Category Archives: ADC FOM

ADC Survey: Spring 2013 update on FOM


Winter seems to be super-glued to Sweden this year, so to illustrate “spring” I had to pick this photo from the archives.

Winter seems to be super-glued to Sweden this year, so to illustrate “spring” I had to pick this photo from the archives: Liverleaf (Hepatica Nobilis) in all its glory.

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

  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  6. B. E. Jonsson, “On CMOS scaling and A/D-converter performance,” Proc. of NORCHIP, Tampere, Finland, pp. 1–4, Nov. 2010.
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ADC Survey: Christmas 2012 update on FOM


ADC FOM UPDATE: I’ve understood that many Converter Passion readers are the very scientists who advance the state-of-the-art for A/D-converters. You are most certainly keeping a close eye on the progress yourselves. But in case you haven’t had time to scan the output of every major conference and top journal lately, this post will summarize the figure-of-merit (FOM) evolution since the Spring 2012 Update.

What’s new?

This update adds coverage for the 2012 versions of Symposium on VLSI Circuits, ESSCIRC and CICC. Also the most recent issues of IEEE Journal of Solid-State Circuits (JSSC), and Transactions on Circuits and Systems pt. I and II. A total of 64 new sources were added to the survey, so that it now includes 3917 experimental data points extracted from 1772 scientific papers published between 1974 and Oct/Dec 2012.

ISSCC/Walden FOM

As mentioned in the previous update, the 4.4 fJ reported by van Elzakker et al. at ISSCC 2008 [1] has been an impressively persistent world record for “The FOM”

F_{A1} = \dfrac{P}{{2}^{ENOB}\times f_{s}}

It lasted for over four years until June 2012 until Tai et al [2] presented a 3.2 fJ SAR ADC at the IEEE Symposium for VLSI Circuits. Congratulations to the team from National Taiwan University, Taipei, Taiwan for their outstanding achievement. With their 0.35 V design, the NTU team were the new FOM champions between June and August 2012.

In September there was ESSCIRC. This year’s ESSCIRC had no less than four ADCs with a sub-10 fJ FOM [3]-[6]. No extra points for guessing the architecture – yes, they are all SAR. Among the four, the 2.8 fJ, 0.7 V, 7–10-b, flexible SAR by Harpe, et al. [3], is the new winner. The Eindhoven-based team behind the impressive world-record FOM are from the Holst Centre and Eindhoven University of Technology, The Netherlands. Excellent job, indeed! Many greetings from Converter Passion.

Beside the winners, all designs that achieved an FA1 < 10 fJ since the last update are listed below. Their combinations of {FA1, fs, ENOB, technology, VDDmax} are shown. In addition to all being variations of the SAR architecture, they are also close to the 9-b sweet spot for FA1, as predicted in “The path to a good A/D-converter FOM” and [7]. Except for the 7.07-b design by Yoshioka, et al. [6], they are all gathered within a 0.5-b slim interval centered just above 9-b. As explained in [7], this is not by accident.

Another clear trend is to operate the ADC at a lower-than-nominal supply voltage. As you can se from the table, the CMOS nodes range from 180 to 45 nm, but all six are run at low or ultra-low voltage. This is directly beneficial as it reduces the digital switching power. It is also likely to cause the converter to become limited by analog noise, which is pretty much a requirement when you’re aiming for energy-optimal operation.

FOM [fJ] Speed [S/s] ENOB Node [nm] VDD [V] 1st Author Ref
2.8 2M 9.31 90 0.7 Harpe [3]
3.2 100k 9.06 90 0.35 Tai [2]
3.9 2M 9.29 65 0.7 Yin [4]
4.5 1k 8.80 65 0.6 Zhang [5]
6.1 1.3M 7.07 45 0.4 Yoshioka [6]
8.0 200k 9.33 180 0.6 Huang [8]

What’s in the future?

It seems that a larger body of research efforts are now catching up with the rather extreme step taken by van Elzakker et al. The region below 10 fJ is rapidly becoming more densely populated. Within a six months period we saw two new world records, and with so much focus on this particular performance measure, we are likely to see more. In fact, judging from the titles in the ISSCC 2013 advance program, there are already two designs below 2.8 fJ lining up to be presented there. Perhaps more. Wish I could go there too.

