Talk:Analog-to-digital converter/Archive 1

Archive 1

Stubness

I agree this article needs some rewriting and re-engineering, but why was it marked as a stub? -- NIC1138 21:23, 17 December 2005 (UTC)

Resolution

Updated wikilink from Resolution to Resolution (logic) this might need to point to Resolution (music) or even another page. feel free to change it if you know better. --STHayden 22:35, 6 August 2006 (UTC)

Merge with Digital-to-analog converter

I've posted a merge tag on the article. It would make sense to have the opposite technologies in one article. If you agree or disagree, please post. --Davidkazuhiro 13:03, 9 February 2007 (UTC) I Take that back. The articles are large and well established as it is. --Davidkazuhiro 13:05, 9 February 2007 (UTC)

Analog != Audio

This article is linked to from some general articles on electronics (I got here via the oscilloscope article), yet some authors appeared to have assumed that it was predominantly about audio applications of A to D conversion. While the audio information seems good, its organization is confusing. In several spots the topic shifts without warning from general discussion of an analog signal to very audio-specific applications. General A-to-D material should be edited to keep the discussion general, and audio-specific information should be moved to its own section or article. Chriscorbell 23:26, 11 May 2007 (UTC)

Ramp converter with microcontroller

Adding this here, since it's a bit too long to insert into the body of the article. Given a microcontroller (eg PIC) which does not have any analog IO ability, and something we need to measure (eg the resistance of a potentiometer), we can get a fairly decent measurement (perhaps 5%) by using an RC circuit. The PIC's I/O pin is connected to the junction of R/C; C is grounded; R is taken to +V. Then, the I/O pin is initially set up as an output, at logic 0. The I/O pin is then converted back to an input, which (being CMOS) is fairly high-impedance, and probably switches at Vsupply/2. We poll this pin until it goes high. Within its limitations, this technique works extremely well.

That kind of converter is now briefly mentioned in this article as a "ramp-compare ADC". Would wikibooks:Analog and Digital Conversion be a better place to put detailed information on this technique? --76.209.28.72 18:23, 6 July 2007 (UTC)

Merge from Analog-to-digital conversion with SAR

Would it be worth merging the content at Analog-to-digital conversion with SAR here? Jɪmp 17:22, 8 January 2008 (UTC)

inappropriate example

"For example, to sample audio at 44.1 kHz with 32 bit resolution, a clock frequency of over 1.4 MHz would be required". Implying 32 bit resolution audio in an example that seems to be simple math is misleading and inappropriate. 32 bit audio has never been a goal of any converter manufacturer, it's plain silly. The example uses the number 32 in order to inflate the required clock frequency. Suggest removing or rewriting this paragraph. —Preceding unsigned comment added by 65.115.107.210 (talk) 22:44, 19 December 2008 (UTC)

Oversampling

The section states

a 20 bit ADC can be made to act as a 24 bit ADC with 256x oversampling

, but I believe that it should either read

a 20 bit ADC can be made to act as a 24 bit ADC with 16x oversampling

or

a 16 bit ADC can be made to act as a 24 bit ADC with 256x oversampling

. The sum of 256 (2⁸) 20 bit samples (i.e. 256x oversampling) would require a 28 bit number to represent all possible values. —Preceding unsigned comment added by 217.40.148.115 (talk) 16:23, 11 March 2009 (UTC)

No, the effective SNR increase is 10*log10(256) = 24dB, which is equivalent to 4*6dB, i.e. a 4-bit increase in resolution. Oli Filth^{(talk|contribs)} 00:22, 12 March 2009 (UTC)

ADC with intermediate FM stage

Many applications require converting some analog quantity at some remote location to a nice digital display at a more convenient, nearby location. I've seen several people do this with several parts:

• an analog transducer-to-frequency converter at the remote location -- perhaps using a linear voltage-controlled oscillator, or perhaps measuring temperature using an oscillator with a known frequency drift;
• a long wire or RF signal to carry that varying-frequency signal to the nearby location; and
• a frequency counter at the nearby location to convert the "instantaneous" frequency to a digital value.

The system as a whole is performing analog-to-digital conversion, although it is difficult to say whether "the ADC" is located at the remote site or at the local site.

