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BELL SYSTEM TECHNICAL JOURNAL 



1.0 

 0.9 

 0.8 

 0.7 

 0.6 



0.3 

 0.2 



1.0 

 0.9 

 O.S 

 0.7 

 0.6 

 0.5 

 0.4 

 0.3 

 0.2 

 0.1 

 

 -0.1 



100 200 300 400 500 600 700 800 900 1000 



FREQUENCY IN KILOCYCLES PER SECOND 



5 10 20 30 40 50 100 200 300 



FREQUENCY IN KILOCYCLES PER SECOND 



1000 



Fig. 6 — Real and imaginary components, ilf„ and Mb, respectively, of the mutual 

 inductance between (1) two pairs of No. 10 A.W.G. wires and (2) two pairs of No. 

 18 A.W.G. wires. Length of wires = 74 inches; interaxial separation = 0.14 inch. 



imaginary. In the last step of the analysis below the mutual im- 

 pedance of two circuits of wires of large ^" cross-section is derived by a 

 method of successive approximations. A first approximation is ob- 

 tained by assuming the field due to each wire of the second pair cir- 



'- The wires of a pair are to be considered "large" for a given frequency (/), 

 lirovided the values of the radius (a), interaxial separation {d), conductivitN' {a) and 

 permeability (mc) are such that the magnitude 



\{2amUz)IUz)y\ 



is not small compared to unity. Here /o and Ji are Bessel functions of the first kind 

 of zeroth and first orders, respectively, and of complex argument, r = ia'^iwanJu. 