Historically, the state-of-the-art FOM has mainly been reported in JSSC and at ISSCC, with the occasional publication at other conferences. As noted above, we can expect more to come out of ISSCC in the future, but ESSCIRC has clearly raised its profile with respect to ADC FOM in this millennium. Looking at the number of unique publications advancing the state-of-the-art FOM over time sorted by source publication, we get the “market share” of world records for each conference/journal, as shown in Fig. 1. Since the data between 2000 and 2012 consists of only 7 unique FOM advancements, we can’t be too sure about the trends. But it certainly makes ESSCIRC look good, doesn’t it?

Pie charts

Fig. 1. Where was the state-of-the-art FOM published? (a) Accumulated total (b) 1982–1999 (b) 2000–2012. [Click to enlarge]

Thermal FOM

As discussed in a previous post, the overall evolution of the “Thermal FOM”

F_{B1} = \dfrac{P}{{2}^{2\times ENOB}\times f_{s}}

over time has slowed down, and as explained in [9] it may not improve much over technology scaling. It is therefore no surprise that the overall FB1 remains unchanged at the 1.1 aJ reported by Xu [10].

Thermal FOM for Nyquist ADCs

New thermal-FOM champions for Nyquist converters are actually the same as the Walden-FOM winners above: First, the design by Tai et al. [2] nudged the previous 6.6 aJ record by Verbruggen et al. [11] down to 6.0 aJ. After a few months, Harpe et al. took the thermal FOM down to 4.4 aJ, which is the current world record.

Final words

All papers highlighted in this update represent considerable efforts and significant achievements with respect to energy efficiency. It was a joy reading them, and it will be exciting to see how far this evolution will take us.

To the blog readers that celebrate Christmas, I wish you a Merry one – to the rest, a Joyful Season. To all of us, a Happy New Year!

Next up is a book review, which I hope to post soon.

<- Previous FOM update

References

  1. M. van Elzakker, E. van Tuijl, P. Geraedts, D. Schinkel, E. Klumperink, and B. Nauta, “A 1.9μW 4.4fJ/Conversion-step 10b 1MS/s charge-redistribution ADC,” Proc. of IEEE Solid-State Circ. Conf. (ISSCC), San Francisco, California, pp. 244–245, Feb., 2008.
  2. H.-Y. Tai, H.-W. Chen, and H.-S. Chen, “A 3.2fJ/c.-s. 0.35V 10b 100KS/s SAR ADC in 90nm CMOS,” Symp. VLSI Circ. Digest of Technical Papers, Honolulu, USA, pp. 92–93, June, 2012.
  3. 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.
  4. G. Yin, H.-G. Wei, U-F. Chio, S.-W. Sin, S.-P. U, Z. Wang, and R. P. Martins, “A 0.024 mm2 4.9 fJ 10-bit 2 MS/s SAR ADC in 65 nm CMOS,” Proc. of Eur. Solid-State Circ. Conf. (ESSCIRC), Bordeaux, France, pp. 377–380, Sept., 2012.
  5. D. Zhang, and A. Alvandpour, “A 3-nW 9.1-ENOB SAR ADC at 0.7 V and 1 kS/s,” Proc. of Eur. Solid-State Circ. Conf. (ESSCIRC), Bordeaux, France, pp. 369–372, Sept., 2012.
  6. K. Yoshioka, A. Shikata, R. Sekimoto, T. Kuroda, and H. Ishikuro, “An 8bit 0.35-0.8V 0.5-30MS/s 2bit/step SAR ADC with Wide Range Threshold Configuring Comparator,” Proc. of Eur. Solid-State Circ. Conf. (ESSCIRC), Bordeaux, France, pp. 381–384, Sept., 2012.
  7. B. E. Jonsson, “Using Figures-of-Merit to Evaluate Measured A/D-Converter Performance,” Proc. of 2011 IMEKO IWADC & IEEE ADC Forum, Orvieto, Italy, June 2011. [PDF @ IMEKO]
  8. G.-Y. Huang, S.-J. Chang, C.-C. Liu, and Y.-Z. Lin, “A 1-μW 10-bit 200-kS/s SAR ADC With a Bypass Window for Biomedical Applications,” IEEE J. Solid-State Circuits, Vol. 47, pp. 2783–2795, Nov., 2012.
  9. B. E. Jonsson, “On CMOS scaling and A/D-converter performance,” Proc. of NORCHIP, Tampere, Finland, pp. 1–4, Nov. 2010.
  10. 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.
  11. B. Verbruggen, M. Iriguchi, and J. Craninckx, “A 1.7mW 11b 250MS/s 2× Interleaved Fully Dynamic Pipelined SAR ADC in 40nm Digital CMOS,” Proc. of IEEE Solid-State Circ. Conf. (ISSCC), San Francisco, California, pp. 466–467, Feb., 2012.

