A DSD DAC with no chip

DonH50

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The paper didn't load for me but my Internet connection has been flaky tonight (I haven't managed to clear my outbox either, keeps bombing out, argh). I'm not sure where you're going, presumably disputing my statement, but that statement has been proven over and over again. Different architectures will exhibit different sensitivity to different types of jitter as related to their bandwidth and noise shaping properties, over their entire bandwidth, but as far as random jitter is concerned the SNR change is related to the signal and resolution only (for any converter, ADC or DAC). This is very easy to prove theoretically and measurements have correlated with theory. At least IME and papers I have read over the past few decades. YMMV - Don
 

opus111

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Do you have any links to the papers where you've drawn that conclusion? - its totally at odds with my own understanding and that of Bob Adams in the linked paper.

In brief the SNR sensitivity depends (he considers a multibit S-D loop) on how many DAC (quantization) levels the signal occupies vs how many levels are occupied by the noise. For DSD (a special, limiting case that Adams doesn't raise) the noise occupies the whole 1bit, any signal has to squeeze in beside it. He says explicitly that there are only two ways to combat this extreme jitter sensitivity - increase the ratio of signal to noise in the loop as far as possible, or adopt a discrete time (in practice it means switched capacitor) analog filter at the output. The latter approach was the one chosen by Philips for 'Bitstream' - the TDA1547 uses this.
 

DonH50

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Not now and I am swamped at work and home (getting ready for a concert). The basic jitter derivation is in many converter and signal-processing texts and is derived several different ways, some using probability (expectation integrals), others Bessel functions, some simply use a straight-line approximation of the sine wave around an lsb, calculate the area of the resultant triangles for quantization noise, then relate to changes in area with jitter time to calculate SNR reduction, etc. I believe it is in the Oppenheim and Schaffer seminal texts Digital Signal Processing and Discrete-Time Signal Processing, etc. Honestly, I have known that for so long, and had it drilled into me through so many college classes, workshops, work experience (theoretical and practical lab measurements), etc. over a variety of ADC/DAC designs I have worked on (SAR, flash, encoded-flash, delta-sigma, binary, unary, segmented, etc.) that I have not thought about it (the basic derivation) in ages. Converter companies like ADI, TI/Burr-Brown, Comlinear/National, etc. have app notes that discuss it. I am sure I have it in my notes but don't have the time to dig them up right now. One of my jitter threads here on WBF goes through a hand-waving explanation. It is related to aperture time, the time it takes a signal to pass through one lsb. It turns out clock frequency drops out and all you are left with is resolution and signal frequency, so the jitter deviation (in time) is related to signal frequency and resolution only.

The number of levels the signal and noise level is the heart of it, as well as how long (in time or UIs) the jitter deviates, but that is independent of the clock rate and architecture. Jitter is a problem in a delta-sigma loop due to both noise shaping and loop stability issues; it does not change the fundamental relationship between wideband random jitter and the signal with respect to quantization levels in-band. Note: I use delta-sigma, DS or D-S, because Gabor Temes once said the original paper was mistranslated and it should be D-S, not S-D; this is because the differencing element (D) comes before the summer (S) in the loop. For that matter, I am pretty sure I have his notes, or his and John Candy's, showing the same conclusion about jitter, from my long-ago grad classes.

I suspect we are getting mixed up on random jitter and other timing errors in the loop. I am not sure what you mean when you say the noise occupies the "whole 1bit" -- most schemes assume a limiter so jitter impacts only the edges.
 

opus111

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Not now and I am swamped at work and home (getting ready for a concert). The basic jitter derivation is in many converter and signal-processing texts and is derived several different ways, some using probability (expectation integrals), others Bessel functions, some simply use a straight-line approximation of the sine wave around an lsb, calculate the area of the resultant triangles for quantization noise, then relate to changes in area with jitter time to calculate SNR reduction, etc. I believe it is in the Oppenheim and Schaffer seminal texts Digital Signal Processing and Discrete-Time Signal Processing, etc. Honestly, I have known that for so long, and had it drilled into me through so many college classes, workshops, work experience (theoretical and practical lab measurements), etc. over a variety of ADC/DAC designs I have worked on (SAR, flash, encoded-flash, delta-sigma, binary, unary, segmented, etc.) that I have not thought about it (the basic derivation) in ages. Converter companies like ADI, TI/Burr-Brown, Comlinear/National, etc. have app notes that discuss it. I am sure I have it in my notes but don't have the time to dig them up right now. One of my jitter threads here on WBF goes through a hand-waving explanation. It is related to aperture time, the time it takes a signal to pass through one lsb. It turns out clock frequency drops out and all you are left with is resolution and signal frequency, so the jitter deviation (in time) is related to signal frequency and resolution only.

