Frequency domain approach to the steady state, stability, and phase noise analysis of externally injection-locked optoelectronic oscillators

Optoelectronic oscillators (OEOs) can produce ultra-low phase noise oscillations much better than electronic oscillators (EOs), especially at high microwave and millimeter wave frequencies. Making an OEO injection locked to an EO provides benefits such as reducing the well-known spurious peaks in the phase noise, preventing frequency hopping, and the ability to tune the frequency of the OEO by changing that of the EO. The current paper aims to provide a steady-state analysis of injection-locked OEOs, assess the stability of the solutions, and compute their phase noise power spectral density. The conversion matrix approach formulation is used for phase noise and stability analysis. Also, a formula based on the phase transfer approach (PTA) is derived to accurately characterize the EO phase noise to output phase noise conversion. No limitations are assumed regarding the injection strength, frequency detuning, or the value of the loop delay. This overcomes the shortcomings of the previously presented works. Also, the runtime is much faster than the time or envelope domain methods. The accuracy of the analysis is verified by comparing its results with those of other methods presented in the literature and the PTA formula extracted here.