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aaron_do

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Does Dynamic Element Matching in ADCs and DACs really work?
Jan 09^th, 2014, 1:45am

Hi all,

in dynamic element matching (DEM), nonlinearity due to component mismatch is averaged out into white noise by dynamically switching the usage of different elements. There's a paper entitled, "Why Dynamic-Element-Matching DACs Work" in IEEE TCAS-II, Feb 2010.

Anyway I have a doubt about the idea. Suppose my system consists of a non-ideal DAC whose non-linearity is averaged by DEM followed by an ideal ADC. If I run a two-tone test on the system, I believe the IMD would be corrected by the DEM. However, I think the BER of the system could be as bad as the actual non-linearity of the DAC without DEM. My reasoning is that BER looks at the system on a sample to sample basis while looking at the spectrum is observing the long term average (two wrongs don't make a right?).

So if the linearity problem is causing you to fail spectrum emissions then DEM would be helpful, but if your linearity problem is causing your BER to degrade, it wouldn't work.

Am I right in my analysis?

thanks,
Aaron

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carlgrace

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Re: Does Dynamic Element Matching in ADCs and DACs really work?
Reply #1 - Jan 10^th, 2014, 6:11pm

I think you're right. DEM directly trades noise floor for effective matching so if you're noise-limited it isn't going to help you.

Where it really DOES work is in cases where linearity is critical and is limited by capacitor matching. Two places where it is used routinely is in multi-bit delta-sigma ADCs and in unit-element DACs.

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aaron_do

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Re: Does Dynamic Element Matching in ADCs and DACs really work?
Reply #2 - Jan 12^th, 2014, 7:32am

Hi carlgrace,

I guess my question wasn't worded very well...definitely if you're noise-limited, DEM would aggravate the problem.

My doubt is that for whilte noise, you have a normal distribution in the voltage levels. When the voltage noise exceeds a certain level, you may have a bit-error. However, that only happens once in 10,000 samples (for example).

For DEM, the problem is linearity, not noise. So if you design for 9b linearity and then use DEM to improve the linearity to 12b, each individual sample still only meets the 9b linearity requirement. My concern is that if your modulation scheme has a large number of amplitude levels, then each individual sample could potentially be wrong.

Or is my analysis wrong. Perhaps, as you suggest, the net effect is simply an increase in the noise level.

thanks for the help,
Aaron

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Frank Wiedmann Community Fellow Offline Posts: 678 Munich, Germany	Re: Does Dynamic Element Matching in ADCs and DACs really work? Reply #3 - Jan 13^th, 2014, 12:48am I guess that you need to have a low-pass filter in front of your BER sampler to take advantage of DEM. Like this, you will always look at the average of several DAC samples.
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carlgrace

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Re: Does Dynamic Element Matching in ADCs and DACs really work?
Reply #4 - Jan 13^th, 2014, 11:38am

aaron_do wrote on Jan 12^th, 2014, 7:32am:

Hi carlgrace,

I guess my question wasn't worded very well...definitely if you're noise-limited, DEM would aggravate the problem.

My doubt is that for whilte noise, you have a normal distribution in the voltage levels. When the voltage noise exceeds a certain level, you may have a bit-error. However, that only happens once in 10,000 samples (for example).

For DEM, the problem is linearity, not noise. So if you design for 9b linearity and then use DEM to improve the linearity to 12b, each individual sample still only meets the 9b linearity requirement. My concern is that if your modulation scheme has a large number of amplitude levels, then each individual sample could potentially be wrong.

Or is my analysis wrong. Perhaps, as you suggest, the net effect is simply an increase in the noise level.

thanks for the help,
Aaron

Hi Aaron,

It's hard to interpret your statement "each individual sample only meets the 9b linearity requirement". If you're taking a sample out of context the idea of linearity doesn't make sense because linearity is defined as a measurement involving an ensemble of measurements.

Remember, with DEM if you could magically fix the input EXACTLY, you would still get various voltage levels due to the DEM. On average they would be more accurate.

Here's an intuitive way to see what is going on.

