Dear comp.dsp, Our recent "daily quiz" thread has caused me to think more about ADC converter measurements, especially about the suitableness of using the dynamic range measure to quantify converter performance. I would like to bounce some of these thoughts off the group. First of all, for the purposes of this thread, let us assume we have a theoretically perfect ADC, i.e., one with no non-linearities other than the quantization process itself. Also let us define dynamic range as follows: DR = 10 * log(P_Strongest / P_Weakest) [dB], where P_Strongest is the power of the strongest signal the ADC can convert and P_Weakest is the power of the weakest (non-zero) signal the ADC can convert, at the output of the converter. I will purposely leave the terms "signal" and "can convert" loosely defined at this point. Part I, Measuring DR Without Dither ----------------------------------- If we use a sine wave for the input signals, then one issue that comes up is the "sine'edness" of the resulting ADC output at the lowest possible input sine wave amplitude, e.g., q/2 * cos(omega * t), where q is the converter's quantization step. Namely, that's just going to be a square wave. 1. How does one get off referring to this as a sine wave? 2. How does one handle the fact a square wave has more power than the sine wave? Part I, Measuring DR With Dither ----------------------------------- For this part we use the theoretically perfect non-subtractive dither Robert Wannamaker outlined in his PhD thesis, namely uncorrelated TPDF with endpoints at -q/2 and +q/2. In this case the output is perfectly linearized and the dynamic range is INFINITE since, no matter how small the input sine amplitude is, it can be "detected" at the output (detection method unspecified). Conclusion ---------- Dynamic range is NOT the right parameter to use for ADC resolution measurement! SNR (or SINAD) is mo' better. -- Randy Yates, DSP/Embedded Firmware Developer Digital Signal Labs http://www.digitalsignallabs.com
Dynamic Range as a Measure of ADC Converter Resolution and Accuracy
Started by ●March 18, 2016
Reply by ●March 19, 20162016-03-19
On 3/18/2016 10:15 PM, Randy Yates wrote:> Dear comp.dsp, > > Our recent "daily quiz" thread has caused me to think more about ADC > converter measurements, especially about the suitableness of using the > dynamic range measure to quantify converter performance. I would like to > bounce some of these thoughts off the group. > > First of all, for the purposes of this thread, let us assume we have > a theoretically perfect ADC, i.e., one with no non-linearities other > than the quantization process itself. > > Also let us define dynamic range as follows: > > DR = 10 * log(P_Strongest / P_Weakest) [dB], > > where P_Strongest is the power of the strongest signal the ADC can > convert and P_Weakest is the power of the weakest (non-zero) signal the > ADC can convert, at the output of the converter. I will purposely leave > the terms "signal" and "can convert" loosely defined at this point. > > Part I, Measuring DR Without Dither > ----------------------------------- > > If we use a sine wave for the input signals, then one issue that comes > up is the "sine'edness" of the resulting ADC output at the lowest > possible input sine wave amplitude, e.g., q/2 * cos(omega * t), where q > is the converter's quantization step. Namely, that's just going to be > a square wave. > > 1. How does one get off referring to this as a sine wave?Who cares? It represents the signal as best can be done within the limitations of the number of bits.> 2. How does one handle the fact a square wave has more power than > the sine wave?Who said it is a square wave? All you can do is work with the information you have. I believe an RMS equation is pretty simple and appropriate.> Part I, Measuring DR With Dither > ----------------------------------- > > For this part we use the theoretically perfect non-subtractive dither > Robert Wannamaker outlined in his PhD thesis, namely uncorrelated TPDF > with endpoints at -q/2 and +q/2. > > In this case the output is perfectly linearized and the dynamic range is > INFINITE since, no matter how small the input sine amplitude is, it can > be "detected" at the output (detection method unspecified). > > Conclusion > ---------- > > Dynamic range is NOT the right parameter to use for ADC resolution > measurement! SNR (or SINAD) is mo' better.Why would either of those measurements be better when using the "perfect" dither outlined above? -- Rick
Reply by ●March 19, 20162016-03-19
