Long-term and short-term frequency stabilities in sinusoidal oscillators

Deterministic considerations addressing linear sinusoidal oscillators are presented. The considerations are complex-frequency-domain ones and start with the fact that every oscillator can be represented as a closed loop of positive feedback. On the basis of such a model, a simple expression for variations in oscillation frequency ω₀ is developed. Since the model is a general, unified representation of various oscillators, it makes it possible to compare properties of circuits of different types and classes. Examples of RC oscillators with a passive feedback network and examples of active RC oscillators are discussed as particular cases of the general concept. Long-term changes in ω ₀, are considered as variations under conditions of fixed oscillation amplitude, while short-term changes in this frequency are considered as variations under conditions of varying oscillation amplitude