ADC performance evolution: Thermal figure-of-merit (FOM)


Figure 1. Evolution of best reported thermal FOM for delta-sigma modulators (o) and Nyquist ADCs (#). Monotonic state-of-the-art improvement trajectories have been highlighted. Trend fit to state-of-the-art points for DSM [1984–2000] (dotted), and Nyquist [1982–2012] (dashed). Average trend for all designs (dash-dotted) included for comparison.

POWER EFFICIENCY TRENDS (continued): As mentioned in the previous post, a slightly different FOM, sometimes labeled the “Thermal FOM” [1]-[2], has been proposed in order to better compare high-resolution ADCs limited by thermal noise. The thermal FOM, FB1, is expressed as

(1) : F_{B1} = \dfrac{P}{{2}^{2\times ENOB}\times f_{s}}

The thermal FOM considers error power rather than amplitude (as in the Walden FOM), and therefore the value of FB1 improves by 4× (rather than 2×) for every additional bit of resolution. This matches the theoretical 4× minimum increase in power if ENOB is limited by kT/C-noise [3] and the architecture remains unchanged [4]. It was shown in [5] that the thermal FOM represents a better description of the state-of-the-art power-resolution tradeoffs according to empirical data than the Walden FOM for ENOB ≥ 9.

As seen in Fig. 1, there is a significant difference between DSM and Nyquist ADCs with respect to FB1. With the exception of two early 14-b designs [6]-[7], the global state-of-the-art is defined entirely by delta-sigma modulator implementations while Nyquist ADCs lag distinctly behind. A possible explanation could be that the thermal FOM favors converters whose power dissipation is truly limited by thermal noise, and that high-resolution ∆-∑ ADCs are more distinctly driven into the thermal noise limit than their Nyquist counterparts. Another point is that many scientific DSM implementations use an off-chip (i.e., zero power) decimation filter implemented in software. This will give DSM an unfair advantage over Nyquist, although it can hardly be the only explanation for a one order of magnitude FOM difference.

Since the thermal FOM for Nyquist converters has evolved over a rather uneven path, I’ll not make any elaborate interpretations of its shape. The trend (dashed) is simply fitted to all the state-of-the-art points from 1982–2012, revealing an average improvement rate of 2× every two years. The DSM envelope appears to have three main segments with breakpoints at 1990 and 2000, respectively. For simplicity, a single trend was estimated for the envelope until Naiknaware [8], after which the thermal FOM has evolved significantly slower. From Fiedler [9] to Naiknaware, the average improvement rate is 2× every 17 months (1.4 years) – again faster than Moore’s Law [10]-[11] – whereas from year 2000 to present day [12], the state-of-the-art points fit to a more modest /5.5 years slope. Even if the latter is from a fit of only four data points, and the exact slopes can be discussed, it is clear from Fig. 2 that the thermal FOM for DSM experienced a distinct slowdown after year 2000. This coincides with the breakpoint where the relative noise floor – approximately the denominator in (1) – also goes into saturation. It can further be noticed that it coincides with the accelerated evolution of FA1 as well. A possible, but perhaps speculative interpretation is that the ADC community first focused on thermal noise performance and related design optimization, and after hitting the noise floor around year 2000 moved on to focus on power efficiency.

If you wish to suggest other explanations, please share them below.

This concludes a series of ten posts on ADC performance and technology trends. If you want to go back and read them all from the beginning, these are the topics and the order in which they were posted:

  1. CMOS node adoption
  2. Low-voltage operation – part 1
  3. Low-voltage operation – part 2
  4. Thermal noise
  5. Jitter
  6. Relative noise floor
  7. Linearity (SFDR)
  8. Sampling rate and resolution
  9. Walden FOM
  10. Thermal FOM (this post)

As a small postlude, a follow-up post will list known prior art ADC surveys for those of you that (like myself) have an insatiable appetite for technology trend estimations and empirical data dots.