I think this kind of ADC structure should be mentioned in the Analog-to-digital converter#ADC structures section of this article.

Is there a standard name for this type of ADC structure? "voltage-to-frequency ADC"? "frequency modulation ADC"? --68.0.124.33 (talk) 06:51, 18 August 2009 (UTC)

This sounds like it's just a transmission method. From the way you describe it, there's no digits involved until the final stage. Oli Filth^{(talk|contribs)} 07:32, 18 August 2009 (UTC)

It could be viewed as a form of pulse-density modulation though, since the receiving end is just counting pulses. SpinningSpark 17:26, 20 August 2009 (UTC)

Yes, frequency modulation and pulse-frequency modulation are used for transmission in this kind of ADC, which is very closely related to pulse-density modulation.

So what is the name of the whole ADC structure?

Yes, there are no digits involved until the final stage -- much like several of the ADCs already described in the article, which convert the analog signal into a pulse-width modulation signal in their early stages. But those ADCs are not named "PWM ADCs", they have other names.

This system has a continuous analog signal at one end. This system has digital digits displayed at the other end. That meets the definition in this article, "a device which converts continuous signals to discrete digital numbers."

I'm going to stick it in the article now; I have plenty of references. But alas, none of my references give it a name more specific than "ADC" or less specific than a list of the parts ("a V/F converter" and "a frequency counter").

The Bob Pease reference says that voltage-to-frequency converters are "a kind of ADC".

Is he trying to point out that the V/F converter -- by itself -- converts an analog voltage level to a (relatively) digital signal? In which case, the frequency counter is technically not part of the ADC, and this article should list the V/F converter -- by itself -- as a kind of ADC.

Or is he naming the entire ADC structure (the V/F plus the frequency counter) as a "voltage-to-frequency converter"?

Is there a standard name for this particular type of ADC structure? --68.0.124.33 (talk) 08:53, 30 August 2009 (UTC)

Unless you can reference that this is an ADC it shouldn't be in the article. FWIW I agree it is, but it still shouldn't be added: 'verifiability over truth'.- (User) Wolfkeeper (Talk) 13:09, 30 August 2009 (UTC)

Agree with that sentiment.

To me, it sounds like a tightly-coupled combination of an ADC and a comms system; we need to be careful to distinguish the two (otherwise, the combination of my landline telephone, the copper cable and exchange forms an ADC!). Oli Filth^{(talk|contribs)} 17:48, 30 August 2009 (UTC)

I agree that this article needs to be clear that the "long wire or opto-isolator or RF signal" is not an essential part of this kind of ADC structure. Please improve the definition in the article if it does not sufficiently distinguish them.

The article has verifiable references (Robert Pease, Walter Kester, AN795, etc.) that says this is "a kind of ADC". Are the references in the article enough to meet our WP:VERIFY policy? --68.0.124.33 (talk) 00:58, 2 September 2009 (UTC)

exact reconstruction ?

This article says that a sampled bandlimited signal can be "EXACTLY" reconstructed, but I think there are some who would dispute this. There is some talk going on at Talk:aliasing that suggests that the Nyquist sampling theorem is only an approximation. The maths is beyond me, so I'm hoping that someone will explain the problem in words. I'm guessing that it has to do with the twin impossibilities of building a perfect brick-wall filter and taking an instantaneous sample. -- Heron 09:16, 2 Apr 2004 (UTC)

A bandlimited signal CAN be EXACTLY reconstructed. The problem is that it is impossible to have a truly bandlimited signal. This is because a signal that is truly bandlimited (i.e. has exactly zero power above a given frequency) cannot be simultaneous limited in time, and is therefore non-causal. Think of this as Heisenburg's Uncertainty Principle for signals. The amount of aliasing can always be controlled, however, to be below the SNR of the signal in question. So, calling Nyquist an approximation is silly, and not useful. It is more accurate to say that the Nyquist's criterion can only be approximately satisfied, rather than the theory itself is an approximation.

Think about band-limited periodic signals. They are composed by a group of impulses in the frequency domain, so it's easy to see that they are band-limited. If you multiply this periodic (therefore unlimited) signal by a step function, we convolve the impulses in the frequency domain by an unlimited 1/s function, and the signal is not band-limited anymore.

