SINGING ON TWO-WIRE CABLE CIRCUITS 603 



63 per cent of the total return losses measured. Sh is determined 

 entirely from the fractional deviations of the capacitances and in- 

 ductances. Sw is determined by the proximity of the frequency in 

 question to the cutoff frequency of the line facilities. Sa is determined 

 by the attenuation of the cable circuit and is, in effect, the summation 

 function of the different sources of irregularity. 



Figure 2 shows the distribution curve Sp from the paper referred to 

 above. In a similar manner the distribution curve of several repeater 

 sections in tandem or in parallel ^ may be determined. This is known 

 as an active return loss. Referring to Fig. 1 the return loss measured 

 across the west hybrid coil of repeater C will be determined not only 

 by the irregularities in the immediately adjacent repeater section but 

 also by the irregularities in the other repeater section to the west of 

 repeater C as seen through the intervening losses and gains of the 

 circuit. Strictly speaking, the return losses on the east sides of 

 repeaters A and B will also affect the active return loss because cir- 

 culating paths around each repeater and around various combinations 

 of repeaters will exist. However, these circulating paths have so much 

 loss in any practical field circuit in which the other requirements are 

 satisfied, that the return losses on the east side of A and B need not 

 be considered. 



Appendix I derives the formula for the distribution curve of an 

 active return loss when the passive return losses of which it is made 

 up are of the form given above, assuming no returned currents from 

 beyond the terminal repeater. This distribution function is: 



5i - F{N, T) + Sf. 



In this case it is assumed that the value of Si is the same for the passive 

 return losses of each repeater section, but from the appendix, the more 

 general case where there is a different value of ^i for each section may 

 be determined. 



Figure 3 gives values of F{N, T) for the specific case where each 

 repeater section has the same loss and each intermediate repeater has 

 the same gain. The value of this function is also derived in Appendix I. 



Referring again to Fig. 1 there will be an active return loss which 

 may be measured on the west side of repeater C and also an active 

 return loss which may be measured on the east side of repeater C. 

 Assuming that the distribution function of the active return loss 

 toward the west is ^u -f Sp (not including path A) while the dis- 



2 While this paper develops the theory specifically for the case of repeater sections 

 in tandem, e.g., in a single two-wire circuit, it is generally applicable also to the case 

 of repeater sections in parallel, e.g., in a toll conference connection. 



