The single-sideband phase noise 
of free running oscillators
can be calculated by solving Eq. (
)
and using a perturbation approach (Kärtner [])
The first term on the right hand side of Eq. () describes
the phase noise
caused by the white noise sources. 
is the left-sided
eigenvector of the eigenvalue 1
of the fundamental matrix 
.
The matrix 
denotes the correlation
matrix of the white noise sources. The second term
of Eq. () describes the phase noise
caused by the baseband noise.
The factor 
characterizes
the upconversion of the baseband noise to the carrier frequency
.
The
modulation of the 
noise source due to the oscillation is taken
into account as well as the upconversion of the baseband noise caused by
the nonlinearities in the circuit.
The factor c is derived from baseband noise measurements.
is the offset frequency
where the single-sideband phase noise is to be calculated.
The functions 
and 
depend on
the design parameters 
of the circuit
(e.g., capacitors and inductors of the linear network)
by the system of 2 n nonlinear
differential equations derived from ()
and 2n+1 boundary conditions
