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Oscillator Linewidth in the presence of 1/f noise (Read 46 times)
singhk
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Oscillator Linewidth in the presence of 1/f noise
May 20th, 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.
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Ken Kundert
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Re: Oscillator Linewidth in the presence of 1/f no
Reply #1 - May 20th, 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 Sv will be flat. Remember that the amplitude of Sv is constrained by the amplitude of the signal. In particular, Sv 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 Sv 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
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Frank Wiedmann
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Re: Oscillator Linewidth in the presence of 1/f no
Reply #2 - May 21st, 2003, 4:41am
 
An analytical treatment by Alper Demir can be found at http://www.sigda.org/Archives/ProceedingArchives/Iccad/Iccad98/papers/1998/iccad... 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.
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