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BELL SYSTEM TECHNICAL JOURNAL 



means. It appears likely in most cases that the expression of these results 

 in terms of a single integral is the most advantageous form for practical 

 purposes, since the integrands are relatively simple, while evaluations in 

 terms of tabulated functions, where possible, often lead to complicated 

 terms. Numerical evaluation of the double integral is also a possible method 

 in cases where neither integration can be performed in terms of functions 

 suitable for calculation. 



One integration can always be accomplished for the integer power-law 

 case, since the function / (P cos x -\- Q cos y — J) in (1.12) then becomes a 

 polynomial in cos x and cos y. Cases of most practical interest are the 

 zero-power, linear, and square-law detectors, in which /(z) is proportional 

 to z", z , and z" respectively. The zero-power-law rectifier is also called a 

 total limiter, since it limits on infinitesimally small amplitudes. We shall 

 tabulate here the definite integrals for a few of the more important low-order 



Fig. 13. — Response of biased total limiter to two-frequency wave. 



coefficients. To make the listing uniform with that of our earlier work, we 

 express results in terms of the coefhcient Amn, which is the amplitude of the 

 component of frequency mp ± nq. The coefl&cient Amn is half of «„„ when 

 neither m nor n is zero. When w or » is zero,, we take Amn = a^n and drop 

 the component with the lower value of the i sign. When both m and n 

 are zero, we use the designation Aqq/I for ooo, the d-c term. In the tabula- 

 tions which follow we have set/(z) = otz' with v taking the values of zero 

 and unity. 



We first consider the biased zero-power-law rectifier or biased total 

 limiter. This is the case in which the current switches from zero to a 

 constant value under control of two frequencies and a bias as illustrated 

 by Fig. 13. The results are applicable to saturating devices when the 

 driving forces swing through a large range compared with the width of the 

 linear region. It is also to be noted that the response of a zero-power-law 

 rectifier may be regarded as the Fourier series expansion of the conductance 



