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How to Design a Class-D Amplifier

 Child With Blocks

This is a very tricky topic.  Any simple article is never going to be enough for a novice to really be able to design a class-D amplifier.  However in this article I attempt to outline the basic requirements and considerations for designing a class-D amplifier.  It isn’t complete, but it’s a good start!

Also, in the article I attempt to draw a parallel between some of the familiar elements of a linear amplifier and the perhaps not-so-familiar elements of a class-D amplifier.  The comparison isn’t perfect, but I hope it will serve as a springboard to those not yet familiar with the intricacies of class-D amplifier design.

Level Matching for AB Testing

Two Glasses of Wine

In order to evaluate two components in an AB test, it is essential that they are carefully level matched.  If the gain differs by only one dB, the louder unit will almost always be perceived as sounding better.  Unfortunately, this phenomena has been exploited by unscrupulous hi-fi dealers to promote overpriced components, as I have personally witnessed:

My friends and I once went to a local hi-fi shop to check out the goodies.  There were some very lovely components we had the opportunity to see and hear, but there was also a one meter length of heavy power cord retailing for about $2,000 (this was over 10 years ago).  The salesman conducting the demos (err…Jim) saved this gem for last – here’s the process he used (I watched very carefully):

  • Carefully set volume knob to specific level
  • Play track from reference CD to completion
  • Turn down volume knob to zero
  • Insert special power cord between power strip (!) and amplifier
  • Carefully set volume knob to specific level
  • Play track from reference CD to completion
  • Turn down volume knob to zero

Sure enough the second time the track was played it sounded significantly better!  It would have been truly amazing if I had not been paying really close attention: When Salesman Jim carefully adjusted the volume knob the second time – the time with the special power cord in circuit – he turned it up just a little bit higher!  It wasn’t enough to notice it was louder, but it was enough for all of us to think it sounded much better.

My friends had unfortunately not noticed this scoundrel’s trick.  I’m sure I only did because I knew to look for it.  I quizzed Salesman Jim on exactly what made this power cord work.  At first he tried to dodge the question, but then it went something like this:

Salesman Jim: “Okay, okay it’s a ‘PFM Circuit’.”
Me: “A ‘PFM Circuit’?  I’ve never heard of that – what’s it mean?”
Salesman Jim: [laughing] “Pure Fricking Magic.” [note: slightly edited]
Me: “Okay, ha ha, seriously what is it?”
Salesman Jim: [growing annoyance with this punk] “Hey Bob, what’s the technology of this [brand] power cord?”
Salesman Bob: “Uh…geometry and metallurgy.”
Me: “Geometry and metallurgy?”
Salesman Bob: “Yup, that’s it.”
Me: [sigh] “Okay, well thank you guys for your time.”

So there you have it folks – the secrets to any mysterious audio gizmo: PFM Circuitry and Geometry/Metallurgy – what will they think of next!

Physics Friday – Blackbody Radiation

 Blackbody Radiation

Please forgive the bitter tone that follows in this post, but recently I came across an “audiophile” device that I feel may damage the already precarious position of the audiophile industry.  First however a little necessary physics background…

A “Blackbody” is an object that does not reflect electromagnetic energy incident upon it, or allow any to pass through it.  Any emission from it is entirely thermal in nature with no characteristic emission/absorption lines from any element.  This is referred to as “Blackbody Radiation”.  Classical theory describes this spectrum with the Rayleigh-Jeans Law:

$$I(\lambda ,T)=\frac{2\pi ckT}{\lambda ^{4}}$$

$$I(\lambda ,T)$$ is the power per unit area
$$c$$ is the speed of light
$$k$$ is Boltzmann’s constant
$$T$$ is the temperature in Kelvin
$$\lambda$$ is the wavelength

This is in agreement with observation at lower frequencies, however the problem with this result is that at higher frequencies (i.e. as $$\lambda \to 0$$) the power approaches infinity!  This is certainly not in agreement with observation and has been referred to as the “ultraviolet catastrophe”.