On Fri, 18 Mar 2016 22:15:57 -0400, Randy Yates <yates@digitalsignallabs.com> wrote:>Dear comp.dsp, > >Our recent "daily quiz" thread has caused me to think more about ADC >converter measurements, especially about the suitableness of using the >dynamic range measure to quantify converter performance. I would like to >bounce some of these thoughts off the group. > >First of all, for the purposes of this thread, let us assume we have >a theoretically perfect ADC, i.e., one with no non-linearities other >than the quantization process itself. > >Also let us define dynamic range as follows: > > DR = 10 * log(P_Strongest / P_Weakest) [dB], > >where P_Strongest is the power of the strongest signal the ADC can >convert and P_Weakest is the power of the weakest (non-zero) signal the >ADC can convert, at the output of the converter. I will purposely leave >the terms "signal" and "can convert" loosely defined at this point. > >Part I, Measuring DR Without Dither >----------------------------------- > >If we use a sine wave for the input signals, then one issue that comes >up is the "sine'edness" of the resulting ADC output at the lowest >possible input sine wave amplitude, e.g., q/2 * cos(omega * t), where q >is the converter's quantization step. Namely, that's just going to be >a square wave. > > 1. How does one get off referring to this as a sine wave? > > 2. How does one handle the fact a square wave has more power than > the sine wave? > >Part I, Measuring DR With Dither >----------------------------------- > >For this part we use the theoretically perfect non-subtractive dither >Robert Wannamaker outlined in his PhD thesis, namely uncorrelated TPDF >with endpoints at -q/2 and +q/2. > >In this case the output is perfectly linearized and the dynamic range is >INFINITE since, no matter how small the input sine amplitude is, it can >be "detected" at the output (detection method unspecified). > >Conclusion >---------- > >Dynamic range is NOT the right parameter to use for ADC resolution >measurement! SNR (or SINAD) is mo' better.For your hypothetical case where there are no other non-linearities, then, maybe. However, it's still going to be application dependent, since different systems try to squeeze different things out of "signals". And you haven't defined "noise". The hypothetically completely linear ADC, such that it has no spurs or other distortions due to intermods or anything else, could theoretically support small signals down to whatever other noise limit (which is unspecified), might begin to impair them. Is it the noise of the converter? And all that's really needed to get signals below the LSB is that the composite input signal adequately decorrelates the quantization noise from the small signals. Dither does that so that it works independent of whatever else might be there, but if the composite input signal has sufficient entropy then small signals may be able to be recovered without dither. I say that only to make the point that "noise" may be context dependent, so even the "noise" of the converter may or may not drive the spec. But no ADC is completely free of non-linearities, so this is only an academic exercise for many applications. Eric Jacobsen Anchor Hill Communications http://www.anchorhill.com
Reply by ●March 22, 20162016-03-22
rickman <gnuarm@gmail.com> writes:> On 3/18/2016 10:15 PM, Randy Yates wrote: >> Dear comp.dsp, >> >> Our recent "daily quiz" thread has caused me to think more about ADC >> converter measurements, especially about the suitableness of using the >> dynamic range measure to quantify converter performance. I would like to >> bounce some of these thoughts off the group. >> >> First of all, for the purposes of this thread, let us assume we have >> a theoretically perfect ADC, i.e., one with no non-linearities other >> than the quantization process itself. >> >> Also let us define dynamic range as follows: >> >> DR = 10 * log(P_Strongest / P_Weakest) [dB], >> >> where P_Strongest is the power of the strongest signal the ADC can >> convert and P_Weakest is the power of the weakest (non-zero) signal the >> ADC can convert, at the output of the converter. I will purposely leave >> the terms "signal" and "can convert" loosely defined at this point. >> >> Part I, Measuring DR Without Dither >> ----------------------------------- >> >> If we use a sine wave for the input signals, then one issue that comes >> up is the "sine'edness" of the resulting ADC output at the lowest >> possible input sine wave amplitude, e.g., q/2 * cos(omega * t), where q >> is the converter's quantization step. Namely, that's just going to be >> a square wave. >> >> 1. How does one get off referring to this as a sine wave? > > Who cares? It represents the signal as best can be done within the > limitations of the number of bits. > > >> 2. How does one handle the fact a square wave has more power than >> the sine wave? > > Who said it is a square wave?It's not a question of who, but what. It *is* a digital square wave, 0, 0, ..., 1, 1, ..., 0, 0, ... etc.> All you can do is work with the information you have. I believe an RMS > equation is pretty simple and appropriate.So it's ok that _something_ gets produced in the output even if it has little resemblence to the input?!?