Electronic Design
Bob Adams: Navigating The Sigma-Delta Roadmap

Bob Adams: Navigating The Sigma-Delta Roadmap

Adams (2011)

Bob Adams is an Analog Devices fellow. He is known for his contributions to the invention of log-domain filters, the design of the first monolithic asynchronous sample-rate converters for digital audio, and the development of groundbreaking multi-bit sigma-delta converters. Yet he began as “one of those kids who from the earliest age was fiddling with electronics,” he said.

“The 1960s were the era of Heathkits, ham radio, and the space program. I was taking apart and fixing TVs and radios from an early age, and I wandered into ham radio in the sixth grade or so,” Adams said.

“So when it came time to go to college in 1972, I didn’t have to think very hard about what I was going to do. I arrived at Tufts University with a fairly good hobbyist background in the electronics of the day. Back then, Tufts had a pretty heavy lab component to the EE classes, and I liked that. I remember I got particularly excited about digital filters. That was pretty early days for them.”

Adams acknowledges that he got off to a shaky start with some of the more analytical aspects of electronic engineering, but by tackling them on his own time, he got a firm grasp on them.

“I have to admit that all that stuff about differential equations and LaPlace transforms didn’t jell for me until I left school and started to use it,” he said. “I guess I was dissatisfied that I was using this math that I didn’t really understand. So I went back to it and closed the loop, got my fundamentals more in order.”

The Real World

His engineering career has always had a focus on professional audio, perhaps because of another interest—he’s a talented amateur saxophone player.

“When I first got out of school, I worked for a small audio company called ADS. It made speakers and automotive hi-fi systems. I only worked for them for about a year before I went to a company called DBX, an early competitor to Dolby,” Adams said.

“They made noise-reduction systems and a lot of analog processing gear, largely based on novel log/antilog-based voltage-controlled amplifiers and RMS detectors. So, I got a good dose of analog signal processing,” he said.

“One of the early things that fired up my imagination—when I arrived, they were designing RMS detectors using this funny little diode circuit that no one really understood. It just seemed to work. I tackled that from a mathematical point of view and ultimately realized that it was actually a linear filter operating in the log domain,” he said.

“That was one of the earliest things that I got really excited about. I presented a paper about the technology at the AES conference, but the concept lay dormant for 15 years until it was rediscovered in the nineties, and log-domain filters became a hot topic with hundreds and hundreds of papers.”

But that wasn’t sigma-delta. Sigma-delta analog-to-digital technology was known, thanks to Bell Labs, and its use in telecommunications. But it wasn’t ready for high-end audio.

“As audio started to drift into the digital world,” Adams said, “the state of a-to-d and d-to-a conversion was pretty primitive. You could buy these big hybrid bricks from several companies, including Analog Devices, for 40 or 50 dollars each. They’d be manually laser trimmed to maybe a 16-bit level if you were lucky.”

Those were the converters used in some of the earliest digital recorders for audio professionals. At that time, he became interested in the whole topic of oversampled sigma-delta modulation.

“They were used extensively in telecom applications, but no one had ever tried to extend that technology to the professional audio level. I got pretty excited about trying to do that at DBX. I designed a digital recorder based on companded delta modulation and that product was sold into the studio market,” he said.

“That was back in the days when the only other digital recorder was one from Sony. It was a box that converted digital audio into a video signal and then recorded that signal on a video recorder. So I did a 1-bit sigma-delta version of that. It was moderately successful, though not necessarily high-volume. Then I tried to make a more general a-to-d converter based on the same concept with the addition of a decimation filter.”

Semiconductor Strategizing

That was where Adams began his education in semiconductor design and manufacturing.

“Because DBX did not have an integration capability, we teamed up with NEC in Japan. I went over there for sometimes weeks at a time and worked alongside their VLSI guys. I did the system-level design and the decimator design and they did most of the circuit-level analog work,” he said.


“That led to a chip set offered by both companies and we presented a paper at ISSCC about what was probably the first audio converter with greater than 16-bit resolution.”

Not that Adams was the only person thinking about sigma-delta in those days.

“I didn’t know it at the time, but the folks at Crystal Semiconductor were working at the same pace, and we came out with products at roughly the same time,” he said.

“The main guy behind their early converters was Dave Welland, who had also worked at DBX. Later, he came to Analog Devices and we worked together again. Then he went off to become one of the founders of Silicon Labs. Also, back in the early days, you’d have to say that Philips Research did a lot of groundbreaking work.”

The ISSCC paper and good marketing led to respectable sales of the DBX/NEC chipset. But by 1988, DBX had run into financial troubles and Adams sensed that it was time to move on. The move from a small company to a big one was a heady experience.

“When I started at Analog Devices I went from being a big fish in a small pond to being thrown in with a bunch of world experts on everything you could imagine,” Adams said.

