1026 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER, 1953 



of links. The mathematical expression for the combination of these 

 three standard deviations is: 



Dl = Dl + D] + NDl 

 = 2.5' + 3' + N2' 



From this equation Table II can be constructed. 



In line with the principles stated at the outset, the mathematics will 

 be worked out on the basis that 99 calls out of 100 will be free from echo; 

 then margins will be added. The mathematics are as follows: (1) In 

 order to meet 99 per cent of the cases, 2.33 standard deviations must be 

 used, or: Avg. Rd. Trip Loss = Avg. Echo Tol. - Avg. Ret. Loss + 2.33 

 Std. Dev. (2) The average one-way loss is the loss to be assigned and is 

 one-half the average round-trip loss. 



Table II 



Permissible average losses with several different numbers of links, 

 based on this equation, are given in Table III. These data are for four- 

 wire circuits and four-wire switching. It will be noted from Table III 

 that for a given total round-trip delay the necessary increase in over-all 

 loss for increasing numbers of links varies somewhat for different con- 

 ditions but for the more severe cases it is about 0.4 db per link. 



Because, as stated at the outset, the relationship between round-trip 

 delay and permissible circuit loss is not linear, Table III can not be used 

 directly in selecting the working net loss of a circuit to be used in switched 

 connections. An example will make this clear: 



(a) From Table III, the permissible loss of a circuit with 20 ms round- 

 trip delay is 5.0 db. 



(b) If this were used as the basis for designing the circuit, the loss 

 of four such circuits in tandem would be 20.0 db whereas the table shows 

 that four links with a total round-trip delay of 80 ms could be operated 

 at 14.6 db. 



