56S BELL SYSTEM TECIIMCAL JOIRXAL 



II such amplifiers are connected in tandem is that the compression charac- 

 teristic is the same as with one amphtier but occurs at outputs 10 log // db 

 lower. Thus, the power level must be reduced 10 log ;/ db and this penalt}' 

 accrues over and above the noise accumulation penalty. 



In (2) only noise accumulation occurs. 



In (3) and (4) it is assumed that minimum power conditions are attained 

 and the operation has reached the straight part of the minimum (marginal) 

 power curves. Without reshaping, the system must be powered so that, at 

 the tinal repeater, the accumulation of noise does not exceed the marginal 

 \'alue. With reshaping at each of the ii repeaters each span may be mar- 

 ginal. Making each span marginal with the same bandwidth would be 

 accomjilished with 10 log ii db less power and would make the signal-to- 

 noise ratio 10 log // db lower. This can be made up by using more band- 

 width. In marginal PPM-AM the signal-to-noise ratio improvement occurs 

 at the rate of 20 db per decade of bandwidth and thus the bandwidth must 

 be increased by -\///. This requires, to keep the operation marginal, an 

 increase in power of 10 log ;/ " = 5 log n db. In the case of marginal FM, 

 signal-to-noise ratio is improved at the rate of 30 db per decade, and the 

 bandwidth must accordingly be increased by \/ii. To keep the operation 

 marginal, the power must be increased 10 log ;/ ' = 333 log ;/ db. The 

 entries in Tables II and III invoke these relationships. There, n may be 

 thought of as having values 1, 5 or 133. 



Equation (5) reflects the fact that where PCM regenerative repeaters are 

 employed no accumulation of noise occurs with number of spans. 



With pietallic conductors, the span loss in decibels is proportional to the 

 length of span. If A denotes the span loss in decibels per mile and .S* denotes 

 span length in miles, the circuit length L = nS and 



M = — + .V log ;/ (6) 



II 



or, 



.M-—- log ;/ (/) 



where x is the appropriate coetticient, 20, 10, 5 or 3.33. In this e.xpression 

 there is an optimum value of ii corresponding to a maximum value of circuit 

 length L. Figure 28 is a plot of circuit length for .v = 20 (Eq. 1), showing 

 the maxima. Figures 29 to 32 show the optimum values of ;/ and the result- 

 ing maximum circuit lengths for each of the relations expressed in equations 

 (1), (2), (3), (4). 



Considerations affecting transmission over metallic circuits are different 

 from those afTecting radio relay in at least the following four ways: 



1. Interference from other routes substantially vanishes with coaxial and 



