PART IV 

 NOISE THROUGH NON-LINEAR DEVICES 



4.0 Introduction 



We shall consider two problems which concern noise passing through 

 detectors or other non-linear devices. The first deals with the statistical 

 properties of the output of a non-linear device, that is, with its average 

 value, its fluctuation about this average and so on. The second problem 

 may be stated more definitely: Given a non-linear device and an input 

 consisting of noise alone, or of noise plus a signal. What is the power 

 spectrum of the output? 



There does not seem to be much published material on the first problem. 

 However, from conversation with other people, I have learned that it has 

 been studied independently by several investigators. The same is probably 

 true of the second problem although here the published material is somewhat 

 more plentiful. This makes it difficult to assign credit where credit is due. 

 Much of the material given here had its origin in discussions with friends, 

 especially with W. R. Bennett, J. H. Van Vleck, and David Middleton. 

 Help was obtained from the recent paper by Bennett, and also from the 

 manuscript of a forthcoming paper by Middleton. 



4.1 Low Frequency Output of a Square Law Device 



Let the output current / of the device be related to the input voltage V by 



/ = aV^ ■ (4.1-1) 



where a is a constant. Wlien the power spectrum of V is confined to a 

 relatively narrow band, the power spectrum of / consists of two portions. 

 One portion clusters around twice the mid-band frequency of V and the 

 other around zero frequency. We are interested in the low frequency 

 portion. The current corresponding to this portion will be denoted by 

 / tf , and is the current which would flow if a low pass filter were inserted 

 in the output to remove the upper portion of the spectrum. It is convenient 

 to divide I if into two components: 



It( = he + Uf (4.1-2) 



"Loc. cit. (Section 3.10). 



*" Cruft Laboratory and the Research Laboratory of Physics, Harvard University, 

 Cambridge, Mass. In the following sections references to Bennett's paper and Middle- 

 ton's manuscript are made by simply giving the authors' names. 



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