It's good to think about periodic signals, because the values of the impulses in the time domain will be different depending on the delay between the sampling and the signal. Even so, the reconstruction will bring the same wave shape, delayed.

You can even have semi-periodic samplings, where the sampling frequency is not a rational multiple of the signal frequency. The reconstruction will bring the original signal, but you need an unlimited number of time samples, what implies in infinite frequency resolution.

Every band-limited function is unlimited in time. -- nwerneck 22:10, 1 Dec 2005 (UTC)

I've just come to this article, and I'm confused about the apparent inconsistency between exact signal reconstruction and the problems of aliasing. I don't understand the discussion above about what a bandlimited signal is. It would be nice if this could be made a little more layman friendly. Tim Richardson (talk) 23:43, 2 November 2009 (UTC)

Actually, following around a few links and arriving at the bandlimited page sorted me out. bandlimited signals are a subset of waveforms that don't have higher frequency components when Fourier transformed (eg sinewaves). Tim Richardson (talk) 23:53, 2 November 2009 (UTC)

Does 16-bit audio exist?

What is the minimum voltage that an ordinary, consumer-grade 16-bit ADC can sample?

I have looked at the Wikipedia article "Line Level", and consumer grade audio peaks at 0.447 volts. Since 16 bits equals 65536, dividing into 0.447 you get 0.0000068 volts. That is 0.0068 millivolts, or 6.8 microvolts (edit: was nanovolts).

Is the average consumer card capable of measuring microvolts? Is any card capable of this? Even if you use the "pro audio" specification of 1.737V, you still get 0.0000265 volts, or 0.0265 millivolts, or 26.5 microvolts.

I have come across the phrase ENOB, or Effective Number of Bits (which has its own article). What is the ENOB of the average 16-bit card? What VOLTAGE range is it designed to measure? -mjs 173.68.190.122 (talk) 04:41, 4 October 2009 (UTC)

Your initial assumptions are mistaken. Nominal consumer level is 0.316 volts but its peak levels can go higher, depending on the actual piece of gear. Certainly, 1.58 volts is possible for quite a lot of consumer or semi-pro gear if pushed to its limits. The CD Redbook standard is to 2.0 volts rms at full scale, but this isn't always met by manufacturers. Some common ADC chips can take 4.0 volts peak to peak. Most recording gear will have pads or gain stages with volume knobs between the inputs and the ADC chip, so you can't always tell what voltage it is getting at full scale. Yes, all 16 bits are being used by modern decent quality gear. Some early CD gear had a 12- or 14-bit bottleneck, but those days are long past. Binksternet (talk) 14:59, 4 October 2009 (UTC)

I mentioned that pro audio is 1.7 volts and you went on to say that some consumer gear handles 2.0 volts, not a huge difference. The real question is can it detect 2.0 volts divided by 65536, or 30.5 microvolts? I'm more of a digital person, not an EE person, but 30 microvolts seems like amazing accuracy for any circuitry. Got any docs that show that an $80 Creative Labs or $150 M-Audio card can sample this? -mjs 72.89.228.177 (talk) 07:48, 8 November 2009 (UTC)

Voltage levels down that low will always be dancing around relative to noise levels, and it doesn't matter whether you're looking at analog gear or digital gear. If you put a 100-microvolt signal into an analog zero gain op-amp or a digital ADC, both of them may output a signal which is more or less than 100 µv. Binksternet (talk) 16:53, 8 November 2009 (UTC)

Application to music recording

I've just applied what I think is the third revert - i.e. we have hit 3RR. To avoid warring, let's discuss this. The text I have (re)removed was:

Some people in the business sometimes believe this an overkill or marketing hype, because with some kind of music you don't see the difference (typically electronic music made from 48Khz numerical synths won't make any difference when mastered at 192khz). They think that the analog waveform does not have enough information in it to necessitate such high sampling rates. However, the continuation of the LP as a audiofile format on one side, and the new market of the SACD on the other side, tends to show that it more the mythical "CD quality" which is a marketing hype since the eighties.

