Tag Archives: trends

ADC Energy Efficiency Trends


Fig. 1. State-of-the-art energy per sample vs. ENOB in five-year steps from 1983 to 2013.

Fig. 1. State-of-the-art energy per sample vs. ENOB in five-year steps from 1983 to 2013.

ADC ENERGY EFFICIENCY EVOLUTION: What are the trends for ADC energy efficiency and why did the “Walden” figure-of-merit get almost canonical status when it doesn’t fit to current data? Read on, and you’ll know.

Evolution front

Figure 1 shows how the state-of-the-art boundary for energy-per-sample (Es) vs. effective-number-of-bits (ENOB) has progressed over time in 5-year steps from 1983 to 2013. The energy vs. resolution dependencies suggested by the Walden and Thermal figures-of-merit (FOM) have been indicated as the Walden and Thermal slope, respectively.

Snow cone scatter

The most immediately striking feature in Fig. 1 is that the curves are increasingly more separated at lower resolutions, and tend to group more closely together as ENOB increases. With the Thermal and Walden slopes overlaid as in Fig. 1, you get a kind of “snow cone scatter plot”. It means that the energy efficiency has improved far more for low-resolution ADCs than for high-resolution converters during the 30 years of research covered by Fig. 1. A possible explanation for that is the fairly low number of attempts reported above 15-b ENOB. Another reason could be that the power dissipation at ultra-high resolution almost inevitably becomes limited by thermal noise constraints, and that the few reported designs were carefully optimized. As an example, the work by Naiknaware et al. [1] is the only scientific ADC reporting an ENOB > 20-b (other works only report static linearity or measures that did not resolve to an SNDR value). Although Naiknaware’s design was reported as early as year 2000, it is still on par with today’s noise-limited state-of-the-art. That’s quite impressive!

Slope twist

A second distinct feature in Fig. 1 is that the slope for Es vs. ENOB has changed over time from an almost perfect Walden FOM model (doubling of Es per additional bit) to an almost perfect Thermal FOM model (quadrupling of Es per additional bit).

This explains the great mystery of the Walden FOM and its near-canonical status: Even as late as 2003, the state-of-the-art edge aligned very well with a Walden model. In fact, the Walden model remained true to empirical data all the way to 2007. By 2008, however, the experimental data had started to break away from the Walden slope – something that was also noted by Murmann in his well-known CICC 2008 paper [2] – and by 2013 the experimental data fits more or less perfectly with the thermal-noise model.

The van Elzakker leap

The single most influential contribution to this shift is probably that by van Elzakker et al. [3] as it represented nothing less than a quantum leap in energy efficiency for ADCs in the lower mid-range of resolutions. It gave us a new experimental data-point that completely redefined the energy landscape as it showed their medium-resolution design to be pushed all the way to the thermal-noise power limit of 2008. I believe their contribution broke a mental barrier for many regarding how far you can actually go, and what is the real energy limit. Over the last five years, other authors have followed by reporting more experimental data – both filling the gap created by the van Elzakker leap and pushing efficiency even further [4]-[6].

Low-resolution plateau

As always, we have the low-resolution plateau. There is a slight tendency towards a plateau already in the 1998 curve, and by 2003 it was fully visible – although at a much higher Es level than today’s plateau. Figure 1 also shows us that there has been significant progress at resolutions below 9-b over the 20 years from 1988 to 2008, but almost no movement at all during the last 5 years. The relative amount of attempts below 9-b (~35%) has remained the same both before and after 2008, so it should not be due to lack of interest.

Any explanations you might have would be very interesting to hear. Pure speculations are fine too 😉

Hopes and expectations for the future

In coming years I would expect to see progress in the 10–13 bit region, which seems to be a bit underexplored at the moment. We saw an extension in this direction by the most recent state-of-the-art work by Harpe et al. [4]. I hope that future authors will continue to push the resolution for ultra-efficient ADCs. It should be possible to “iron out the wrinkles” on the current state-of-the-art border. It would be particularly nice if we could populate the border with evenly spaced SAR implementations spanning all the way up to the high resolution of commercial SAR ADCs.

