PURIFI Audio and the Audiophile Style reader's Q&A with Lars Risbo & Bruno Putzeys

Audiophile Style has already introduced to you PURIFI Audio in a quick manner last month, when we reported from a sneak listening on their prototype Class D amplifier board and the newly developed long-hub transducer in Munich.

Two of the principal owners of the Danish High End upstart, Lars Risbo and Bruno Putzeys from Belgium, then have agreed to the idea of an Q&A with you, our readers, in respect to all the questions that come along with new products and advancements in Class D amplification and transducer technology. You have left us with a bunch of great & challenging questions, however, Bruno and Lars have delivered answers with grace, passion and fire.

Before we start with the entertaining excursion into the world of audio engineering, I think we should show some love and respect to the people behind the enterprise called PURIFI Audio ApS. which happens to have its headquarters in of the most mystical places in Denmark when it comes to music performance arts.

This is the moment to ask you for some of your precious time reading about the people behind the scenes, an extraordinary conglomerate of senior engineers in the audio industry, which share an important background in work and education since more than 25 years. 

Beyond the obvious duality of these respected audio engineers and inventors, the company PURIFI Audio ApS could also be seen as a "supergroup" of Danish engineering knowledge, however with an important Belgian flavour. I'd suggest "Twin Peaks & Les Purifiens"

If you imagine them as band set up, you could see the co-founder, Danish entrepreneur Peter Lyngdorf, as the music loving manager of this exciting instrumentalists. A well-networked personality and guiding light, who takes care that all that virtuosity will find its place in real life products.

The rhythm section may consist of Claus Neesgaard, the CEO of PURIFI, on bass, and Carsten Tingaard, co-owner of the subsidiary PURIFI Transducer Technology ApS, on drums controlling the pace and the backbeat. The guitar section would include the experienced Kim Madsen on rhythm guitar and Sören Paulsen on lead. Lars Risbo would play the cello (as he does in real life!); piano and lead vocals are  contributed by Bruno Putzeys, while Morten Halvorsen takes on the Light and Sound engineering department. 

Like any supergroup dedicated to artistic success, they may grow as an entity, that respects the special virtues of all members for their common goal "Building a Straight Wire to the Soul of Music", never forgetting that in the best of outcomes, the whole will be more than the sum of its parts.

This is a special moment to cite Aristotle's work on metaphysics (book VIII, 1045a.8–10)

"The totality is not, as it were, a mere heap, but the whole is something besides the parts".

Mission accomplished!

Hence, this band would definitely play the mystical Roskilde Open Air in Denmark, the biggest festival in Northern Europe, as local headliner. My safe bet would be, they'll open the festival on the Orange Stage in front of 60.000 people. Why, you may want to ask?  Just because the opening act for that extraordinary moment is natively dedicated to local bands from the region. And, in my imagination,  they would start with  a Cello-adapted version of the “John Coltrane’s Class D Stereo Amplifier Blues” from The Dream Syndicate! … I got some fine wine in the freezer mama … 😉

Roskilde 2019 opens on June 29th, this time sporting Bob Dylan, Robert Plant as well as The Cure for headliners, and in real life, "Twin Peaks & les Purifiens" are as close as it gets:

Less than a mile as the crow flies!!! 

There's literally just the transportation corridor, that cuts the direct access from their headquarters to the festival area.

The premises were once the facilities and the laboratory of Point Source Acoustics, which Carsten Tinggaard incorporated into PURIFI as co-owner of the subsidiary PURIFI Transducer Technology. Carsten, MSc in engineering from DTU (Technical University of Denmark in Copenhagen), who loves rainforest /jungle trekking and mountain walking, does not only look like fit in his 40s (he's born in '71), though he has already achieved an impressive career as Head of R&D and audio engineering with Danish speaker brands Peerless, Tymphany, ScanSpeak and Vifa. In Denmark he is well known for his collaboration with Danish design furniture manufacturer Montana in 2013/14, which yielded in the smart furniture integrated music system that was called Montana by Pointsource, connecting in-built speaker with amplifier and Airplay / DLNA endpoint to your personal streaming device.

The second, and we are not finished yet, alumnus from DTU, is Claus Neesgaard, co-owner and CEO of PURIFI since October 2017, when the company secured enough "local" expertise from TI Denmark to get into stealth mode for active product development. Claus started his career in 1998 with Toccata Technology, which was founded by Lars Risbo in 1996, until the year 2000, when the company was bought in an act of European engineering talent acquisition by Texas Instruments from Dallas, USA. Since then, he made the steps towards the experienced industry veteran he is now after 17 years with TI Denmark, acquiring skills and personal development within senior positions in Site/Business/R&D Management apace with Lars. He is co-owner of PURIFI Audio ApS since May 2018 and holds an MSc in Engineering and 7 audio related patents.  

Claus is the executive leader of PURIFI Audio, which principally is a highly specialized R&D facility and patent holding company. Their focus lies on monetizing their inventions based on the numerous patents that are involved and upcoming within their product lines. Beyond licencing their technologies to manufacturers like NAD or Lyngdorf Audio, a DIY line of products is in the running. Claus allowed me to announce that there are a 40A version of the Eigentakt ("Big Brother") and a family planning around the woofer, with 4' and 10' driver, in the making. They look vivaciously forward to an exciting 2020 ...

At PURIFI, Claus was joined by Kim Nordtorp Madsen, a specialist in Class D Power stages and SMPS development and a longtime colleague at TI, as Application Manager. Kim received his MSc E.E. already in 1991, worked for Alcatel and Dynatech previously to joining Toccata Technology in 1998. Before siding with PURIFI, he had been with Lars and Claus at TI Denmark for 17 years. Kim holds 5 US patents and several patent disclosures.

Søren Poulsen, the "lead guitarist", has received his PhD from DTU in 2004, but worked part-time with Toccata during his M.SC.EE and joined the band - don't be surprised - in 2004 @ TI Denmark -  where he held the role as lead system designer for more than 11 years. He holds as well 5 US patents in audio related technology.

The youngest alumnus from DTU is Morten Halvorsen. Morten worked as Senior Acoustic Engineer at PointSource Acoustics, where he co-developed both, the loudspeakers and the sound unit of the Montana Sound, and Sound By PointSource products. He holds an MSc.E.E with specialization in acoustics  and has significant expertise in electromagnetic simulations, measurements and procedure optimization..

We have already heard with a short flicker of my eyes in April that Class D stands possibly for Denmark, and what looks like a reasonable joke, proofs quite seriously different in reality.

No joke at all, but hard facts: Deputy Head for the Department of Electrical Engineering @ the DTU, Professor Michael A.E. Andersen, had been the academic mentor for majority of the Purifiens as well as for legions of other Danish audio inventors, having guided Claus, Kim, Sören and Lars into Class D and prepared them for their journey through their M.Sc. EE respectively PhD projects during the Nineties.

