So, what is a good figure-of-merit (FOM) for analog-to-digital converters (ADC)? What is technically sound? What makes a figure-of-merit relevant, and what is good practice when using it? I’ll not able to cover everything in one post, so the plan is to keep returning to this subject over a number of posts.
What is a figure-of-merit?
“… a quantity used to characterize the performance of a device, system or method, relative to its alternatives. In engineering, figures of merit are often defined for particular materials or devices in order to determine their relative utility for an application. In commerce, such figures are often used as a marketing tool to convince consumers to choose a particular brand.”
Another quote from the Wikipedia entry touches on the question of relevance and proper use:
“When used in deceptive advertising, the deception lies more in the question of relevance rather than truth since the number quoted as a figure of merit may not be enough to determine performance when comparing products.”
As a consumer of whatever is marketed or assessed with a FOM – be it commercial ADC parts or scientific results – I also want to know that the FOM is designed so that anything awarded a state-of-the-art value is what actually has the best performance or is more useful to me. That is a well-conceived FOM. A well-conceived FOM also gives equal value to all objects that have equivalent performance with respect to whatever the FOM is supposed to measure, while an ill-conceived FOM can give widely different values for equivalent actual merits. In short, I would say that:
A good figure-of-merit should accurately reflect the merits of the ADC in the context and for the purpose which the figure-of-merit is used.
You are welcome to share your thoughts on this. What would you expect from a good FOM? What criteria do you use to identify an ill-conceived FOM?
Purpose & context
A figure-of-merit is used for a purpose and in a context. Common purposes include:
- Product performance comparison
- Comparison of scientific achievement
- Identifying the best component for a particular task
The context is also important. If you want to apply a FOM to a set of commercial part specifications to find out which part is the best for your current project, then you can define pretty much any FOM expression you’d like, as long as you know it will help you detect the best circuit. The context is local – your project and your organization. You only have to convince your project team and perhaps the steering group that the FOM is technically sound and will do the job.
If, on the other hand, you wish to propose a FOM that can be universally applied to compare the merits of widely different circuits, the context is global. The demands will be higher – both with respect to the mathematical expression and your ability to convince others that the FOM is sound. We will focus on this latter case.
Universal comparison of merits in a global context
Universal comparison of merits can be divided by at least two major purposes: (I) product comparison and (II) comparison of scientific achievement. When comparing the merits of a product, it doesn’t matter if a FOM is biased towards certain design parameter values. If the FOM correctly represents end user satisfaction, it is irrelevant whether or not you can always achieve a better FOM by reducing power, increasing the voltage supply, or by using a more recent manufacturing technology. If new technology makes the design easier each year, who cares? For the end user it doesn’t matter how easy or hard it was for the engineers to develop the product – as long as the FOM measures how good the product is for the user, it is all well.
When a FOM is used to measure or claim scientific achievement and progress, it does matter if certain corners of the parameter space always gives the best results. Then the FOM becomes a measure of how close you are to that corner, rather than a measure of some universal achievement. This is actually the case with the most commonly used FOM today
It was shown in  that a distinct feature of is that it improves with every step of CMOS scaling. Roughly improves by 100 times for every 10 times of process scaling, as seen in the FOM vs. CMOS node plot above. In practice, it means that organizations that have the possibility to use the latest technologies will always win the race with respect to , while those that refine their design in other ways (without moving to a newer technology node) have practically no chance. Its usefulness as a universal measure of scientific achievement in power-performance trade-off can therefore be questioned.
That said, it should be understood that designing in deeply scaled nanometer technologies is certainly not without challenges. Quite the contrary – it has many design challenges, and it is a scientific or engineering achievement to break new ground and design ADCs in the most recent CMOS nodes. But the point here is the particular FOM and that process scaling almost automatically improves it. A research group that develop innovative architectures or circuit techniques that improve the power-performance trade-off within the same node is therefore much less likely to publish state-of-the-art values than a group that focus on the problems of porting its design to newer technologies. Hence , the most commonly used FOM today, heavily promotes the use of new process technology, and this should be understood when comparing the FOM reported in different papers.
