CEA RA CT ERISTICS OF TOLL TELEPHONE CABLES 3 13 



istics were given for impedance, attenuation and delay distortion by Pierre 

 Mertz and K. W. Pfleger'*. 



Closely allied to these effects is the possibility of temperature differences 

 across the section of cable in actual installed cables. Splicing usually takes 

 care of this, too, but there are traces of such a lag in cases where the pairs 

 remain in the outer part of the cable for a long distance and then pass to the 

 inner group for the remaining part of the line. No such cross-sectional 

 variation entered into the laboratory measurements as the temperatures 

 were sufl&ciently well maintained close to given desired values. 



Atlenualion 



The propagation constant y is given by the familiar formula 



7 = a +y^ = V(i?+ycoL)(G+icoC) 



= >Vxy(l+^4)(n-,^) (9) 



The real part, a, is the attenuation in nepers and the imaginary part, /3, is 

 the phase in radians. Expressing the attenuation in terms of reals, gives 



2a' = V{R'-\-c,'L'){G' + co'C') - (co'XC - RG) 



= co'ZCVd + R'/J'L'Xl + G'/co'C') - {c/LC - RG) (10) 



In cables, G/coC is small as compared to unity, in which case (10) may be 

 reduced to the approximate form 



2«' = w'ZCVl + R'/c/L' - (co'ZC - RG) (11) 



The formula for /3 is the same as for a except for the sign of the last two 

 terms in (10) and (11), that is, the sign in front of the parenthesis is + 

 instead of — . 



By expanding the square root term in (10) and using only first order terms 

 in the expansion, another approximate form, frequently found useful in 

 checking high-frequency values, is obtained, viz., 



. R fC , G fl (R , G\ r— 



(12) 



(Terms neglected in this approximation all include powers of w in their 

 denominators and so become negligible at high frequencies.) The first 

 term is commonly called the "resistance component of attenuation" and 

 represents series losses. The second term represents shunt losses and is 

 called the "leakage component of attenuation". The quantity \/L/C, as is 

 well known, represents the nominal characteristic impedance of the circuit. 



" Pierre Mertz and K. W. Pfleger, "Irregularities in Broad-Band Wire Transmission 

 Circuits," B.S.T.J., XVI (Oct. 1937) pp. 541-559. 