There is plenty to say about music quality, what a human can/cannot distinguish, and whether CD quality is enough. It would be good to include something sensible on the subject, with sources. An unsourced ramble about 'some people think...' isn't suitable for Wikipedia - we can do better than that. By all means, please add something concrete - it would improve the article - but I will invoke Nyquist if required. 192kHz needs some justification. GyroMagician (talk) 21:46, 9 March 2010 (UTC)

An ADC with wide LSB (>1)

In the article, fig. 3 depicts ADC transfer function with wide LSB: code length is not of unit and found as Q=2^{n-1}/2^{n}), where n is ADC resolution, bits, code shift is of -1/2Q. My questions are to SpinningSpark: Tell please where did you get this picture? What is it sourced from? Such transfer function is very intresting, but i did not see it in practice and in books/datasheets accessible to me. Did you see ADC with such transfer function in your practice? Beforehand thanks. —Preceding unsigned comment added by 87.253.7.84 (talk) 12:53, 18 August 2010 (UTC)

Figure 6.13 SpinningSpark 16:59, 18 August 2010 (UTC)

Thanks for fast answer, but it is not the case you shown in Figure 3. In the book, the midtread one has an odd number of code intervals, while in your picture, such number is even. Also, in the book's midtread, all the code intervals are of the same length, in your figure, they are of two lengths: Q and Q/2. The ADC transfer function your shown is a new one, but it has the right to exist, therefore please don't drop it from the article. It's so smile, you had contrived new transfer function. I had modelled, your function is very powerful and practiceful. One thing that disturbs me, there are no IC employing it. —Preceding unsigned comment added by 95.86.251.33 (talk) 06:49, 22 August 2010 (UTC)

My main aim here was to provide a set of diagrams that illustrated and made sense of the text. There was no intended reference to any specific manufactured devices. Prior to the diagrams being inserted, the text had been edited in the past on the grounds that the formulae that relate to diagram 3 are incorrect (although I have found several sources using this formula), but left the text inconsistent and contradictory. I have provided the diagrams just to make it clear what is being discussed and which formula relates to which scheme. I am fine with diagram 3 being deleted as long as the text is amended appropriately and the formulae still make sense afterwards. SpinningSpark 09:25, 22 August 2010 (UTC)

Dear SpinningSpark, because of i'm not native English speaker, it is difficult to me to express my thinks clear. Therefore, to exclude any misunderstanding, i'm repeating my position in other words: Figure 3 must be presented in the article. The fact that the transfer function it depicts exists theoretically only is not a cause to delete the figure from the arcticle. I think, if it will useful, the article text may claim that: "...there are many adc transfer functions possible, but not all are employed in practice now..." —Preceding unsigned comment added by 85.113.196.189 (talk) 06:33, 24 August 2010 (UTC)

Modem

There is an obvious problem on Modem that most people think a Modem converts digital signals to analog signals. The modem article is already too long to include a tutorial on the difference between analog and digital signals, and there isn't any good place to reference -- so any suggestions would be welcome.203.206.162.148 (talk) 08:03, 8 September 2010 (UTC)

Anti-aliasing filters and FM stages

I've just undone an edit by 80.100.243.19. The (good faith) edit suggests that an anti-aliasing filter isn't needed in the ADC uses a V-to-F converter and a counter. I undid for two reasons. First, I think the integration time of the counter is a low pass filter. But also, trying to introduce exception to a clear story, early in the article, is confusing. But I thought I'd bring it up here for discussion - I won't be offended if you all tell me I'm wrong ;-) GyroMagician (talk) 20:45, 24 September 2010 (UTC)

I am in agreement with both points. Thanks for your thoughtfulness.

--Bob K (talk) 21:58, 24 September 2010 (UTC)

Fatal1ty?

On the picture of the adc on the sound card, the card is labelled as a Xi-Fi Fatal1ty Pro. I get the feeling this is incorrect, so i figured i'd point it out. However it also happens on that particular sound card's page. —Preceding unsigned comment added by 121.209.39.143 (talk) 07:11, 28 September 2010 (UTC)

E_FSR ?