I'm not disputing the standard approaches to jitter theory, those make sense. What's been our difference for as long as I've been on WBF is how S-D ( or D-S in your parlance) needs to be treated slightly differently. The claim you're making is for PCM only - where there's no appreciable noise being reproduced by the DAC. Hence I would modify what you say in the last sentence - the jitter sensitivity is related to total DAC output (signal plus any noise) and resolution only. in the case of S-D, we cannot consider 'signal frequency' because the audio band signal is being swamped by wideband noise. its the jitter's impact on this wideband noise which is at issue because jitter will cause some of this noise to 'fold down' into the audio band.

I suspect we are getting mixed up on random jitter and other timing errors in the loop.

I suspect there's a more fundamental misunderstanding.

I am not sure what you mean when you say the noise occupies the "whole 1bit" -- most schemes assume a limiter so jitter impacts only the edges.

Here I am talking about the total energy that the DAC is able to deliver, and how it gets partitioned between wanted stuff (signal) and unwanted (noise). A 1bit DAC can only put out a constant total energy so how a signal gets to be reproduced is by moving some of that HF energy down to lower frequencies. Which is the essence of noise shaping. At digital silence the partitioning is 100% noise and 0% signal. As the signal level increases so the total non-audio band noise decreases a little - up until the point where the loop is deemed to be 'overloaded'.
 

DonH50

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I don't have time for this at this time, sorry. I will just say that most of my experience has been with non-DS converters (ADCs and DACs) and the theory clearly worked. It also worked with the few (very high-frequency) DS ADCs and DACs I helped design. I have no idea what you mean by "no appreciable noise produced by the DAC". I have never seen a DAC like that... There is wideband thermal, shot, flicker, etc. etc. etc. noise as well as added jitter (random and deterministic). I have not observed differences in this between DS and any other ocnverter.

If the audio band was swamped by wideband noise then no signal would ever appear. Are you talking about a delta-sigma loop or something else? At the output of a DS DAC is a bit stream, which does look like wideband noise until you add an output filter, which "averages" the pulses to produce a lower-frequency signal. DSD is also a bit stream, same result. Jitter varies the samples' energy and can create in-band spurs, but again related to the signal frquency (note PCM or DSD also modulates the pulse stream with the signal, that's the point).

BTW, jitter at the output of a DAC does not alias (fold down); that only happens at the ADC (where the sampling process takes place). There are images generated at the DAC's output, whether it is noise-shaped or not, and wideband noise, but no aliasing.

I am not sure how you reckon energy when you say a 1-bit DAC can only put out constant energy.

I have a very hot project and work plus a concert to prepare for so don't have my usual evening time windows, sorry. I think we are so apart on this it'd better be to agree to disagree and move on...
 

opus111

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I don't have time for this at this time, sorry.

No worries - but perhaps other readers will gain some more clarity about the issues by our deliberations.

I will just say that most of my experience has been with non-DS converters (ADCs and DACs) and the theory clearly worked. It also worked with the few (very high-frequency) DS ADCs and DACs I helped design.

Yep and I have no issues with the theory whatsoever. I use the theory to reach the conclusions I have.

I have no idea what you mean by "no appreciable noise produced by the DAC". I have never seen a DAC like that... There is wideband thermal, shot, flicker, etc. etc. etc. noise as well as added jitter (random and deterministic).

Yeah and I wasn't referring to any of those. I was referring to the noise moved out of the audio band by the noise shaping process. Its that process that permits use of a much lower resolution DAC (1bit for DSD or in the case of most S-D architectures nowadays, 5 or 6bits).

