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Enter Dithering How It Works For D/A Conversion Too Filling In Values

Errors that occur during analog-to-digital (A/D) conversion can cause weird effects when input-signals are at, or near, the MSB transition level. The same is true for input-signals at or near any other major bit transition level, such as 1/4, 1/2, or ý scale. Using a dither method of data conversion, you can sidestep those problems.

By Dr. Kenneth F. Hatch, Principal Engineer
KLA-Tencor, 1 Technology Drive, Milpitas, CA 95035

Problems occur because most significant bit (MSB) transitions are usually quite noisy. That's usually because most of the digital bits are switching nearly simultaneously, which can cause ground differentials, power supply pulling, radiated noise, and more—all of which can wend their way into the analog portion of an A/D and cause erratic behavior. In successive approximation A/Ds, the MSB transition level requires maximum analog precision, resulting in more temperature drift and noise sensitivity at that level.

Enter Dithering
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The dither technique described here for doing A/D conversion was originally developed to improve the cosmetic appearance of nuclear medicine images. These images were created from digitized data developed from so-called gamma cameras.

In the nuclear medicine application, a small error (a fraction of a bit) in the digitization of the analog signal resulted in an ominous black or white stripe traversing the length or breadth of the picture. By using the dither method of conversion, the stripes don't appear. That's because the picture coordinates that correspond to the offending bit transition vary randomly over a given area of the picture.

This technique is also applicable to the case of a small analog signal that's exhibiting erratic harmonic spurs due to the crossing of a major bit, say the MSB. When the signal is sufficiently small, the errors associated with crossing the MSB can be substantial. Worse, harmonic distortion can vary wildly as dc drift causes the signal to drift in and out of the MSB area.

By using dither, the small signal can be presented to the analog input of your A/D at randomly varying dc levels. That can greatly reduce the probability of experiencing anomalies due to major MSB transition errors. Harmonic distortion is substantially reduced, and is steady.

How It Works
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Let's look at the operation of an A/D using the dither method. With each conversion clock a random number is changed to a new value. This random number is applied to a digital-to-analog converter (DAC), with proper gain to generate an analog signal equivalent to the random number. The analog signal from the DAC (let's call it the dither DAC) is summed with the main analog signal coming in that's to be converted.

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Here's a block diagram of a typical A/D converter that makes use of dither to improve nonlinearity.

For a constant dc input voltage (or very small signal voltage), the signal applied to the main A/D varies over a substantial range, depending on the size of the random number. It's recommended that the dither cover about 1/4 of the main A/D range. Therefore, each conversion done by the main A/D will have an error at its output that's equal to the random number. However, since the random number is known for each conversion, that value is simply subtracted digitally from the A/D digital output to arrive at the correct digital number for the conversion.

In this way, the converted output is always correct, but the A/D code (or "channel" or "bin") that's used for the conversion is "dithered" randomly, over about a quarter of the A/D's range. In this way the differential nonlinearities and instabilities are averaged out.

Of course, the range of the A/D must be increased to accommodate the dither voltage that's added to the incoming signal. In essence an extra bit will be needed for the A/D.

For D/A Conversion Too
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A corresponding technique can be used for D/A conversion. Again, with each conversion clock, a random number is changed to a new value. The random number can be two bits less than the digital word length, which will cause a dither of 1/4 of the range.

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This diagram shows the architecture of a dithered DAC.

For this case, the random number is digitally added to the incoming digital word to be converted, and the result is sent to the DAC, which must allow for 1/4 over-range (an extra bit). As with the A/D example discussed above, the analog output is in error by the amount of the random number. That number is then sent to a second D/A that has the resolution of the random number (2-bits less than the incoming digital word). The output from the second DAC is subtracted, using an op-amp, from the first D/A's output, thus yielding the correct analog result.

The advantage is that quantization errors from the main DAC are averaged out over 1/4 of the DAC range. Hence, differential linearity is vastly improved.

Filling In Values
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Another opportunity presents itself: if the random number has extra length (more bits than two-less-than the incoming digital number) the extra bits can be used to fill in the missing analog values between codes of the main DAC. Since the extra bits are random, the space between main DAC codes will be randomly filled in with 2^m levels, where m is the number of extra bits.

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If the random number generator has extra length, the extra bits can be used to fill in missing analog values between codes of the main DAC.

 

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