What does E_FSR mean? The voltage at the frequency sampling rate? What does that even mean? —Preceding unsigned comment added by 99.159.44.37 (talk) 18:26, 26 January 2011 (UTC)

Digital number listed at Redirects for discussion

An editor has asked for a discussion to address the redirect Digital number which was recently added pointing to this article. Editors here might want to participate in the redirect discussion (if you have not already done so). SpinningSpark 20:40, 4 March 2011 (UTC)

Sources for the different transfer functions

The "Resolution" section has diagrams of three possible transfer functions, and describes two of them mathematically (mid-tread with a small 0 and a large max code, and mid-rise with offset with all steps equal width). It states that “The exception to this convention seems to be the Microchip PIC processor, where all M steps are equal width, as shown in figure 1.”. There are painfully few references here, especially no references for the claim that PICs' ADCs use mid-rise-with-offset; interestingly, a Google search for the phrase “mid-rise with offset” seems to turn up nothing more than a lot of verbatim copies of the text shown on this page. What's the deal? Where did this information come from? Hawk777 (talk) 04:49, 26 March 2011 (UTC)

I propose we delete figure 2 and 3 and the text and math associated with them. At best, this is an unimportant implementation detail. At worst it is simply fabricated. --Kvng (talk) 22:36, 28 March 2011 (UTC)

support. The different figures are confused. With variations gone, the fencepost issue would be clearer. Glrx (talk) 02:38, 29 March 2011 (UTC)

Aperture Error: Table with examples misleading

In the example table the headline says input frequency: e.g. 44.1kHz (typical sample rate for an audio stream). Then the largest permissable jitter is worked out correctly for an input frequency of 44.1kHz. But due to the sampling theorem you must not have frequencies beyond 22kHz in your audio stream, hence the permissable jitter is a factor of 2 larger for an audio stream. To have more realistic examples, one should say input frequency 22kHz for the audio stream, etc... It would be helful to mention that this requires a sample rate of 2x the input frequency... — Preceding unsigned comment added by 86.3.141.168 (talk) 17:46, 6 August 2011 (UTC)

ADC history

There should be history of analog-to-digital converter development. — Preceding unsigned comment added by 76.17.115.184 (talk) 02:32, 4 November 2011 (UTC)

Inventor of Wilkinson converter?

Was it Sir Denys Wilkinson? — Preceding unsigned comment added by 71.191.185.32 (talk) 01:13, 22 June 2012 (UTC)

Jitter issues misrepresented

The claim that it's not worth using 24 bits for sound recording if jitter is not ultra low is somewhat clueless. One reason for using 24 bits is to have extra headroom before clipping. If the recording level is reduced, then the effect of jitter is also reduced: more jitter is needed to make a one-bit error in a quiet signal than in a loud one! So for instance if you record using only 16 bits out of the available 24, then the jitter requirement is that for 16 bits. But there is 8 bits of headroom for transients.192.139.122.42 (talk) 20:08, 30 July 2012 (UTC)

Badly needed introductory section on basic concept of sampling

This article badly needs an opening section on the basic idea of sampling, even if just a continuous waveform overlaid with a stepped waveform. Seriously. As it is now, it just starts out with a discussion of resolution and the reader who knows nothing of A/D converters (and this is probably a large proportion of people who would be using Wikipedia to read about them) is rudely thrown into a discussion of resolution. Resolution of what, he/she might ask, before clicking on to something else more interesting. — Preceding unsigned comment added by Oscarruitt (talk • contribs) 03:56, 31 July 2012 (UTC)

I have some trouble the other way. I think sampling is overstressed. An ADC "is a device that uses sampling to convert a continuous quantity to a discrete time representation in digital form" is heavily loaded on sampling and discrete time. Many ADC architectures do not take a single instantaneous sample: integrating converters, for example. The notion of discrete time is also forced. (Delta modulators fit the discrete time representation, but I'm not sure that is what the definition intends -- oversampled with a 0/1 output stream.) The definition seems DSP-centric.

The basic ADC converts a analog quantity to a digital quantity. There is truncation error in a digital representation. If the input quantity changes slowly, then sampling is not an issue. When I'm measuring a supply voltage, my DVM is updating every so often, but I don't really care when it updates as long it tracks the changes. I don't even need a fixed rate. A real time processor might do a measurement when it is idle rather than every 200 milliseconds. Accuracy can be discussed with a stable input.

When the input is changing quickly, then conversion speed and sampling become an issue. Aperture error. Using a classic sample and hold can convert the ADC problem to the steady input state. But the SH is a different signal processing block.

Other applications, such as DSP, place higher demands on the system. Those demands should be discussed, but it is not fundamental to many ADC architectures.

