656 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 



The foregoing results lead to the conclusion that the effective djlS ratio 

 along the length of a cable pair can be determined from formula (1) using 

 1000 cps inductance, with an accuracy equal to that of the inductance tests. 

 Since d is generally known or can be found with greater precision than the 

 inductance, S can likewise be found with an accuracy dependent on the 

 precision of the inductance tests. This conclusion appUes regardless of the 

 type of conductor insulation. However, it should be noted that formula (1) 

 would not be accurate if there happened to be magnetic materials in close 

 proximity with the pair under test, such as, for instance, pairs surrounding 

 a core of steel tape bound coaxials. 



The Dielectric Constant 



The dielectric of a cable pair consists of a non-homogeneous mixture of 

 solid insulating material and air. The dielectric constant of a cable pair can 

 be defined as the ratio of the actual mutual capacitance of the pair to the 

 mutual capacitance which would result if the solid insulating material were 

 removed leaving a 100% air dielectric in the otherwise undisturbed cable. 

 The problem is, of course, to find out what the mutual capacitance would be 

 with an air dielectric, or with any other homogeneous dielectric of known 

 dielectric constant. Because of the complex configuration of the cable struc- 

 ture it is not calculable. 



The shielded balanced pair (referred to herein as the "ideal" pair) structure 

 and its components of mutual capacitance are illustrated in Fig. 1. Although 

 the cable pair structure is different from that of the ideal pair, it has es- 

 sentially the same components of mutual capacitance. The static shield 

 for the cable pair is not solid and perfectly cyhndrical but consists of the 

 other cable pairs or sheath which are immediately adjacent to the pair 

 under consideration. The direct capacitances of the two wires to this ground 

 or shield are very nearly equal. 



Rigorous mathematical formulas have been derived by Mrs. S. P. Mead 

 of the Bell Telephone Laboratories for the mutual capacitance (Cmut) and 

 the capacitance to ground (Co) of the ideal pair. These formulas are given in 

 Appendix I. For discussion purposes they can be written as follows: 



Cmut = 7"^ ^ (2) 



^\2S' d) 



