DETECTION OF TWO MODULATED WAVES 



An expression of this type will accurately represent a small portion of 

 any continuous characteristic. The present analysis requires that the 

 impressed e.m.f. shall be of small amplitude in order that the limits of 

 the portion of the characteristic thus represented may not be exceeded. 

 This restriction is necessary in treating square law detectors. 



The audio frequency output of the detector will be due entirely to 

 the second order term in (2). Hence it will be sufificient, for our 

 purposes, to square the expression for v. We are interested primarily 

 in the ratios of the amplitudes of the various undesired audio fre- 

 quencies produced to the amplitude of the desired signal of frequency 

 Pi lit. Such a ratio will be designated as a relative amplitude. Neg- 

 lecting circuit constants, etc., which will apply equally in all the 

 expressions for the various frequencies, the amplitude of the desired 

 component of the audio frequency output is readily shown to be E-M. 

 The expression for v- is reduced to first power sinusoids and the ampli- 

 tude of each frequency converted to a relative amplitude by dividing 

 by E~M. The case in hand >ields twelve undesired audio frequencies, 

 the relative amplitudes of which are listed in table I. Before com- 

 menting on these results we shall consider the straight line detector. 



TABLE I 



in which 11 = 0:1 — coo. 



The Straight Line Detector 



In making analyses of rectification by a straight line detector it is 

 customary to reduce the sum of the various impressed radio frequencies 

 to a single radio frequency, the amplitude and phase angle of which are 

 slow functions of time. The most common example of this type of 

 treatment is a combination of the carrier and two side bands of single 

 frequency modulation into the familiar expression for a modulated 



