How to use thermal noise to your advantage

RE: How to use thermal noise to your advantage

Dawea Wang — Thu, 13 Mar 2014 09:54:37 GMT

Hi Mike,

Get your article, but I didn't know your mail address, so I have to write to you here.

I have another question about your applicaiton datasheet of ADS1118(Precision Thermocouple Measurement with the ADS1118), you mensioned how to get the actual temperature of thermocouple by using tempearture and voltage lookup table, and you also said that the entries of the lookup table 16 and 32 for k-type thermocouple would be enought for presion and draw a comparasion figure for your idea. My question is what is the detailed point for 16 and 32 entries table? I think these points should be scientific and I also didn't the details from TI website, so I have to write to you. Could you send the details to me? thanks very much.

My mail address: wylinder@163.com

RE: How to use thermal noise to your advantage

Mike Beckman — Thu, 14 Nov 2013 20:09:18 GMT

Golden Warrior,

To your comment, "abandoned by the rotation to the right four times, how can it be used if the four bits still dithering?"

The short answer is because the final output rate of the data is much slower and effectively averaged. If you think about the statistical nature of the unmodified 16-bit result for DC signals between two codes you should notice that the LSB should tend toward whichever code is closest to the actual signal. This will happen proportionally to how close the signal actually is to the code. The process of oversampling (adding and rotating right), while actually smooth out some of the noise added for the dither and will actually provide a very stable result. However if the dithering noise is too high, it is possible that those extra bits will be toggling. For gaussian noise, every averaging of two datapoints into one slower data point results in a factor of roughly sqrt(2) reduction in noise.

For your second question, "is there enough noise to create digital codes varying between each other, if the device runs at 128 samples-per-second?"

It really depends on how noisy the input signal is. If the noise of the input signal is very small, a sample rate of 128SPS may not be sufficient to cause toggling of the LSB. One option, as long as your input range can allow it, would be to increase the gain of the PGA in front of the modulator. This will double the size of the signal entering the modulator, and also double the noise coming in from the outside. This might increase the noise just enough to use the dither at 128SPS. For the ADC alone (shorted inputs on a clean design), you should see a peak-to-peak noise of almost 1LSB at gain of 1. This wont quite be enough noise use the technique, but if you increase the gain, you'll cut each LSB step size in half, which should just barely provide enough bits toggling to use the technique. 128SPS is right on the edge of having enough noise for this technique.

RE: How to use thermal noise to your advantage

Golden Warrior — Mon, 21 Oct 2013 03:57:29 GMT

Hi,Mike,

"The ADS1118 can perform conversions at rates up to 860 samples per second", is there enough noise to create digital codes varying between each other, if the device runs at 128 samples-per-second?

Under which sample rates yield a stable result with no digital code changes?

RE: How to use thermal noise to your advantage

Golden Warrior — Mon, 21 Oct 2013 03:35:55 GMT

Glad to read your share. Here are two quetions?

1 Why is it told that "the result is closer to the actual value than a lower noise front end that is causing no change in codes"?

2"These extra 4 bits are usable resolution. Same data rate, with more resolution because of a little noise", As the four bits are to be

abandoned by the rotation to the right four times, how can it be used if the four bits still dithering?

RE: How to use thermal noise to your advantage

JOSEPH MCELROY — Tue, 01 Oct 2013 20:59:43 GMT

It's great to see this pop up every so often. FYI, my first encounter with it was in 1990, discovered while browsing the university library stacks. Found this intriguing article in a Physics Journal from the 1970s that described this method.

RE: How to use thermal noise to your advantage

Mike Beckman — Mon, 23 Sep 2013 05:27:20 GMT

Richard,

You are correct that a periodic signal could introduce an undesired tone of an undesired frequency if it is not phase locked to the sampling of the ADC. A pseudo random pattern would be a better way to avoid a tone as long as it is of sufficient length.

Clemens,

By increasing the sampling rate of many 16-bit delta sigma ADCs, the decimation ratio of the ADC decreases and a wider bandwidth of signal is converted. This increases the RMS noise of the ADC. If the ADCs noise is smaller than 1 LSB at low data-rates, sometimes increasing the data-rate is sufficient to increase the RMS noise to exceed 1 LSB, which would provide the dither. This is the case for the ADS1118. For other architectures, this is not necessarily true that noise can be induced through increasing speed.

RE: How to use thermal noise to your advantage

clemens kloeck — Tue, 17 Sep 2013 12:55:45 GMT

Hi Mike,

great article. Could you explain me why an increase sample rate of an 16 bit ADC make the LSB flicker?

RE: How to use thermal noise to your advantage

Richard Cappels — Mon, 16 Sep 2013 05:52:49 GMT

Correction: The two noises will add, not beat.

RE: How to use thermal noise to your advantage

Richard Cappels — Sun, 15 Sep 2013 16:00:27 GMT

That is very cool.

A potential problem from using a periodic dither signal is that it can beat with any periodic noise in the input, thus defeating the purpose of dithering. Using random noise or analog pseudo random noise avoids that problem.

RE: How to use thermal noise to your advantage

Mike Beckman — Wed, 28 Aug 2013 20:20:14 GMT

Otto,

Great Question. You are absolutely correct, the signal doesn't have to be gaussian noise, it can be any signal that can encompass the LSB as long as a full period of the signal can be windowed within the set of averaged samples. For example, if a partial period of 1 or multiple sine waves was used, there would be a small skew toward one or the other LSBs so you would want that period to be syncronized to the sampling to make sure it's balanced. What you've suggested could be done with a simple DAC and a weighted summer. Great suggestion!

RE: How to use thermal noise to your advantage

Otto Hunt — Wed, 28 Aug 2013 19:49:15 GMT

Why does it have to be statistically random or Gaussian noise? Could the added noise be simply a sine wave or triangle wave with amplitude large enough to encompass the LSB of the ADC?