I also hope that someone will explore the empty space below the low-resolution plateau. It seems to be a lot of data points missing there that could give us a better understanding of the true energy limits.

More data at ultrahigh resolution – please!

Finally, I want to plead to those of you designing ultrahigh resolution ADCs to start including traditional dynamic performance measures (at least SNDR) even if the target application you’re imagining doesn’t care about it. If nothing else, it would increase your visibility in my scatter plots, but the main benefit for our science is that we would get more experimental data and a better understanding of the design space for “20-b and beyond”.

So, please … 🙂

References

  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  6. 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.

New minor revision: A/D-converter performance evolution (v1.1)


T13001-ThumbNote that the recently released A/D-converter performance evolution “eBook”/PDF, has been incremented to v1.1 due to a mistake with Figure 6.3. The latest release can always be reached from the Document Download page. If you pass links around, be sure to link to that page instead of any direct link to a specific release.

My sincere apologies to the 38 readers who downloaded the document during the first hours.

Now as a free eBook/PDF: A/D-converter performance evolution


Updated (see below)!

I’m happy to see that the “A/D-converter performance evolutionarticle has become the most popular content on Converter Passion. There’s a huge amount of research work put into those ten posts, so I’m glad you liked it.

T13001-ThumbBut even the most die-hard fan of scatter plots and performance trend estimates may find it tiresome to have to click their way through the ten blog posts.  I even feel a bit lost myself from time to time. For your convenience (and mine too), I have therefore made the whole lot available as an “eBook”/PDF, which you can download here (4.8MB). It’s an almost exact replica of the original on-line content, so if you’ve read the original Converter Passion article there’s nothing new here. But it’s likely you find the format much easier to read. I certainly do.

If you’re working with ADCs, you have probably already clicked the link – it’s an absolute no-brainer: A 50-page fully functional PDF with 44 pages of content, 24 illustrations and 92 references. All for free.

Happy reading!

Update 2013-01-07: My sincere apologies to the 40 or so that have downloaded it already, but there was a bug with Fig. 6.3 (it was 6.2 duplicated). The correct graph has now been inserted in v1.1. of the document. Many thanks to EJ & Henk at Catena!

Book Review: Advanced Data Converters


BOOK REVIEW: Are you looking for a more complete data converter overview than you get from Converter Passion blog posts or by maintaining your own library of recent papers? Perhaps you’re just wishing to catch up on the latest technology or get a helicopter view to see what’s outside of your own patch in the data converter field? Have you been longing for a contemporary data converter summary that is easy to read, yet rich with technical detail? Read on to know if Advanced Data Converters by Gabriele Manganaro is the book you’ve been looking for.

Book at a glance

Advanced-Data-ConvertersAdvanced Data Converters is not the regular tech tome. The actual content only spans slightly more than two hundred pages, followed by a comprehensive reference section listing over 400 relevant works. Of the five chapters, two are introductory in nature, and the remaining three respectively covers ADC, DAC and Trends. On first glance this made me wonder if there was actually anything in the book. Don’t worry, though. Advanced Data Converters is a masterpiece of lossless information compression that may even go beyond the limits of information theory as we know it 🙂

Let me say right from the start that this is a really good book. The author is clearly a gifted writer and has delivered a text that simply flows. It reads more like an interesting story than a technical lecture. Although the topic is advanced, the form never gets in the way. It is concise, professional in style, yet sufficiently relaxed and easy on the brain. Most of us can appreciate what an achievement that is.

Key chapters

The chapter on A/D converters includes a review of underused classic architectures now brought back into the game to overcome the challenges imposed by CMOS scaling. Time-interleaving, calibration, and emerging architectures and techniques – often introduced for the same reason – are also discussed. The story told in this chapter is so in tune with what I’ve observed through my own survey that I actually don’t have a single suggestion as to what could have been added or taken out. It is indeed a very accurate and insightful description of how the field has developed lately. The number of different architectures and techniques covered in a relatively limited space is truly impressive.

