# Monthly Archives: July 2011

## 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.

## What parameters should be reported in a good ADC paper?

If you’re anything like me and try to draw as much information as possible out of scientific experiments done by others, you may have been frustrated from time to time over the huge variation in reporting practices between individual scientific authors. Having surveyed over 1600 papers by now, I’ve noted that measurement data reporting philosophies range from having a full set of relevant design and performance parameters (sometimes even including the variation over all circuit samples) down to reporting SNR-only performance for a single input frequency near DC and no mention of things like full-scale range, input amplitude, supply voltage, or anything else that could help the reader to interpret the results. It makes you wonder …

I’ve been contemplating the fact that authors may spend 9-12 months (or 1–1.5% of their lifetime) conceiving, modeling, designing and measuring their ADCs, but when they finally write their papers, some choose to make as little impact as possible by omitting nearly everything that could be of interest to the scientific and engineering community. Imagine yourself spending 1-1.5% of your life earnings on something (that’s like 5 to 7 months salary). Then you’d want it to make a difference, right? So, why not in (some) papers?

I can understand that companies may want to hide some information to avoid helping competitors, and I do understand that academic competition can sometimes be just as fierce. But if neither corporations nor universities feel they can openly report their results, where does that leave our field? Do we really want a “science” where everybody is competing to be the first to come up with something of which they tell nothing?

If not, what can be done about it, and what parameters do you expect to see in a good ADC paper?

## Going to Linköping … Yes, Yes, Yes!!

Curves like these can be really useful if you're going for small chip area. Those who attend ECCTD 2011 will get the full picture and learn what's on the X and Y axes.

You’d be forgiven to think that, with all the praise I recently gave to Italy and the IWADC conference, there’s no room in my heart for any other conference or location. But going to the European Conference on Circuit Theory and Design in Linköping, Sweden will be very special. The location isn’t nearly as exotic to me as Italy – quite the opposite in fact. I used to study in Linköping, and I was also a PhD student at the very department that is hosting the conference. What is special with Linköping is that it’s the city I used to call home for about 15 years of my life – 15 good years filled with memorable moments, good friends and talented engineers and scientists. It’s a nice Swedish town, and I highly recommend you to go there. ECCTD 2011 offers the perfect excuse.

If, like me, you’re also interested in what’s actually presented at the conference, it too is an excellent reason to go there. I guess there will be a conference program up on the conference site sooner or later. Until then I can only tell you about my contribution “Area Efficiency of ADC Architectures”, which I was very glad to get accepted. No extra points for guessing the general topic of the paper, and I’m not going to spoil the fun by telling you everything about it. Suffice to say that it’s another huge survey of scientific A/D-converter achievements. This time we’ll take a first look at the area-efficiency of various ADC architectures at different speed/resolution specifications. It exemplifies a small fraction of the EDO methodology used by ADMS Design AB, and gives you some overall guidelines to get you started with area-optimized ADC design.

So, if you design ADCs for high volume production and a low manufacturing cost is important … don’t miss this paper.

## Converter Passion Citation Boost

Stuff like this makes a tech-blogging nerd happy …

A very pleasant recent observation is that this blogs scientific citation frequency just improved by ∞ % (from zero to one), thanks to an IWADC paper [1] referring to a Converter Passion post [2]. It may be a humble start, but it was good news to see that someone out there trusts the data on this blog enough to include it as a reference in a scientific publication. To the best of my knowledge that was a first for Converter Passion, but let me know if you get a paper published that cites Converter Passion. Should it become a trend, I might have to compile a list of citations here, but I’ll wait until we have at least two … 😉

Update: Now there are more than one, so I’ve now added a citation list.

#### References

[1]    F. Fuiano, L. Cagnazzo, and P. Carbone, “Data Converters: an Empirical Research on the Correlation between Scientific Literature and Patenting Activity,” Proc. of Int. Workshop on ADC Modelling, Testing and Data Converter Analysis and Design (IWADC), Orvieto, Italy, June, 2011.

[2] B. E. Jonsson, “Who has done all that A/D-converter research?,” Converter Passion, Nov. 6, 2010, Available: https://converterpassion.wordpress.com

Views from Orvieto (click to enlarge)

I’m completely in love with Italy now. It was my first time there, and I was impressed by just about every aspect of the visit – the beautiful landscape, the fascinating history embodied in ancient buildings, and of course by the people. Perhaps it was accentuated by me going through the “vanilla phase” with Italy, but it did seem very easy to get a kind smile from just about any Italian I met throughout the entire trip.

A fraction of the big happy family of IWADC delegates

Attending IWADC 2011 was every bit as pleasant: The conference itself ran like clockwork, the medieval city of Orvieto was a decidedly pretty conference location, and the relatively small size of the conference contributed to the relaxed and friendly character of the event. Almost like a family event – a big happy Italian family, I could imagine :-). The feeling of being welcome and surrounded by “family” was very much accentuated by the hospitality shown by the conference general chair, professor Paolo Carbone (University of Perugia), members of the organizing committee, and other delegates. During the conference dinner when we were also treated with one tasty Italian dish after another, I remember uttering something like “all conferences should be in Italy”. That’s how good it felt to be there.

Who doesn’t love Italian food? I was late to some sessions because I tried to eat all the Salatini before they cleared the tables …

# CWCP winner

A winner: Yu Lin

Now being a solid tradition, each conference I attend needs to have an opportunity to connect with Converter Passion. To motivate conference delegates to not be shy we came up with the Connect with Converter Passion (CWCP) prize. The rules are simple: First blog reader to find me at the conference and claim the prize is the winner, and for IWADC 2011 the winner is Yu Lin, a PhD student at Technical University of Eindhoven who was also presenting the paper “An Input Signal Statistics Aware Design Approach and Examples for Analog-to-Digital Converters for communication systems” at the conference [co-authors: Kostas Doris (NXP), Hans Hegt and Arthur van Roermund (TU Eindhoven)]. It was a pleasure to meet such a motivated blog reader. Yu aimed for victory and did not hesitate to claim the prize already at the informal pre-conference reception at restaurant Maurizio. Definitely the right spirit and a worthy winner indeed. Congratulations! Normally, the competition is only for the glory, but this time a small surprise memento was added in the form of a handmade key ring in black leather produced by “Boothill Bob” from Boothill Bob Holsters.

# The conference

Scientific discussions

Of my own contributions, the first (An empirical approach to finding energy efficient ADC architectures) was about using the measured performance of chips made by others to better optimize your own design, and the second (Using Figures-of-Merit to Evaluate Measured A/D-Converter Performance) treated how to assess the quality of figures-of-merit often used to make comparisons of measured performance.