When the company was founded in its actual form in 2017, our guests in the Q&A, Lars Risbo and Bruno Putzeys, teamed up with Peter Lyngdorf, the Danish audio industry legend, who knew Lars since 1998, when he based the TacT Millennium on technology developed by the Toccata team, prior to the TI acquisition. TacT could be seen as the company that laid the foundation of Lyngdorf Audio as we know it today, with its innovative development and use of digital room correction. Here is a website that gives you some background on the work of Tact Technology and a comprehensive description of the TacT Millenium Mk2 (German only, please use Chrome with translate to view in English).

Mr. Lyngdorf, who owns one of the biggest audio retail chains in Europe, HiFi Klubben (The HiFi Club), Snell Acoustics (USA), AudioNord, DALI and Steinway-Lyngdorf Audio amongst other investments, is the most senior industry figure you could imagine in Danish audio. As former owner and CEO of Gryphon Audio Designs and NAD Electronics (1991-1999) he may have been significantly involved with the cooperation of NAD and PURIFI, that was announced during the Munich High End 2019. Beside his entrepreneurial relevance, it's understood that his passion for technology and the pursuit for best possible musical reproduction were the main drivers for implementing PURIFI Audio.

Finally we arrive at the lead protagonists of this article, the Twin Peaks (or Yin and Yang? Glimmer twins? Soul brothers?) of Class D amplification, Bruno and Lars.

Meeting them in person in Munich made me feel like a fanboy, overwhelmed with an endless fluid of tech & maths from some really smart people. Working with them on this publication has shown how well these brilliant minds blend in science with a fundamental positive attitude.

In my personal opinion, their catalogue of answers represent an enlightening case about how much fun serious science can be. Both have several time accentuated, that PURIFI Audio is a group activity, not a personal show of solo-ists, as it would appear on first glance.

Lars Risbo, who learned his instrument at the age of 10, had been the former principal cellist of the Copenhagen Youth Symphonic Orchestra (KUSO) for 10 years. His departure coincided with the final year of Toccata Technology, before the company was incorporated by Texas Instruments. Lars describes himself as "in love with life and learning". Bruno told me that his "twin" still continues with his passion by playing in professional orchestras.  Lars is the perfect example of a passionate musician that turned into an inventing engineer of highest degree. He was then - in university - on his personal mission, creating the sonic experience he felt inside the symphonic orchestra with electronic devices for sound reproduction. He says this quest is still his personal driver for his involvement in Purifi Audio.

If you're into merits, look at his CV, it could be a blueprint for talent, hard work, ambition and virtue (which is equally the case for Bruno !). Lars impressed me deeply in Munich with his sense of details, effortlessly recalling the source of a citation from my latest article, mellowing a smart opening challenge from Bruno with that information.

One of his notable lifetime achievements has been the TI fellowship @ Texas Instruments, when he was elected for two years by his peers and TI’s senior leadership team in 2012. The TI fellow is an outstanding distinction, which represents less than 0,2 percent of the company's total eligible population.
Prior to establishing Toccata Technology in 1996,  Lars has worked 2 years with Harman Europe. He has a rich output on research papers in audio engineering and holds MSc.E.E and Ph.D in engineering from DTU as well as approx. 35 patents family.

The other twin, like the first second to none, is Bruno Putzeys from Belgium.

He is, as Lars, one of the most respected audio engineers in the High End community, his workbook contains leading roles with Philips BV, Hypex and Grimm Audio, before he took the role as CTO with Mola-Mola and Kii, which he co-founded. His invention, the nCore Class-D family drives zillions of DIY’ed speakers and amplifiers and o good number of  High End power mono blocks like Mola Mola, Lindemann or Veritas.

Bruno is still actively engaged at Kii, while he left Mola-Mola in 2018. If you meet him in person, now in his 40s, he impresses you impromptu with his impeccable blue eyes, which are perfectly set in motion by his stylish sterling beard. IMHO, he should never be allowed to wear shades (even if it's only for that ZZ Top effect, I could imagine)!

If you talk with Bruno, you can feel his passion and the drive, that has led him grow into one of the most important inventors in the European audio industry. Bruno Putzeys seems absolutely like minded with Lars Risbo, just as a personality he is a bit more present in the room, which may refer to the fact, he is not of "laid back" Danish nature, but Flemish by design originating from Belgium.

As with Lars, it was a pleasure to work with him on this article, and both have contributed not only answers to your questions, in addition to their cooperation with Audiophile Style they have provided a list of specific literature list  to our reader for acquiring deeper knowledge on the related topics. 

Before they have received all questions from the forum, I have structured them by topics to avoid unnecessary double entries/encounters of topics. Bruno and Lars were free to choose in which order they would answer to the queries.

This shout-out goes to LARS RISBO! And BRUNO PUTZEYS! And "LES PURIFIENS" !!! MAY CLASS D RULE & ENJOY ROSKILDE !!!

The other one goes to our readers and active forum members, who provided so much interest and challenge to our guests! YOU ARE AWESOME !!!

The Q&A, answered by Lars & Bruno:

@Sagittarius : Where is class D heading? Where are further improvements going to come from? There are companies which now use gallium nitride transistors and are pushing the switching speed into the MHz region. Is this the way forward in your view?

Bruno: Well, with the sort of audio performance we’re getting I’d say that we’re asymptotically approaching “perfect”. One could argue that we passed the point of diminishing returns a few years ago already. I’m not saying that a next step won’t have any audible benefits, but in the grander scheme of things, the margin is shrinking.

Lars: That’s if you stick to audio performance alone. Otherwise we wouldn’t have bothered going to class D to begin with. You don’t do that for audio quality. You do that to get better efficiency, make the amp smaller and yadda. And then you get a new set of problems to fix, such as what it sounds like. And then there’s reliability, manufacturability and so on. I wouldn’t say that GaN is going to be the answer to those things, and neither is upping the switching frequency.

Bruno:  Well for a given efficiency you could probably increase the switching rate, but if I’m going to shell out as much for a pair of FETs as what you’d normally pay for the whole amp, I’d rather benefit from that in terms of higher efficiency. Of course, not everyone is able to make that choice. I’ve spent my career honing control loops, most audio designers haven’t and so have to rely on simpler control loops. In that case, increasing the switching frequency is definitely helpful to reduce distortion.

Lars:  We’re as fanatic about audio quality as anyone else, but because we’ve got feedback down to a T now we’re not forced to resort to higher switching frequencies.

Bruno:  If we need to be geeky and I guess that the folks who are going to read this interview can handle that -eh Thomas?- lets grab the specs for the FET in our 400W Eigentakt module and its closest GaN equivalent. So that’s the FDP42AN15A0 (OnSemi) on our left and the EPC2033 on our right. Rdson: 36mOhm vs 7mOhm. Clear win for GaN here. 

