Wide-band amplitude control of the second-order oscillator circuit

In this paper, a new analysis technique of an ordinary second-order oscillator which is based on multi-time concept is proposed. This mathematical analysis results in a new closed-form solution of a system complete response. It is found that amplitude of the natural response is not constant but varied with the forced response of the system. For a constant forcing function proposed, the new analysis is identical to the conventional analysis. In the case of time-varying forcing function, however, it is different from the conventional approach. Based on such analysis, it implies that the amplitude of a second-order oscillator can easily be controlled by forced response of the system. Hence, the obtained result based on the proposed analysis technique provides a proper mathematical solution for the system, especially in a time-varying forcing function. Moreover, the mathematical analysis for the wide-band characteristic of a second-order oscillator is also described. The experimental results demonstrate the responses of the oscillator which agree well between the theoretical and simulation results.