A comparison of two models for an oscillator with an amplitude control system

Two models are compared which describe amplitude transients in an oscillator with an amplitude control system. The approximate model is a linearization of the more complicated exponential model. Using an amplitude control system that employs squaring circuits to derive the control signal, the two equations are solved in closed form and the transient responses are compared. It is found that the transient duration for the approximate model is longer and that the difference between the two models increases as the initial amplitude decreases. When a loop filter, with time constant , is introduced similar results are found.