>> Part I, Measuring DR With Dither >> ----------------------------------- >> >> For this part we use the theoretically perfect non-subtractive dither >> Robert Wannamaker outlined in his PhD thesis, namely uncorrelated TPDF >> with endpoints at -q/2 and +q/2. >> >> In this case the output is perfectly linearized and the dynamic range is >> INFINITE since, no matter how small the input sine amplitude is, it can >> be "detected" at the output (detection method unspecified). >> >> Conclusion >> ---------- >> >> Dynamic range is NOT the right parameter to use for ADC resolution >> measurement! SNR (or SINAD) is mo' better. > > Why would either of those measurements be better when using the > "perfect" dither outlined above?Because "infinity" doesn't tell you much about the resolution of a converter. -- Randy Yates, DSP/Embedded Firmware Developer Digital Signal Labs http://www.digitalsignallabs.com
Reply by ●March 22, 20162016-03-22
> >> > >> Conclusion > >> ---------- > >> > >> Dynamic range is NOT the right parameter to use for ADC resolution > >> measurement! SNR (or SINAD) is mo' better. > > > > Why would either of those measurements be better when using the > > "perfect" dither outlined above? > > Because "infinity" doesn't tell you much about the resolution of a > converter. >I will add that this "problem" with the defintion of dynamic range, applies not only to A/Ds but to anything that has an upper signal capability, carries a signal and adds some noise to it....... which is just about everything. M
Reply by ●March 22, 20162016-03-22
makolber@yahoo.com writes:>> >> >> >> Conclusion >> >> ---------- >> >> >> >> Dynamic range is NOT the right parameter to use for ADC resolution >> >> measurement! SNR (or SINAD) is mo' better. >> > >> > Why would either of those measurements be better when using the >> > "perfect" dither outlined above? >> >> Because "infinity" doesn't tell you much about the resolution of a >> converter. >> > > I will add that this "problem" with the defintion of dynamic range, > applies not only to A/Ds but to anything that has an upper signal > capability, carries a signal and adds some noise to it....... which is > just about everything.Are you aware of a more useful definition? Interesting that this article defines it essentially as 1 + SNR: https://en.wikipedia.org/wiki/Amplifier_figures_of_merit -- Randy Yates, DSP/Embedded Firmware Developer Digital Signal Labs http://www.digitalsignallabs.com
Reply by ●March 22, 20162016-03-22
On Tue, 22 Mar 2016 11:38:03 -0400, Randy Yates <yates@digitalsignallabs.com> wrote:>makolber@yahoo.com writes: > >>> >> >>> >> Conclusion >>> >> ---------- >>> >> >>> >> Dynamic range is NOT the right parameter to use for ADC resolution >>> >> measurement! SNR (or SINAD) is mo' better. >>> > >>> > Why would either of those measurements be better when using the >>> > "perfect" dither outlined above? >>> >>> Because "infinity" doesn't tell you much about the resolution of a >>> converter. >>> >> >> I will add that this "problem" with the defintion of dynamic range, >> applies not only to A/Ds but to anything that has an upper signal >> capability, carries a signal and adds some noise to it....... which is >> just about everything. > >Are you aware of a more useful definition? Interesting that >this article defines it essentially as 1 + SNR: > > https://en.wikipedia.org/wiki/Amplifier_figures_of_merit >-- >Randy Yates, DSP/Embedded Firmware Developer >Digital Signal Labs >http://www.digitalsignallabs.comIf I understand your questions correctly, I think it comes down to what limits the small signal case. It might be noise, it might be distortion, it might be spurs, but *something* starts to get in the way that limits small signal detection. Whatever that happens to be, it makes a reasonable reference as a limit and therefore a potential definition of the lower limit for a DR spec. Likewise at the top end, a hard-limiting system may wind up with a different max signal than something that has a softer limit, due both to the limiting mechanisms as well as the application's sensitivity to that limiting.. So, yeah, it is kind of expected that there isn't a truly universal definition of DR. Eric Jacobsen Anchor Hill Communications http://www.anchorhill.com
Reply by ●March 22, 20162016-03-22
Eric Jacobsen wrote: <snip>> > So, yeah, it is kind of expected that there isn't a truly universal > definition of DR. >There are perfectly useful definitions constrained by domain. This is true with most things.> > Eric Jacobsen > Anchor Hill Communications > http://www.anchorhill.com >-- Les Cargill
Reply by ●March 22, 20162016-03-22
