The Response of Biased, Saturated Linear and Quadratic Rectifiers to Random Noise

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Abstract
Spectral distributions and powers associated with the output of biased, saturated linear and quadratic rectifiers are determined according to the method of Rice when the incoming disturbance is random noise. Three classes of input spectra are considered: (I), broad band noise, where the central frequency is equal to or less than the spectral width, (II), semi‐broad band noise, for which the central frequency exceeds the width by a moderate amount, and (III), narrow band noise, where the width is much less than the central frequency. Rectification of types I and II yields spectra having roughly the same distribution as that of the incoming waves, but for type III an infinite number of separate noise bands are generated and appear in the output, centered about harmonics of the central frequency. It is found that clipping, whether at the ``top'' or ``bottom'' of the incoming wave, always spreads the spectrum and reduces the output power. Further, it is shown that clipping due to cut‐off alone produces a greater spectral spread than clipping with saturation in addition, for types I and II, but not necessarily for spectra of type III. Symmetrical clipping for classes I and II yields little broadening of the spectrum, even in extreme cases, and for class III waves, the even‐harmonic regions are completely missing except for a d.c. component, and only the odd‐harmonic zones appear. The behavior of linear and quadratic rectifiers is qualitatively similar in most cases. The powers in the d.c. and continuous portions of the output spectrum are shown to be independent of the spectral shape of the incoming noise. Some examples of extreme clipping are considered, numerous curves are included, and a general analysis is outlined.

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