Lars:  It’s also got a higher current rating (24A vs 48A) so if we want to be fair we should be scaling by about 2:1

Bruno: Oh erm well, that’s still a minor win for GaN because after scaling it’d come up at 14mOhm. Gate charge is of course magnificently low (30nC vs 6nC after scaling) so driver losses would be low and you can turn them on fast. GaN also has zero Qrr so you can do that if you want. But the main thing that sticks in my throat here is output capacitance. Our good old FDP42, which is from 2002 mind you, has an output capacitance at 100V of 70pF whereas the EPC device puts in a whopping half nanofarad (or 250 puff after scaling). That means your idle losses will go up, or you will have to increase dead time to allow the output inductor to recover the extra stored energy at its leisure. And isn’t it just idle losses that more or less determine real-life power consumption in full? And if power consumption isn’t something to care about, why not just stick with class A…?

Lars:  And high dead time combined with high switching frequency sounds even less attractive. That just increases open-loop distortion.

Bruno:  In applications like motor controllers and high density SMPS GaN and SiC devices are a breakthrough, mind you. It’s just that audio is this weird application where average power is very low and where dead time actually affects performance.

Lars:  And GaN is going to mature so this picture is bound to shift at some point. Just not now.

Bruno: True. On the other hand, silicon is doing the same. More recent devices are getting frightfully close to GaN. Sadly they only come in SMD packages that require fairly expensive methods to get the heat out. Like most GaN devices. It looks terribly ancient, but the good old TO220 package is still a neat compromise in terms of performance for the price.

Lars:  It’s just a game of tradeoffs. The fact that we’re using normal parts, and the reason why we chose to do so doesn’t make for a sexy story. We all like to believe in a magic bullet but when you’re an engineer you have to make choices based on tangible grounds. So the sexy story we’re trying to push about Eigentakt is that we think it’s a bloody clever design.

@Sagittarius: Class D has achieved very low levels of distortion, but is it possible for class D amplifiers to continue their evolution into something close to a straight wire with gain, i.e. minimal phase shift in the audio band? (A similar question from maty).

Bruno:  The 1ET400 module has the frequency and phase response of a 2^nd order Butterworth filter cornering at 60kHz. If you look at the phase shift of that, it’s very nearly “linear phase” in the audio band. To take some rough numbers, it if you have a circuit that has a 0.2 degree phase shift at 200Hz, 2 degrees at 2kHz and 20 degrees at 20kHz, that’s the same as saying it has “0.001 degree per Hertz” phase shift. That’s another way of saying that the whole signal is simply delayed by 2.8 microseconds. If you plot phase shift on a linear frequency scale that’s immediately obvious because you get a straight line. Of course a simple delay doesn’t change the sound. It’s literally the same as starting your music a few microseconds later.

Lars:  My dad used to say that if you left a CD in its case without playing it back, it’d just sit there accumulating massive amounts of phase shift as time went by.

Bruno:  What that matters to sound is how much phase shift differs from a pure delay. Anyone who’s ever done phase measurements on speakers will remember that you have to remove the time-of-flight delay from the data, for instance by marking the leading edge of the impulse response. Otherwise the linear phase shift corresponding to the distance between the speaker and the mic completely clouds the picture. In the case of the 1ET400 module it’s just under 1 degree at 20kHz. There never was a phase shift problem in class D, it’s simply a trick of the light that happens when you plot the phase response on a log scale without removing the fixed delay. 

@Sagittarius: Are you using the same feedback scheme which was developed for Ncore in the new amplifiers?

Bruno:  Well it’s a self-oscillating loop with global feedback and integrator-windup prevention. Does that mean it’s the same? That depends on the amount of detail. For instance the fact that Eigentakt has a well-behaved, load-independent second order closed loop response is a rather valuable novelty and it took a new topology to get there.

Lars: I rather recall you pulling your hair out fearing you wouldn’t be able to find something better than Ncore.

Bruno:  I grew a beard to compensate.

Lars:  Then there’s the “little matter” of the mathematical model.

Bruno:  Oh yes. The new loop has two more orders and the result was initially that it developed some unexpected instability near clip. Unexpected in that it wasn’t predicted by the formulae I used before to dimension the loop. So apart from the bits that people will surely be poring over once the patent applications get published, a lot of IP is in a discrete time model for self-oscillating amps that is valid for all duty cycles and that predicts this sort of large-signal behaviour exactly. We can now let Matlab do the component tweaking, knowing that what the model predicts will match the actual behaviour of the circuit exactly.

Lars:  That’s something we’re quite hot on at Purifi in general. The motor geometry we use for drive units is also automatically optimised. You put the desired specs into a Matlab script, let it stew over the coffee break and within material tolerances the resulting design will get as close as possible to the specs as possible and, once built, do exactly what was expected. This is quite a step up from general practice where simulators are simply used in lieu of experimentation. It’s only when you have a mathematical description that you get fundamental insights. Merely simulating will not get you further than tinkering in the lab.

@Sagittarius: Does the high damping factor of class D amplifiers negatively affect the subjective sound quality of some types of speakers as some reviews seem to suggest?

[Damping factor is defined as 8 ohms divided by output impedance, high DF means low output impedance and vice versa -ed]

Bruno:  Oi, we had to battle for this high damping factor! Before anyone worked out how to put global feedback around the output filter, the damping factor of class D amplifiers was actually much lower than that of class A/B. And much good did that do… In particular, the big problem was at high frequencies, where the frequency response became enormously load dependent. Most speakers have a highish impedance in the top octave, and early class D amplifiers would thereby produce a very clear lift in the top end, which explains why they were often perceived as sounding harsh.

Lars: Have we got an indication where this idea of high DF being bad for sound might have come from?

Bruno:  I’m not sure. Maybe in the past, high DF was associated with big, sluggish amps? I wonder what speaker they were using. If they’re listening with a broadband speaker with no crossover filter for instance, a high output impedance could bring some of the benefits of current drive and reduce hysteresis distortion in the iron in the speaker motor.

Lars:  You’d have to really go overboard.

Bruno:  An SET amp with no feedback typically has an output impedance equal to the rated load impedance so you’d be looking at nearly 6dB less hysteresis distortion in the midrange. But for any other speaker this trick is quite useless. Crossover filters are simply designed with the assumption of a voltage source. It’s a matter of standardisation. Otherwise how this particular speaker sounds when connected to that particular amp becomes rather unpredictable.

Lars:  Isn’t that precisely why hi-fi shops do all that mixing and matching?