On Fri, 18 Mar 2016 22:15:57 -0400, Randy Yates wrote:> Dear comp.dsp, > > Our recent "daily quiz" thread has caused me to think more about ADC > converter measurements, especially about the suitableness of using the > dynamic range measure to quantify converter performance. I would like to > bounce some of these thoughts off the group. > > First of all, for the purposes of this thread, let us assume we have a > theoretically perfect ADC, i.e., one with no non-linearities other than > the quantization process itself. > > Also let us define dynamic range as follows: > > DR = 10 * log(P_Strongest / P_Weakest) [dB], > > where P_Strongest is the power of the strongest signal the ADC can > convert and P_Weakest is the power of the weakest (non-zero) signal the > ADC can convert, at the output of the converter. I will purposely leave > the terms "signal" and "can convert" loosely defined at this point. > > Part I, Measuring DR Without Dither ----------------------------------- > > If we use a sine wave for the input signals, then one issue that comes > up is the "sine'edness" of the resulting ADC output at the lowest > possible input sine wave amplitude, e.g., q/2 * cos(omega * t), where q > is the converter's quantization step. Namely, that's just going to be a > square wave. > > 1. How does one get off referring to this as a sine wave? > > 2. How does one handle the fact a square wave has more power than the > sine wave? > > Part I, Measuring DR With Dither ----------------------------------- > > For this part we use the theoretically perfect non-subtractive dither > Robert Wannamaker outlined in his PhD thesis, namely uncorrelated TPDF > with endpoints at -q/2 and +q/2. > > In this case the output is perfectly linearized and the dynamic range is > INFINITE since, no matter how small the input sine amplitude is, it can > be "detected" at the output (detection method unspecified). > > Conclusion ---------- > > Dynamic range is NOT the right parameter to use for ADC resolution > measurement! SNR (or SINAD) is mo' better.Objection: If properly qualified (spurious-free, 3rd-order intermod, etc.), dynamic range is a _good_ parameter to use to qualify an ADC for a specific task. I agree that it's not a good method for ADCs in general. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com
Reply by ●March 22, 20162016-03-22
On Tuesday, March 22, 2016 at 2:18:31 PM UTC-4, Tim Wescott wrote:> On Fri, 18 Mar 2016 22:15:57 -0400, Randy Yates wrote: > > > Dear comp.dsp, > > > > Our recent "daily quiz" thread has caused me to think more about ADC > > converter measurements, especially about the suitableness of using the > > dynamic range measure to quantify converter performance. I would like to > > bounce some of these thoughts off the group. > > > > First of all, for the purposes of this thread, let us assume we have a > > theoretically perfect ADC, i.e., one with no non-linearities other than > > the quantization process itself. > > > > Also let us define dynamic range as follows: > > > > DR = 10 * log(P_Strongest / P_Weakest) [dB], > > > > where P_Strongest is the power of the strongest signal the ADC can > > convert and P_Weakest is the power of the weakest (non-zero) signal the > > ADC can convert, at the output of the converter. I will purposely leave > > the terms "signal" and "can convert" loosely defined at this point. > > > > Part I, Measuring DR Without Dither ----------------------------------- > > > > If we use a sine wave for the input signals, then one issue that comes > > up is the "sine'edness" of the resulting ADC output at the lowest > > possible input sine wave amplitude, e.g., q/2 * cos(omega * t), where q > > is the converter's quantization step. Namely, that's just going to be a > > square wave. > > > > 1. How does one get off referring to this as a sine wave? > > > > 2. How does one handle the fact a square wave has more power than the > > sine wave? > > > > Part I, Measuring DR With Dither ----------------------------------- > > > > For this part we use the theoretically perfect non-subtractive dither > > Robert Wannamaker outlined in his PhD thesis, namely uncorrelated TPDF > > with endpoints at -q/2 and +q/2. > > > > In this case the output is perfectly linearized and the dynamic range is > > INFINITE since, no matter how small the input sine amplitude is, it can > > be "detected" at the output (detection method unspecified). > > > > Conclusion ---------- > > > > Dynamic range is NOT the right parameter to use for ADC resolution > > measurement! SNR (or SINAD) is mo' better. > > Objection: If properly qualified (spurious-free, 3rd-order intermod, > etc.), dynamic range is a _good_ parameter to use to qualify an ADC for a > specific task. > > I agree that it's not a good method for ADCs in general. > >OK to continue the daily quiz in the context of receiver front ends.... what is generally meant when one refers to the INSTANTANEOUS dynamic range? Mark