A physicist by the name of Max Plank made an amazing assumption that was to prove instrumental not only for resolving the paradox of the Rayleigh-Jeans law, but for all of quantum mechanics.  The assumption is that radiation can only only assume discrete energy values:


$$n$$ is the energy level
$$h$$ is Planck’s constant
$$f$$ is the frequency.

Therefore the energy between two adjacent energy states is given by:


The power per unit area spectrum that results from this important assumption agrees with observation and is given by the following expression:

$$I(\lambda ,T)=\frac{2\pi hc^{2}}{\lambda ^{5}(exp(\frac{hc}{\lambda kT})-1)}$$

Now I return to the bitter part of my post.  As I make clear in my Engineering Perspective article, I am not a big fan of overpriced audio interconnects.  I am not saying there isn’t a subjective improvement, but that it may not provide the greatest benefit to cost ratio for the audiophile.

However, at least these overpriced interconnects are functional.  At worst, they get the signal from point A to point B.  Even something as esoteric as a special wooden volume knob that improves your sound at least allows you to turn up the volume!  But a product that claims to dramatically improve your system by acting as an electromagnetic blackbody for your equipment is a complete waste.

There are people in this world with incredible perception that can detect “impossible” subtleties.  The purpose of the audiophile industry is to cater to these individuals – those for whom minute differences matter.  Please try to give these gifted individuals the audio experience they deserve and not just another piece of junk backed up with horrible pseudoscience.

Snake Oil

Personal Goals

John Performing the Iron Cross 

I love to set personal goals.  The feeling of always reaching for something that you can just barely touch with your fingertips.  The above picture is my father-in-law John performing the “Iron Cross” on the gymnastic rings.  He used to perform the “Flying Rings” on Muscle Beach back in the day.  Wow.  Gymnasts make it look so easy, but the most humbling experience you can have is to actually try it.

Like I said I love to set goals for myself, and not just in audio endeavors (e.g. design a great new amp).  I’m not what you would call an “in-shape” person – in fact just two months ago I couldn’t do a single chin up!  Now I can do a single good one (no kicking, swinging, etc.)  I have installed a pair of gymnastic rings in the garage and my personal goal is: to perform a single “Muscle Up” on the rings!

My next goal is to someday perform the Iron Cross on the rings…hey, it’s important to have dreams!  🙂

Grounding and Layout for Audio

Ground Symbol

There is much debate about optimum grounding strategies in audio electronics.  This article explores a “Star Ground” versus a “Ground Plane”.

It may come as a surprise that, despite the common use of the star ground approach in audio electronics, the ground plane is superior.

Also included in the article is a list of helpful advice for a successful layout, particularly for high-power switching audio designs.


Happy Belated Birthday!


Oops, time flies and I didn’t notice that an entire year has passed since Hephaestus Audio was officially founded!  I guess that means we should be walking now?  😉

A lot has happened in that time.  I’ve had some great feedback and some very happy customers, but I’ve also come face-to-face with the realities of juggling a startup, a day job, and a family.  They say most startups fail within the first year and now I have experienced exactly why: it’s far too easy to just give up!

The most important part however is that we’re still here and we’re still making one of the finest amplifiers you’re likely to come across.  Happy birthday to us!

Hephaestus Audio Announcement


Following on the heels of my previous announcement I have a much better announcement: my brother, Mike White, has joined the Hephaestus Audio team!  His strong business background will be perfect for directing  sales, marketing, and business development (i.e. all of the things I’m not so good at).  I will now be able to focus more on what I do best: the manufacturing and R&D of audiophile class-D amplifiers.

I can’t express how excited I am to find somebody that not only complements my abilities so well, but also somebody I’ve known all my life!  We’ve got the start of a killer team here – the best is yet to come.  🙂

Hephaestus Audio Transition


Well, it’s been nothing if not interesting.

In trying to more or less single-handedly start my own audio company, I have discovered something: I have absolutely no clue how to market and sell a product!  No doubt it is obvious to those with sales and marketing savvy that a designer might be ill-suited to this task.  Such being the case, I will transition Hephaestus Audio from a commercial site to a site devoted to those who love audio and audio electronics.  Really though, it’s been that all along…kind of like the Tin Woodman and his heart.