See also …

ADC survey data

References

  1. A. M. A. Ali, C. Dillon, R. Sneed, A. S. Morgan, S. Bardsley, J. Kornblum, and L. Wu, “A 14-bit 125 MS/s IF/RF sampling pipelined ADC with 100 dB SFDR and 50 fs jitter,” IEEE J. Solid-State Circuits, Vol. 41, pp. 1846–1855, Aug, 2006.
  2. C. Wulff, and T. Ytterdal, “Design of a 7-bit, 200MS/s, 2mW pipelined ADC with switched open-loop amplifiers in a 65nm CMOS technology,” Proc. of NORCHIP, Aalborg, Denmark, Nov., 2007.
  3. B. Murmann, “A/D converter trends: Power dissipation, scaling and digitally assisted architectures,” Proc. of IEEE Custom Integrated Circ. Conf. (CICC), San Jose, California, USA, pp. 105–112, Sept., 2008.
  4. K. Bult, “Embedded analog-to-digital converters,” Proc. of Eur. Solid-State Circ. Conf. (ESSCIRC), Athens, Greece, pp. 52–60, Sept., 2009.
  5. B. E. Jonsson, “Using Figures-of-Merit to Evaluate Measured A/D-Converter Performance,” Proc. of 2011 IMEKO IWADC & IEEE ADC Forum, Orvieto, Italy, pp. 1–6, June 2011. [PDF @ IMEKO]
  6. R. J. van de Plassche, and H. J. Schouwenaars, “A Monolithic 14 Bit A/D Converter,” IEEE J. Solid-State Circuits, Vol. SC-17, pp. 1112-1117, Dec., 1982.
  7. T. Sugawara, M. Ishibe, H. Yamada, S.-I. Majima, T. Tanji, and S. Komatsu, “A Monolithic 14 Bit/20 µs Dual Channel A/D Converter,” IEEE J. Solid-State Circuits, Vol. SC-18, pp. 723-729, Dec., 1983.
  8. R. Naiknaware, and T. Fiez, “142dB ∆∑ ADC with a 100nV LSB in a 3V CMOS Process,” Proc. of IEEE Custom Integrated Circ. Conf. (CICC), Orlando, USA, pp. 5–8, May, 2000.
  9. H. L. Fiedler, and B. Hoefflinger, “A CMOS Pulse Density Modulator for High-Resolution A/D Converters,” IEEE J. Solid-State Circuits, Vol. SC-19, pp. 995-996, Dec., 1984.
  10. G.E. Moore, “Cramming more components onto integrated circuits,” Electronics, Vol. 38, No. 8, Apr. 1965.
  11. G. E. Moore, “No exponential is forever: but “forever” can be delayed!,” IEEE ISSCC, Dig. Tech. Papers, San Francisco, CA, Feb. 2003, pp. 20–23.
  12. 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.

ADC Survey: Spring 2012 update on FOM state-of-the-art


Will reading tons of ADC papers grow your brain — or wear it out?

Well folks, its the time of year when an A/D-converter survey update is due. Since a significant effort is still invested in the quest for ever-improving figures-of-merit (FOM), I’ll start by firing up the Converter Passion FOM-o-meter  and apply it to the body of ADC science. The latter is here approximated by my pet project – the ADC performance survey.

Including the papers added since last year, the updated survey now has 3628 experimental data points extracted from 1708 scientific papers published between 1974 and April/May 2012. The number of unique ADC implementations will be slightly less, since some papers are full-length versions of conference contributions. The source publications monitored are listed here.

What a difference a year makes …

… or not?

ISSCC/Walden-FOM

Can you believe this: With all the current competition to get a great ISSCC/Walden-FOM

F_{A1} = \dfrac{P}{{2}^{ENOB}\times f_{s}}

the state-of-the-art (4.4 fJ) reported by van Elzakker et al. at ISSCC four years ago [1] is still number one. Their design really went the extra mile with respect to getting a low energy per sample, and I guess that paid off big time. Well done!

