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BELL SYSTEM TECHNICAL JOURNAL 



where Ki is a Bessel's function of the second kind (see " Theory of 

 Bessel Functions " by G. N. Watson). 

 Now 



= anti-Iogio 



2kik 



20 



where Si is the return loss obtained from the two in series. 



Let 



Sp = — 20 logio a = — 5ii — 5i2 + Si, 

 Si = 511 + ■5'i2 4" Sp. 



(38) 



(39) 

 (40) 



This last expression is the distribution curve of the two return losses 

 in series. 



APPENDIX III 



Addition of End Path to Active Singing Points 

 (16 Ca. H-44-25 2-Wire Cable Side Circuits) 



The different tests using the same number of repeaters are different 

 circuits and different testing repeaters. Columns (2) and (4) are 

 measured singing points. Column (3) is the sum of the measured 

 losses from the measuring point to the drop side of the terminal 

 repeater and back, plus the return loss of resistance termination 

 applied at the drop side of the repeater. 



