General oscillator characterization using linear open-loop S-parameters

From a practical standpoint, oscillator design using linear open-loop S-par ameters is attractive to designers due to the ease of use and widespread av ailability of linear S-parameter-based analysis software, However, the easi est and, therefore, most common approach is based on intuition and rules of thumb. The intent of this paper is to obtain quantitative expressions that characterize oscillator performance in terms of the linear open-loop S-par ameters, A characteristic equation is derived that determines oscillator st ability. The Nyquist stability criteria can be applied to this equation dir ectly from the open-loop Bode plot, A closed-loop gain parameter is derived , which describes how the open-loop circuit self-connects, From this parame ter, the startup time, oscillation frequency, and loaded Q can be predicted . A prediction of actual oscillation frequency can be made based on a simpl e oscillator model with known saturation characteristics. It will be shown under what conditions these expressions simplify to more readily applicable forms. In many cases, the designer can adjust analysis parameters to allow the use of the simplified expressions.