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BELL SYSTEM TECHXICAL JOURNAL 



xj/o being the average value of V'y . Equation (4.2-3) follows from the 

 formulas (3.10-12) and (4B-9). WTien x is large the asymptotic expansion 

 (4B-3) of the iFi gives 



2P 8P^ 



Similarly, the mean square value of I if is 



I-f = -,R'= - [P- + 2^o) 



(4.2-5) 



(4.2-6) 



and the mean square value of the low frequency current I(f , excluding the 

 d.c, is given by 



T- " 



Pif = I'd — I'dc 



^0 



2P2 



\Mien X is large we have 



4^0 — 

 IT- i_ 



and when x = 0, 



4, =^^„I2-;, 



IT- l_ iX 



(4.2-7) 



(4.2-8) 



Curves for Idc are given in Figures 1, 2 and 3 of Bennett's paper. He 

 also gives curves, in Fig. 4, showing l}f versus .v. These show that the 

 effect of the higher order modulation terms is small when Iff is computed 

 by adding low frequency modulation products. 



\Mien V consists of two sine waves plus noise, 



V = Vn + P cos pt -{- Q cos ql, (4.1-4) 



the average value of Itf is, from (3.10-25), a sort of double iFi function: 



1/2 00 00 / i\ 



Idc = - R = OL 



1-K k=o m=o klklmlml 



EZ 





(4.2-9) 



where 



P^ 



2tAo' 



y = 



2^0 ' 



Piciz) = Legendre polynomial (4.2-10) 



If X is large and y < x, we have from (3.10-27) the asymptotic expression 

 hc^-P± ^~^!^^~^^' 2F, (k-hk-h 1; -") (4.2-11) 



TT k=0 



klx'' 



