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…).**

**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?**

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) [3].

**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:**

**1. Oversampling **

**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.

**2. Noise-shaping**

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 **

**4. If an integrator is chosen to be the loop filter**

We do a plot of H(f), STF(f), and NTF(f) (Matlab ‘*fvtool’* is used):

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**

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.

References:

[1] B. Murmann, “ADC Performance Survey 1997-2014,” [Online]. Available: http://www.stanford.edu/~murmann/adcsurvey.html.

[2] K. S. Kim, J. Kim, and S. H. Cho, “nth-order multi-bit \Sigma-\Delta ADC using SAR quantiser”, *Electronics Letters*, vol. 46, 2010.

[3] 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.

[4] R. Schreier and G. C. Temes, *Understanding Delta-Sigma Data Converters*, 2005.

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Hey, I’m really fortunate to find your blog. It seems you’re an expert in SAR ADC design! 🙂

I did research on Sigma-delta and Incremental ADCs, and now I want to use some special SAR structures in my design. But I’m new in this field and I even don’t know how I can simulate a SAR or a noise-shaping SAR ADC in system level! 😦

Should I write Matlab codes? Or better to use Simulink? Or maybe there are some other simulators which work better with this special type of ADC?!!

I’ll be very grateful if you could help me in SAR ADC design and simulation.

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