A frequency-domain evaluation of multiple-nonlinearity systems exhibiting jump-resonance responses

A generalized two-nonlinearity feedback system is used to develop a numerical sequence capable of fully depicting all features of acuminating jump-resonance characteristics. This is achieved by recognizing the importance of the shape of the response of the input error signal at a nonlinear element. The curve is traced by iterating on the system equation and the describing-function integral while judiciously adjusting step sizes in accordance with the contour. Complete amplitude and phase responses can hence be extrapolated and critical-jump-resonance conditions predicted. Practical verification is provided by a simple bandpass active-filter circuit.