**ADC FOM UPDATE**: It’s now “post-ISSCC”, which is a more than sufficient reason to update the survey. If you were lucky enough to attend ISSCC this year, you may be familiar with the progress in A/D-converter *figure-of-merit* (FOM) since the Christmas 2012 Update. If not, I will summarize it here. This update also covers the most recent issues of *IEEE Journal of Solid-State Circuits* (JSSC), *Transactions on Circuits and Systems* pt. I and II, and ADC papers from ISOCC 2012. Unfortunately, the 2012 version of A-SSCC doesn’t seem to have made it into IEEE Xplore yet, so the 11 or so ADC papers that were published there will have to wait until next update. Even without the A-SCCC 2012, the survey now includes **4057** experimental data points extracted from **1810** scientific papers published between 1974 and Q1-2013.

# ISSCC/Walden FOM

Already from the paper titles in the ISSCC 2013 *Advance Program*, it was clear that the previous 2.8 fJ world record by *Harpe* et al. [1] wasn’t going to stand for long. Of the two papers reporting an improved Walden FOM, the 10-b SAR by *Liou* and *Hsieh* [2], National Tsing Hua University, Hsinchu, Taiwan, achieves an impressive **2.4 fJ**. Nevertheless, *Pieter Harpe* and coauthors *Cantatore* and *van Roermund* from Eindhoven University of Technology, The Netherlands, keep the leader position through their new 10/12-b SAR [3], achieving **2.2 fJ** in 12-b mode.

Clearly, both of the above designs are outstanding works. Something I particularly liked with the *Harpe* ADC was the elegant way they reduced the impact of comparator noise only for the decision(s) when it is really needed (i.e., when the comparator input is weak). Check it out, and enjoy the beauty of it all.

Another highlight is that *Harpe* et al. were able to set the new FOM world record and *simultaneously* push ENOB to 10.1 bits. Since the Walden FOM does not correctly model the energy vs. resolution trade-off for thermal noise limited designs, it is more difficult to achieve a good FOM the higher resolution you have. We’ll take a deeper look into that very soon in future posts. For now we can just conclude that the effort represented by their result is therefore even more admirable.

### Additional observations

As observed in the Christmas 2012 Update, state-of-the-art Walden FOM is typically reported at lower-than-nominal supply voltages. This is true also for the present update. If you are aiming to win the FOM race you obviously need to make a really good design in the first place. Then, when you’re measuring, it seems that a good advice would be to sweep the VDD downwards, accept that the circuit becomes slower and noisier, and simply search for the VDD sweet spot where you get the best FOM to report.

Another striking feature is that sub-10fJ Walden FOM has so far been reported from only a handful of countries, of which *The Netherlands* and *Taiwan* currently seem to have the initiative. I will probably focus on this geographical aspect in a separate post, so I’ll just leave you with this teaser for now.

# Thermal FOM

As in the previous update, no progress is reported beyond the Thermal FOM of 1.1 aJ reported by *Xu* [4], but for Nyquist ADCs, the Walden FOM winner above [3] is also the new Thermal FOM winner with a new world record of **2.0 aJ**. So, double gold medals for *Harpe*, *Cantatore* and *van Roermund* from Eindhoven University of Technology. Excellent job!

I also want to mention that the design by *Liou* and *Hsieh* [2] – the silver medalists in the Walden FOM category above – also weigh in as the third best Thermal FOM ever reported for Nyquist ADCs.

There are a few more designs now becoming visible on my “sub-10aJ radar”. Of these, I’d like to point out the ring-amp based ADC by *Hershberg* et al. [5]. First of all it’s **not a SAR**. Among low-energy Nyquist ADCs, that’s unusual in itself. Secondly, the authors suggest that Ring Amp realization of ADCs could be a way to beat the noise-floor vs. technology scaling limits predicted for example by myself in [6]. And, as much as I like to be right in my predictions, I still prefer that I am wrong and the ADC field continue to evolve beyond all limits we can see today. So I hope they are right about the Ring Amp ADC, and will follow up with more experimental results to establish that once and for all.

Or … that someone else of you has something even better in your drawer.

# Upcoming posts

Unless I get too fascinated with the geographic aspects of low-energy ADC research, the plan is to start looking at the energy vs. performance limits from a mostly empirical perspective. I hope to deliver something that is useful for those of you active in this race.

#### References

- P. Harpe, G. Dolmans, K. Philips, and H. de Groot, “A 0.7V 7-to-10bit 0-to-2MS/s Flexible SAR ADC for Ultra Low-Power Wireless Sensor Nodes,”
*Proc. of Eur. Solid-State Circ. Conf. (ESSCIRC)*, Bordeaux, France, pp. 373–376, Sept., 2012. - C.-Y. Liou, and C.-C. Hsieh, “A 2.4-to-5.2fJ/conversion-step 10b 0.5-to-4MS/s SAR ADC with Charge-Average Switching DAC in 90nm CMOS,”
*Proc. of IEEE Solid-State Circ. Conf. (ISSCC)*, San Francisco, USA, pp. 280–281, Feb., 2013. - P. Harpe, E. Cantatore, and A. van Roermund, “A 2.2/2.7fJ/conversion-step 10/12b 40kS/s SAR ADC with Data-Driven Noise Reduction,”
*Proc. of IEEE Solid-State Circ. Conf. (ISSCC)*, San Francisco, USA, pp. 270–271, Feb., 2013. - J. Xu, X. Wu, M. Zhao, R. Fan, H. Wang, X. Ma, and B. Liu, “Ultra Low-FOM High-Precision ΔΣ Modulators with Fully-Clocked SO and Zero Static Power Quantizers,”
*Proc. of IEEE Custom Integrated Circ. Conf. (CICC)*, San Jose, California, USA, pp. 1–4, Sept., 2011. - B. Hershberg, S. Weaver, K. Sobue, S. Takeuchi, K. Hamashita, and U.-K. Moon, “Ring Amplifiers for Switched Capacitor Circuits,”
*IEEE J. Solid-State Circuits*, Vol. 47, pp. 2928–2942, Dec., 2012. - B. E. Jonsson, “On CMOS scaling and A/D-converter performance,”
*Proc. of NORCHIP*, Tampere, Finland, pp. 1–4, Nov. 2010.

Dear friends,

Bengt made a nice ADC FOM update. FOM is very useful for judging the ADC development. It turns out that thermal FOM ca be theoretically predicted (see Sundström, Murmann, Svensson, TCAS I, 56, 509; and Zhang, Svensson, Alvvandpour, ECCTD 2011). A simplified view of Nyquist SAR is that the comparator dominates power for n>10, and that the thermal FOM can be estimated to about 24nkT (see Zhang), which with n=10 and room temperature gives 1aJ. So we are obviously very close to the theoretical limits!

Thank you for the kind words, and for sharing your insight with us.

Interesting that your theoretical predictions for SAR fit so well with current state-of-the-art. I just tried in Photoshop to overlay your ECCTD Fig. 4 with my Fig. 1 in the next post, and they fit very nicely together. It seems, like you say, that we are very close to theoretical limits.

It makes me wonder if “

that’s it” and we’re stuck here, or if someone will still figure out a way to go further. Research is truly interesting!Thanks also for reminding me about the ECCTD paper. I’ve updated the next post with a reference [13], so that the two works you mentioned above are now listed as [10] and [13], respectively.

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