Bruno:  It’s quite possible that shop owners would have less fun if all amps had sensibly low output impedance. But beyond “sensible”, damping factor is completely overrated in my view. Once output impedance is low enough to keep response changes due to load variations to within a small fraction of a dB it’s low enough. The term damping factor is seriously misleading because some folks think that an amp with a DF of 1000 is ten times better at stopping a moving cone than one with a DF of 100. It doesn’t make a jot of difference. In both cases the resistance of the voice coil, the crossover filter and even the speaker cable will dominate totally. In actual fact you wouldn’t even want to have infinite damping because the speaker designer counts on the natural resonance to define the bass response. So it’s rather a good thing that the speaker has its built-in resistance in series with the amp.

Lars:  Having a super low output impedance does have one real benefit: it makes bi-wiring work. The whole point of bi-wiring is to isolate the tweeter and woofer portions electrically. If you have a common impedance in series with the speaker, distorted currents produced by the woofer will turn into a distorted output voltage which in turn is seen by the tweeter section. So if you want bi-wiring to work its magic you really do need an extremely low output impedance, which is the same as super high DF of course.

Bruno:  Good point, a hundred might not be enough then. I think people resort to bi-amping when their amps don’t have low enough output impedance for bi-wiring to do the trick. So for a serious audiophile having really high DF is a real advantage, if only financially. 

@barrows: Why not develop the newest tech with Hypex as before?  Why start a new company?

Bruno: Is that about out “bromance” as Thomas called it? We’d been on each other’s radar for 15 years or more and whenever we met we kept saying “we should do something together”. By 2014 I was feeling more than usually entrepreneurial (I was an employee at Hypex, not a partner, few people realise that) when the matter came up again. So basically we both left our respective jobs in order to make this work. Having to build up manufacturing and all that is perhaps more than I signed up for but on the upside we got three of Lars’ TI colleagues into the bargain. Søren, Kim and Claus are enormously experienced senior engineers and managers who are responsible for getting hundreds of millions of chip-based class D amplifier units out there. Their approach to industrialisation, verification and product reliability is second to none and I’m just grateful to have that sort of backing.

Lars:  We weren’t thinking of putting amp modules on the market when we started though. The first idea was to do an intelligent digitally controlled amplifier that could sense and correct distortion in standard loudspeaker drivers. But that work ended up showing  us how we could easily (well, relatively) fix the most important distortion mechanisms in the driver itself. We had already involved Carsten Tinggaard, on account of his peerless (pardon the pun) knowledge in driver design and manufacture, and that now gave us the chance to start dreaming of actually building our own low distortion speaker drivers. Carsten is now a partner and we’ve started shipping samples. Anyhow, that’s why we’re doing drivers and amplifiers as separate projects, for now. Note those last two words.

Bruno: Then to wrap up this perfect storm there’s Peter Lyngdorf who’s enthusiastically backing us. He and Lars go back quite long while too.

Lars:  That’s putting it mildly. He also funded my first startup, Toccata, where I developed the TacT Millennium amplifier. Kim, Claus and Søren were also involved in that. So by the time Bruno and I started floating ideas about smart amplifiers, Peter was pretty much jumping up and down to get involved.

@crenca: Now that THD measurements have been driven so low, what else are you hoping to achieve in this and future designs that relate to the unmeasured quality of the sound of Hi Fi amplification gear?  Not looking for a high level debate about measurements, but I am assuming that not everything related to SQ has been measured and/or is not seen in the standard measurements.  

Bruno:  I like the way you put it, “unmeasured”. Because that’s really the point when measurements and ears diverge. Measurements are scientific experiments: to test a hypothesis. Remember that you can’t ever prove a hypothesis, the best thing you can do is try very, very hard to disprove it. Every time you fail to prove your hypothesis false, it becomes more solid. So if your hypothesis is that “this is a good amplifier” you try to make it do things you don’t want it to do. It’s not enough to run a handful of standardised tests, you have to invent all sorts of tests that you target specifically at weaknesses you expect.

Lars:  Like a 20kHz THD test in its own right is not very useful because the harmonics are inaudible. So you do an IMD test with 20kHz and 19kHz tones and all of a sudden the whole audible spectrum clutters up with distortion. The silly thing is that the standard CCIF test that this signal came from then ignores all of that and only looks at the lone second order product at 1kHz… You have to look at the whole spectrum and that’s really enlightening. It’s one of the major tests that really tell you which is the better amp. Probably a reason why this test isn’t commonly included in amplifier data sheets.

Bruno:  The nice thing is that this high frequency IMD test is about the worst thing you do to an amp with an input that’s still technically an audio signal. Of course you can make an amplifier go completely mad by feeding it radio frequency signals but that’s not going to tell you anything about the sound. But to come back to your question, I’m always looking for test methods that are within the remit of audio and that somehow make amplifiers do unexpected things. Admittedly that well has dried up a little. Even a class D amplifier is simple enough that with two sine waves you can pretty much probe all there is to probe. The only real surprise we had recently was to do with the output choke. Magnetic materials have something called hysteresis, but there is precious little information about what this really does. If you test a magnetic core with a sinewave the distortion looks a little like soft clipping, perfectly benign. But what came out of tests on iron parts in loudspeakers was that hysteresis has a long term memory so you can get intermodulation between things that happen now and things that happened 10 minutes ago. With music this distortion sounds like half correlated noise.

Lars: Crackling. You hear when each magnetic domain flips.

Bruno:  When you put the coil inside the amplifier’s feedback loop that distortion gets reduced along with the distortion of the power stage and everything else. We have a strong suspicion here that the most audible distortion in typical class D amplifiers may very well be that. 

Lars:  The TacT Millennium had, of course, no feedback and we had to resort to an air-cored inductor which, apart from being expensive, was an enormous problem in terms of radio interference. It’s a solution of sorts, just not a very practical one. Or very sensible even.

Bruno:  It would certainly explain why the Eigentakt circuit sounds so much cleaner: the extreme amount of loop gain reduces the sonic footprint of the output choke. The low harmonic distortion, most of which is power stage related, is simply a side benefit. It would also mean that directly trying to reduce power stage distortion, say by using faster FETs, is not going to improve the sound anywhere near as much as improving loop gain.

Lars: Wouldn’t you say that speakers with drive units that explicitly tackle hysteresis distortion like ours and like DALI’s, are much more revealing of the differences between class D amps?

Bruno:  I’d say so.

Lars: I’m going out on a limb here but maybe there is a wider class of “memory” distortion effects that are completely ignored when you do sine wave tests. Why shouldn’t similar effects occur in capacitors? And thermal effects in class AB amplifiers are also notable for being very audible without showing up on a THD plot.

Bruno:  They do on an IMD test with a low and a high frequency but I take your point. There could be more ahead when we go looking for memory effects. On the other hand, the Eigentakt amplifier has so far survived all subjective shoot-outs so let’s say that any undiscovered effects must be rather subtle.

Lars:  Not subtle maybe, but sitting inside a feedback loop with 75 dB gain and therefore subtle now. It helps when you have that, it can save you a lot of discovering and fighting every individual distortion mechanism. I’d rather put that effort in the speaker driver where sadly we haven’t got feedback or suchlike.

