RESPONSE OF RECTIFIER TO SIGNAL AND NOISE 

 The value of this mtegral is shown in Appendix I to be 



99 



/ = ayj/|^"e-«'^""|/oaF./2fF„) 



+ 



pHw)-"m 



(10) 



This form is particularly convenient for calculation since Watson's Theory 

 of Bessel Functions, Table II, gives c~'[Jz) and f""-/i(c) directly. 



0.6 0.8 1.0 1.2 



RMS. NOISE INPUT 

 RMS. SIGNAL INPUT 



1.4 1.6 l.a 2.0 



Fig. 1 — Variation of direct-current component in response of linear rectifier with ratio 

 of noise input to signal input. 



Limiting forms of this equation may be expressed in terms of series in 

 powers of 11^/11',, when the signal power is small compared with the noise 

 power and in powers of TF,, Tr,. when the noise power is small compared 

 with the signal power. The ascending series for small signal is: 



K-i) {w,f 



V^"[ 



^" 1 + 



1 w 



+ 



2(1!)MF„ 22(2 !)2 (PF„) 



l(-l)(-3) {Wjf 

 2^(3 !)2 (IFn) 



■] = VI"'^'(t-.'^^-) 



(11) 



The asymptotic series, which is available for computation when the signal 

 is large, is 



(-1)^.1=^ (IFn)^ 





^ (-1)^1^3^ i^y ^ 



2! (4IF,) 



(_1)2. 12.32.52 i^Wr)' 



(12) 



3! 



(4IF.) 



4! 



(4IF,) 



+ 



Curves of I have been plotted in three ways. Fig. 1 shows the ratio of 

 7 to Iso = aPo/TT, the average current in the absence of noise, as a function 