A slightly different approach was used in the D/A converter chapter, where “precision” DACs where left out in favor of current-steering DACs. Instead, these are given a more thorough treatment – essentially you get a complete rundown on the key design issues for this type of DAC. This worked very well for me. Ending the chapter is an update on the latest developments on high-performance and specialized DACs.

Finally, there’s a chapter on data converter trends. As the faithful Converter Passion reader may suspect, I’m not easily impressed with scatter plots and survey data trends. Quite unsurprisingly, this is the chapter where I’m instantly itching to jump into the discussion, add a few graphs, discuss what the plots actually show, etc. That’s not necessarily a bad thing, though. Just as the previous two chapters inspire the reader to look deeper into emerging ADC/DAC architectures, it is a good thing if this chapter encourages the reader to become a more active and educated user of survey data. Analogous to the rest of the book, the author has managed to collect an impressive amount of information in a very limited space. The ADC part is split between a summary of several surveys by other authors, and some original work using the Murmann data set. The DAC part reflects the present lack of any large DAC survey, and therefore the trends are estimated from a very small set of data.

The more colors, the better ...

The more color, the better …

The book as a whole

Advanced Data Converters does not start from scratch, but from a point where the reader is assumed to be familiar with the basics of data conversion, sampling, signal processing and IC design. There are numerous references to where the basics are treated, and even if the level is “advanced”, it never gets scary or impenetrable. If you’re relatively new to the field, you could very well enjoy the book anyway.

For more senior scientist, designers, or data converter end users, the book is a veritable goldmine of information. It successfully captures just about everything necessary to catch up with the latest data converter developments. It allows you to understand the essential technical issues and driving forces that shape the data converter field. None of the topics are treated in great depth, but the amount and quality of references for further reading is impressive. The book delivers a feature-rich helicopter view of the entire data converter field that encourages further exploration. It also provides you with a solid framework – a “grid of knowledge” – in which you can place your own bits and pieces as you pick them up.

This is not a book that will bypass the 6–8 years it is said to take becoming a reasonably good data converter IC designer. Neither will any other book. But keeping it as a companion will probably ease the pain of those years considerably. It will also make the constantly changing data converter landscape a bit less confusing. This book is both educational and a source of inspiration for new adventures to all of us that feel we have more to learn. If you truly believe you know it all, then it might still be worth buying it solely for the excellent list of references.

FiveYou can probably guess by now, what the rating will be. Since this is the first book review on Converter Passion, I had made a firm decision to save some headroom at the upper end of the full-scale range. That was the plan. But Advanced Data Converters is one of the best written tech books I’ve ever read, so it would not be correct to give it anything but the highest grade – 5 out of 5.

BTW: If your grandmother gave you money for Christmas, this book might be what she had in mind 😉

Find the book at Cambridge University Press

A survey of ADC surveys


Figure 1. Accumulated publication count for scientifically reported ADC implementations in mainstream IEEE sources. The number of publications equivalent to 20% of total is indicated for reference.

SURVEYS GALORE: If the ten posts long A/D-converter survey just concluded did not fully satisfy your desire for scatter plots and tech trends, then this post will provide a list of prior ADC survey works as suggested “further reading”. In fact, I’d recommend everyone serious about data-converter technology trends to get hold of these documents. The list will also serve as a brief history of the ADC survey field. But first some thoughts on surveys:

Survey characteristics

When is it a “survey”? — I’m not going to spend too much energy on a stringent definition of a “survey”. My guideline is that a survey should be based on a significant amount of data, and that the visualization, discussion and interpretation of the data is the main work. Many scientific papers nowadays include a scatter plot that compares a particular design with 5–20 relevant prior efforts. While it’s a good idea to do so, these papers are not considered surveys in this context. Others use large amounts of empirical data to validate or derive a model, but the focus is more on the model.

