Linear time-invariant (LTI) phase noise theories provide important qualitat
ive design insights but are limited in their quantitative predictive power,
Part of the difficulty is that device noise undergoes multiple frequency t
ranslations to become oscillator phase noise. A quantitative understanding
of this process requires abandoning the principle of time invariance assume
d in most older theories of phase noise. Fortunately, the noise-to-phase tr
ansfer function of oscillators is still linear, despite the existence of th
e nonlinearities necessary for amplitude stabilization, In addition to prov
iding a quantitative reconciliation between theory and measurement, the tim
e-varying phase-noise model presented in this tutorial identifies the impor
tance of symmetry in suppressing the upconversion of 1/f noise into close-i
n phase noise, and provides an explicit appreciation of cyclostationary eff
ects and AM-PM conversion. These insights allow a reinterpretation of why t
he Colpitts oscillator exhibits good performance, and suggest new oscillato
r topologies, Tuned LC and ring oscillator circuit examples are presented t
o reinforce the theoretical considerations developed, simulation issues and
the accommodation of amplitude noise are considered in appendixes.