There will be some changes to the website soon.  I will change the product section to a project section that shares various projects I have worked on, such as the HMA-1000 monaural amplifier and the VK-1 dipole loudspeaker.  Also, I will keep chugging away with audio-related posts and articles at my relatively glacial pace.  I hope these are useful and enjoyable for my fellow audio enthusiasts.  You can still reach me via email (iris@hephaestusaudio.com) with any questions or just to chat about this great hobby.

We tend to be good at what we’re passionate about (or is it the other way around?) so I’m going to stick with what I’m good at: audio design.  Who knows, maybe someday down the road I’ll be fortunate enough to meet up with somebody who shares my vision, has a gift for sales and marketing, and is just crazy enough to love the audio industry.  Anything is possible.  🙂

Food for Thought

Leonardo da Vinci Sketches

When I stop and think – imagine – the most fantastic images come to mind.  I know I’m getting the smallest sliver of a glimpse inside of my subconscious and my conscious mind is futilely attempting to make sense of it in the terms it understands: vision, hearing, etc.  This process is so amazing that I’ve never been able to convey it very well, although I’ve no doubt that other designers have a similar experience.  Most likely even more so.

That’s the first step.  Thinking.  Imagining.  However, for others to benefit from this process it is necessary next to do something.  A former professor of mine, Carl Pavarini, once said “Ideas are worth their weight in gold.”  After the class full of engineers enthusiastically agreed, Dr. Pavarini then posed the question “How much does an idea weigh?”  Ouch.  It’s a tough pill to swallow, but it’s painfully true.  You must do something – whether your medium is paint, words, code, or solder.

I’m not sure what’s more incredible: the fact that I have the great joy of experiencing these creative visions or the fact that so many others have as well!  The following quotes provide terse insight to the inner workings of great minds.  These are the thoughts of the giants on whose shoulders we have all stood.  The best innovators distinguish themselves by not fearing to stand at such a great height.


“I do not think there is any thrill that can go through the human heart like that felt by the inventor as he sees some creation of the brain unfolding to success… such emotions make a man forget food, sleep, friends, love, everything.” — Nikola Tesla

“But I think Steve’s [Jobs] main contribution besides just the pure leadership is his passion for excellence. He’s a perfectionist. Good enough isn’t good enough. And also his creative spirit. You know he really, really wants to do something great.” — Andy Hertzfeld

“People take the longest possible paths, digress to numerous dead ends, and make all kinds of mistakes. Then historians come along and write summaries of this messy, nonlinear process and make it appear like a simple, straight line.” — Dean Kamen

“An essential aspect of creativity is not being afraid to fail.” — Edwin Land

“One of the unfortunate things about our education system is that we do not teach students how to avail themselves of their subconscious capabilities.” — Bill Lear

“One always has to remember these days where the garbage pail is, because it’s so easy to make sounds, and to put sounds together into something that appears to be music, but it’s just as hard as it always was to make good music.” — Robert Moog

“With all the knowledge and skill acquired in thousands of flights in the last ten years, I would hardly think today of making my first flight on a strange machine in a twenty-seven mile wind, even if I knew that the machine had already been flown and was safe.” — Orville Wright

“Knowing is not understanding. There is a great difference between knowing and understanding: you can know a lot about something and not really understand it.” — Charles Kettering

“Opportunity is missed by most people because it is dressed in overalls and looks like work.” — Thomas Edison

“The real secret of success is enthusiasm.” — Walter Chrysler

Physics Friday – Calculus of Variations

Calculus of Variations

“I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely in your thoughts advanced to the state of Science, whatever the matter may be.” – Lord Kelvin

I do not completely agree with Lord Kelvin’s assertion, but there is no doubt that you must understand a subject really, really well in order to translate it into the language of mathematics.  Once you have done so however, a whole world of tools opens up.  Not only the vast array analytical tools of past generations, but the powerful simulation tools of the present.  The Calculus of Variations is one such tool – one that allows you to determine what is optimum, whether in terms of cost, time, quality, etc.

Please refer to this article for more background on the Calculus of Variations, as well as the derivation of the Euler-Lagrange Equation.