Oscillator phase noise
Oscillators inherently produce high levels of phase noise. That noise increases at frequencies close to the oscillation frequency or its harmonics. With the noise being close to the oscillation frequency, it cannot be removed by filtering without also removing the oscillation signal. And since it is predominantly in the phase, it can be removed without any limiter.
All well-designed nonlinear oscillators have stable limit cycles, meaning that if perturbed, the oscillator will naturally return to its limit cycle. This is depicted in the figure on the right (removed due to unknown copyright status). Here the stable limit cycle is shown in state space as a closed orbit (the ellipse). When perturbed, the oscillator responds by spiraling back into the limit cycle. However, by observing the time stamps, it is easy to see that while the oscillation returns to its stable limit cycle, it does not return at the same phase. This is because the oscillator is autonomous; it has no stable time reference. The phase is free to drift. As a result, any perturbation of the oscillator causes the phase to drift, which explains why the noise produced by an oscillator is predominantly in phase.
There are two different ways commonly used to characterize noise in an oscillator. Sφ is the spectral density of the phase and Sv is the spectral density of the voltage. Sv contains both amplitude and phase noise components, but with oscillators the phase noise dominates except at frequencies far from the carrier and its harmonics. Sv is directly observable on a spectrum analyzer, whereas Sφ is only observable if the signal is first passed through a phase detector. Another measure of oscillator noise is L, which is simply Sv normalized to the power in the fundamental.
As t → ∞ the phase of the oscillator drifts without bound, and so Sφ(Δf) → ∞ as Δf → 0. However, even as the phase drifts without bound, the excursion in the voltage is limited by the diameter of the limit cycle of the oscillator. Therefore, as Δf → 0 the PSD of v flattens out, as shown in Figure 3(removed due to unknown copyright status). The more phase noise, broader the linewidth (the higher the corner frequency), and the lower signal amplitude within the linewidth. This happens because the phase noise does not affect the total power in the signal, it only affects its distribution. Without noise, Sv(f) is a series of impulse functions at the harmonics of the oscillation frequency. With noise, the impulse functions spread, becoming fatter and shorter but retaining the same total power.
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