As Michiel commented, it is just a matter of time before someone goes below 4.4 fJ. This is also reflected in the scientific output over the last twelve months. Although the current F_{A1} world record didn’t change, there are several designs that reported an F_{A1} < 10 fJ, and that’s not bad either. They are:

FOM [fJ] Speed [S/s] ENOB Architecture 1st Author Ref
8.7 2M 8.27 SAR Sekimoto [2]
6.8 1k 8.52 SAR Lu [3]
6.5 4M 9.4 SAR Harpe [4]
6.1 1.1M 7.48 SAR Shikata [5]
6.8 10M 10.0 SAR Verbruggen [6]
9.7 250M 9.45 SAR Verbruggen [6]

The most striking feature is probably that they are all SAR ADCs. Secondly, while they are all impressive efforts, the one that stands out a bit is the design by Verbruggen et al. It maintains a sub-10fJ FOM at a significantly higher sampling rate (250 MS/s) while also reporting the highest resolution [6].

Although it’s beyond the scope of this post, it can be good to keep in mind that there are other aspects to factor in than simply the FOM value when analyzing energy efficiency. It was pointed out by Verbruggen [6] that previous ultra-low FOM ADCs have been reported only at rather low sampling rates or moderate resolution. It is a greater challenge to maintain a low F_{A1} for high sampling rates. Hence, pragmatic limits to the state-of-the-art F_{A1} are speed-dependent. It has also been shown that the limits are both scaling- and resolution-dependent [7, 8], so a perfectly fair comparison between designs is difficult to make. I can pretty much guarantee that I’ll get back to this topic in the future, but for the remainder of this post we’ll just look at the raw FOM numbers as they are.

Thermal FOM

It would have been boring to read another 100+ papers and still have nothing new to report, so I’m very glad to see that the so called “Thermal FOM

F_{B1} = \dfrac{P}{{2}^{2\times ENOB}\times f_{s}}

has been improved by over a factor of two through the switched-opamp (SO) based ∆∑ design reported by Xu et al. [9]. Previous state-of-the-art – 2.7aJ reported by Perez et al. [10] – will assume its well-earned place in the Hall of Fame, while we applaud the 1.1 aJ achieved by the Chinese team from Zheijan University and Analog Devices, Shanghai. You’re the best now. Enjoy!

Thermal FOM for Nyquist ADCs

There has also been some evolution among the Nyquist ADCs: The 250MS/s SAR ADC by Verbruggen et al. mentioned above, is actually the new Thermal-FOM champion for Nyquist ADCs as it nudges the previous F_{B1} record [11] from 7.6 to 6.6 aJ. The authors are with imec, Belgium, and Renesas Electronics, Japan. Congratulations!

Old and new winners are always found in the halls of fame for Thermal and Walden FOM, respectively. If you are only interested in checking for the current leaders, the FOM-o-meter gives you both with a single click.

As always: I do believe the information here is correct, but if I’ve misrepresented anyone or forgotten to mention someone that should have been included, just send me an email or post a comment below.

<- Previous update | Next update ->

References

[1] M. van Elzakker, E. van Tuijl, P. Geraedts, D. Schinkel, E. Klumperink, and B. Nauta, “A 1.9μW 4.4fJ/Conversion-step 10b 1MS/s charge-redistribution ADC,” Proc. of IEEE Solid-State Circ. Conf. (ISSCC), San Francisco, California, pp. 244–245, Feb., 2008.

[2] R. Sekimoto, A. Shikata, T. Kuroda, and H. Ishikuro, “A 40nm 50S/s – 8MS/s Ultra Low Voltage SAR ADC with Timing Optimized Asynchronous Clock Generator,” Proc. of Eur. Solid-State Circ. Conf. (ESSCIRC), Helsinki, Finland, pp. 471–474, Sept., 2011.

[3] T.-C. Lu, L.-D. Van, C.-S. Lin, C.-M. Huang, “A 0.5V 1KS/s 2.5nW 8.52-ENOB 6.8fJ/Conversion-Step SAR ADC for Biomedical Applications,” Proc. of IEEE Custom Integrated Circ. Conf. (CICC), San Jose, California, USA, pp. 1–4, Sept., 2011.

[4] P. Harpe, Y. Zhang, G. Dolmans, K. Philips, and H. De Groot, “A 7-to-10b 0-to-4MS/s Flexible SAR ADC with 6.5-to-16fJ/conversion-step,” Proc. of IEEE Solid-State Circ. Conf. (ISSCC), San Francisco, California, pp. 472–473, Feb., 2012.