Glrx (talk) 22:12, 2 August 2012 (UTC)

If you're sampling a DC signal, then you're right. But if it's not then you're firmly in DSP land and you need a Nyquist filter; otherwise it's much too easy for a signal to alias down and give you entirely spurious results. A sample and hold will not get you out of trouble.

That's WHY it's useful that the DVM is integrating; that integration step forms a low pass Nyquist filter.Teapeat (talk) 06:39, 29 March 2013 (UTC)

Metastability

Teapeat (talk · contribs) has added a brief section on metastability. I don't have access to the ref provided. That ref appears to be narrowly focused. Here is a more general discussion of metastability issues in ADCs [1]. -—Kvng 05:17, 29 March 2013 (UTC)

This looked very good to me, so I replaced it. Well found!Teapeat (talk) 06:26, 29 March 2013 (UTC)

I don't believe this ref says anything about clock synchronization or high sample rates. I have reverted. If you like the new ref, the text needs to be conformed to what it actually says about metastability. I have not done this myself because this paper is talking about an internal error condition in flash converters and it is not clear that is what you were trying to introduce with your edits. If this is spot on, I think it best discussed under a BER heading. -—Kvng 14:22, 1 April 2013 (UTC)

Should this section even be included? Metastability is a very general electronics and DSP concept that is not directly related to ADCs, and probably not of interest outside of a very narrow range of applications. Or if it is of interest somehow, the page should probably give some context. Right now the mention is only useful to people who already understand the concept. 18.62.28.248 (talk) 17:07, 24 June 2013 (UTC)

It certainly shouldn't be included if it has problems. I have removed it for now. ~KvnG 06:27, 28 June 2013 (UTC)

Decibels per bit?

"One effective bit of resolution changes the signal-to-noise ratio of the digitized signal by 6 dB" -- wouldn't it be 3 dB? That is 10 log_10(2). — Preceding unsigned comment added by 91.137.20.132 (talk) 18:20, 20 March 2014 (UTC)

Comparison of quantizing a sinusoid to 64 levels (6 bits) and 256 levels (8 bits). The additive noise created by 6-bit quantization is 12 dB greater than the noise created by 8-bit quantization. When the spectral distribution is flat, as in this example, the 12 dB difference manifests as a measurable difference in the noise floors.

Each bit changes the width of the uniform probability disribution of the quantization error amplitude by a factor of 2, which changes the variance = mean-squared error = power by a factor of 4.  $\scriptstyle 10\cdot \log _{10}(4)\ =\ 6\ \mathrm {dB} .$  So an added bit gives a 6 dB improvement, and a removed bit gives a 6 dB degradation.

--Bob K (talk) 01:10, 31 March 2014 (UTC)

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Resolution and number of levels

Josecampos did some changes regarding the number of levels of the digitalization. I agreed only with some of his modifications... There are 256 levels in a 8 bit digitalization, from 0 to 255. But the difference from level to level is actually (V+-V-)/(2^8 - 1). So I fixed the article making a distinction between the number of levels and the number of "intervals"... Comments? -- NIC1138 18:44, 1 May 2007 (UTC)

12.47.224.7 15:57, 26 September 2007 (UTC) Jim Bach 12.47.224.7 15:57, 26 September 2007 (UTC) From: James.C.Bach@Delphi.com Date: 26-SEP-2007

The difference from level to level is (V+ - V-) / 2^N . . . . NOT (V+ - V-) / 2^n -1 . . . for a 3-bit ADC that is (V+ - V-)/8 not V+ - V-)/7!

In a 3-bit ADC there might only be 7 transitions from code-to-code . . . but the input voltage range (i.e. V- to V+) has 8 regions in it, representing codes "0" thru "7" ("000" to "111" for bit-bangers :-) ). These regions can be equal-width (at 1/8th of Vsupply) like the MicroChip PIC controllers, or they can have a 1/2-width "0" code and a 1.5-width "7" code like just about everyone else's ADC on the planet. Look at the diagrams (and in some cases, equations) provided in the URLs cited below.

