Transient Responses to Relaxation Oscillations in Multivibrators

The multivibrator is an electronic circuit that has three oscillation states: astable, monostable, and bistable; these circuits typically contain opamps. These states are often modeled using hybrid systems, which contain characteristics of both continuous and discrete time. While an ideal opamp possesses both continuous and discrete characteristics, actual opamps exhibit continuous properties, which necessitate in-depth modeling. The relaxation oscillations produced by the multivibrator, characterized by periodic, rapid state changes, are typically modeled by considering slow–fast dynamical systems. In these systems, the phenomenon whereby the amplitude of the signal changes rapidly is referred to as a “canard explosion”. By considering this phenomenon, it is possible to understand the process of relaxation oscillations in the multivibrator. In this work, we model the multivibrator by considering a slow-fast dynamical system and observe canard explosions through numerical experiments. This study indicates that the oscillatory changes in the multivibrator are continuous, which explains the onset of relaxation oscillations. Additionally, circuit experiments are conducted using affordable opamps; in this experimental work, canard explosions are observed.

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