What is “a significant amount of data”? — The size of the survey should be related to the total amount of data available at the time of the survey. A survey of 200 papers would have been exhaustive in 1990. Today it represents less than 12% of all scientific publications. The accumulated amount of scientific papers over time is shown in Fig. 1. While this is not the absolute total number of ADC publications, it covers the ADC implementations reported in nearly all journals and conferences central to the A/D-converter field, and shall for simplicity be referred to as the “total” amount here. The number of sources equivalent to 20% of the accumulated total at any given time is also shown in Fig. 1.

So, how much of the total do I need? Well, it depends on what you’re trying to do. When it comes to survey data, I’m a firm believer in “the more the merrier”, but there are tasks which can be done with a fairly small subset. For example, if you want to get an idea of the overall trend for one parameter vs. another or just make a quick sanity check.

Small subsets do have some limitations though. For the subset to function as a reasonably generic approximation of the exhaustive set, its data must span roughly the same chunk of parameter space, and have similar distribution of values in all dimensions. This is difficult to achieve unless you make a random sampling of the exhaustive set. A smaller set also risks running out of data, for example when dividing it further according to some parameter such as resolution or architecture.

How quickly will a survey become dated? — I really don’t know. I guess it depends on what you wish to study. But we can observe, as in Fig. 2, how the accumulated total at any given time relates to the overall total (here 1708 papers), and what percentage of currently available works were yet unpublished at any given time (e.g., at the end year of a particular survey). It is seen that approximately 50% of all currently available papers (~Q1-2012) were published in the last 8–8.5 years, i.e., after 2003, and almost 30% were not yet published in 2007. By the end of 1997, 70% of today’s body of empirical data was still unpublished.

You can use Fig. 2 to assess how old a survey can be before it’s no longer useful for your purpose. Can you make business decisions based on trend estimates where the most recent half of the data set is missing? Probably not. Most recent 30/20/10%? If so, you need a survey that’s less than approximately 4/3/1 years old.

It is clear that continuously updated surveys, such as Murmann’s, or the one used here at Converter Passion are preferable over single-shot attempts, since the former allows for continuously updated trend estimations.

Figure 2. Paper “yield”. The fraction of current total already published (blue) and yet to be published (red) at the end of any given year.

Known ADC surveys

Author Size Years Type What Ref
Walden 100 ≤ 1994 Both Perf. limits, FOM [1]
Walden 150 1978-1997 Both Perf. limits, FOM, jitter, evolution [2]
Merkel 150 1993-2002 Both Perf. limits, SFDR, power, VDD, scaling, device, arch. [3]
Le 1000 1983-2004 Parts Perf. limits, jitter, cost, arch., no. chan, N [4]
Walden 175 1978-2007 Both Update++ [5]
Walden n/a 1978-2008 Both Update [6]
Murmann ~260 1997-2008 Sci Perf. limits, VDD, scaling, FOM, evolution [7]
Jonsson 1400 1974-2010 Sci Perf., VDD, scaling, FOM, evolution [8]
Jonsson 1100 1976-2010 Sci Perf. & FOM vs. CMOS scaling, evolution [9]
Fuiano 5540 1970-2010 Sci Data-converters, research/patent correlation [10]
Jonsson 1400 1974-2010 Sci Energy/sample by arch [11]
Jonsson 1500 1974-2011 Sci Area eff by arch [12]
Murmann ~350 1997-2012 Sci Online survey data [13]
Jonsson 1700 1974-2012 Sci Perf., VDD, scaling, jitter, SFDR, FOM, evolution [14]

