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trond

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relationship autocorrelation of SDM o/p AND spurs at frac-N-synthesizer o/p
Sep 30^th, 2008, 1:32am

Hello all,

My question concerns the spurs occurring in fractional-N-PLLs.
More specifically spurs coming from the sigma-delta modulator.

Is there a relationship between the output of the autocorrelation estimate of the sigma-delta ADC and the power of the spurious tones at the output of the synthesizer?

I use a PLL model (mostly VerliogA). I found that even for autocorrelation estimates which are �close to that of white noise (dithering), tones are present at the synthesizer output. �The tones must be coming from the SDM, but the autocorrelation plot shows no significant periodicity, i.e, normalized coeff. values of less than 0.05.

Thanks

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Berti Community Fellow Offline Posts: 356	Re: relationship autocorrelation of SDM o/p AND spurs at frac-N-synthesizer o/p Reply #1 - Sep 30^th, 2008, 4:08am Do the spurs not come from charge pump non-ideality?
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trond

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Re: relationship autocorrelation of SDM o/p AND spurs at frac-N-synthesizer o/p
Reply #2 - Sep 30^th, 2008, 5:17am

I have an ideal charge pump, ideal PFD, VCO, FBdivider...... So I would not expect spurs in the synthesizer o/p at multiples of the fractional part, would I?
The fractional input to the SDM is 1/512 with the reference clock being 26M. I am getting spurs at multiples of 26M/512 which are below the PLL BW of 1MHz.

But when I look at the spectrum of the SDM o/p and also at its autocorrelation, I can see no significant spurs.

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« Last Edit: Sep 30^th, 2008, 7:03am by trond »

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trond Senior Member Offline Posts: 168 Glasgow, Scotland	Re: relationship autocorrelation of SDM o/p AND spurs at frac-N-synthesizer o/p Reply #3 - Oct 4^th, 2008, 7:51am So are you saying that even with an ideal charge pump and dithered 3rd order sigma delta modulator I will see spurs at the synthesizer o/p? I am, that's what's puzzeling me. I would not expect any spurs, but might overlooking something. Any hints are appreciated.
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rf-design

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Reiner Franke

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Re: relationship autocorrelation of SDM o/p AND spurs at frac-N-synthesizer o/p
Reply #4 - Oct 6^th, 2008, 2:07pm

Depend on the number of states of your divider!

You use a 26MHz reference and a possible high number dual-modulus divider. The issue is that it creates a bad number distribution. If you take the spectrum of the open-loop SDM output the FFT is like a an ideal brickwall lowpass filter with the FTT lenght. But the PLL is something third-order. The integer+1/2^k division is critical. I found that only a multibit output SDM works. It could generate a nearly gaussian distribution also for these numbers. I discuss this some times ago here:

http://www.edaboard.com/viewtopic.php?t=147586

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trond

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Re: relationship autocorrelation of SDM o/p AND spurs at frac-N-synthesizer o/p
Reply #5 - Oct 7^th, 2008, 1:54am

Thanks for your response.

I use a multi-modulus divider. The PLL-order is 2 and the MASH topology is 3rd order. As a result the divider chooses between 8 divisions, N-3 to N+4. I attached a figure of the distribution of the division values. The distribution should resemble a gaussian.

Could you please elaborate your comment "If you take the spectrum of the open-loop SDM output the FFT is like a an ideal brickwall lowpass filter with the FTT lenght. But the PLL is something third-order."

Thanks,

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trond

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Re: relationship autocorrelation of SDM o/p AND spurs at frac-N-synthesizer o/p
Reply #6 - Oct 7^th, 2008, 1:59am

Also, here is a spectrum plot of the 26MHz clock at the output of the divider. I sampled the clock output at 1GHz and exported it to Matlab. I used a hanning window.

The plot shows the difference between using dither and not using dither. As you can see even with dither there are tones at 26.202kHz (multiples of 202k away). The fractional input was 1/256 which would create tones at multiples of 1/256*26MHz = 101kHz.

I cannot see the tones in the autocorrelation of the dithered o/p. But the PSD of the feedback clock shows even multiples of 101kHz. Hence I was wondering where they might be introduced.

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rf-design

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Reiner Franke

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Re: relationship autocorrelation of SDM o/p AND spurs at frac-N-synthesizer o/p
Reply #7 - Oct 7^th, 2008, 12:18pm

The argument that the PSD of the SDM output does not show spurious but the closed PLL is the following:

If the PLL in time continous phase domain with linear behaviour get a SDM number distribution without spurs the closed loop should also be spurious free!

But the model of operating the PLL in phase domain is not true:

1. The frequency step, which is a ramp in phase domain is applied somewhere within the phase cycle. That lead to memory effects where the cycle period time depend on previous times.

2. The frequency step is no addition of a phase ramp to the loop input. Instead the loop gain change too.

Both effects are typical neglated because these does not fit into a linear time continious PLL model. A simulation is the way to work with. I think Ian Galton describe in an article the differencies.

http://ispg.ucsd.edu/pubs/Wang_ISSCC2008_slides.pdf

Hope that helps. Dither was also a small piece to improve.

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trond Senior Member Offline Posts: 168 Glasgow, Scotland	Re: relationship autocorrelation of SDM o/p AND spurs at frac-N-synthesizer o/p Reply #8 - Oct 12^th, 2008, 10:45pm Thanks for your feedback rf-design. It has been very helpful. I'll digest gathered information and may post back if I have more questions. Cheers
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