Sometimes it is much easier to become a fan of something when you only know something about it. Just like Sigma-Delta ADC, it is so complicated that even though I have learned it for several times I still can’t fully understand it!
Nevertheless, I am still a fan of it ;-).
Sigma-Delta ADCs dominate in the high-resolution domain (though they are not extremely fast, actually kind of slow…).
I am currently doing successive-approximation-register (SAR) ADC.
Fig. 1 Signal-to-noise-and-distortion ratio (SNDR) versus sampling frequency of Sigma-Delta ADCs and other Nyquist ADCs (SAR, Pipeline, and Flash). The data were reported in ISSCC, and collected by Murmann’s ADC survey .
SAR ADCs are quite energy-efficient, but less accurate than Sigma-Delta ADCs.
In order to achieve high resolution, can SARs shape the noise just as Sigma-Delta ADCs do?
Fig. 2 Energy (P/fs) versus SNDR of SAR ADCs, Sigma-Delta ADCs, and other Nyquist ADCs (Pipeline and Flash). The data were again extracted from Murmann’s ADC survey .
People have tried to imploy noise-shaping technique into the SAR architecture [2, 3], but so far the reported performance (with chip measurement) is not very compelling (SNDR = 62dB , Power = 806uW, Bandwidth = 11MHz, FoM = 35.8fJ/conv) .
Nevertheless, the idea of noise-shaping SAR is so intriguing.
Before entering into this topic, I would like to do some warm-ups – some basics of Sigma-Delta ADCs (yes, that’s all I know about it).
Some basics of Sigma-Delta ADCs:
Fig.3 Brief illustration of oversampling (OSR is the abbreviation of oversampling ratio)
Doubling the sampling frequency gives 3 dB increase of SNR. However, oversampling is seldom used alone, and it is commonly used together with the noise-shaping technique.
Fig.4 Brief illustration of noise-shaping and the sigma-delta modulator
Filtering is introduced into the ADC to further suppress the in-band quantization noise power. At the same time, the filtering does not affect the input signal. By applying a loop filter before the quantizer and introducing the feedback, a sigma delta modulator is built.
3. Linear model of a sigma-delta modulator
Fig.5 Linear model of a sigma-delta modulator, STF and NTF are abbreviations of signal transfer function and noise transfer funcion, respectively. (More information can be referred to Schreier’s book)
According to STF and NTF, if the transfer function of the loop filter H(z) is designed to have a large gain inside the band of interest and small gain outside the band of interest, the signal can pass the modulator and the noise can be greatly reduced.
4. If an integrator is chosen to be the loop filter
Fig. 6 Modulator with an integrator as the loop filter and its STF and NTF
We do a plot of H(f), STF(f), and NTF(f) (Matlab ‘fvtool’ is used):
Fig. 7 Magnitude response of H(f), STF(f), NTF(f)
Bingo! The signal is passed to the output with a delay of a clock cycle, while the quantization noise is passed through a high-pass filter.
Doubling the sampling frequency gives 9 dB increase of SNR for 1st order noise shaping.
5. Get more aggressive on the order
Fig. 8 Magnitude response of NTF from 0th – 3rd order
This post tells the basic story of noise-shaping. In the next post, I will try to learn how noise-shaping can be used in SAR ADCs.
 B. Murmann, “ADC Performance Survey 1997-2014,” [Online]. Available: http://www.stanford.edu/~murmann/adcsurvey.html.
 K. S. Kim, J. Kim, and S. H. Cho, “nth-order multi-bit \Sigma-\Delta ADC using SAR quantiser”, Electronics Letters, vol. 46, 2010.
 J. A. Fredenburg and M. P. Flynn, “A 90-MS/s 11-MHz-Bandwidth 62-dB SNDR Noise-shaping SAR ADC”, JSSC, vol.47, 2012.
 R. Schreier and G. C. Temes, Understanding Delta-Sigma Data Converters, 2005.