“Besides myself, there were a few other young upstarts who were interested in pushing the sigma-delta concept. Paul Fergusson was one. His knowledge of circuit design and the IC design process was greater than my own. I was playing more of a system role then, while he was more circuit-oriented.”

One major design issue being attacked at multiple companies was the stabilization of high-order loops.

“The early telecom parts that we all started from came out of Bell Labs. They were second-order loops. A guy by the name of Jim Candy did a lot of that work. So, myself, and some folks at Phillips, as well as Dave Welland at Crystal Semiconductor, all three of those companies were, in isolation, tackling this challenge of how to stabilize a high-order loop,” Adams said.

“I had done a fourth-order loop, and later when I came to ADI, Paul and I did a fifth-order loop. There were some companies that might have done even higher-order loops. That was the name of the game back then.”

Then things changed.

“People realized that somewhere between a 16-bit SAR (successive approximation register) and a 1-bit sigma delta, there could be an in-between stage, where instead of a 1-bit sigma delta, you could make a 3- or 4-bit sigma delta,” he said.

“There were all sorts of benefits that came with that, one of which was that, suddenly, you could go back and implement simpler loop filters—like a second-order loop, which was easier to stabilize,” he said.

“That meant you had traded in one set of problems for another. Instead of stabilizing high-order loops, all of a sudden, you had to worry about matching—a problem that we’d gotten away from with the 1-bit sigma deltas.”

But Adams and others “figured out how to do this so-called mismatch shaping, where you sort of scramble the elements around in such a way that any mismatch error turns into shaped noise,” he said.

“I was working with Tom Kwan at the time and he and I jointly cracked that nut and published some papers.”

Today And The Future

In the last 10 years, Adams has drifted into audio DSP architectures and algorithms and was responsible for starting the “sigmaDSP” line of graphically programmed audio processors. He also has some opinions about contemporary challenges in analog design.

“One of the bigger practical problems today arises when you want to make a mixed-signal part that has high-performance, high-resolution converters on the same die as a big monster digital section,” he said.

At extremely small design rules, the area of the analog portion doesn’t really scale down, so you wind up with very expensive converters, just based on the silicon real estate. In addition, you also have to contend with the mediocre performance characteristics of the transistors that are available to you at those nodes as well as the very noisy environment.”

That leads to some insights about matching converter design to process technology.

“If you’re just making a standalone converter, you might choose a different process node than if you are making a converter that’s integrated with a huge DSP. The approach you take at the system level for the conversion architecture may be dramatically different in each of those two cases,” he said.

“For example, in the case with the big digital core next to you, you might decide to use some of the power of that DSP to correct for the deficiencies in the converter. So the trick becomes a sort of co-design effort where you allow the analog part of the design to be sloppy in areas where the digital processing can fix things up,” Adams explained.

“But that means also knowing where you actually have to hold the line and do things properly in the analog domain. I’d say that’s the biggest problem—how you marry high performance analog at these very small process nodes.”

Adams also has some opinions about how things have changed since he got out of college, though he looks for some particular qualities in new college graduates.

“We’ve had good luck with new hires. We have a fairly rigorous interview process and give some pretty detailed technical quizzes. There used to be a joke around here that you may be hiring someone for a software position, and they’re still going to have to be able to draw an op amp, but that’s changed recently,” Adams said.

“We do tend to get candidates who are circuits-oriented, though, and we look for people who have an intuitive ‘feel’ for the circuits, whether or not they can write out the equations. You have to do more than just write out the equations, you have to be able to interpret them.”

Selected Works

Bob Adams was a frequent author and contributor to journals and conferences. Here is a small, select list of some of his most influential works.

  • “Filtering in the Log Domain,” Fall AES, 1978: This paper, rediscovered in 1990, was the first discovery of the log-domain filtering principle and has resulted in 100 IEEE papers and numerous thesis works.
  • “Companded Predictive Delta Modulation: A Low-Cost Conversion Technique for Digital Recording,” Spring AES, 1983
  • “Design and Implementation of an 18-bit Audio A/D Converter using Oversampling Techniques,” Spring AES, 1985
  • “A New Windowing Technique for Digital Harmonic Distortion Measurement,” 1986 IEEE Workshop on applications of Signal Processing to Audio and Acoustics
  • “One-Bit Higher Order Sigma-Delta A/D Converters,” ISSCC 1990 (co-author)
  • “Design of Single-bit Noise-shaping Loops with High-order Loop Filters,” Fall AES, 1990
  • “Theory and Practical Implementation of a Fifth-Order Sigma-Delta A/D Converter,” Spring AES, 1991
  • “Jitter Analysis of Asynchronous Sample-Rate Conversion,” Fall AES, 1993
  • “Spectral Noise-Shaping in Integrate-And-Fire Neural Networks,” International Conference on Neural Networks, 1997
  • “Integrated stereo Delta-Sigma Class-D amplifier,” JSSCC, Dec. 2005
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