If the audio band was swamped by wideband noise then no signal would ever appear. Are you talking about a delta-sigma loop or something else? At the output of a DS DAC is a bit stream, which does look like wideband noise until you add an output filter, which "averages" the pulses to produce a lower-frequency signal. DSD is also a bit stream, same result.

That's my meaning yes - the bitstream contains the audio signal within it, but its swamped by wideband noise until a filter's applied.

Jitter varies the samples' energy and can create in-band spurs, but again related to the signal frquency (note PCM or DSD also modulates the pulse stream with the signal, that's the point).

Here the problem with how I understand your approach is in this phrase you use: 'signal frequency'. That's not applicable in the noise shaped case because the dominant content at the DAC's output is wideband noise, not audio band signal.

BTW, jitter at the output of a DAC does not alias (fold down); that only happens at the ADC (where the sampling process takes place). There are images generated at the DAC's output, whether it is noise-shaped or not, and wideband noise, but no aliasing.

How can you be so sure that jitter-induced sidebands of the wideband noise won't appear in the audio band? If this indeed is the case then you've been right all along, and both Bob Adams and myself are mistaken. The phrase 'fold down' that I used wasn't intended to imply aliasing btw, perhaps it was an inappropriate use.

I am not sure how you reckon energy when you say a 1-bit DAC can only put out constant energy.

Simply because there are only two levels it can output. The output is a pulse train with variable duty cycle, the RMS value is completely constant. What's changing is the distribution of this constant energy stream - between in-band and out-of-band.
 

DonH50

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Jun 22, 2010
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I have not the time now, but I think we are closer than I thought.

Note quantization noise is shaped, wideband noise is not (or at least not in the same way; it comes in at the input of the loop in an ADC, not the output). I think I actually have a thread in the tech forum that plots the transfer functions fo several low-order DS loops.

Jitter at the sampling point, which is before or often part of the input differencing cell of a DS ADC, acts just like "regular" jitter with the same results and follows the theory. For a DS loop, and for several other architectures, jitter inside the loop (or inside the pipeline) can influence the output in different ways depending upon the transfer function from that (inner) point to the output. Jitter isshaped by the loop dynamics, and that often includes multiple sampling points (e.g. for a switched-capacitor design). I think that is the fundamental point we got sideways about. At the output of a DAC, no matter the "flavor", the only way for higher-frequency anything to get back to baseband is for there to be some sort of mixing (nonlinear, multiplication) function at the output. That can happen in the buffer circuits, other electronics, speakers, even our ears. I have always seen and used the term "folding" in this context to refer to aliasing, so I was confused when you used that term differently (i.e. "mixing" or "modulation" of the output). Different definitions...

One other side comment: Converters that use multibit converters in the loop give up the "perfect" 1/0 states implied by a 1-bit loop and have more noise and stability issues. Accuracy is also a concern; a multibit DAC in the feedback path of a first-order loop must be as accurate as the final resolution, even if it is just a few bits. That is, a 5-bit DAC in the ADC's DS loop must have 16-bit accurate levels for a 16-bit result. This leads to trimming, dynamic element matching, and various other schemes to ensure high resolution. Some of these schemes inject their own noise and distortion, further complicating matters. The trade for lower clock rates and lower-order loops must be made with great care by DS designers.
 

Audiophile Bill

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Geardaddy

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Well, well. Competition is a good thing. It looks like they are meticulous and fabricate pretty things. Their 300B integrated is a beauty. Time will tell...
 

Geardaddy

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The question is what part of the Amare design is proprietary? Much of it looks like a derivate of previous designs (and there is nothing intrinsically wrong with that....its the history of science and engineering)....
 

Joel

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Newcomer at home : one single ethernet input, four speaker biding terminals, that's it.
For 1,990 $, the new Lumin M1 offers nice performances with a very pleasing LP sound, and streams up to DSD 128. Not too shabby...



This small digital amp is able to drive convincingly my Vivid G1s. It's certainly not the ultimate amplifier for high end systems but I could nevertheless live with that one...
A bit too expensive to be included on the new Andre Marc's topic of gears under 1,500 $
 

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