Bruno:  People are shouting “motional feedback” at their computer screens now.

Lars:  Motional feedback systems are quite band limited. I haven’t seen any that work above 200Hz. So the IMD that the bass would cause in the mid-band is completely impossible to solve using just motional feedback. And then there’s the Bode Inequality you know. Things get worse outside the loop bandwidth. And even with perfect motion there is still output from the surround which, shall we say, is not necessarily linear. By the way, maybe you ought to stress that the 75 dB loop gain of Eigentakt is all the way up to 20 kHz.

Bruno:  Yes otherwise it doesn’t sound all that impressive, does it? I suspect most basic class AB amps have a loop gain of 75 dB, but only up to 100Hz or so, then it starts dropping. For a linear amp design with a standard 1^st order compensation to hit 75 dB at 20 kHz it’d have to have a Gain Bandwidth Product of 110MHz. Two-pole compensation is the highest I’ve ever seen in a class AB amplifier and even then 76 dB at 20 kHz is pretty astronomical. I doubt if anyone with strong opinions against feedback has ever heard an amp with a lot of feedback.

@crenca: Right. So how do these new amps sound?  What is your goal around sound?

Bruno:  No sound at all. The output signal should be indistinguishable, by ear, from the input signal. I’m stressing the “by ear” thing here because we as audio nerds, and that includes all interviewers here, are often conflicted about what it means to measure and what it means to listen. For me, measurements are lab tools. Measurements tell you technically what your circuit is doing. Before you heat up your soldering iron to, say, change a resistor, you need to have something numerical to point to the right resistance value. Ears don’t help there. Your ear should be used instead to figure out what to measure so as to make those measurements meaningful for sound quality.

Now, if someone wants a particular sonic character, they can still use measurements by first understanding what their desired sound looks like technically and then using lab tools to achieve that result efficiently. That’s not what I’m after personally. My personal goal is to build stuff that I can’t hear at all. It’s a matter of respect for the artists who make recordings.

Lars:  I want to be able to hear all those differences in recording styles, rooms and all that. If an audio system has an obvious sound of its own, all recordings start sounding the same. And with a bit of luck, if our work gets into recording studios as well, it will help the professionals hear what they’re doing much more easily. We actually took our demo speaker and the Eigentakt demo amp to Danish Radio and the reaction we got was “these speakers really respond well”. Meaning that anything they changed was directly audible without second guessing.

Bruno:  What I also need to get off my chest here is the confusion between accuracy and clinical “analytical” sound. What’s implied there is that you have to choose between accuracy and joy. That runs completely counter to my experience. When something sounds “clinical” or “analytical” it always turns out to be totally inaccurate. Overhyped highs and thin mids have nothing to do with accuracy. An accurate system will sound warm, lush and emotionally engaging provided that these characteristics are actually in the recording. Low distortion sound can be incredibly moving.

Audiophilestyle: As an engineer, at which point you accept audible proof of your mathematical model?

Bruno:  Well you can’t prove a mathematical model by ear, you verify that by measurement. If it does on the bench exactly what it did on paper, you’re done for the modelling part. But I take it you’re wondering when I’m satisfied with what I’m hearing? If at all possible, I’ll try to do a direct A/B comparison with the input signal. That’s not very practical to do with a power amplifier so I try to learn as much about the sound difference between the input and output of small-signal circuits like preamps and AD/DA converters. Most of that knowledge extrapolates quite nicely to power amps. So mostly when I actually listen to power amps that’s not so scientific, it’s more a matter of looking for sonic artefacts I wasn’t expecting.

Audiophilestyle: What’s your signal chain when listening to the amp? Do you, for example, use a Mola-Mola input stage or suchlike?

Bruno:  Our current listening setup is a Mola-Mola Makua (with internal DAC) driving the 1ET400 directly without further stages in-between. The Makua has enough headroom.

@barrows, @Matias: Now you mention it, is there any chance of Purifi releasing a Bruno Putzeys designed DIY DAC module using the 100 MHz 1 bit discrete FIR approach used by Mola-Mola?

Bruno:  I have a twin brother in this venture, he’s called Lars and he knows at least as much about DACs as I do. It would be quite a waste not to invent something cleverer together. Our dream is to do an IC. We can but hope. 

Lars:  With this kind of amplifier performance it would be nice to have a matching DAC. I feel that audio DAC chips have largely stagnated, it’s not an area that draws much investment.

Bruno:  SNR’s are going up all the time, but some of the fundamental problems (birdies, tone-like artefacts) keep being ignored so there’s space in the market for a new chip.

@crenca: Have the various distortions of modern amplifiers (when used normally) of all almost all designs not already become so low as to no longer matter - in other words it's transducers, rooms, and recordings that are "responsible" for the "sound"?"

Bruno: To use that lovely German word, jein. The distortion mechanisms of loudspeakers and amplifiers are so different that they don’t cover each other up necessarily. But I would agree with the general sentiment that tinkering with electronics whilst ignoring the speaker and all the rest is not good use of one’s time. By all means the acoustics, including the speaker driver are the long pole in the tent.

@jabbr: Since you've said that you like the sound quality of your analogue Class D amps as opposed to your own direct digital/power DAC ... why? What is the electrical correlate?

Bruno:  Oh that thing. Well, if you want poetic justice, this was it. This power DAC ticked all the boxes in the audiophile canon: all-digital, directly DSD driven, no feedback. Even now people are dreaming about true DSD, DD amplification and few know it’s been done already. Like DSD itself it was one of those apparently great ideas that went straight from the future to the past without ever passing through the present. Sound-wise this amp was barely hi-fi. The reasons? All of the above I would say. It had a ferrite output inductor which, as I mentioned is fine so long as a massive feedback loop is there to prevent you from hearing it. It had thermally induced timing shifts causing low-frequency distortion. And though I never bothered to look for precise technical reasons it was ridiculously sensitive to the types of capacitors used throughout, especially in the power supply. For something that was supposed to be a “digital” amplifier it was the most remarkable jumble of entirely analogue sonic contributors. The takeaway of the whole exercise is that either you can try improving all of these elements separately, which would be a huge and maybe impossible undertaking in analogue circuit design, or you could admit that the thing is by its nature analogue and accept that the one thing analogue does best -feedback- will work its magic on any type of imperfection you put inside the loop.

Lars:  I sometimes wonder if the major part of the good sound of the Millennium -and no offence meant but it must have sounded rather better than your power DAC- wasn’t mostly the PWM algorithm where I really went out of my way to get rid of various tonal artefacts that plagued just about any DAC available in those days. It certainly was a better DAC than it was an amplifier.

Bruno (harrumphs): none taken, after all the output filter I used wasn’t terrifically thought through. It might have sounded nicer with an air cored inductor like yours.

