Noise shaping article or book?

Dear all:

I need to learn about the gory details of noise shaping in delta-sigmas and (especially) fractional-N synthesizers, as pioneered by HP back in the early '90s. Not just descriptive stuff, but something that will help me learn how to do it myself in new situations.

What are your favourite references for this?

Thanks

Phil Hobbs

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Dr Philip C D Hobbs
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Phil Hobbs
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In the case of a linear modulation such as PCM or Delta-Sigma, noise shaping can be seen as a digital feedback loop and the standard H(z) math applies. Ideally, you want the noise transfer function to be flat both in the passband and in the stopband; this corresponds to the minimum of noise boost. Usually, the noise transfer function is found by brute force optimization.

In the cases of nonlinear modulation such as FM or PWM, the noise shaping theory is tough.

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It also has some good references.

Vladimir Vassilevsky DSP and Mixed Signal Design Consultant

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Vladimir Vassilevsky

Thanks. Where I'm going with this is mostly fractional-N PLLs. HP came up with a really cute trick back in the '90s that used noise shaping instead of a DAC to get rid of the reference frequency ripple in a fractional-N loop:

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(P. 44)

This is probably old hat to the hard core DSP folks here, but I hadn't seen it before, and thought it was cute, besides being potentially very useful. There's no math in the article, so I was hoping to learn how to synthesize the correct pattern for each value of N.

Cheers

Phil Hobbs

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Phil Hobbs

You should post this to comp.dsp, also -- there's a number of folks who hang out there that don't here.

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Tim Wescott

The concept of noise shaping could be applied to the frequency dividers in PLL, however you should be careful about that.

There are two issues:

  1. The analog loop filter should have enough of attenuation at the high frequencies so the noise boost would not affect the output spectrum of the VCO. This implies the filter of the higher order, with the corresponding negative effect on the loop dynamics.

  1. The shaped phase noise affects the output spectrum in the non-linear manner. That is, the noise which is supposed to be outside the band of interest, is partially converted back in the band. This effect can be accounted for.

I don't know of a book with the exact analysis of the effects of the noise shaping inside the fractional-N PLL, however it isn't very difficult to draw some estimates, then do the simulation and optimize it.

Tim Wescott already suggested to post in the comp.dsp, that would be a good idea.

Vladimir Vassilevsky DSP and Mixed Signal Design Consultant

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Vladimir Vassilevsky

If you look at the HP Journal article, the cute part is that they vary the division ratio among the 8 ratios [N-4, N+3] some fixed number of times within each reference cycle.

If it were just a straight delta-sigma modulator, that wouldn't be hard at all--it's figuring out just what pattern to use for each of probably

10**5 choices of average modulus that's the parlor trick--it's like a delta sigma with a limit cycle of a predetermined (short) length. Simulation is sort of difficult because of the number of choices.

I'll try comp.dsp too.

Cheers

Phil Hobbs

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Phil Hobbs

Maybe I sort of understand what you're talking about:

Instead of a straight divide-by-N in a PLL feedback, and instead of a fixed-ratio pulse swallower (divide by N some times, divide by N+1 some times) you could use a stream of pseudo-random N's, from some longish lookup table, and convert the predictability of the pulse swallower into a random noise floor, like PWM versus delta-sigma. The phase detector becomes a delta-sigma dac.

Is that the idea?

Instead of a lookup table, you could do a delta-sigma dac sort of feedback algorithm to compute the stream of Ns that average to the divisor you need. FPGA for sure.

Fun but mathematically messy when it comes to computing the final phase noise.

Why not have a smart phase detector drive a real dac?

John

Reply to
John Larkin

So it is like 3-bit delta sigma. The concept is the same: they feed back the phase error via the noise shaping filter. The output of the filter sets the division ratio.

The length of the limit cycle could be rather long depending on the shaping filter order and the division ratio. I'd rather do a noise shaping filter then calculate fixed pattern. With the filter, you can also add dither to smear the periodic pattern.

