INVESTIGATION OF RELAXATION OSCILLATIONS IN THERMISTOR–CAPACITOR SYSTEMS

Abstract

It is known that a thermistor displays 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 threshold for oscillation, to a strongly relaxational type when a large shunt capacitance is employed.The investigation 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 thermal time constant for which special very-low-frequency techniques were developed.The oscillations were studied over a wide range of capacitance covering the transition from sinusoidal to relaxational type. The voltage extrema and period were measured as functions of capacitance, voltage supply resistance, and operating point.An investigation was made of the features of the differential equations describing the behavior of the system, especially for limit cycles corresponding to relaxation oscillations. The asymptotic form of the cycles was 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 approximative methods were found to be necessary. However, in the case of sinusoidal oscillations of small amplitude, the period can be expressed exactly in terms of the system parameters (Burgess 1955b) and this result was confirmed experimentally.