From Allan variance to phase noise: A new conversion approach

A new mathematical method is proposed to convert the oscillator instability parameters from Allan variance to Spectrum Density (SD) of random phase fluctuations, which is the inversion of the classic transformation formula from SD to Allan variance. Due to the fact that Allan variance does not always determine a unique SD function, Power-law model of the SD of oscillator phase fluctuations is introduced to the translating algorithm. And that a constrained maximum likelihood solution is presented. Considering that the inversion is an ill-posed problem, a regularization method is brought forward in the process. Simulation results show that the converted SD of phase fluctuations from Allan variance parameters agrees well with the real SD function. Furthermore, the effects of the selected regularization factors and the input Allan variances are analyzed in detail.