getting 16 bit from 8 bit ADC in software

• Your instructor is cruel and evil, or doesn't really understand what he's asking, or he really cares about you and is sneaky to boot.

• A 256-step to 65536-step increase in accuracy is not a doubling of accuracy, it is an increase of 256 times.

• You probably aren't increasing the accuracy by anything close to 256 times.

• You may be increasing resolution by 256 times, though, and sometimes that's good enough --
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You can make a pretty good ADC by integrating and timing how long it takes to get to a limit (search on "single-slope ADC"). You can improve this by integrating up and then down again, timing each segment, and doing some math (search on "dual-slope ADC").

You're being asked to build something akin to a single-slope ADC. You should be able to get pretty good resolution by sampling your ADC every one or two milliseconds then doing a linear curve fit to get your "enhanced" data.

Note that while you are most certainly going to increase resolution and accuracy your accuracy is limited by a heck of a lot more than your resolution is; you can probably count on getting a good honest 16 bits of resolution, and probably significantly enhanced nonlinearity, but you will bump into the other things that limit your accuracy.

You can investigate your resolution enhancement by simulating the thing in a good math package like MatLab, MathCad, Maple, SciLab, etc. I highly recommend this. Verifying accuracy means understanding all of the accuracy drivers in the ADC and investigating their effect on the accuracy of your result. This is a worthwhile goal if you want to make a thesis out of it.

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Tim Wescott
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It's not just quantization, though -- there should be timing information available from the slope; merely averaging isn't all there is to it.

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Tim Wescott
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I thought I understood until I read this. If the signal is stable and the A/D is stable, you should get the SAME reading every time??? To get improved ACCURACY or RESOLUTION, don't you first need a system that's stable to much better than the quantization interval then to perturb the input with a signal of known statistics?

If you're counting on system instability or (uncontrolled) noise to do the deed, you're just collecting garbage data. yes? no? mike

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No, because the input signal is being applied to an integrator, so you should see a monotonically increasing ramp. The rest is weird science.

In this case it's neither uncontrolled nor noise. You can, however, count on random noise to increase the effective resolution of an ADC as long as it's PDF is wide enough. I've done this very successfully in control systems that need high resolution and short-term repeatability, but that don't need terribly high accuracy -- so you can take a 16-bit ADC that's really only _accurate_ to 15 bits or so, and get 18 or 19 bits of _resolution_ out of it by oversampling like mad and averaging the hell out of it. Note that the accuracy doesn't change -- only the resolution.

-snip-

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Tim Wescott
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I don't know whether the author was being sloppy with his terminology or just didn't know what he was talking about, but this is altogether wrong as stated.

Under certain circumstances you can get 16-bit _precision_ by averaging many readings froma an 8-bit ADC, but you can never get _accuracy_ better than your reference, no matter what tricks you try.

Now, if you're allowed to add a reference known accurate to that level, or you can add a 16-bit _accurate_ DAC, and you can add an amplifier to amplify your differences, and, finally, your signal is stable long enough that you can get through all this process before it changes, you can eventually cobble together a measurement to that accuracy.

Note the long list of "if's". Especially the signal stability. That alone can make it impossible to get even a measurement to 16-bit _precision_, much less 16-bit _accuracy_.

Some of the other comments are also appropriate.

John Perry

Hello Toby,

Have the authors validated that claim with some hardcore measurements, such as detecting and restoring a signal that was, say, 13 or 14 dB below 5Vpp?

Regards, Joerg

SAME

you

quantization

The usual name for the perturbing signal is "dither". There is a fair amount of literature on the subject if you can find it. My "Comment on 'Noise averaging and measurement resolution" in Review of Scientific Instruments, volume 70, page 4734 (1999) lists a bunch of papers on the subject.

do

IIRR random noise isn't too bad as a dither source - there is an ideal distribution, but Gaussian noise is pretty close.

My own experience of getting 16-bit accuracy out of a quasi-quad-slope integrator-based ADC was that it took a while, but I had to find out about "charge soak" in the integrating capacitor the hard way, and also started out relying on the CMOS protection diodes to catch signals spiking outside the power rails.

Switching to a polypropylene capacitor and discrete Schottky catching diodes solved both those problems. A colleague of mine once built a

20-bit system based on a similar integrator, using Teflon(PTFE) capacitors and a feedback system that minimised the voltage excursions across the integrating capacitor in a much more intricate and expensive unit.

------ Bill Sloman, Nijmegen

Aside from the other comments, you might look at the technique described for the Burr Brown DDC101, I believe. It might add another thing to consider.

Jon

Its not possible the way you described it.

Exactly, you would need to add a small signal, 1lsb sawtooth, and sample over the sawttoth period. Getting a 16 bit absolute reading is very very difficult, just about impossible, from a simple setup like this even if you had a real

16bit adc.

This can, at most, increase signal accuracy by a factor of 16 (four bits), being the square root of 256. And that's assuming a number of things about the behaviour of the converter.

To increase accuracy to 16 bits, you need to take 256*256 samples at least, based on random distribution of quantisation errors.

Clifford Heath.

You make it sound like that's a bad thing.

:)

He is apparently not selling it.

Rene

The blind leading the blind, I think it is called.

'Precision' - meaning what? 1/2 bit of noise in the reading?

If this was written by someone at your school you may want to transfer schools.

It is possible to oversample with a V/F or other integrating A/D to increase _resolution_: accuracy is out the window.

To pick up one usable bit of resolution you will have to increase the measuring interval by 4. Homework: why? Hint: the readings have to be independent.

To get from 8 bits to 16 bits will require a 4^8 integration period increase, or 65,564 readings.

This is a very profound area of inquiry. Talk to someone in signal processing in the EE department.

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"CBarn24050" wrote

This happens automatically if you use an asynchronous V/F converter: If there are, say, 4.5 V/F periods in the sampling interval then 1/2 the time the reading is 4 and half the time it is 5. Since the reading is noise based you have to measure 4x to drop the noise by 2x and pick up an extra bit [of resolution].

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No, weird science is fun and sometimes lucrative.

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Tim Wescott
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