If you have linearity problems then you will have strong peaks in the output spectrum of your converter. DEM chops off the tops of those peaks and distributes the power among all the other bins. Since the overall power is the same, it has to raise the noise floor to do it. This isn't exactly correct mathematically, but it gets the intuition of the process.

I agree with Frank that DEM may not be super helpful if BER is your #1 concern. BER depends a lot on the noise and DEM increases noise (in exchange for improved linearity)

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aaron_do

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Re: Does Dynamic Element Matching in ADCs and DACs really work?
Reply #5 - Jan 13^th, 2014, 4:52pm

Hi all,

thanks for the replies.

Quote:

I guess that you need to have a low-pass filter in front of your BER sampler to take advantage of DEM. Like this, you will always look at the average of several DAC samples.

I haven't seen any work mentioning a LPF before, but I suppose that you're implying that the rest of the system following the DAC would LPF the signal...I don't know, that's not what I understood from the papers. Maybe I'm wrong, but I don't think a LPF is necessary...

Quote:

If you have linearity problems then you will have strong peaks in the output spectrum of your converter. DEM chops off the tops of those peaks and distributes the power among all the other bins. Since the overall power is the same, it has to raise the noise floor to do it. This isn't exactly correct mathematically, but it gets the intuition of the process.

Yeah, I've heard, and understood this explanation before. My problem with it is that when you look at a signal's spectrum, you are looking at its time average, but for BER, each sample matters. Anyway I think the only way I'm gonna convince myself is through system simulations.

BTW, if anybody happens to know, roughly how much power does the DEM encoder require?

thanks,
Aaron

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RobG

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Re: Does Dynamic Element Matching in ADCs and DACs really work?
Reply #6 - Jan 13^th, 2014, 8:07pm

aaron_do wrote on Jan 13^th, 2014, 4:52pm:

Yeah, I've heard, and understood this explanation before. My problem with it is that when you look at a signal's spectrum, you are looking at its time average, but for BER, each sample matters. Anyway I think the only way I'm gonna convince myself is through system simulations.

You are correct that DEM won't help if each sample matters - but you are assuming that the mismatch is large enough to cause a bit error. That mismatch causes other problems: harmonics (and DEM eliminates the harmonics). I know eliminating harmonics is very important in communication systems. I'm not 100% sure why, but here is a guess. Say you were trying to get all the information around "Fo". If your ADC had a large 3rd harmonic distortion due to mismatch, and there was an unwanted signal at Fo/3, the ADC distortion would upconvert the Fo/3 signal to Fo. The error from the signal at Fo/3 could be much larger than the error due to the mismatch. Thus it is more desirable to randomize the noise than to have distortion upconvert an undesirable signal onto your desired signal.

I hope this makes sense...

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aaron_do

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Re: Does Dynamic Element Matching in ADCs and DACs really work?
Reply #7 - Jan 13^th, 2014, 9:12pm

Hi RobG and others,

thanks for the help.

Quote:

but you are assuming that the mismatch is large enough to cause a bit error

Yeah, that's why I was saying that the usefulness of DEM is signal dependent. In other words, I need to check how well it works for my specific modulation scheme. However, what others (including the authors of several papers) seem to be saying is that the effect of DEM can be modeled as simply an increase in the noise level. I can kind of see how that might be true also.

I think when we look at harmonics, we are not necessarily concerned with the harmonics themselves (although they could be important, in the situation you mentioned for example). Instead, the harmonic distortion level is an indication of the linearity of the design. It could be used as an indication of how much intermodulation or spectral regrowth to expect. For transmitters its mostly about meeting spectral emissions requirements, and for receivers I suppose its mostly about intermodulation.

But imagine if you had a temperature sensor that took a 14b accurate reading every second, and the number kept jumping around because of DEM. This might not be tolerable. As Frank mentioned, you might need to average the results. I wonder if such a situation could occur in a communications system.

thanks,
Aaron

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Frank Wiedmann

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Re: Does Dynamic Element Matching in ADCs and DACs really work?
Reply #8 - Jan 14^th, 2014, 2:04am

aaron_do wrote on Jan 13^th, 2014, 4:52pm:

Quote:

I guess that you need to have a low-pass filter in front of your BER sampler to take advantage of DEM. Like this, you will always look at the average of several DAC samples.

