Phase noise in oscillators-leeson formula revisited

In the field of linear feedback-systems formalism, the Leeson formula is a useful tool for the determination of phase noise in feedback oscillators. Nevertheless, a direct application of the Leeson model without care can lead to erroneous results because the formula contains hidden parameters that are generally unwittingly ill evaluated or neglected. Thus, a brute-force calculation of phase noise with the Leeson formula can lead to errors of several orders of magnitude (i.e., several tens of decibels). A detailed analysis enables us to enlighten the hidden parameters leading to a modified Leeson formula that is valid for all oscillator circuits. It explicitly takes into account all the parameters needed for phase-noise calculation. In order to demonstrate the ease of use and accuracy of the new formula, we apply it to several oscillator circuits with lumped elements, transmission lines, and high-Q resonators. Finally the analytical results are confirmed by numerical simulations with a nonlinear transistor model.