2 BELL SYSTEM TECHNICAL JOURNAL 



trum which occurs in the receiver output, in terms of the intensities 

 and degrees of modulation of the input signals. 



It is to be expected that the results obtained will depend, to some 

 extent at least, on the type of detector which is used. The square law^ 

 characteristic is a fair approximation to that of any detecting device 

 which is worked over only a small range and hence an analysis of this 

 characteristic may be expected to serve as an excellent guide to general 

 detector performance. When large signals are impressed on the 

 detector the functioning of the device may approximate more closely 

 to that of the ideal straight line detector. It has been felt that a study 

 of these two types would furnish data from which the performance of 

 any intermediate type of detector could be inferred without great error. 

 As the problem of the square law detector is very nmch the simpler it 

 will be considered first. 



Mathematical Analysis 

 There will be assumed two broadcasting stations transmitting on 

 frequencies which differ by a relatively small amount, the beat fre- 

 quency being restricted to the audible range or less. Each of the 

 carriers will be assumed to be modulated by a single audio frequency, 

 the modulating frequencies at the two stations being, in general, 

 different. The total signal impressed on the receiving detector will 

 then be of the form 



V = £(1 + -1/ cos pt) cos (joit + c{\ -\- m cos qt) cos oi-J, (1) 

 in which 



V is the total alternating voltage impressed on the detector. 



E is the amplitude of the desired carrier. 



e is the amplitude of the undesired carrier. 



M is the degree of modulation of the desired signal. 



m is the degree of modulation of the undesired signal. 



a;i/27r is the frequency of the desired carrier. 



co2/27r is the frequency of the undesired carrier. 



pjlir is the frequency of the desired modulation. 



5/2 TT is the frequency of the undesired modulation. 



Square Law Detector 

 We shall first suppose this signal to be impressed on a detector which 

 will be assumed to have a characteristic in the neighborhood of the 

 operating point, of the form 



i = Ao + A,v+A,v\ (2) 



