1174 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1952 



given by (472) as 



AP, = 



TtHoHoPj^I 



dYi 



X'pCoixppj-i) + 0T4 C'i(XpPj-i) 



Apj. (481) 



The total power AP dissipated per unit length in the whole stack is 

 obtained by summing APj o\'er j. Approximately the sum by an in- 

 tegral, we have 



AP = 



ttHoHo 

 9 



irHoHoXp 



j pixlClixpp) + ~ Ci(xpp)] dp 



2g 



1 + 



3xp5i_ 



(482) 



[b^Cl(xph) - a'Clixpa)]. 



The average transmitted power P when the laminae are infinitesimally 

 thin is 



Re 



i [ f E,Hlpdpd<t> 



Jo Ja 



= tta/'^ HoHt I pCl(xpp) dp 



= h^AAHoHtlb'Clixph) - a'Clixpo)]. 



(483) 



If we assume the same value for P when the laminae are of finite thick- 

 ness, then from (482) and (483) the attenuation constant of the line is 



AP 



2 

 Xp 



2P 2 Vm/^ g L 



1 + 



3xl5t_ 



(484) 



The similarity of equation (484) to equation (468) for the parallel- 

 plane line becomes obvious if we write Xp in the form (476) and denote 

 the total thickness ^(6 — a) of conducting material in the coaxial stack 

 by 22^1 . We then have 



pV^/p(a/6) 



1 + 



u\t\ 



2\/M/e g{h - of 



1 + 



3pV^/p(a/6)6t_ 



4.2rp2 2 2r2-| 



(485) 



and as the ratio a/b approaches unity the function fp(a/b) approaches 

 unity and (485) becomes identical with (468). We recall that fi{a/b) 

 was plotted against a/b in Fig. 12. For the principal mode in a cable 



