Elementary amplitude and distortion evaluation in Wien and phase shift oscillators

Oscillator theory is typically introduced to undergraduate electrical engineers using a quasilinear analysis based on transfer functions for what is, by essence, a nonlinear phenomenon. For negative resistance oscillators, a more rigorous treatment based on differential equations is presented in L.O. Chua et al. (1987), and while it sheds a significant amount of light on the nonlinear dynamics involved, it fails to give an elementary treatment of what is after all the essential difficulty in low distortion sinusoidal oscillator theory: amplitude and distortion evaluation. In this work, under an assumption of low distortion, we compute an asymptotic approximation of the amplitude of oscillation based on an elementary analysis of the evolution of the total energy stored in energy storing circuit elements over a cycle, for both Wien and phase shift oscillators. Interestingly, we show that amplitudes in both oscillators are characterized by very similar transcendental equations involving appropriately defined normalized variables. Also, the procedure herein proposed appears to be generalizable to arbitrary types of low distortion sinusoidal oscillators.