CROSSTALK BETWEEN COAXIAL TRANSMISSION LINES 157 



transfer impedances. Consider a coaxial pair whose outer conductor is 

 either a homogeneous cylindrical shell or a shell consisting of coaxial 

 homogeneous cylindrical layers of different conducting substances. 

 The transfer impedance from the inner to the outer surface of the outer 

 conductor is then defined as the voltage gradient on the outer surface 

 per unit current in the conductor. In a triple coaxial conductor 

 system this transfer impedance is evidently the mutual impedance 

 between two transmission lines, one comprised of the two inner 

 conductors and the other of the two outer conductors. On the other 

 hand the mutual impedance has a quite different value if one line 

 consists of the two inner conductors while the other is comprised of the 

 innermost and the outermost conductors. 



The surface transfer impedance of a homogeneous cylindrical shell is 

 given by the following expression, good to a fraction of a per cent for all 

 frequencies up to the optical range if the thickness / is smaller than 20 

 per cent of the average radius 



Zab =,r-^csch(c7/). (50) 



^^^^|ab 

 In this equation: 



a is the inner radius of the middle shell in cm. 

 b is the outer radius of the middle shell in cm. 

 / is the thickness of the middle shell in cm. 



0- = -^lirgiJifi nepers per cm. 



lirufi . 

 ^— ohms 



g is the conductivity in mhos per cm.* 

 fjL is the permeability in henries per cm.* 

 / is the frequency in cycles per second. 



If the ratio of the diameters of the shell is not greater than 4/3 the 

 following formula correct to 1 per cent at any frequency will hold for 

 the absolute value of the transfer impedance 



\Zab\ — Rdc I , (51) 



Vcosh u — cos M 

 where 



Rdc — the dc resistance of the shell, 

 u = tyf^Tfigf. 



* As in the previous paper by Schelkunofif we adhere throughout this article to the 

 practical system of units based on the c.g.s. system. For copper of 100 per cent 

 conductivity 



g = 5.8005X10^ mhos/cm. and n = iirlO~^ henries/cm. 



