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.
