Negative resistance oscillators revisited

Negative resistance oscillator theory is typically introduced to undergraduate electrical engineers using a quasi-linear analysis based on transfer functions for what is, by essence, a non linear phenomenon. A more rigorous treatment based on differential equations is presented in Chua-Desoer and Kuh, 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. A transcendental equation with normalized variables is obtained which shows that under low distortion conditions, the amplitude of inductance tension can vary from a minimum of V_SAT (minimal distortion) to a maximum of (4/π)V_SAT (maximal distortion), where V_SAT is the operational amplifier saturation voltage for the amplifier used to synthesize the negative resistance. Estimates of third harmonic distortion levels are also given