Lars:  Yes, and since we had the air cored inductor the output stage distortion was once again the most audible part of the sound, so here tightening the switch timing was clearly for the better, sonically. For the same circuit, lower distortion always resulted in more music.

@Em2016: Bruno, you went on record somewhere (link) saying you solved Class D distortion issues within 2 hours, with “no distortion at all, for every reasonable definition of ‘none at all’”. So why keep at it? 

Bruno:  Ah yes I remember that. Actually this was not about amps as a whole. It was strictly about digital PWM algorithms (like the one Lars credits for making the TacT Millennium sound good). I was trying to highlight the futility of making the perfect PWM signal, only to try amplifying it with an open loop power stage with no error correction. I found it hilarious that as late as 2004 folks were still convinced that the PCM to PWM conversion process was the big problem to crack. There seemed to be a race on in the class D industry to invent ever better ways of converting PCM into PWM.

Lars:  I used to hammer on that: the PCM to PWM process is the easy part. The power stage was the hard part. Upon which I started explaining how to convert PCM into PWM…

Bruno:  Right. So one sleepy afternoon a Philips colleague walked through the office shouting “has anyone got something clever to present at the DSP conference in Eindhoven?” So for a laugh I tried and found a new PWM algo in two hours. Mind you, I’d been trying for years by then, but always under some pressure to deliver. Now that I’d basically given up on the idea I was relaxed and that helped. But to be clear: in itself this algorithm did not immediately advance the art of class D design. I finally got to use it in the Mola-Mola DAC though.

Lars:  You might perhaps give your industry colleagues a bit more credit. I didn’t go all digital with the Millennium out of an audiophile belief that negative feedback was bad, or because DD looked good on paper. It was just that in those days nobody knew how to put feedback around a class D amplifier without actually adding distortion. Normally when you build a class D amplifier schoolbook style, with a triangle wave oscillator, you would bend over backward to make the slopes of that triangle wave as straight as possible to minimise distortion in the analogue PWM process. If you then try to close the loop you are feeding back a signal that contains your audio but also a filtered residual from the PWM signal. And then all your effort to make the most beautiful triwave was for nothing because the ripple in the feedback signal makes it severely lopsided. The more feedback you tried to add, the bigger the open loop distortion became. I don’t think anyone had an answer to that in the late 90’s so we decided to go without feedback entirely. The ripple compensation trick you came up with for your PWM algorithm was actually a scheme to get around that problem.

Bruno:  Then here’s a shout out too, because to my knowledge your MAE (Minimum Aliasing Error) trick was the first time I’m aware of that anyone made real headway into this problem.

Lars:  And finally the model for self-oscillating amps added another way to make feedback really work in class D.

Bruno:  The three having in common that you can let the input voltage of the comparator look as bad as you want, provided you still know how fast it’s going to cross through zero.

@psjug and @jabbr: What about digitally controlled amps that use an ADC to take feedback and then do the loop filter digitally?

Bruno:  It’s actually the approach we were planning to take initially, when there was also going to be a lot of speaker DSP involved. Fundamentally, there is nothing wrong with this approach. You’ve got feedback, you’ve got an implicit DAC (hidden inside a feedback loop in the ADC), so you have all the ingredients you need to build the equivalent of a DAC followed by an analogue controlled Class D. For quite long I’ve advocated the approach, not because it’s in any way superior to doing an analogue class D amp (it is equivalent so neither better nor worse) but because in the long run it should be cheaper to do and more flexible too.

Lars:  It benefits from modern large scale integration. A digital integrator is for free, an analogue one costs you at least a capacitor. Of course you keep a few analogue integrators which are now sitting in the feedback loop of the ADC instead of that of the amp.

Bruno:  So as soon as the loop order of the amp exceeds that of the ADC you’re in the money.

Lars: Once you’ve done the investment of a full blown mixed signal IC development of course.

Bruno:  Why isn’t anyone asking about self-oscillating? I’m dying to mention it.

Lars: OK since you ask: why haven’t you continued with ripple compensated fixed frequency amps? That ought to be perfectly suited for a digital implementation like in your collaboration with Toit Mouton?

Bruno:  I wanted to for a long time. The problem was that I could never find a clocked control loop that was anywhere near as robust as any of the self-oscillating stuff I was doing. It completely stumped me why a self-oscillating loop always sorted itself out while the clocked loop could just go unstable when you changed the load. Toit worked around that by starting the amp up with a pulse so as to estimate the loaded Q of the output filter and adjusting the loop filter accordingly. It’s lovely that digital offers you that flexibility but a simple analogue self-oscillating circuit works it out for itself by magic somehow. I’m aware that you presented the noise transfer function of a self-oscillating amp in your 2005 paper but I didn’t understand the math so it kept stumping me.

Lars: That model only worked near 50% duty cycle though.

Bruno:  Yes, but understanding it would have answered most questions I had at the time. I did realise though that we’d need an extension to cover large duty cycles too.

Lars: I’m not sure if it proved that self-oscillating was superior.

Bruno:  I rather think it did because it shows that the region where noise gets amplified is automatically bunched up against the switching frequency where it goes to infinity. So rather than having to spread it out evenly outside the audio band you could just mercilessly park it on the switching frequency.

Lars: You didn’t have to worry about it being unstable. It was designed to be unstable and it oscillated exactly there.

Bruno:  So anyhow, the game you play with a normal noise shaper where you try to minimise the out-of-band noise gain whilst still buying enough gain inside the audio band is no longer needed in a self-oscillating amp. The upshot of that is that to get equally stable operation with a clocked amplifier you would have to run it at a much higher frequency like [names a company with ADC feedback] does, which can’t be good for either headroom or efficiency.

Lars:  Well you certainly redeemed yourself with the new double-sampling model. It had to be possible but someone had to do it…

@HQ-Sound : What is stopping more designers from coming up with competitive solutions? Why aren't they (the large audio brands) trying to produce their own class D solutions?

Bruno:  There’s a range of ways people can get class D amps into their products. If audio performance is not super important, IC based solutions are available. That actually covers most amplification needs. Then, some companies do roll their own because getting acceptable performance is becoming less of a black art with various reference designs floating around. But if you want absolute audiophile performance then it becomes an enormous investment to learn the ropes. The handful of people who do that investment can’t ever hope to recuperate it by selling it just through one audio brand. Even large companies don’t sell a lot of high-end gear.

Lars:  Just think of the years of class D experience that’s accumulated in the Purifi team. Who would want to start from scratch? TI only managed to launch itself on the path to its dominant position in the class D IC market by first acquiring a small joint from Denmark.

Audiophilestyle: What is your opinion about the hybrid designs used with Class D topologies?

Lars:  These always pop up in conferences.

Bruno:  I’ve seen my share over the years. Somehow though the best performing examples never manage do outperform the best pure class D designs that existed at the same time.

Lars:  In theory you should be able to cram a lot of loop gain into those.

