MICROWAVE REPEATER RESEARCH 



199 



Allowing the signal power to fade by a factor M below this value, the maxi- 

 mum gain of repeater "a:" must be 





(II-l) 



The total maximum gain in the circuit is Gj- = Gi X G2 X - - Gn which 

 for the same repeater spacings and fading allowances becomes 



72 > 2 , ^\ n / j2 X 2 , ^\ D/d 



(II-2) 



— (m = m' 



where D is the total length of the circuit. Because of distortion, original 

 costs, and maintenance costs, this total gain should be made as small as 

 possible. 



s 



4-— da— -| 



JS 3,1 



'-REPEATERS-' 



K-dx 



!-^-dn-*" 



TERMINAL 

 (INPUT) 



-I 



, 1 (SIGNAL) 



L riJ^v 



G n __^ 



n ZNx 

 (noise) 

 terminal 



(OUTPUT) 



Fig. II-l. — Repeater circuit with n links. 



The following example illustrates the maximum gain required of the ampli- 

 fier in a repeater: 



For c? = 4 X 10^ meters (25 miles), X = 0.075 meters (/ = 4000 mega- 

 cycles), A = 4.6 meter2 (50 sq. ft.) and M = 100 (20 db), we have 



G = 4.3X 10'(76db) 



The noise output of a repeater due to noise sources in the repeater itself 

 is approximately^^ 



iVx = 4 X 10-21 F BG:, Watts 



or from (II-l) 



N. = 4X 10-'^ FB ^ M, 



i« H. T. Friis, "Noise Figures of Radio Receivers", Proc. I. R. E., vol. 32, pp. 419-22; 

 July 1944. 