[5] A. Shikata, R. Sekimoto, T. Kuroda, and H. Ishikuro, “A 0.5 V 1.1 MS/sec 6.3 fJ/Conversion-Step SAR-ADC With Tri-Level Comparator in 40 nm CMOS,” IEEE J. Solid-State Circuits, Vol. 47, pp. 1022–1030, Apr., 2012.

[6] B. Verbruggen, M. Iriguchi, and J. Craninckx, “A 1.7mW 11b 250MS/s 2× Interleaved Fully Dynamic Pipelined SAR ADC in 40nm Digital CMOS,” Proc. of IEEE Solid-State Circ. Conf. (ISSCC), San Francisco, California, pp. 466–467, Feb., 2012.

[7] B. E. Jonsson, “On CMOS scaling and A/D-converter performance,” Proc. of NORCHIP, Tampere, Finland, pp. 1–4, Nov. 2010.

[8] B. E. Jonsson, “Using Figures-of-Merit to Evaluate Measured A/D-Converter Performance,” Proc. of 2011 IMEKO IWADC & IEEE ADC Forum, Orvieto, Italy, June 2011. [PDF @ IMEKO]

[9] 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.

[10] A. P. Perez, E. Bonizzoni, and F. Maloberti, “A 84dB SNDR 100kHz Bandwidth Low-Power Single Op-Amp Third-Order ΔΣ Modulator Consuming 140μW,” Proc. of IEEE Solid-State Circ. Conf. (ISSCC), San Francisco, USA, pp. 478-480, Feb., 2011.

[11] C. P. Hurrell, C. Lyden, D. Laing, D. Hummerston, and M. Vickery, “An 18 b 12.5 MS/s ADC With 93 dB SNR,” IEEE J. Solid-State Circuits, Vol. 45, pp. 2647-2654, Dec., 2010.

The path to a good A/D-converter FOM


Figure 1. ENOB, power, and sampling rate trajectories showing the evolution path to the current state-of-the art FOM.

If you are participating in the scientific competition to report an ever better ADC figure-of-merit (FOM), you will find some pretty useful information in this post. Basically it will tell you where to start “drilling for oil”, and with a bit of persistence (preferably combined with some skill in the art) it might take you all the way to ISSCC 2013. The deadline for ISSCC 2012 is probably a bit too close for anyone to make a full ADC implementation according to these guidelines and still get it back in time from the foundry. But you can always try. I will give you a set of information about design and performance parameters that will enable you to predict quite accurately where in the design space the next state-of-the-art ADC (with respect to FOM) will be located. Remember that it could be your ADC, if you choose to optimize the speed-resolution-power tradeoff for this particular target.

First, let us clarify that we are talking about the most commonly used ADC figure-of-merit of all:

F_{A1} = \dfrac{P}{{2}^{ENOB}\times f_{s}}

Figure 1 illustrates the trajectories of each of the three parameters in FA1 as FA1 improved over time. Click on the image to enlarge it. Only the data points representing an advance of FA1 state-of-the-art, i.e., the monotonic decrease of FA1 over time are used in the plot. Time was also quantized so that only the single best ADC per year appears in the trajectories. The underlying data set is gathered from 1600 scientific papers, and the same as used in [1]-[5]. The FOM axis and the FOM values for each dot are the same for all three plots, while the x axes show the simultaneous values of ENOB, power dissipation and sampling rate, respectively. These are the three parameters used to calculate the FOM, so any systematic trends in their trajectories are likely to be a good direction for a FOM-optimized design.

Figure 2. Approximate trajectory trends suggested by the plots.

Although there is plenty of noise in some of the trajectories, visual inspection suggests the approximate trends indicated in Fig. 2. At least it is my best guesstimate. It is purely ad hoc, and you are of course invited to discuss and refine my estimates by posting comments below. The most obvious trend applies to power dissipation (P), which has reduced by almost six orders of magnitude – from Watts to micro-Watts. At the same time the effective resolution (ENOB) has followed a more noisy, but visible path towards lower (medium) resolutions – from ~14 to currently 9-b ENOB. The change equals a three orders of magnitude increase in error power. Finally, the sampling rates at which state-of-the-art figures-of-merit were achieved have migrated slowly, from ~100 kS/s to 1–10 MS/s, even if state-of-the-art FOMs have occasionally been reported at several GS/s in the past. Looking at the fs trajectory from a purely mathematical curve-fitting perspective, it would not support the trend suggested by the green curve. Weighing in some understanding of the speed-power tradeoff in actual design (described below), it makes a bit more sense. It appears thus, that the FOM is best improved by lowering the power dissipation and accepting a medium resolution, while running at moderate sampling rates.

