410 



BELL SYSTEM TECHNICAL JOURNAL 



DETECTORS 





iZi^ 



AMPLIFIERS 



1 





le":'x( 



' tV-'xe 



-nc @ 





IV? 



EoE, 







' e.^ X e. 



Fig. 42 — Circuit employed in the analysis of the effect of detector characteristics 

 upon signai-to-noise ratio. 



the signal-to-noise ratio of the final output is 



e"s.4 + e"sB + 



+ e^,K 





(7) 



Maximizing this expression with respect to u shows that the maximum 

 occurs for u = 2 (square law) and is 



{u = 2) 



(8) 



That this expression represents the maximum signal-to-noise ratio may 

 also be concluded by observing that it is proportional to the square 

 root of the total energy. 



For linear detectors u — 1 and the signal-to-noise ratio becomes 



Es 



+ e,B + 



+ esK 



en^ K 



{u= 1) 

 If the branch signals are all equal, i.e., if e^A = e^a 



(9) 

 = esK, (8) 



