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Measurements >> Phase Noise and Jitter Measurements >> Oscillator Linewidth in the presence of 1/f noise
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Message started by singhk on May 20^th, 2003, 2:48pm

Title: Oscillator Linewidth in the presence of 1/f noise
Post by singhk on May 20^th, 2003, 2:48pm

This is a question with regards to oscillator linewidth and 1/f noise. Hopefully, someone out there can answer this.

All the analysis I've seen thus far is based on white-noise broadening of the oscillator line-width to a Lorentzian form. I understand that even with flicker noise, the linewidth corner frequency can still be calculated by applying the power conservation principle (total integral over all frequencies for phase noise L(dF) = 1.0 ).

However, with flicker noise present, does the spectrum still look Lorentzian (i.e. flat) as delta_F->0 ? If it varies as 1/f, then we are back to the unbounded integral issue again (integral -> infinity as delta_F -> 0 ).

Thanks in advance for all comments.

Title: Re: Oscillator Linewidth in the presence of 1/f no
Post by Ken Kundert on May 20^th, 2003, 4:14pm

As far as I know nobody has been able to analytically do the analysis for flicker noise, and I have not seen experimental results, but it is certainly my expectation that at low frequencies S_v will be flat. Remember that the amplitude of S_v is constrained by the amplitude of the signal. In particular, S_v cannot be proportional to 1/df for small df because the integral of 1/df from 0 to anything is infinity.

If it were me, I would assume that S_v for an oscillator with flicker noise has 3 regions:
~df^-2 for large df (white noise region)
~df^-3 for moderate df (flicker noise region)
~1 for small df (within the linewidth)
And I would determine the linewidth by letting it be a parameter, and then integrating over all three regions. I would then find the value of linewidth that results in the total area equaling the noisefree power of the signal.

-Ken

Title: Re: Oscillator Linewidth in the presence of 1/f no
Post by Frank Wiedmann on May 21^st, 2003, 4:41am

An analytical treatment by Alper Demir can be found at http://www.sigda.org/Archives/ProceedingArchives/Iccad/Iccad98/papers/1998/iccad98/pdffiles/03a_2.pdf or http://home.ku.edu.tr/~aldemir/research/pubs/tcas002.pdf. There is no simple closed-form expression, but the approximations for various special cases confirm Ken's assumptions about the qualitative behavior.