I also want to clarify that I’m not suggesting that those that have defined the state-of-the-art evolution of have effortlessly surfed the wave of CMOS scaling. Many, most, or all of these designs have reached state-of-the-art through a combination of technology scaling and innovative techniques for power reduction. As an example, the design by van Elzakker et al.  currently listed as state-of-the-art on the FOM-o-meter page, combines the advantages of 65 nm technology with a low-energy multi-step switching charge-transfer technique to reach a truly impressive result.
Industrial and scientific relevance
As discussed above, a FOM may have relevance for comparing the performance of commercial products without being suitable for comparison of scientific achievement. In my opinion, has industrial relevance only to the extent that it measures what the buyers truly want from an ADC part. I’m not in a position to fully assess whether is representative of the market demand, or if the market has simply been taught by ADC vendors that “this is what you really want” 🙂 so now the sourcing people keeps asking for it. It would certainly be interesting to hear your thoughts on that – both from a sourcing and from a vendor perspective.
Regarding scientific relevance, , a.k.a. the “ISSCC FOM” has some redeeming features in that it can be shown that an ADC with state-of-the-art is indeed highly optimized with respect to energy per sample. On the other hand, displays such a strong correlation with many design parameters, that it can also be shown that a state-of-the-art can only ever be achieved at certain sweet spots and golden corners within the design parameter space. Its almost canonical status as a global measure of scientific achievement, and possibly even criteria for publication, is therefore in my opinion questionable. Or at least something that needs a serious debate. I’m sure that many of my blog readers have an opinion too, and it would be great to hear what you think. It is no problem if you have a different view, I’d like to hear it anyway. Perhaps you can bring me back to “the narrow path” 😉 …
I hope to get back with more details on sweet spots and corners in future posts, but for now the FOM vs. CMOS node plot can serve as illustration of a “golden corner” with respect to process technology.
FOM discussions in the literature
There are only a few literature references to this post, simply because I’m not aware that any longer discussion of the topic has taken place anywhere. But if you are aware of any scientific papers, business magazine articles, application notes or web pages treating the title question of this post – “What is a good ADC FOM?” – then I’d be very happy to hear about it and to include references to them here. Please use the comment function, or email me.
Bult includes in his ESSCIRC 2009 paper  a brief but good discussion on how the current scientific competition is centered around , and its consequences on power dissipation reporting practices – a topic I will return to in a future post. Bult also reflects on the relevance of and in view of observed and expected correlation between ENOB and P in actual circuits. In Carsten Wulff’s Ph.D. thesis , there is a discussion of figures of merit, and Murmann also discusses the relevance of and briefly in his CICC 2008 paper .
ADC FOM DIY-kit
Now, if after reading this far you are tempted to try your hand at designing your very own and much better ADC FOM, then you have the perfect DIY-kit here at Converter Passion. It will help you to shape and define almost any FOM of your liking. You can always start building it from scratch if you feel adventurous, but why not start with the “Mother of all FOM”, and the generic FOM classes I’ve put together for you.
Enjoy, and don’t forget to share your views on ADC figures-of-merit with the rest of us.
And … if you invent a smashing ADC FOM, or already have published one that I’ve missed, be sure to post it in the comments.
Let me know if you want help getting the WordPress LaTeX to work. It can be used in the comments as well. Here’s an on-line LaTeX equation editor that makes life easier. Because the WordPress LaTeX parser is much less forgiving, the code sometimes need some final polishing before it renders correctly.
 B. E. Jonsson, “On CMOS scaling and A/D-converter performance,” Proc. of NORCHIP, Tampere, Finland, pp. 1–4, Nov. 2010.
 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, IEEE.
 K. Bult, “Embedded analog-to-digital converters,” Proc. of Eur. Solid-State Circ. Conf. (ESSCIRC), Athens, Greece, pp. 52–60, Sept., 2009.
 Carsten Wulff, Efficient ADCs for nano-scale CMOS Technology, PhD Thesis, Norwegian University of Science and Technology, Trondheim, Norway, Dec. 2008.
 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.