A low phase noise is besides the signal properties essential to the design of oscillating electrical circuits. Up to now, a reduction of the phase noise can only be achieved by using empirical rules which, e.g., require additional elements in the circuit or the manufacture of lines of prototypes (trial and error).
A new and general method to minimize the single-sideband phase noise of free running oscillators is presented. It is based on the description of the signal and noise behavior of an oscillator circuit by the Langevin equations
where
are the state variables of the circuit (voltages, currencies), are the white noise sources and y is a nonlinear noise source denoting the baseband noise. The noise sources are assumed to be small compared to the signal amplitudes and the terms of order are neglected.