About the surveys

Walden

The “mother of all ADC surveys”, and the most frequently cited of all, is the pioneering work by Walden [2] where 150 scientific and commercial ADCs were analyzed, and performance trends were extracted. An earlier version was published already in 1994 [1], but this extended work became “The Walden Survey” to most of us. Although the 150 source documents originated from a mix of commercial and experimental designs, the Walden survey had a size equivalent to 30% of all scientific publications available at the time. The methods introduced in [2] are still useful, but Fig. 1 and Fig. 2 suggest that the trends extracted in [2] are unlikely to be valid and applicable today. At least they would have to be confirmed using more recent data. Two updated versions of the survey were published in 2008 – one covering 175 ADCs and data until 2007 [5], and one with an unspecified survey size and data until 2008 [6]. It is unclear how the 175 converters included in [5] were selected. During the time from Walden’s classic survey to 2007, the academic output alone generated another 715 new sources – commercial parts not counted. The +25 increase in source data therefore seems surprisingly incremental. Still, some of the results in [5] align very well with Converter Passion data, so apparently it was a carefully chosen subset.

Merkel & Wilson

Merkel and Wilson surveyed 150 commercial and scientific ADCs with specifications suitable for defense space applications [3]. Their data appear to span from 1993–2002, and the selection criteria for inclusion in the survey was a sampling rate fs ≥ 1 MS/s, and nominal resolution ≥ 12 bits. The paper does not reveal the mix between scientific papers and commercial parts, but gathering 150 sources must have been quite an effort by the authors. The total scientific output matching these specs and the time period is no more than 81 papers, and only 59 in the two sources (ISSCC, JSSC) the authors mention as primary. An additional minimum of 69–91 commercial parts must have been included to reach 150 sources. It is therefore assumed that the Merkel & Wilson data set was close to exhaustive for the spec range surveyed, and exhaustive data sets are always applauded here at Converter Passion.

The analysis and discussion itself is geared towards the stated application and focused on linearity (SFDR) to the extent that noise parameters are not treated at all. Power dissipation, supply voltage, speed, device type, scaling and architecture were observed.

Le, Rondeau, Reed & Bostian

An enormous data set, covering nearly 1000 commercial ADC parts from 1983–2004 was used in the survey by Le, Rondeau, Reed and Bostian [4]. As a comparison, the scientific output from the same years (not included in their survey) is 900 papers. The work is firmly rooted in the Walden tradition, but also considers parameters such as the number of channels per package and cost vs. performance. Additionally, the treatment separates the data by architecture, which adds an interesting extra dimension. Because of the larger volume and time span of the data set, part of the focus is to establish differences between this work and the classic Walden paper. Unfortunately, some exponentially improving parameters were plotted along linear axes, which makes many results from the survey difficult to see or interpret. Nevertheless, the contribution by Le et al. is a gigantic work and a key reference.

Murmann

The survey by Murmann [7] is a significant recent contribution to the analysis of empirical performance data. It covers approximately 260 scientific ADCs reported 1997–2008 at the two conferences VLSI Circuit Symposium and ISSCC. The work analyzes ADC performance trends with a focus on energy per sample and signal-to-noise-and-distortion ratio (SNDR). The impact of process and voltage scaling is considered. If you don’t have this paper already, you should definitely head over to IEEE Xplore and get it right now.

Murmann’s survey has further benefits in that it is continuously updated and the data set is available online [13]. The latter opens up a lot of possibilities for anyone wishing to analyze the data in their own way, and makes the survey a very important contribution to the field. It currently includes around 350 sources.

Fuiano, Cagnazzo & Carbone

A rather different angle is taken in [10], where Fuiano, Cagnazzo and Carbone use survey data to analyze the correlation between scientific literature and patent activity. Compared to more “Waldenesque” surveys, this is a rather different animal. It nevertheless appeals to me as it illustrates an attempt to mine large amounts of survey data for something more unusual than ENOB, fs and FOM.

Jonsson

The ADMS Design data set used here at Converter Passion has also been used in five scientific papers, of which four are “surveys”:

  • ADC trends and performance evolution over time was analyzed in [8].
  • The impact of CMOS scaling on ADC performance was empirically analyzed in [9].
  • ADC architectures were compared with respect to energy efficiency in [11].
  • Area-efficiency of ADC architectures was surveyed in [12].

