THE BIASED IDEA L RECTIFIER 



143 



Then if a single frequency wave defined by 



E = P cos pt, - P < b < P, (1.2) 



is applied as input, the output contains only the tips of the wave, as shown 

 in Fig. 3. It is convenient to place the restrictions on P and b given in 

 Eq. (1.2). The sign of P is taken as positive since a change of phase may 

 be introduced merely by shifting the origin of time and is of trivial interest. 

 If the bias b were less than —P, the complete wave would fall in the con- 

 ducting region and there would be no rectification. If b were greater than 



,-«-Pcos pt 



Fig. 3. — Response of biased rectifier to single-frequencj' wave. 



P, the output would be completely suppressed. Applying the theory of 

 Fourier series to (1.1) and (1.2), we have the results 



Oo 



2 r 



a„ = - 



If Jo 



2 n=l 



arc cos h/P 



-\- Zli (^n COS n pt 



f(P COS X — b) cos nx dx 



(1.3) 



(1.4) 



When two frequencies are applied, the output may be represented by a 

 double Fourier series. The typical coefficient may be found by the method 

 explained in an earlier paper by the author^. The problem is to obtain the 

 double Fourier series expansion in x and y of the function g{x,y) defined by: 



/O, P cos x -\- Q cos y < b \ 



Six, V) = (1.5) 



\f{P cos -T + () COS y — b), b < P cos .v + Q cos v/ 



' W. R. Bennett, New Results in the Calculation of Modulation Products, B. 5. T./., 

 Vol. XII, pp. 228-243, April, 1933. 



