Математична модель мікроелектронного автогенераторного засобу для вимірювання вологості

Abstract

A mathematical model of a microelectronic autogenerating device for measuring the relative humidity of air has been developed. The microelectronic frequency transducer of humidity is developed on the basis of a transistor structure with a negative differential resistance based on two bipolar transistors and a capacitive element that is sensitive to moisture. The negative differential resistance obtained by parallel connection of the impedance with a capacitive component on the collector-collector electrodes of the bipolar transistor structure and inductance leads to the occurrence of electrical oscillations in the circuit of the autogenerating humidity transducer. Using the Maple environment, the adequacy of the developed mathematical model has been proved. It was found that there are periodic oscillations at the output of the autogenerator, the frequency of which changes with a change in the capacitance of the humidity sensitive element. So, at 305 pF the frequency is 64.53 MHz, and at 354 pF the frequency is 58.82 MHz, while the supply voltage is 5 V. To confirm the theoretical results, the autogenerating means were investigated in the LTSpice circuit simulation environment. The studies were carried out in the range of variation of the humidity sensitive capacitance from 305 pF to 354 pF, which corresponds to an increase in the value of the relative air humidity from 20% to 95%. Based on the results of modelling in the LTSpice environment, it was found that with an increase in the capacitance of the humidity sensitive element from 305 pF (W = 20%) to 354 pF (W = 95%), the signal frequency decreases from 64.516 MHz to 58.823 MHz. The results of theoretical and experimental studies have shown that at the output of an autogenerating device for measuring the relative humidity of air, there are periodic fluctuations, the frequency of which will decrease with an increase in the value of the relative humidity of the air. The obtained theoretical and experimental studies are in good agreement, the relative error does not exceed 1.5%.