572 



BELL SYSTEM TECHNICAL JOURNAL 



It is of interest now to return to radio relay transmission and examine the 

 relations derived for metallic conductors, but now assuming that the span 

 attenuation is that associated with an inverse ^-power of distance law 

 (k — 2 for free space attenuation). If we use the symbol E to denote the 

 excess power capacity (in decibels) of the repeater over that required for a 

 unit span of, say, one mile, we get the relation 



lOy^ log L = E-\- (mk - x) log n 



(8) 



where x = 20, 10, 5, 3.33, for the cases described by equations (1), (2), 

 (3), (4), (5) respectively. The equation shows no optimum number of spans 



^- 'H 



< CD 



•- UJ 



20 



Lu q: 

 5 O 



O IL 



6 8 10 20 40 



CIRCUIT LENGTH IN MILES 



60 80 100 



Fig. a — Relation between circuit length, power, and number of repeaters in radio relay 

 systems. 



corresponding to a maximum circuit length. It also shows that when x 

 is less than 10^ the circuit length can be increased indefinitely by adding 

 spans although the spans become shorter with increased circuit length. 

 When X = 10^ the circuit length can not be increased beyond the maximum 

 single span, i.e., it depends solely upon E and is not affected by the number 

 of spans. If X is greater than 10^ the circuit length again cannot be increased 

 beyond the maximum single span and is reduced by employing more than 

 one span. This last case does not occur for free space attenuation. In 

 Fig. 33 is plotted the relationship between L, E and n for the free space 

 attenuation law {k = 2). The curve passing through zero decibels excess 

 power capacity at one mile circuit length applies to one span for any value 



