Irregularities in Loaded Telephone Circuits 



By GEORGE CRISSON 



Synopsis: The development of lonp distance telephone transmission 

 has made the (|iiestion of line irregularities a matter of great im|«)rtanre 

 lieeaiise of their harmful effect in prodiicinR echo currents anil causing ^ 

 the re(H"aters to sing. 



The structure of coil-loaded circuits |H'rmils the calcul.ilion of the 

 prolialiility of obtaining an assigned accuracy of balance between line and 

 network when certain <lata are known or assumed regarding the accuracy 

 of liKtding coil inductance and si-ction capacity. 



Formulae are given and the results of calculations compared with nuasure- 

 ments made on circuits of known accuracy of loading. 



Introdiction 



Tld'i application of ri-|H"atC'rs lo telephone' cimiils in which the 

 speech currents in the two directions of transmission pass through 

 the siinic electrical path, has caused considerable emphasis to he 

 placed on the matter of making the telephone circuits as free as 

 possible from irregularities. This paper aims to present the theory 

 of the relation between the irregularities in coil loaded lines and the 

 effects resulting therefrom, which have an important bearing upon 

 the operation of two-way telephone repeaters. 



The idea of applying the theory of probability to the problem of 

 sutnming up the effects of many small line irregularities was first 

 suggested in 1912 by Mr. John Mills. The effect upon repeater 

 operation of impedance unbalance had been mathematically analyzed 

 by Dr. G. A. Campbell; and the effect upon itnpedance of a single 

 irregularity of any type had been in\estigated by Mr. R. .S. Hoyt. 

 Using a probability relationship which was pointed out In- Mr. \'.. C 

 Molina, Mr. Mills developed a formula which gives the average or 

 probable impedance departure in terms of average or probable irregu- 

 larities in inductance or capacity, which served at the time of the 

 engineering of the transcontinental line (1913-14) and for some 

 years after. 



With the rapid growth of repeatered circuits in cable it became 

 necessary to calculate what fractif)n of a large number of essentially 

 similar lines would give a definite impedance unbalance at a given 

 frequency. The necessiiry mathematical work to indicate the con- 

 ditions for a large group of similar lines was recently carried out 

 independently by Messrs. H. Nyquist and R. .S. Hoyt. 



The theory which has thus been evolved over a period of \cars is 

 now presented in a manner which it is hf)ped will be found relali\ely 

 simple and useful. \'arious charts are given which should be of 



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