708 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1953 



outer conductor and adding the result. Thus: 



„ , ,3 S20S0Ai [ . , Biw'DIfL , 1 1. / • /o1^ 



/Ci + I^ac2 = —^^2 — [1 + — 37lO~ ■ ■ ■ J ^^"^^/"^^' (21) 



where: 



Dl . d! 



„ 2(D,Dt - d,(k){Di - dx)(J>2 - ^2) .„„, 



^' - {Dl -dl + Dl- dl)Dl ■ ^^^> 



From (4) and (5) in the first part of this paper, it is possible to ex- 

 press A i and Bi wholly in terms of <^i , T and U. Thus, Ai and Bi are 

 independent of D2 , and it follows that the first term in (21) is inversely 

 proportional to Dl , while the second term, when multiplied out, is in- 

 dependent of D2 , assuming fixed values of 0i , T and U. 



2.2 Impedance J Inductance and Capacitance 



In a coaxial cable the flux in the space between the two conductors 

 gives the external inductance. The internal inductance is obtained from 

 considering the flux within the walls of the conductors themselves but 

 not that in the space between them. The effective inductance is then 

 the sum of the two. Analogous considerations apply to the external and 

 internal capacitance and the effective over-all capacitance is the value 

 of the two acting in series. 



Similarly in the frequency range where o)L^R and o)C ^ G, but where 

 the ac resistance is nearly equal to the dc resistance, the internal in- 

 ductance and capacitance of the laminated conductors must be taken 

 into account. Since they are in series with the external components they 

 tend to increase the total inductance and decrease the total capacitance. 

 The impedance of the circuit can therefore be expressed as follows: 



Z, = i/| = 7 ^^^+/"^-, ohms, 



./ r CinCex 1 "' (24) 



(I) 



(#3 



Lex = ^ ^n ( ;i ) henries/cm, (25) 



2ir€/ 



^« = 7T\ farads/cm, x^^v 



^^fd,\ (26) 



