MEASUREMENTS IN MULTIPAIRED CABLES 657 



where e = dielectric constant and /„, and /j, are the functions defined in 



appendix I. 



Dividing equation (3) by equation (2): 



Ca/c^^,= r^'^J (4) 



\2S'dJ 



Thus, the Cg/Cmnt ratio is independent of the dielectric constant, being 

 a function only of the dimensional ratios describing the ideal pair configura- 

 tion. The ratio d/2S also appears in formula (1). Therefore, knowledge of 

 L, Cgj and Cmut for an ideal pair is sufficient to find its dimensional ratios 

 and dielectric constant, using the following procedure: 



1. Equation (1) is solved for d/2S, 



2. Knowing Cg/Cmnt and d/2S, equation (4) is solved implicitly for S/D. 



3. Knowing Cmut, d/2S, and S/D, equation (2) is solved for e. 



Curve sheets to faciUtate the solution of equations (2) and (4) for the ap- 

 plicable ranges of d/2S and S/D are shown in Figs. 2 and 3. 



When this same procedure is appUed to a cable pair using its measured 

 1000 cps L, Cg, and Cmut, the dielectric constant value obtained is truly 

 representative of the pair in accordance with our definition of dielectric 

 constant, only if the ideal and actual structures are equivalent. An absence 

 of rigor in this method would be expected due to differences in configuration, 

 and non-homogeneity in the cable dielectric. 



The magnitude of the error in the dielectric constant of a cable pair, when 

 determined by this method, was evaluated by comparison of tests on a cable 

 having a known, homogeneous dielectric with tests on an identical cable 

 structure having a non-homogeneous dielectric but a known dielectric 

 constant. 



These tests were made on a short length of cable containing twenty-two 

 19-gauge pairs. The conductors were insulated with solid polyethylene. The 

 core wrap was polyethylene tape under an alpeth* sheath. A low molecular 

 weight polyethylene compound known as DXL-1 has the same dielectric 

 constant as solid polyethylene (2.26). The compound is in a semi-solid state 

 at room temperature and flows easily at 150° Fahrenheit. By filling the 

 interstitial air space in the cable with DXL-1, a cable having a homogeneous 

 dielectric with a dielectric constant of 2.26 is obtained. The dielectric con- 

 stant of the cable structure before filling with DXL-1 is found from the 

 ratio of mutual capacitance before and after filling, and a check on the 

 accuracy of the ideal pair formulas as applied to cable pairs is available. 



* Bdl Laboratories Record, November 1948. 



