Monday, November 17, 2025

Class-D Tales: The D is For Denmark (a comprehensive overview)

Origins

The origins of switch mode power amplifiers (SMPA) date back well into the era of vacuum tubes [1]. Once there was a website listing some patents of the early days which was quite helpful in order to get an overview over SMPA history [2]. 

My personal impression is that there was not so much momentum in the early days. When switch mode power supplies (SMPS) started to become popular (late 70's to early-mid 80's - most likely fueled by the work of Middlebrook and Ćuk and by the advent of suitable semiconductors [3]) also Class-D technology saw a little boost (e.g. Brian Attwood at Peavey). The whole thing really took off in the late 90's to early 00's (not only but significantly) driven by a group of former PhD students of Michael A. E. Andersen at DTU.

Class-D is called Class-D simply because at the time it arrived the amplifier classes A, B and C were already known and D is the next letter in the alphabet. However, due to the fact that a power sage switching between (at least) two discrete states is at the core of the concept people tend to misinterpret (yes, it is still ongoing) the D as abbreviation for ‚digital‘. Which is horrifically stupid.

D is for Denmark - which is the Class-D hotspot.


Literature

For long years there has been no comprehensive treatise on Class-D technology. Some days ago I found the book of Robert N. Buono on the interweb [4]. 
My first thought was: "woohoo, finally...". Then I read the name of the author and realized two things:
  • I've never heard of that guy
  • Apparently he is not danish
So my second thought was: "please, please, please don't be bullshit". I downloaded the masterpiece on scribd.com. And it was utter crap. Honestly, don't waste your money on this! It is frightening to see that there are people spending years on the topic who afterwards still have no clue about it. Another good example is the dissertation of Verena Grifone Fuchs [5]. 

You could simply read the respective chapters in Bob Cordell's (otherwise very precious) book about linear amplifiers [6] and reach the same level of enlightenment easily - and Bob is clearly no Class-D guy.

After all this page is meant to contain a list of all literature that is relevant according to my impression:
  • Some of the links get you to archive.org - this is the case for everything that I could find somewhere on the internet.
  • The other links get you to a google drive - the files you get from there are password protected. Send me a message and I'll help you.
 After all, there is nothing like a step-by-step guide around a 'blameless' solution.

People


This is me in 2018 taking a little walk through the evening hours of Copenhagen after a fruitful day at the ICEpower office - a time I remember with great joy and pleasure (read [7] !)

Dichotomy and Archetypes

There is this ubiquitous myth that within self-oscillating topologies there is a dichotomy between phase shift controlled (PSC) circuits and hysteresis controlled (HC) circuits. However, Bruno showed that these can be analyzed using one unified framework [PUZ09]. Yes, there are differences when it comes to details but essentially PSC and HC are the same.

The only true dichotomy in Class-D is clocked vs. self-osc. Period.

Still, this circuit below is praised as the archetype of all Class-D amps basically everywhere. 


However, practical implementations of this tend to get quite complex due to several reasons:
  • When you go full digital (which indeed has some powerpoint appeal) you need ADCs, DSPs and what not to in the end still have an analogue amplifier [PUZ06a]
  • When you go analog you need a precision triwave generator.
    • One very well known solution to this problem is a circuit which is known as "Rechteck-Dreieck-Generator" in German. It comes with a nice feature that might be worth to chew on for a while:
      • By adding just one resistor to the circuit which forms an input node this thing starts acting as a full-blown HC-type Class-D modulator in itself. 
      • A fact Stefan Wehmeier thought he figured out himself [ELB98] but I guess the patent office had a different opinion so the application got stuck in A1-phase. 
      • Question: does it really make sense to hide an SMPA inside an SMPA? 
  • In both cases the fed back signal parts will cause the beautiful triangle to be disfigured and so the PWM process itself is not linear anymore (-> distortion). Ripple compensation [PUZ06b] is a way around it (doesn't matter whether analog or digital) but this again adds complexity. 
    • So while it is inevitably true that this circuit is the archetype of clocked SMPAs practical design  it is absolutely no technical minimal system.

What is a 'technical minimal system'? 

I first heard this term during a lecture held by this guy. Actually the concept is fairly easy to understand. Think about an AC supply circuit. All it needs to supply a load is two wires (often referred to as 'live' and 'neutral'). The big benefit over DC (which also required 'just' two wires) it that with AC the voltage can be stepped up/down using transformers so to overcome large distances. But there is one remarkable drawback: as power is the product of voltage and current and both have periodic zero crossings also the transmitted power oscillates between zero and twice the average value (assuming a pure ohmic load). A more steady power at the load can be achieved by adding a rectifier and a smoothing capacitor. But this comes at the cost of high peak currents in the AC line (deformed power / Verzerrungsblindleistung).

Now comes the magic: by adding just one wire it is possible to go from single-phase AC to a three-phase system (a neutral wire is not really needed if the load is well-balanced). Transformation is still possible and the transmitted power is steady again. For sure it is possible to add more wires anb phases - but nothing gets better by doing so.

For my LinkedIn profile I once described it like this: "What drives me is the eagerness to find „minimal systems“ which is the state of a device, circuit or system where removing or altering a single component severely worsens the overall performance but adding components does not lead to significant improvements."


Final words

Finally one might ask: "what is the archetype of self-osc. SMPAs"?. Well (cliffhanger incoming), we'll clarify this in an upcoming post. However, I'm, 100% convinced that the following circuit shows (following the argumentation in [1]) the technical minimal system of an SMPA in general:


Yes, there is a first-order closed loop response - but there is no circuit with less components that yields (at the same time):
  • the same order of robustness
  • the same order of load-invariance
  • the same order of loopgain at higher frequencies (check [PUZ11b] and [7])

Cheers,
P.


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