Understanding the trajectories

In high-resolution ADCs, it can be shown that the power dissipation has a lower limit defined by the size of capacitors sized for a kT/C-noise in line with the target ENOB. The power used to drive these capacitors increase by 4X for every additional bit of resolution – in other words, as {{2}^{2\times ENOB}} . It was shown in [3] and [4] that the break point where power dissipation becomes proportional to {{2}^{2\times ENOB}} is currently @ 9-b ENOB for the most power efficient ADCs. It was also shown in [4] that FA1 will always have a sweet spot at this break point.

Since FA1 (erroneously) presupposes that P is proportional to {{2}^{ENOB}} (rather than {{2}^{2\times ENOB}} ) for P and ENOB to be traded on equal terms, you will always improve FA1 more by lowering P than by increasing ENOB – as long as ENOB ≥ 9. Below the 9-b break point, state-of-the-art P/fs is approximately independent of ENOB [3]-[4],  which makes it meaningless to lower the resolution further, as it would only diminish the {{2}^{ENOB}} factor in FA1 and do very little to reduce P/fs. This is the reason why the trajectories has not migrated to even lower resolutions and dissipations – for example to a pathologically low ENOB with femto-Watt dissipation.

The reason state-of-the-art FA1 values tend to be reported for 0.1–10 MS/s ADCs is perhaps less obvious. A reasonable assumption is that energy per sample (P/fs) increase faster than linearly with fs when sampling rates are pushed further, and therefore moderately fast designs are likely to have a more optimal P/fs at any fixed ENOB.

Cookbook for an optimized FOM

It was shown in [2] that the state-of-the-art FA1 also improves with every step of CMOS scaling. Including the parameter trajectories showed in this post, the recipe for a good A/D-converter FOM would be something like:

  • Use the most deeply scaled CMOS process you possibly can.
  • Aim for 8–9-b effective resolution, and a modest sampling rate.
  • Use the lowest amount of power that will place you at the ENOB sweet spot, and let the measurements decide exactly what fs you should claim in the paper 😉

There are a few more tricks – some of which can be understood from [3] and some that I’ll save for clients and partners – but that’s more or less it. It will obviously help if you’re prepared to go the extra mile with your design, like the current record holders van Elzakker, et al. [6], who introduced multi-step charging of capacitors to further reduce P/fs. Honing your design skills will help too, but essentially you’re now set to go out and design the next big scientific hit … 

Keep trying, and best wishes! 🙂

References

[1] B. E. Jonsson, “A survey of A/D-converter performance evolution,” Proc. of IEEE Int. Conf. Electronics Circ. Syst. (ICECS), Athens, Greece, pp. 768–771, Dec., 2010.

[2] B. E. Jonsson, “On CMOS scaling and A/D-converter performance,” Proc. of NORCHIP, Tampere, Finland, pp. 1–4, Nov. 2010.

[3] B. E. Jonsson, “An empirical approach to finding energy efficient ADC architectures,” Proc. of 2011 IMEKO IWADC & IEEE ADC Forum, Orvieto, Italy, pp. 1–6, June 2011. [PDF @ IMEKO]

[4] B. E. Jonsson, “Using Figures-of-Merit to Evaluate Measured A/D-Converter Performance,” Proc. of 2011 IMEKO IWADC & IEEE ADC Forum, Orvieto, Italy, pp. 1–6, June 2011. [PDF @ IMEKO]

[5] B. E. Jonsson, “Area Efficiency of ADC Architectures,” Accepted for presentation at Eur. Conf. Circ. Theory and Des. (ECCTD), Linköping, Sweden, Aug., 2011.

[6]    M. van Elzakker, E. van Tuijl, P. Geraedts, D. Schinkel, E. Klumperink, and B. Nauta, “A 1.9μW 4.4fJ/Conversion-step 10b 1MS/s charge-redistribution ADC,” Proc. of IEEE Solid-State Circ. Conf. (ISSCC), San Francisco, California, pp. 244–245, Feb., 2008.