and II type cables. From these formulas 

 the various constants entering into the expressions for attenuation, im- 

 pedance and phase as given in Part I are evaluated in terms of the di- 

 mensions of the cables and the frequency. 



In deriving the formulas, certain simplifying assumptions have been 

 made as explained in the test. The effects of these assumptions are 

 examined by comparing the results with those obtained by more rigorous 

 methods. 



1. RESISTANCE IN GENERAL 



A Clogston I cable consists of a laminated inner conductor and a 

 laminated outer conductor as shown in Fig. 1. Each of these may be 

 represented by the laminated conductor shown in Fig. 6. At present, we 

 have no exact formula for the ac resistance of such conductors over a 

 wide range of frequencies. However, S. P. Morgan has shown that for a 

 stack of parallel plates, the resistance per unit cross-sectional area is 

 equal to: 



fl, = R^ !g±l Fi + ('^^ - y5)«>- FL +....], (16) 

 w L 412 J 



where i^dc is the dc resistance of the stack, when completely filled with 



— D-' 



Fig. 6 — Laminated conductor. 



