CROSSTALK BETWEEN COAXIAL CONDUCTORS 361 



proached in as elementary a fashion as possible. In order to do this 

 we shall start with the simple arrangement of two coaxial conductors 

 in free space, a case already covered in previous papers. To the 

 crosstalk equations covering this case will then be added terms to allow 

 for the effects of quads and sheath. In all that follows in Part I the 

 quads and sheath will be considered as one unit referred to as the 

 "sheath." This is a good approximation as will be shown in Part II. 

 The conception of two independent crosstalk components — a direct 

 or transverse component between coaxials in contact and an indirect 

 or interaction component via the sheath tertiary circuit — is not neces- 

 sary for the solution of the problem. It is preserved here, however, as 

 offering a familiar and much simpler approach to a clear understanding 

 of the processes involved in crosstalk summation with length. 



Far-End Crosstalk 



Consider first an elementary section, dl, of a long single coaxial in 

 free space as indicated in Sketch (a) of Fig. 1. If the current at this 

 point in the center conductor is /i the current in the outer conductor 

 is practically — /i since there is no other return path (except through 

 the air dielectric which offers a high impedance especially at the lower 

 broad-band frequencies considered here). Using Schelkunofif's nomen- 

 clature we may state that an open-circuit voltage equal to ei = IiZagdl 

 is developed on the outer surface of the outer coaxial conductor. The 

 term Zas represents the surface transfer impedance (mutual im- 

 pedance) per unit length between the inner and outer surfaces of the 

 outer coaxial conductor. 



Now suppose that we place another long coaxial parallel to the first 

 one and, for generality, insulated from it as shown by Sketch (b) of 

 Fig. 1. The open-circuit voltage ei on length dl of the first coaxial 

 outer conductor will now cause current to flow in the intermediate 

 circuit composed of the two outer conductors. The parameters of this 

 circuit are 73 and Z3 as shown on the sketch. In returning on the 

 second coaxial outer conductor this current causes crosstalk into the 

 second coaxial circuit. 



It is convenient at this point to replace the original impressed voltage 

 ei by the set of emf's shown in Sketch (c) of Fig. 1. The insertion of 

 equal and opposite voltages eijl on the outer surface of the disturbed 

 coaxial outer conductor does not change conditions but enables us to 

 consider certain effects separately. The first effect to be considered is 

 that due to the pair of equal and opposite voltages ei/2 in the loop 

 composed of the two coaxial outer conductors. These voltages com- 

 bine to form a "balanced" voltage ei which tends to drive current 



