Oscillator Phase Noise - Oscillator Voltage Noise and Phase Noise Spectra

Oscillator Voltage Noise and Phase Noise Spectra

There are two different ways commonly used to characterize noise in an oscillator. S_φ is the spectral density of the phase and S_v is the spectral density of the voltage. S_v contains both amplitude and phase noise components, but with oscillators the phase noise dominates except at frequencies far from the carrier and its harmonics. S_v is directly observable on a spectrum analyzer, whereas S_φ is only observable if the signal is first passed through a phase detector. Another measure of oscillator noise is L, which is simply S_v normalized to the power in the fundamental.

As t → ∞ the phase of the oscillator drifts without bound, and so S_φ(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, S_v(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.

The voltage noise S_v is considered to be a small signal outside the linewidth and thus can be accurately predicted using small-signal analyses. Conversely, the voltage noise within the linewidth is a large signal (it is large enough to cause the circuit to behave nonlinearly) and cannot be predicted with small-signal analyses. Thus, small-signal noise analysis, such as is available from RF simulators, is valid only up to the corner frequency (it does not model the corner itself).