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A theoretical and experimental investigation of sinusoidal and relaxation oscillations in thermistor - capacitor systems Morley, Gordon Arthur

Abstract

It is known that a thermistor displays inductive reactance and negative resistance at low frequencies when biased with a current greater than turnover current. Thus when shunted by a capacitance in this condition sustained oscillations are possible. These oscillations range from a sinusoidal small - amplitude character, when the system is just above the threshold for oscillation, to a strongly relaxational type when a large shunt capacitance is employed. The investigation described in this thesis involved a study of the dynamic properties of these oscillations and their relation to the static properties of the thermistor. The relevant thermistor parameters which were measured included the dependence of resistance on temperature, the thermal conductance and the thermal time constant. For the determination of the latter, special very low frequency techniques were developed. Thermistors of high resistance and low thermal time constant were selected in order to avoid the necessity for very large capacitances in the study of relaxation oscillations. The oscillations were studied over a wide range of capacitances covering the transition from sinusoidal to relaxation type. The voltage extrema and period were measured as functions of capacitance, voltage supply resistance and operating point. Also, in order to elucidate the dynamic processes involved, the transient phenomena produced by abrupt pertubations were investigated. In parallel with the experimental program, an investigation was made of the features of the differential equations describing the behaviour of the system, especially for the limit cycles corresponding to relaxation oscillations. The asymptotic form of the cycles were derived for the case where the circuital time constant greatly exceeds the thermal time constant of the thermistor. The complicated nature of the equations precluded a solution in a closed form and approximational methods were found to be necessary. However, in the case of sinusoidal oscillations of small amplitude, the period can be exactly expressed in terms of the system parameters (Burgess, Nov. 1955) and this result was confirmed experimentally.

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