Start with the trivial noise shaping filter like [-1] or [-2 +1] or [-3

+3 -1], then optimize it.

Vladimir Vassilevsky DSP and Mixed Signal Design Consultant

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Vladimir Vassilevsky

The idea is to avoid all that squishy analogue stuff. ;) The DAC approach came from the original Dana Labs Digiphase synthesizer, back in

1969 or thereabouts.

Depending on the loop BW, you could do pretty well with either method, I think, and HP's trick is cool enough that I got motivated to actually learn the math if possible. Really good DACs have gotten a lot cheaper since 1993, of course, which may make that approach effectively obsolete.

I don't think that using a straight delta-sigma would have the same result, because you might easily have beats between the limit cycle period and the reference period, for some values of N. It seems a bit like Don Lancaster's 'magic sine wave' idea.

Cheers

Phil Hobbs

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Phil Hobbs

Reminds me of cpu clock ditherers designed to spread the clock spectrum a bit while maintaining a design average in to reduce EMI peaks so that devices could skate under the approvals' "radar."

Jon

Reply to
Jon Kirwan

Yes, it's a bit like that, except that they claim that the noise shaping they're using moves almost all the reference ripple into the loop filter's stopband. Also since the spur power is proportional to the phase deviation of the VCO, which goes like 1/f_mod, merely moving it further out is a help.

Beyond the loop BW, you can be much more aggressive about rolling off the skirts of the filter because you don't care too much about the phase shift.

Cheers

Phil Hobbs

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Dr Philip C D Hobbs
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Phil Hobbs

It is not so simple. The noise shaping is like digging a hole in the flat noise floor. If the vertical axis is the log(amplitude), and the horizontal axis is frequency, then you put the same volume of soil above the ground as you took away from the hole. Notice the log scale! You might need the analog filter of the high order. For the loop to be stable, the cutoff of the filter should be about x4 of the loop bandwidth or so.

Vladimir Vassilevsky DSP and Mixed Signal Design Consultant

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Vladimir Vassilevsky

Sure. I often use bandstop filters in FB loops, because their phase shift is much less outside their stopbands. This works great with resonant actuators such as piezo bimorphs--they have a Q of about 30, which means your loop gain has to be less than -30 dB. A bandstop filter can get you a factor of 10 in closed loop gain.

Cheers

Phil Hobbs

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Dr Philip C D Hobbs
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Phil Hobbs

Wasn't the Digiphase a notorious nightmare+failure? I recall reading a fun and horrifying article about it. In one of Jim Williams' books, I recall.

Fast DACs and ADCs and FPGAs are all affordable nowadays. The pipeline ADCs in particular are an amazing bunch of performance in a cheap package.

Our digital delay generators have a PLL that uses a pipeline ADC to digitize the output of a triggered oscillator, does a bunch of math on it, and drives a DAC+varicap to close the loop. The idea is to lock it to a crystal reference (of a different frequency!) but still have the triggered oscillator stay phase coherent to the random input trigger. I invented that myself, in a fevered burst of brain activity. The point being that an ADC gives you a lot more information about a signal than just fooling around with its edges.

John

Reply to
John Larkin

Chekout:

How the MASH works:

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Simulating fractional-N phase noise:

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An new FPGA-based design with much lower phase noise and no integer-N boundary spurs:

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Reply to
Andrew Holme

Who invented this is actually a bit controversial. The multi-stage noise shaping structure (MASH) can be drawn in two ways. The 1990 IEEE paper by Miller and Conley shows one way; but it was originally invented by John Wells of Marconi Instruments in 1984. See US patent 4609881. My write-up on the MASH shows how the two forms are equivalent:

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See also:

Simulating fractional-N phase noise:

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An new FPGA-based design with much lower phase noise and no integer-N boundary spurs:

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Reply to
Andrew Holme

Brilliant, thanks.

Cheers

Phil Hobbs

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Phil Hobbs

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