The largest survey for which this data set has been used so far is the recently published series of posts on A/D-converter performance evolution [14].

Other survey-related literature

A few other prior publications that are “survey-ish”, or otherwise use a large set of empirical data for their analysis are listed here:

  • Vogels and Gielen used a multidimensional regression fit to derive an ADC power dissipation model/FOM based on ≥ 70 empirical data points divided by architecture [15]. A similar approach was recently used by Verhelst and Murmann to analyze power dissipation and area vs. scaling based on Murmann’s data set [16] .
  • Sundström, Murmann, and Svensson derived theoretical power dissipation bounds in [17], and used the Murmann set to compare theory with empirical reality.
  • In [18], it was illustrated how the quality of a figure-of-merit (FOM) can be assessed by testing it against a large set of empirical data.

If you feel that I’ve left out any contributions that could have been mentioned in this post, just add a comment below.

See also …

ADC survey data

A/D-converter performance evolution

EveryNano Counts: “Those ADC Literature Surveys”

References

  1. R. H. Walden, “Analog-to-digital converter technology comparison,” in Proc. of GaAs IC Symp., pp. 228–231, Oct., 1994.
  2. R. H. Walden, “Analog-to-digital converter survey and analysis,” IEEE J. Selected Areas in Communications, no. 4, pp. 539–550, Apr. 1999.
  3. K. G. Merkel, and A. L. Wilson, “A survey of high performance analog-to-digital converters for defense space applications,” in Proc. IEEE Aerospace Conf., Big Sky, Montana, Mar. 2003, vol. 5, pp. 2415–2427.
  4. B. Le, T. W. Rondeau, J. H. Reed, and C. W. Bostian, “Analog-to-digital converters [A review of the past, present, and future],” IEEE Signal Processing Magazine, pp. 69–77, Nov. 2005.
  5. R. Walden, “Analog-to-digital conversion in the early twenty-first century,” Wiley Encyclopedia of Computer Science and Engineering, pp. 126–138, Wiley, 2008.
  6. R. H. Walden, “Analog-to-digital converters and associated IC technologies,” in Proc. Compound Semiconductor Integrated Circuits Symp., Monterey, Oct. 2008, pp. 1–2.
  7. 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.
  8. 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.
  9. B. E. Jonsson, “On CMOS scaling and A/D-converter performance,” Proc. of NORCHIP, Tampere, Finland, Nov. 2010.
  10. F. Fuiano, L. Cagnazzo, and P. Carbone, “Data Converters: an Empirical Research on the Correlation between Scientific Literature and Patenting Activity,” Proc. of 2011 IMEKO IWADC & IEEE ADC Forum, Orvieto, Italy, pp. 1–6, June, 2011.
  11. 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.
  12. B. E. Jonsson, “Area Efficiency of ADC Architectures,” Proc. of Eur. Conf. Circuit Theory and Design (ECCTD), Linköping, Sweden, pp. 560–563, Aug., 2011.
  13. B. Murmann, “ADC Performance Survey 1997-2012,” [Online]. Available: http://www.stanford.edu/~murmann/adcsurvey.html.
  14. B. E. Jonsson, “A/D-converter Performance Evolution,” Converter Passion, Aug., 2012, Available: https://converterpassion.wordpress.com/articles/ad-converter-performance-evolution/.
  15. M. Vogels, and G. Gielen, “Architectural Selection of A/D Converters,” Proc. of Des. Aut. Conf. (DAC), Anaheim, California, USA, pp. 974–977, June, 2003.
  16. M. Verhelst, and B. Murmann, “Area scaling analysis of CMOS ADCs,” El. Letters, Vol. 48, No. 6, pp. 315–315, Mar., 2012, IEE.
  17. T. Sundström, B. Murmann, and C. Svensson, “Power dissipation bounds for high-speed Nyquist analog-to-digital converters,” IEEE Trans. Circuits and Systems, pt. I, vol. 56, no. 3, pp. 509–518, Mar. 2009.
  18. 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.