Phase noise phenomenon explanation based multi-time variables differential equation technique

In this article, the mathematical analysis is proposed to describe phase noise phenomenon. The principle of this proposed scheme is based on the multi-time variables differential equation technique. The analytic result clearly shows that noise is composed of multiplicative noise that spread around an oscillated frequency and additive noise acts as a noise floor of a system. To verify the proposed analysis, the computer simulation results are given which demonstrate that the obtained results agree well with the theoretical counterpart.