Active Q-Factor and Equilibrium Stability Formulation for Sinusoidal Oscillators

Quality factor (Q-factor) and stability criterion of sinusoidal oscillators are formulated from the viewpoints of energy equilibrium and spectrum purity. Complex power works as an objective function to determine the steady-state oscillation amplitude and frequency. Conjugate product of amplitude and frequency slopes of the function dominates equilibrium stability. Logarithmic derivative of oscillator´s output impedance defines active Q-factor, which takes into account effects of positive power generated by active devices, while keeping its non-divergent property. Transfer Q -factor is also defined for oscillating networks involving noise sources on different branches from the port of spectrum observation. Presented formulas can be applied to the entire oscillator circuit without de-embedding active devices, and thus they enable frequency-domain CAD simulators to numerically evaluate oscillator performance.