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Transcript
A/D Converters Input-referred noise improves A/D converter resolution By Walter Kester, Staff Applications Engineer, Analog Devices, Inc. All analogue-to-digital converters (ADCs) have a certain amount of input-referred noise. In most cases, less input noise is better. There are some cases, however, where input noise can actually be helpful in achieving higher resolution. In precision, low-frequency measurement applications, the effects of this noise can be reduced by digitally averaging the ADC output data, using lower sampling rates and additional hardware. While the resolution 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-band noise dither can improve the differential nonlinearity (DNL) of the ADC (see Figure 1, below) and increase its spurious-free dynamic range (SFDR). The effectiveness of this method depends highly on the characteristics of the ADC being considered. As the analogue input voltage to an “ideal” ADC is increased, the output remains constant until a transition region is reached. At that point, it instantly jumps to the next value, remaining there until the next transition region is reached. A theoretically perfect ADC has zero code-transition quantization noise and a transition region width equal to zero. A real-world ADC has a certain amount of code transition noise, and thus, a finite transition region width. All ADC circuits produce a certain amount of rms noise because of resistor noise and “kT/C” noise. This input-referred noise is characterized by examining the histogram of many output samples taken with constant DC input. The output is typically a distribution of codes centred on the nominal value of the DC input. The noise is approximately Gaussian, so the standard deviation of the histogram corresponds to the effective input rms noise. The DNL of the ADC will cause deviations from an ideal Gaussian distribution. A code distribution that is significantly non-Gaussian usually indicates a bad printed circuit board (PCB) layout, poor grounding techniques or improper powersupply decoupling. Another indication of trouble is when the width of the distribution changes drastically as the DC input is swept over the ADC input voltage range. The noise-free code resolution of an ADC is the number of bits of resolution beyond which it is impossible to distinctly resolve individual codes. Multiplying the rms noise by 6.6 converts it to peak-to-peak noise. The term “effective resolution” is used if the root mean square (RMS) noise (rather than peak-to-peak noise) is used to calculate resolution. Under identical conditions, effective resolution is larger than noisefree code resolution by approximately 2.7bits. The effects of input-referred noise can be reduced by digital averaging. Consider a 16bit ADC that has 15 noise-free bits at a sampling rate of 100 ksps (samples per second). Averaging two measurements of an unchanging signal for each output sample reduces the effective sampling rate to 50Ksps—and increases the signal to noise ratio (SNR) by 3dB (decibels) and the number of noise-free bits to 15.5. Averaging four measurements per output Figure 1: Noise enhances A/D signals. Staying outside of the band is key. sample reduces the sampling rate to 25ksps, and increases the SNR by 6dB and the number of noise-free bits to 16. Averaging process The averaging process also helps smooth out the differential nonlinearity (DNL) errors. This can be illustrated for the simple case where the ADC has a missing code at quantization level k. Even though code k is missing because of the large DNL error, the average of the two adjacent codes, k-1 and k+1, is equal to k. Averaging can increase the dynamic range of the ADC at the expense of the sampling rate and extra digital hardware. But it will not correct the ADC’s inherent integral nonlinearity. Maximizing SFDR requires minimizing both the distortion produced by the front-end amplifier and the sample-and-hold circuit, and that produced by nonlinearity in the encoder. Nothing can be done to significantly reduce the front-end distortion. But distortion caused by DNL can often be reduced by using dither, defined as external noise that is intentionally summed with the analogue input signal. One approach is to add a large amount of dither to randomize the ADC’s transfer function. Here, a pseudorandom number generator drives a DAC. The analogue signal is subtracted from the ADC input and its digital equivalent is added to the ADC output, so no significant SNR degradation occurs. A disadvantage of this technique, however, is that the input signal swing must be reduced to prevent overdriving the ADC. Another way to increase SFDR is to inject a narrowband dither signal outside the signal band of interest. Signal components are not typically located near DC, so this low-frequency region is often used for such a dither signal. Another possible location for the dither signal is slightly below fs/2. The dither signal occupies only a small bandwidth relative to the signal bandwidth, hence no significant degradation in SNR occurs. Dither noise can be generated in many ways. Noise diodes can be used, but simply amplifying the input voltage noise of a wideband bipolar op amp provides a more economical solution. EE Times-India | November 2006 | eetindia.com