authors develop the viewpoint of phase noise as being 5 Note that this list just intends to give some leads. It is by no means exhaustive. 5.2.2 Phase noise analysis random perturbations Oscillator orbit frequency offset (Hz) Figure 5.8: Appearance and operation of oscillator phase noise. (a) Phase noise causes the energy contained in an oscillating signal to spread all over the frequency band. (b) Phase noise is caused by random perturbations (noise) that make the oscillator (phase-)shift along its own orbit. caused by random perturbations (noise) that make the oscillator (phase-)shift along its own orbit in the phase space. To compute the "force" that drives these phase shifts, they project the perturbations onto the tangent line to the orbit. This results in a phase noise equation that is structured as (5.4) Here, 0 is the oscillator's phase, n(t) is the vector containing the perturbing noise sources while T (t) is the oscillator's perturbation projection vector (PPV) [Dem00a]. At this point, we do not go into further detail on (5.4). A more rigorous explanation is given in section 5.7 where (5.4) is shown a special case of the theory presented in this chapter. We only mention that when there is only a single noise source involved, i.e. n(t) = b.n(t), (5.4) reduces to (5.5) Here, T(t)=vT(t). b is called the impulse sensitivity function (ISF, a name introduced in [Haji98]6) corresponding to n(t). The phase noise theories and methods in [Dem00a, Dem00b, Kae90] are very generic in a sense that they make little assumptions about the structure of the equations that 6In [Haji98], the author simply conjectures the approximate phase noise equation This approximate phase noise equation neglects the right-hand-side's dependence on the phase 0 that is present in the exact equation (5.5). The validity of this simplification is discussed in [Vana02d]. PRIOR ART model the oscillator. As such, they can be applied directly to circuit-level netlists. How- ever, by nature, these phase noise theories are only concerned with an o