Analysis of Output Loading Effects in Autonomous Circuits

A methodology is presented to analyze the impact of the termination load on the oscillation frequency and output power of autonomous circuits. Variations of this load can also lead to an extinction of the oscillation signal, due to their effect on the impedance seen by the active device(s). The new methodology enables an efficient analysis and mitigation of the pulling effects, in the case of undesired output mismatch, as well as an efficient oscillator synthesis in large-signal conditions, for specified values of oscillation frequency and output power. The method is based on the calculation of constant-amplitude and constant-frequency contours, traced in the Smith chart. Oscillation extinctions and some forms of hysteresis can be predicted through the inspection of these contours. However, the stability properties will generally depend on the frequency characteristic of the termination impedance. In an oscillator synthesis, the selected impedance, providing the specified values of oscillation frequency and output power, must be implemented in order to guarantee a stable solution. The dependence of the phase-noise spectral density on the particular implementation is predicted, combining an analysis based on the variance of the phase deviation with the conversion-matrix approach.