528 BELL SYSTEM TECHNICAL JOURNAL 



(3) To minimize both linear and non-linear distortion it is necessary 

 that the sequence 



A, (IV (1- 



be rapidly convergent from the start. 



The first term of (58) is simply direct current and has no significance 

 as regards the recovered signal. When we come to consider the 

 problem of noise in the next section, we shall find that its elimination is 

 important. This can be efi'ected by a scheme which may be termed 

 balanced rectification. Briefly described the scheme consists in termi- 

 nating the transducer in two frequency detectors ji and y^ in parallel ; 

 these are so adjusted that 3'i(icoc) = — y^iiooe) and dyi/dc^c = dyz/dojc. 

 oji is therefore of opposite sign in the two frequency detectors. The 

 rectified outputs of the two parallel circuits are then differentially 

 combined in a common low frequency circuit. Corresponding to (58), 

 the resultant detected output is 



2 — cos a- sit). (59) 



This arrangement therefore eliminates first order non-linear distortion, 

 as well as the constant term. 



Rectification is the simplest and most direct mode of detection of 

 frequency-modulated waves. However, in connection with the problem 

 of noise reduction other methods of detection will be considered. 



Note 

 As a specific example of the foregoing let the terminal frequency 

 detector, specified by the admittance y{iui), be an oscillation circuit 

 consisting simply of an inductance L in series with a capacitance C. 

 Then 



/. x ■ [C COJOJR 



where wr^ = l/LC. 



Then, if ojc/cor is nearly equal to unity, that is, if 



we have approximately, 



Wfi = (1 + 5)coc, 

 |5|«1, 



J_ ^ n\ 



y{ioic) = 7^ 



ZCOR — iOc 