Think about it this way . . . let's say the width of your hand represents the voltage range your A/D covers (i.e. HandWidth = V+ - V-) . . . and each finger represents an output code ("0" thru "4", you pick which hand and whether the thumb is LSB or MSB :-) ) . . . you have (presumably) 5 fingers . . . how many cracks (i.e. voltage transitions) do you have between the fingers? 4, right? So, would you estimate that the width of each of your fingers is HandWidth/(N-1) (i.e. HandWidth/4) OR HandWidth/N (i.e. HandWidth/5)? Obviously it is HandWidth/5, which is HandWidth/N. And, if you used your left hand your pinky reasonably approximates the "0" code of a real-world ADC (i.e. 1/2-width) and your thumb reasonably approximates the "4" ("max") code of a real-world ADC (i.e. 1.5-width).

Checkout: http://www.freescale.com/files/microcontrollers/doc/app_note/AN2438.pdf?fsrch=1 http://www.embedded.com/columns/technicalinsights/60403334?_requestid=213222 http://www.maxim-ic.com/appnotes.cfm/appnote_number/1080/ http://zone.ni.com/devzone/cda/tut/p/id/3016

12.47.224.7 15:57, 26 September 2007 (UTC) Jim Bach 12.47.224.7 15:57, 26 September 2007 (UTC)

That formula is wrong...Q = (span)/(number_of_levels) ... —Preceding unsigned comment added by 87.16.20.206 (talk) 10:34, 3 May 2010 (UTC)

The formula is not wrong, the divisor needs to be the number of intervals, which is not 2^M. The argument above is that this does not take into account the common practice of fractional intervals at the extremes. This only makes even the slightest practical difference at very low number of bits - so lets consider the extreme example of one bit and a one volt full scale signal. With no fractional intervals there is only one interval and the resolution is 1.0V. It is stated above, however, that a common practice is 1.5 intervals after the top level and 0.5 intervals below the bottom level. This now makes 3.0 intervals altogether and a resolution of 0.33V. The formula with 2^M as the divisor which has been repeatedly inserted gives an answer of 0.5V which is incorrect for both cases. It only actually gives the correct answer in the special case when the top and bottom interval are both 0.5. This still does not make it a correct formula, it just happens to be spewing out the right answer by a coincidence. The article should either be left as it is, not dealing with fractional intervals, or else they should be properly explained and specifically included in the formula so that it always gives the right answer. SpinningSpark 13:26, 3 May 2010 (UTC)

Every literature says that Q = (span) / (number_of_levels). Mistake is because you consider that max voltage can read from ADC is Vref (and not Vref -1LSB). Then, for your example, when you have and ADC with a resolution of 1bit and a full range of 0..1V, you have 1LSB=1/2=0.5V -So the voltage that corresponds to D=1 is 0.5V (of course always +/- 1/2LSB in ideal case) not 1V Sorry for my english -- Frank Rossi —Preceding unsigned comment added by 87.16.20.206 (talk) 14:12, 3 May 2010 (UTC)

There is a lot of confusion in this area. Check out this book for instance. The formula is quoted as $\scriptstyle E_{\mathrm {fsd} }/2^{N}$ but then sneakily subtracts one when the calculation is actually carried out, effectively using $\scriptstyle E_{\mathrm {fsd} }/(2^{N}-1)$. SpinningSpark 15:03, 3 May 2010 (UTC)

Check this one, instead: http://www.analog.com/library/analogDialogue/archives/39-06/data_conversion_handbook.html (the bible of A/D D/A). That book you linked above is IMHO wrong (page 228): max input voltage not produce all one bits...but (vref-1LSB) voltage produce all ones...as you can read at analog.com link - That formula is anyway correct because the max number we can representate is always (2^number_ov_levels - 1) since we start from 0. In case of 1bit we have 2 levels so max number is 1 ( (2^1) -1 ) - But every step is always (span) / 2^number_of_level —Preceding unsigned comment added by 87.16.20.206 (talk) 15:39, 3 May 2010 (UTC)

Can you give me a chapter and page number? I don't want to read the whole book. If levels are equally spaced (including a whole level at the top and bottom) then the number of intervals will be 2^N+1. Everybody who uses 2^N is assuming half intervals at the end. Many of the references linked above in this post claim an interval of 1.5 at the top and 0.5 at the bottom, also resulting in 2^N+1. SpinningSpark 06:43, 4 May 2010 (UTC)

