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trond

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is jitter and phase noise in VCOs really random?
Aug 29^th, 2005, 8:09am

I was wondering whether the phase noise and/or the jitter in voltage-controlled oscillators is random and uncorrelated with the input signal?

I know that there exits deterministic jitter and random jitter, but I do not know how the input signal to a VCO affects these two types.
In the paper �Predicting the Phase Noise and Jitter of PLL-Based Frequency Synthesizers� it says on page 30 that �The essential characteristic of simple accumulating jitter is that the incremental jitter that accumulates over each cycle is independent or uncorrelated. But this does not apply to independency to the input signal of a VCO, does it? Furthermore, often noise is often considered to be random so that it can be modelled easier. But in real life this is not the case. For example, the quantization error in comparators is strongly dependent on the input signal but is often assumed to be random and white for analysing purposes.

Any thoughts on this topic?

Thanks,
Sven

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Ken Kundert

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Re: is jitter and phase noise in VCOs really rando
Reply #1 - Aug 29^th, 2005, 9:59pm

Phase noise and jitter in oscillators that results from white noise sources is uncorrelated over time once you account for the fact that the phase error accumulates. This is because the white noise itself is uncorrelated over time.

If you have some slowly varying perturbation (such as on the input or the supplies, or perhaps through the substrate) then the resulting phase noise/jitter is correlated over time because the input itself is correlated.

-Ken

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trond

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Re: is jitter and phase noise in VCOs really rando
Reply #2 - Sep 16^th, 2005, 9:16am

I am not certain what upconversion means in an oscillator. Maybe someone can help me understand the following:
Flicker noise falls at 10 dB per decade in a typical spectral density plot. When the noise is up-converted by the oscillation frequency in a VCO, it is characterized by the spectral density of the oscillator falling at 30 dB per decade.

I do not understand the process of up-conversion and see how the noise changes from 10db per decade to 30db per decade.

Thanks

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Ken Kundert

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Re: is jitter and phase noise in VCOs really rando
Reply #3 - Sep 16^th, 2005, 11:47pm

As a nonlinear circuit with a large periodic operating point, oscillators translate signals between frequencies. Noise injected at baseband will appear near the carrier (and its harmonics). Similarly, noise near the carrier or harmonics will appear at baseband. Essentially the oscillation signal periodically modulates the characteristics of the nonlinear components and causes signals to mix up and down in frequency.

Furthermore, since oscillators are autonomous, it is their nature to amplify any injected signal. The closer the signal is in frequency to the carrier or any of its harmonics, the greater the gain. In fact, if we just consider signals that end up near the fundamental, the gain increases with 1/delta f. This is explained in section 3.2 of www.designers-guide.org/Analysis/rf-sim.pdf. Thus, signals that are injected at baseband and up converted to the carrier are amplified with a transfer function that has a -20dB/dec slope. If the signal that is injected is flicker noise, which naturally as a -10dB/dec slope, then the noise that appears near the carrier will have a -30dB/dec slope.

-Ken

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trond

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Re: is jitter and phase noise in VCOs really rando
Reply #4 - Sep 19^th, 2005, 6:10am

Thanks for the response.
Now I do understand how the different noise sources are up-converted to produce slopes of 20db and 30db per decade. These are internal or device noise sources, aren�t they?
What I do not understand, however, (I might be just confused), is why phase noise in a PLL application is sometimes modelled as an additive noise source at the output of the VCO and sometimes at the input of the VCO. Could it be that in one case the VCO is ideal and white and flicker noise are an input signal and in the other case the ideal VCO input is noise free, but 1/f^2 and 1/f^3 noise sources are added at the output?

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