Bruno:  Absolutely, there’s no reason why a hybrid solution shouldn’t work as well as the best possible class A/B amp. It’s just that for some reason, historically, they never did.

Lars:  So, if we simply accept that at a given time the best pure class D amps tend to be no worse than the best hybrids, hybrids are an overly complicated way of doing stuff.

Audiophilestyle: What did you invent to increase the reliability of the design? I've read that some ancient Class D models had some bad karma.

Bruno:  Dire experience, painstakingly (often painfully) acquired. I have to say that this part has become a lot more pleasurable of late. One of our colleagues (Søren) was the class D product architect and testing guru at TI and as you can imagine, when you’re selling millions of units of a certain chip, you want to be sure it’s unbreakable. The testing regime that the Eigentakt modules go through is pretty gruelling. Every time something went up in smoke I knew I had work.

Lars:  Well for us that was painstaking and dire and all that too you know. This sort of experience only comes through having angry CEO’s of large Korean conglomerates calling up TI’s CEO about some chip that was going kafoom.

@fas42: What sort of testing was done to ensure that the units are intrinsically resistant to interference, noise factors? That is, how much work needs to be done by implementers to fully shield the modules from anomalies in their electrical environment?

Bruno:  I am assuming you’re asking about EMC? Basically the modules get pre-compliance and compliance tested as though they were end-user products. And because one end-user product potentially contains a large number of channels we take a lot of margin over the legal requirements. 

Lars: These tests are done with no shielding or anything, which as you can imagine takes a fair bit of careful circuit lay-out and judicious use of local filtering.

Bruno:  Local filtering is amazingly cheap when you compare it to fixing the problem on a finished product level.

@Shadders: What power supply was used for testing the module? Are the powers listed RMS powers, or peak sine wave powers?

Lars:  Would it be a rear-guard battle to point out that “RMS power” ought to be called “Average power”? You typically measure it by measuring RMS voltage and then calculate what that does in the load impedance.

Bruno:  So “400W” means that the power goes twice from 0W to 800W over one cycle of the sine wave. The peak voltage corresponding to 400W into 4 ohms is 56.56V. That’s the nits picked. Data sheet measurements are taken with lab power supplies, because that’s the easiest way to make sure customers can repeat the test.

@Shadders: What is the maximum current capability of the output devices ?

Bruno:  That gets complicated rather quickly because it depends on temperature and time etc. The overcurrent and overtemperature protections make sure that we stay well within the safe limits.

@psjug: Can you explain how your clipping recovery is better than with typical amplifier designs as stated in your literature?

Bruno:  I should stress that the clipping behaviour is better than typical class D amplifier designs, but only about as good as a well designed class A/B. You can’t get better than that. Basically what you want is that when the output signal hits the rail it sticks there only for just as long as the wanted output voltage is higher than the rail voltage, and that normal amplification resumes immediately as soon as the clipping is over. That’s amazingly difficult to do in a high order loop because when the amp clips the error is suddenly very large and the loop filter goes crazy trying to push the output signal further. So when the signal comes back in range the loop filter is in a state far away from where it would have been had clipping not occurred.

Lars:  In some forum thread people were speculating that we were pre-clipping the input signal so as to keep the amp in its linear range.

Bruno:  That sounds complicated but I can see why someone would take such a desperate measure. No, we don’t pre-clip and the amp goes all the way to the rail until it stops switching. Basically the trick is that you actually know what state the integrators in the loop filter ought to be in (minus normal distortion) at any given time, so you keep them from wandering too far off the expected trajectory. If you can render that trajectory trivial, so much the better.

@Shadders: Why does the Purifi amplifier clip or distort significantly at a specific voltage which is much less than the supply rail?

Lars:  Actually I think the question was answered by pointing out that 400W means 800W peak and hence 56.56V, which is not “much less” than the supply rail.

Bruno:  Still worth answering why it doesn’t go all the way to 65V which some linear amplifiers pull off. For a linear amp that’s pretty much required because wasted headroom = wasted power which isn’t the case with a class D amplifier for reasons that I hope are obvious (it’s a power converter). Maximum duty cycle is a fundamental restriction to class D amps because getting arbitrarily close to the rails means creating impossibly short pulses. That’s mitigated by the self-oscillating nature which also drops the switching frequency so you can stretch duty cycle a bit further than with a fixed oscillation frequency. Eigentakt actually operates nicely to a higher duty cycle than most thanks to the whole mathematical rigmarole I’ve been through.

The basic takeaway from our clipping story is that the Eigentakt amp does not exhibit the kinds of instabilities that you often see in other class D amps when they go into and out of clip.

@Shadders: Your amp modules generally tend to have low gain and input impedance, it looks like you need 9Vrms or so to drive this one. Why? How do you drive it? Is that 9V differential or single ended?

Bruno:  That’s to maximize the SNR of the module. It’s then up to the user to decide whether they need such a high SNR and accordingly, what buffer stage to add (if any). Someone integrating our module, for instance, with a super low noise DAC would want to design the DAC’s external filter so that it can drive the amp directly without any further gain stages. An optional 5x gain buffer is included in the eval kit, but we don’t use it for measuring specs. The input of the Eigentakt module is differential so all that matters is the voltage between the two input pins, not what each of them does relative to ground (whatever that is!). So you can drive them with one output that delivers the full 9Vrms swing to one input and tie the other input to your source’s ground reference, or you can use two outputs that each deliver 4.5Vrms in opposite phase, or anything in-between for that matter. It’s the same: volts is volts, and it’s measured strictly between the input pins.

Audiophilestyle: A quick-fire round of market related questions?

@Rt66indierock: Will there be a reference amplifier design for the DIY market?

Bruno:  The eval kit that we supply to industrial customers will also become available for DIY. That’s an I/O board and two 1ET400 modules to make a stereo amp.

@Nordkapp: Besides NAD, what manufacturers have committed to and/or expressed serious interest?

Lars:  Interest has been overwhelming and several more deals have been closed of which we’re awfully proud. But it’ll be up to the respective customers to make the announcement when they’re ready for it.

@Matias: Will the Purifi modules be pin compatible with their competitors for easy swap of modules? 

Lars:  “We try to adhere to industry standards wherever there are standards”.

Bruno:  Not on purpose. I2C control of the 1ET400 is different, for instance, so if you were planning on swapping modules on something you happen to have in the house I’d be careful.

@Matias: What other power ratings are you planning to release? All-in-one modules? Finished products like active speakers? Switching power supplies?

Bruno:  We’re still solidifying the road map. Power is probably going up and down by factors of two. Kim is working hard on an SMPS, integrated modules will then come as a matter of course too. We won’t become a consumer brand, there’s little sense in competing with our industrial customers. They’re already grumbling about our being open to DIY.

