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THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 



APPENDIX II 



It has been shown that if there is a dielectric constant for capacitance to 

 ground (e^) which is different from €mut, then values of €mut as found from the 

 ideal pair formulas will be in error. This appendix describes results of an 

 attempt to evaluate the e^nut/^g ratio for paper ribbon and pulp insulated 

 cable using a method suggested by Mr. M. C. Biskeborn. It was reasoned 

 that whatever non-homogeneity exists in the cable dielectric would be caused 

 by variations in the insulation density in various portions of the dielectric 

 space. Compressive forces encountered in twisting and stranding the pairs 

 tend to make the density for the space between wires of a pair high as com- 

 pared with an average density for the total dielectric space. Since (e — 1) 

 and the power factor, or simply G/C, go to zero approximately in direct 



Table A 

 Evaluation of eg/emut for Pulp Insulated Cable 



proportion to the amount of soUd dielectric material, the following equation 

 may be used to find an approximate value for eg/emut: 



€g — 1 Power Factor of Grounded Circuit 

 €mut ~ 1 Power Factor of Balanced Circuit 



in ~ r — 7r — ~ ^ (power factor ratio) 



€mut -1 tjmut/v-'mut 



Dividing by €mut and rearranging: 



€mut 



= F + 



\ Cmut / 



Substituting 1.50 for Cmut on the right hand side introduces but small error 

 in the eventual result since F is known to be closely equal to unity and 

 permits solution for €(,/€mut as follows: 



= 1 



Cmut 



C-i-O 



