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

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.

#### 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.

### 5 responses to “ADC Survey: Spring 2012 update on FOM state-of-the-art”

1. Hi, I wonder about ENOB and fs? ENOB should include of course noise & distortion, so SINAD-based. fs should be the analog input frequency (so max. fNyquist=fsampling/2), and ENOB should be taken at this frequency, not at low frequencies!! For most ADC it makes a significant difference (well-known fror flash-ADC). But I wonder if all reported FOM use these correct more pessimistic numbers.

• You’re right, ENOB is calculated from SINAD according to the standard definition ENOB = (SINAD – 1.76)/6.02. Perhaps I should have included that expression somewhere.

fs is simply the sampling rate. Analog input frequency is not considered at all by these FOM.

I agree with your remarks above, but unfortunately this has established itself as the current de facto standard for power/performance comparison. In this particular post, I therefore chose to report the FOM exactly as they are most commonly used in the literature – i.e. any input frequency is acceptable. In practice, it means that the current competition takes place at near-DC input frequencies. As you say, going to the Nyquist frequency can give very different results, depending on how well the ADC was designed.

In other blog posts, and even a conference paper [8], I have tried to discuss the broader issue of how to best use and define relevant figures-of-merit. But this post is simply reporting the latest on the FOM that seems to be of interest to many in the field.