Laplace transform of waveforms with hysteretic distortion

Abstract

A brief account of the exponential model introduces the reader to one of the mathematical descriptions of the double non‐linearity of the hysteretic phenomena. The model described here satisfies the requirement for calculating the Laplace transforms in closed form for excitation waveforms constructed of straight lines. The method is demonstrated by applying it to a triangular excitation in the hysteretic process. It is shown that the Laplace transform of the induction waveform can also be calculated when the same excitation waveform is being applied in an anhysteretic process. It is also shown that when the excitation is small and falls within the limits of the Rayleigh region the calculation becomes simpler. This is demonstrated by formulating the Laplace transform of the induction waveform that resulted from triangular excitation in the Rayleigh region for both the hysteretic and anhysteretic cases.