THE BIASED IDEAL RECTIFIER 



169 



The values of the fundamentals and third-order sum and difference 

 products for the biased zero-power-law rectifier have been calculated by the 

 formulas above for the cases ki — .5 and ^i = 1. The resulting curves are 

 shown in Fig. (15) and (16). The values of the auxiliary integrals Zo, ^i , 

 and Zo are shown for ^i = .5 in Fig. (17). These integrals become infinite 

 at kit = I — ki so that the formulas for the modulation coefficients become 

 indeterminate at this point. The limiting \-alues can be evaluated from 

 the integrals {^.3), etc., directly in terms of elementary functions when the 

 relation ^o = 1 — ^i is substituted, except for the H-function. 



Limiting forms of the coefficients when k„ is small are of value in calcu- 

 lating the effect of a small signal superim[)osed on the two sinusoidal com- 

 ponents in an unbiased rectifier. By straightforward power-series expan- 

 sion in ^oi we find : 

 Zero-Power- Law Rectifier, ko Small: 



Aro = -„£ - 



2£ 



7r2(l - k'') 



kl + 



Aoi = ~ [£ - (1 - kl)K\ + -^^^ 



r^-^)^» + 



[ (3.37: 



A21 = - -,r, [(1 



+ 



TT'^l 



K - 



2k\)E 



1 - 2k\ 

 1 - k\ 



(1 - k\)K\ 



'^kl 



+ 



In the above expressions, the modulus of K and E is ki. When k^ = 0, 

 these coefficients reduce to half the values of the full-wave unbiased zero- 

 power-law coefficients, which have been tabulated in a previous publication. 



Acknowledgment 



In addition to the j)ersons already mentioned, the writer wishes to thank 

 Miss M. C. Packer, Miss J. Lever and Mrs. A. J. Shanklin for their assistance 

 in the calculations of this paper. 



" R. M. Kalb and W. R. Bennett, Ferromagnetic Distortion of a Two-Frequency 

 Wave, B. S. T. J., Vol. XIV, .\pril 1935, Eq. (21), p. 336. 



