Analytic Solution of Amplitude Controlled Digital Oscillator Using Multi-Time Variables Technique

In this paper, new solution analysis of difference equation for amplitude controlled digital oscillators based on multi-time variables technique is presented. In general, when the forced input is static signal, the natural response depends only on the value of forced response at initial time. Alternatively for dynamic forced input, the magnitude of natural response gained by using such assumption is different from the simulation results. Thus, the multi-time variables technique for dynamic forced response is therefore introduced. Based on this technique, it is found that the forced response at any arbitrary time is occurred in a term of natural response. This implies that the amplitude of natural response is therefore directly controlled by forced response. To confirm the theoretical analysis, simulation results have been demonstrated and agreed well with the analysis results