I tried to explain that formula is wrong. I'll make another time the same example. M=1 (A/D 1bit). VREF=1V so, according that formula, Q=1/( (2^1) - 1 ) and Number of intervals=1. We haven't one interval, but two intervals: [0...1/2LSB[ and [ (VREF/2) - 1/2LSB...VREF]. The first interval is coded with "0", the second interval is coded with "1". Infact, when I want to get volts from ADC result I have to do: Volts = VREF*ADC/(2^number_of_bits)...according you formula Volt would be VREF*ADC/1 !!!!! The proof that formula is wrong -- 87.18.147.138 (talk) 11:02, 4 May 2010 (UTC)Frank Rossi

The analog value represented by the all one codes is VREF -1LSB , so with 1bit of resolution and VREF=1V you have 1LSB = 1/2 = .5V and infact VREF - 1LSB= (1-.5) =.5V while,according your formula this "all-one-codes" value would be 1V and not .5V (source: http://www.analog.com/library/analogDialogue/archives/39-06/Chapter%202%20Sampled%20Data%20Systems%20F.pdf - page 2.4) --Dontronix (talk) 07:15, 5 May 2010 (UTC)

Have a look at: http://www.national.com/appinfo/adc/files/ABCs_of_ADCs.pdf too. --Dontronix (talk) 07:56, 5 May 2010 (UTC)

The issue seems to be that there is without doubt 2^N-1 intervals between 2^N code values, but that is not the way resolution is defined. It is volts per step, not volts per interval which are not the same thing, because there are 2^N steps. I think a diagram is needed to make this clear in the article. I will see if I can produce something over the weekend. SpinningSpark 17:28, 6 May 2010 (UTC)

No, resolution is simply related to the number of steps; you talk about 8 or 16 or 24 bit resolution.- Wolfkeeper 19:12, 6 May 2010 (UTC)

Accuracy may be expressed in volts or decibels or whatever. There's a big difference between say, resolution and accuracy; the actual numbers associated with the input voltage are often not entirely linearly related.- Wolfkeeper 19:12, 6 May 2010 (UTC)

I appreciate the difference between accuracy and resolution and that resolution is normally expressed in bits. However, our article is currently stating that resolution can also be expressed in volts. Do you take issue with that? If so it would be an argument for removing the passage in its entirety, not just correcting the formula. SpinningSpark 20:24, 6 May 2010 (UTC)

I have had a try at editing this section into sense, including some new diagrams. Please let me know if I have got anything wrong. SpinningSpark 16:57, 16 May 2010 (UTC)

Regarding discussion on number of levels in an 8 bit A/D or D/A. The first coded level is zero. Therefore there are (256-1)or 255steps. The word steps is often used in A/D, D/A talk and is less confusing terminology than talking about intervals. — Preceding unsigned comment added by Alan Bate SEA (talk • contribs) 13:47, 22 February 2012 (UTC)

The use of 2^M-1 is incorrect. Even the source that is used for defining the resolution in bits uses 2^M . Another way to think of A/D conversion is the division of the full-scale range in half where a comparator is used to determine if the MSB is 1 or 0; then the next range is divided in half again, and again, until M times; thus the full-scale range is divided a total of 2^M times to give a final resolution size of the full-scale range divided by 2^M.75.174.53.165 (talk) 05:13, 24 January 2017 (UTC)

Yes, 0 is a useful and valid coding so a digital signal of M bits represents 2^M possible states. I have made minor corrections to the #Resolution section. ~Kvng (talk) 18:49, 3 February 2017 (UTC)

I just did some research into this, because I had the same issue myself when I saw the formulation in practice. Range/2^n is correct. The reason is that each bit doesn't represent a discrete analog value. It represents a small range of value and generally sets at the center of that range. For instance, if you're converting 3-bit to a range of 0-8 volts, then: 000 -> 0V-1V (0.5V) 001 -> 1V-2V (1.5V) 010 -> 2V-3V (2.5V) 011 -> 3V-4V (3.5V) 100 -> 4V-5V (4.5V) 101 -> 5V-6V (5.5V) 110 -> 6V-7V (6.5V) 111 -> 7V-8V (7.5V)

LordQwert (talk) 17:21, 13 March 2017 (UTC)

References