@Matias: Would it make sense to use Eigentakt for low power amplifiers like desktop or portable headphone amps, or even embedded IC chips (DAPs, smartphones) or opamps?

Bruno:  At those power levels there’s no point in going to class D (whose fundamental attraction is efficiency). Life is hard enough as it is.

Lars: Class D is used in cell phones.

Bruno:  For reasons of loud, not good.

@Matias: Will you also go after pro audio customers, MI, live sound?

Bruno:  High end studio monitors, absolutely. MI: unlikely because the price pressure is enormous there. Live sound: ooh yes please. Must be amazing to see 20000 people dancing to Eigentakt amps and Purifi drivers. Did we tell you we’re based in Roskilde?

@Matias: Besides amplification and drivers, possibly DACs as I have also asked before, any other product lines they have in mind?

Bruno:  No, but since drivers were a bit underemphasized in this interview, let’s mention them again. Drivers!

@Paul R: What amplifier does each of you use at your home, for when you just want to relax with some music? If not one of the Purifi products, do you plan to replace whatever you are using with one of the new Purifi Audio products? Be that a reference implementation, a third party device, or a DIY homebuilt job?

Bruno:  I have a pair of Kii THREEs.

Lars: Kii THREEs. A friend recommended them. I wouldn’t mind having our Munich demo system too. Otherwise I have no plans to go DIY – what I want to see is audio manufacturers buying our tech to do amazing stuff with it.

For further reading:

• Risbo, Lars, Field-Programmable Gate-Array-Based 32-Times Oversampling Eighth-Order Sigma-Delta Audio DAC, Audio Engineering Society Convention 96, Feb. 1994, http://www.aes.org/e-lib/browse.cfm?elib=6424 
• Lars’ first DAC design based on his PhD Thesis work on very high order 1-bit control loops.
• Risbo, Lars and Mørch, Thomas, Performance of an All-Digital Power Amplification System, Audio Engineering Society Convention 104, May 1998, http://www.aes.org/e-lib/browse.cfm?elib=8485
• Describes the TacT Millennium design.
• Putzeys, Bruno Johan and de Saint Moulin, Renaud, A True One-Bit Power D/A Converter, Audio Engineering Society Convention 112, April 2002, http://www.aes.org/e-lib/browse.cfm?elib=11439 or https://www.hypex.nl/img/upload/doc/an_wp/WP_AES112BP_A_true_one-bit_power_DA_converter.pdf
• Describes the DSD Power DAC.
• Risbo, Lars, Discrete-time Modeling of Continuous-time Pulse Width Modulator Loops, Audio Engineering Society Conference: 27th International Conference: Efficient Audio Power Amplification, Sep 2005, http://www.aes.org/e-lib/browse.cfm?elib=13263.
• Describes PWM feedback loops as sampled systems, including a self-oscillating loop.
• T. Ido ; S. Ishizuka ; L. Risbo ; F. Aoyagi ; T. Hamasaki, A Digital Input Controller for Audio Class-D Amplifiers with 100W 0.004% THD+N and 113dB DR, 2006 IEEE International Solid State Circuits Conference - Digest of Technical Papers, https://ieeexplore.ieee.org/document/1696185
• Reports a TI test chip project on integrating a high performance DAC and high-order loop class D controller on one chip.
• Groenenberg, René and Putzeys, Bruno and van der Hulst, Paul and Veltman, André, All Amplifiers are Analogue, but Some Amplifiers are More Analogue than Others, Audio Engineering Society Convention 120, May 2006, http://www.aes.org/e-lib/browse.cfm?elib=13494 or https://www.hypex.nl/img/upload/doc/an_wp/WP_All_amps_are_analogue.pdf 
• Educational piece debunking the misconception that there should be something digital about class D.
• Neesgaard, Claus and Risbo, Lars, PWM Amplifier Control Loops with Minimum Aliasing Distortion, Audio Engineering Society Convention 120, May 2006, http://www.aes.org/e-lib/browse.cfm?elib=13497. 
• Article detailing the principle of Minimal Aliasing Error [MAE] loop design.
• Putzeys, Bruno, Simple, Ultralow Distortion Digital Pulse Width Modulator, Audio Engineering Society Convention 120, May 2006, http://www.aes.org/e-lib/browse.cfm?elib=13498 or https://www.hypex.nl/img/upload/doc/an_wp/WP_AES120BP_Simple_ultralow_distortion_digital_PWM.pdf.
• Article using low distortion PCM-PWM conversion as a vehicle to introduce the concept of ripple cancellation to solve the aliasing error problem
• Risbo, Lars and Høyerby, Mikkel C. W., Suppression of Continuous-Time and Discrete-Time Errors in Switch-Mode Control Loops, Audio Engineering Society Conference: 37th International Conference: Class D Audio Amplification, Aug 2009, http://www.aes.org/e-lib/browse.cfm?elib=15221 
• A follow-up paper on the one from 2005, showing how the same loop responds rather differently to dead time distortion and continuous time errors.
• Putzeys, Bruno, Globally Modulated Self-Oscillating Amplifier with Improved Linearity, Audio Engineering Society Conference: 37th International Conference: Class D Audio Amplification, Aug 2009, http://www.aes.org/e-lib/browse.cfm?elib=15213 or https://www.hypex.nl/img/upload/doc/an_wp/WP_Globally_modulated_self-oscillating_amplifier.pdf. 
• Article explaining part of how to optimise self-oscillating feedback loop for minimal inherent distortion.
• Mouton, Toit and Putzeys, Bruno, Digital Control of a PWM Switching Amplifier with Global Feedback, Audio Engineering Society Conference: 37th International Conference: Class D Audio Amplification, Aug 2009, http://www.aes.org/e-lib/browse.cfm?elib=15218
• Describes an amp with ADC feedback that makes use of ripple cancellation.
• Putzeys, Bruno, The F word or Why there is No Such Thing as Too Much Feedback, Linear Audio Magazine vol 1, https://linearaudio.net/sites/linearaudio.net/files/volume1bp.pdf
• Educational article explaining why feedback has such a reputation problem in audio, and why this is undeserved. Contains, amongst others, a rebuttal of “TIM” and what “a lot of feedback” actually means.
• Risbo, Lars et al, Digital Approaches to ISI-Mitigation in High-Resolution Oversampled Multi-Level D/A Converters, IEEE Journal of Solid State Electronics, Dec. 2011, https://ieeexplore.ieee.org/document/6032045
• Explains the problem with birdie tones common to most D/A converter chips and shows a solution.
• Putzeys, Bruno, The G Word or How To Get Your Audio Off the Ground, Linear Audio Magazine vol 5, April 2013, https://linearaudio.net/volumes/786 or https://www.hypex.nl/img/upload/doc/an_wp/WP_The_G_word.pdf
• Attempts to clear up the confusion about balanced/unbalanced/single-ended/differential etc. Includes a DIY preamp that has gained some popularity.