I haven't seen any work mentioning a LPF before, but I suppose that you're implying that the rest of the system following the DAC would LPF the signal...I don't know, that's not what I understood from the papers. Maybe I'm wrong, but I don't think a LPF is necessary...

If you directly sample the DEM signal, you will get the combined effects of nonlinearity and noise, which are just as bad as the original nonlinearity. DEM does not magically reduce the total error, it only causes a different spectral distribution of the error.

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aaron_do

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Re: Does Dynamic Element Matching in ADCs and DACs really work?
Reply #9 - Jan 14^th, 2014, 5:44am

Hi Frank,

Quote:

DEM does not magically reduce the total error, it only causes a different spectral distribution of the error.

yes I was thinking the same thing. But if you design for 9b linearity, and you add DEM, you're probably gonna get more than 9b SNR right? Otherwise I doubt it would be effective...anyway system simulations pending.

I may have misunderstood your point about the LPF though. Are you saying that the LPF should be just after the DAC? Assuming the DEM doesn't include noise shaping, how effective could this be? If you want to operate the DAC up to the nyquist rate, you're not going to filter the DEM noise very much...

thanks,
Aaron

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boe

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Re: Does Dynamic Element Matching in ADCs and DACs really work?
Reply #10 - Jan 14^th, 2014, 7:19am

aaron_do wrote on Jan 14^th, 2014, 5:44am:

Hi Frank,

Quote:

DEM does not magically reduce the total error, it only causes a different spectral distribution of the error.

yes I was thinking the same thing. But if you design for 9b linearity, and you add DEM, you're probably gonna get more than 9b SNR right? Otherwise I doubt it would be effective...anyway system simulations pending.

I may have misunderstood your point about the LPF though. Are you saying that the LPF should be just after the DAC? Assuming the DEM doesn't include noise shaping, how effective could this be? If you want to operate the DAC up to the nyquist rate, you're not going to filter the DEM noise very much...

thanks,
Aaron

Aaron,
if you periodically cycle through N different DEM settings, you have effectively a fs/N-periodic system with DEM-errors around n*fs/N. The signal level around these frequencies is given by the mismatch between the N settings.
Essentially, the "DEM gain" depends on how much of that is filtered away by the LPF characteristics of your system.
- B O E

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Frank Wiedmann

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Re: Does Dynamic Element Matching in ADCs and DACs really work?
Reply #11 - Jan 14^th, 2014, 7:24am

The total error power will not be changed by DEM. You can use DEM either to more evenly distribute the error over the spectrum (in order to reduce peaks and maximize SFDR) or to move the error to frequencies outside the signal bandwidth and then filter it out (which is of course not possible if your signal needs the entire bandwidth of the DAC).

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aaron_do Senior Fellow Offline Posts: 1398	Re: Does Dynamic Element Matching in ADCs and DACs really work? Reply #12 - Jan 14^th, 2014, 4:47pm Hi boe and Frank, thanks for your replies. Essentially what you're saying is that SFDR remains the same unless you add a filter. Is the one-to-one equivalence an exact relationship? thanks, Aaron
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Frank Wiedmann

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Re: Does Dynamic Element Matching in ADCs and DACs really work?
Reply #13 - Jan 15^th, 2014, 6:26am

I did not say that the SFDR remains the same but that the total error power (or SNDR for a given signal) remains the same.

The relationship is only approximate, for details see http://www.diva-portal.org/smash/get/diva2:395/FULLTEXT02.pdf (section 3 of appendix 6 and also chapter 4) and maybe http://www.scribd.com/doc/20488185/Dynamic-Element-Matching as an introduction.

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aaron_do Senior Fellow Offline Posts: 1398	Re: Does Dynamic Element Matching in ADCs and DACs really work? Reply #14 - Jan 15^th, 2014, 6:32am Sorry that was a typing error...I meant SNDR. thanks for the references. Aaron
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