158 BELL SYSTEM TECHNICAL JOURNAL 



The expression (51) is plotted in Fig. 3, p. 559 of Schelkunoff's 

 paper. ^ 



As it has been already mentioned, (50) and (51) represent the mutual 

 impedance in a triple conductor coaxial system. One might anticipate 

 that if the arrangement is not coaxial the mutual impedance has a 

 different value. This is indeed the case if all three conductors have 

 different axes. But if one transmission line is a strictly coaxial pair, 

 then its own current remains substantially uniform around its axis and 

 from equation (81) of Schelkunoff's paper we immediately conclude 

 that the mutual impedance will be the same as if all three conductors 

 were coaxial. Both transmission lines must be eccentric before their 

 mutual impedance becomes affected by their eccentricities. Thus the 

 mutual impedance Zn between a coaxial circuit and the circuit 

 consisting of its outer shell and a cylindrical shell parallel to it is given 

 very accurately by (50) and (51). 



The surface transfer impedance across a shell consisting of two 

 coaxial homogeneous layers is given by 



7 {Zah)l{Zah)2 , rn,s 



^12—— 7^ , \0^) 



where Z„6 is the transfer impedance for each layer and Z is the series 

 impedance per unit length of the circuit consisting of the two layers 

 insulated from each other by an infinitely thin film, when one layer is 

 used as the return conductor for the other. 



The mutual impedance between two coaxial pairs the outer con- 

 ductors of which are short-circuited at frequent intervals is also given 

 by (52) provided Z is interpreted as the distributed series impedance of 

 the intermediate transmission line comprised of the outer shells of the 

 given coaxial pairs. This Z is the sum of the internal impedances of 

 the two shells {Zhb)i and {Zbb)i and of the external inductive reactance 

 coLe due to the magnetic fiux between the shells. If the proximity 

 effect is disregarded, the internal impedance of a single cylindrical shell 

 is the same as that with a coaxial return and various expressions for it 

 are given in equations (75) and (82) in the previous paper. ^ The 

 inclusion of the proximity effect does not complicate the formulae if the 

 separation between the shells is fairly large by comparison with their 

 radii, but in this case the proximity effect is not very large either. 

 The more accurate determination of Z leads to complicated formulae; 

 for these the reader is referred to a paper by Mrs. S. P. Mead.^ How- 

 ever, at high frequencies the important factors in the mutual impedance 

 are the transfer impedances in the numerator of (52). 



