RESPOXSE OF RECTIFIER TO SIGXAL AND NOISE 



107 



fraction of noise power received compared to the limiting noise when the 

 mean signal input power is made indefinitely large compared to the mean 

 input noise power. Some experimental points given by Williams are shown 

 for comparison. ^^'iUiams gives the intercept at zero signal power as 35%; 

 the theoretical value deduced here is tt/'S or 39.27%. It will be noted that 

 the inclusion of the higher order products improves the agreement between 

 experimental and theoretical curves, even though the value of the intercept 

 is unaffected bv them. It shold also be stressed that our analysis applies 



< 0.9 



O 0.5 



3 4 5 6 7 



MEAN SIGNAL INPUT POWER 



MEAN NOISE INPUT POWER 



Fig. 4 — Calculated noise power in audio band of output of linear rectifier when noise 

 and signal are applied in a relatively narrow high-frequency band. The direct-current 

 component is excluded. 



strictly to purely resistive networks. The conventional radio detector 

 circuit (which was used b}' Williams), in which a condenser is shunted across 

 a resistance in series with a diode, departs from the conditions here assumed 

 because of the reactive element, the condenser. The customary approxima- 

 tion made in treating this circuit is that the condenser has infinite impedance 

 in the audio frequency range and zero impedance at the radio frequencies. 

 This leads to a bias on the detector which depends on the signal. The 

 methods given here may be applied, but the resulting formulas are much 

 more difficult from the standpoint of numerical computation. 

 A recent paper by Ragazzini^ gives an approximate solution based on 



^F. C. Williams, "The Response of Rectifiers to Fluctuation Voltages," Journal I. 

 E. E., 1937, Vol. 80, pp. 218-226. 



^John Ragazzini, "The Effect of Fluctuation Voltages on the Linear Detector," Proc. 

 I. R. E., June 1942, Vol. 30, p. 277-288. 



