Using input-referred noise to improve analog-to-digital converter resolution

All analog-to-digital converters (ADCs) have a certain amount ofinput-referred noise. In most cases,less input noise is better. There are some cases, however, where inputnoise can actually be helpful in achieving higher resolution.

In precision, low-frequency measurement applications, the effects ofthis noise can be reduced by digitally averaging the ADCoutput data,using lower sampling rates andadditional hardware. While theresolution of the ADC can be increased by this averaging process,integral nonlinearity errors are not reduced.

In certain high-speed applications, adding some out-of-bandnoisedither can improve the differentialnonlinearity (DNL) of the ADC (seeFigure 1, below) andincrease its spurious-free dynamic range (SFDR). The effectiveness ofthis method depends highly on the characteristics of the ADC beingconsidered.

Figure1: Noise enhances A/D signals. Staying outside of the band is key.

As the analog input voltage to an “ideal” ADC is increased, theoutput remains constant until a transition region is reached. At thatpoint, it instantly jumps to the next value, remaining there until thenext transition region is reached. A theoretically perfect ADC has zerocode-transition quantization noise and atransition region width equal to zero. Areal-world ADC has a certain amount of code transition noise, and thus,a finite transition region width. All ADC circuits produce a certainamount of rms noise because of resistor noise and kT/C” noise.

This input-referred noise is characterized by examiningthe histogram of many output samples taken with constant DC input. Theoutput is typically a distribution of codes centered on the nominalvalue of the DC input. The noise is approximately Gaussian, so thestandard deviation of the histogram corresponds to the effective inputrms noise.

The DNL of the ADC will cause deviations from an ideal Gaussiandistribution. A code distribution that is significantlynon-Gaussianusually indicates a bad printed circuit board (PCB) layout, poorgrounding techniques orimproper power-supply decoupling. Another indication of trouble is whenthe width of the distribution changes drastically as the DC input isswept over the ADC input voltage range.

The noise-free code resolution of an ADC is the number of bits ofresolution beyond which it is impossible to distinctly resolveindividual codes. Multiplying the rms noise by 6.6 converts it topeak-to-peak noise.

The term “effective resolution” is used if the root mean square(RMS) noise (ratherthan peak-to-peak noise) is used to calculate resolution. Underidentical conditions, effective resolution is larger than noise-freecode resolution by approximately 2.7bits.

The effects of input-referred noise can be reduced by digitalaveraging. Consider a 16bit ADC that has 15 noise-free bits at asampling rate of 100 ksps(samples per second). Averaging twomeasurements of an unchangingsignal for each output sample reduces the effective sampling rate to50Ksps—and increases the signal tonoise ratio (SNR) by 3dB (decibels) and the number ofnoise-free bitsto 15.5. Averaging four measurements per output sample reduces thesampling rate to 25ksps, and increases the SNR by 6dB and the number ofnoise-free bits to 16.

Averaging process
The averaging process also helps smooth out the differentialnonlinearity (DNL) errors. This can beillustrated for the simple case where the ADC has a missing code atquantization levelk . Even though code k is missingbecause of the large DNL error, the average of the two adjacent codes,k-1 and k+1 , is equal tok .

Averaging can increase the dynamic range of the ADC at the expenseof the sampling rate and extra digital hardware. But it will notcorrect the ADC's inherent integral nonlinearity.

Maximizing SFDR requires minimizing both the distortion produced bythe front-end amplifier and the sample-and-hold circuit, and thatproduced by nonlinearity in the encoder. Nothing can be done tosignificantly reduce the front-end distortion. But distortion caused byDNL can often be reduced by using dither, defined as external noisethat is intentionally summed with the analog input signal.

One approach is to add a large amount of dither to randomize theADC's transfer function. Here, a pseudorandom number generator drives aDAC. The analog signal is subtracted from the ADC input and its digitalequivalent is added to the ADC output, so no significant SNRdegradation occurs. A disadvantage of this technique, however, is thatthe input signal swing must be reduced to prevent overdriving the ADC.

Another way to increase SFDR is to inject a narrowband dither signaloutside the signal band of interest. Signal components are nottypically located near DC, so this low-frequency region is often usedfor such a dither signal. Another possible location for the dithersignal is slightly below f s /2. The dither signal occupiesonly a small bandwidth relative to the signal bandwidth, hence nosignificant degradation in SNR occurs. Dither noise can be generated inmany ways. Noise diodes can be used, but simply amplifying the inputvoltage noise of a wideband bipolar op amp provides a more economicalsolution.

 Walt Kester is corporateStaff Applications Engineer at Analog Devices Inc.

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