565 BELL SYSTEM TECHSICAL JOURNAL 



electrical irregularities are due principally to the deviations of the 

 inductance of the coils and the capacity of the sections from their 

 a\erage values for the line, it is possible to calculate by a fairly simple 

 method the \alue of the return loss of a coil loaded line if the repre- 

 sentati\e \alues of these deviations and the electrical properties of 

 the line are known or assumed. 



Since the return loss depends upon the accidental combination of 

 a large number of unbalance currents there will not be one definite 

 value applying to all circuits, but an application of the theory of 

 prot)abilities makes it possible to compute what return loss will 

 probably be surpassed by any assigned fraction of a large group of 

 lines having the given de\'iations. 



The method of calculating the return loss of coil loaded lines will 

 now be described. The symbols used in this description and their 

 meanings are given in the following table: 



TABLE I 



A = Attenuation Factor per Loading Section = Ratio of the Current Leaving a 



Loading Section to the Current Entering it. 

 C = Normal Capacity per Loading Section in Farads. 

 F = Fraction of a Large Group of Lines. 

 / =Any Frequency for which a Return Loss is to be Found. 



/, = -^^-^ = Critical or Cutoff Frequency of the Line. 

 ■K\LC 



He = r<epresentative' Deviation of the Capacity of Loading Sections. 



he = Deviation of the Capacity of a Particular Loading Section. 

 Hi, =Representative= Deviation of the Inductance of Loading Coils. 



hi, = Deviation of the Inductance of a Particular Loading Coil. 



// = V//c+-''Z = Representative' Combined Deviation. 



/. = Current Entering the Line. 



/' = Representative- Total In-Phase Returned Current at the Sending End. 



/" = Representative' Total Quadrature Returned Current at the Sending End. 



/,■ = Value of Returned Current which will be Exceeded in a -Specified Fraction F 

 of a Large Group of Lines. 



i' = Total In-Phase Current at the Sending End of the Line. 



i" = Total Quadrature Current at the Sending End of the Line. 



«i. U, it, - - - '■ = Currents Returned from the 1, 2, 3, and Hth Irregularities. 



«i'. »V. «i'i '»' = In-Phase Components of ii, i-, I'j, - - - i„ 



ii", it", ii", '," = Quadrature Com|X)nents of ii, Vg, I3, - - - J, 



k ='\ 7; = Nominal Characteristic Impedance of the Line. 



L = Normal Inductance of a Loading Coil. 



n = Number of Irregularities. 



P = Probability Function for the Absolute \alue of the Total Returned Current 



at the Sending End. 

 p' = Probabilitv Function of the Total In-Phasc Returned Current. 



