Approximations for Digital Computers. By Cecil HastingsJr. 32s. 1955. (Princeton University Press. London, Cumberlege)

Modulation Products and Optimum Frequency Conversion for an n-Frequency Input

A nonlinear device characterized by a noninteger power-law equation is considered. Amplitudes and phases of output harmonic and mixing components are determined for the case where the device is driven by several arbitrarily phased frequency components. The resulting expressions are shown to have close ties with the Gaussian hypergeometric function.

Large-signal analysis of semiconductor circuits with multifrequency excitation

http://ieeexplore.ieee.org/iel5/5/31072/01445773.pdf

Note on Fourier coefficients of power-law devices

Integral representation of zero-memory nonlinear functions offers promise as an analytical method for nonlinear control systems study. A review of work performed at Bell Laboratories and elsewhere on the use of these representations is presented, with particular emphasis on nonlinearities often encountered in feedback control systems. In general, the integral representations are useful only insofar as the resulting expression can be readily evaluated. The use of Bennett functions systematized the formulation of these integrals. The numerical results of a large class of the integrals can then be given by the tabulated Bennett functions. A comprehensive bibliography is appended.

http://ieeexplore.ieee.org/iel7/6731005/6773673/06773680.pdf

Integral representation of zero-memory nonlinear functions

The nonlinear problem of the multiple Fourier analysis of the output from a cut-off power-law rectifier responding to a two-frequency input, reviewed in general in Part I of this study [1], is further scrutinized here for the special case of a zero-power-law device; i.e., a bang-bang device or a total limiter. Solutions for the modulation product amplitudes or multiple Fourier coefficients as in Part I appear as Bennett functions, and line graphs of the first fifteen basic functions for the problem are given. The new functions Amnw(h, 7c) studied, being based on a discontinuous device, then, together with the functions Amnn)(h, k) studied in Part I, provide approximate solutions to the two-frequency modulation product problem for an arbitrary piecewise continuous nonlinear modulator, and the solution for this general problem is outlined. Finally, numerical tables of the zeroth-kind functions Amnm (h, k) graphed have been prepared and arc available separately in the United States and Great Britain. As before, the entire theory is based on the original multiple Fourier methods introduced by Bennett in 1933 and 1947.

/pdf/multiple-fourier-analysis-in-rectifier-problems-ii-4yhpis93an.pdf

Michael R. Sheets

Papers

Multiple Fourier analysis in rectifier problems. II