The Leeson Effect: PM and AM noise and frequency stability in oscillators, including OEOs and lasers

Simply stated, an oscillator consists of a loop in which a resonator sets the oscillation frequency and an amplifier compensates for the resonator loss. The oscillation amplitude is set by clipping or other gain-saturation mechanisms, usually in the amplifier. When phase noise is introduced in the loop, the oscillator converts it to frequency noise through a process of time-domain integration. The consequence is that the oscillator phase fluctuation diverges in the long run. The first part explains the phase-to-frequency conversion mechanism as a general phenomenon inherent in the feedback, following an heuristic approach based on physical insight. There follow the relationships between the noise of the internal components (sustaining amplifier, resonator, etc.) and the phase noise at the oscillator output, or equivalently the frequency stability. The second part is the analysis of the phase noise spectra found in the data-sheet of commercial oscillators: dielectric-resonator oscillator (DRO), whispering gallery oscillator (WGO), 5–100 MHz quartz crystal oscillators, opto-electronic oscillator (OEO). The analysis gives information on the most relevant design parameters, like the quality factor Q and the driving power of the resonator, and the flicker noise of the sustaining amplifier. The last part shows the derivation of the oscillator phase noise formulae from the elementary properties of the resonator. Interestingly, the amplitude non-linearity, necessary for the oscillation amplitude to be stable, splits the resonator relaxation time into two time constants. The approach shown in this last part is general. It applies to all oscillators, including quartz, RLC, microwave cavity, delay-line, laser, etc.