The Clarification of Average Negative Resistance with Extensions of Its Use

A treatment of the subject of negative resistance and the application to the problem of nonlinear oscillations shows the necessity of clarifying the meaning attached to the commonly used term "average" negative resistance. An average effective resistance R
n
, based on a simple energy consideration, is introduced which when applied to the above problem affords a correct prediction of the amplitude of oscillation and supplies a meaning for the term "average" negative resistance. An earlier method known as the secant method of predicting the amplitude of oscillation is investigated and found to yield results not in accord with experimental behavior. The quantity R
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, being a function of the oscillation voltage V suggests a new type of curve called the R
n
-V curve which serves to predict the possible amplitudes of oscillation when the negative resistance device is connected to a parallel R, L, and C circuit. Following this a criterion for amplitude stability is deduced which allows one to determine whether or not a possible amplitude is also stable by simply observing the slope of the R
n
-V curve at the point corresponding to the possible amplitude. A problem of so-called "oscillation hysteresis" earlier reported in the literature is described, and it is shown how the R
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-V curve for this particular case offers a simple explanation of the phenomenon.