568 BELL SYSTEM TECHNICAL JOURNAL 



The crosstalk between two parallel pairs (this applies to twisted 

 pairs as well) can be reduced by enclosing each pair in a cylindrical 

 metallic shield. It is the object of this and the following two sections 

 to develop a theory for the design of such shields. 



This theory is based upon an assumption that in so far as the radial 

 movement of energy toward and away from the wires is concerned we 

 can disregard the non-uniform distribution of currents and charges 

 along the length of the wires. No serious error is introduced thereby 

 as long as the radius of the shield is small by comparison with the wave- 

 length. The field around the wires is considered, therefore, as due to 

 superposition of two two-dimensional fields of the types given by 

 equations (4) and (5). 



The actual computation of the effectiveness of a given shield will 

 be reduced to an analogous problem in Transmission Line Theory. 



Equations (4) and (5) are too general as they stand. Strictly 

 speaking the effect of a shield upon an arbitrary two-dimensional 

 field cannot be expressed by a single number. The field at various 

 points outside the shield will be reduced by it in different ratios. 

 However, any such field can be resolved into "cylindrical waves," 

 each of which is reduced by the shield everywhere in the same ratio. 

 Moreover, to all practical purposes the field produced by electric 

 currents (or electric charges) in a pair of wires is just such a pure 

 cylindrical wave. 



Since both E and H are periodic functions of the coordinate <p, 

 they can be resolved into Fourier series. The name "cylindrical 

 waves" will be applied to the fields represented by the separate terms 

 of the series. As the name indicates the wave fronts of these waves 

 are cylindrical surfaces, although owing to relatively low frequencies 

 and long wave-lengths used in practice the progressive motion of 

 these waves is not clearly manifested except at great distances from 

 the wires. 



Turning our attention specifically to magnetic cylindrical waves 

 of the nth order, and writing the field components tangential to the wave 

 fronts in the form E cos tup and H cos n(p, we have from equations (5) : 



dE . ^^ d{pH) 



dp dp 



From these we obtain 



{g -f icoe)p + 



twjxp 



E. (108) 



d'^F dE 



'j^+ P^- pcoM(g + icoe)p2 + n^-}E. (109) 



