Archive for June, 2009

Class-D PWM Harmonics

Wednesday, June 24th, 2009

PWM Harmonics versus Duty Cycle

Features to note in this plot of the PWM harmonic content versus the duty cycle:

  • At idle (D=0.5) only odd harmonics are present, as expected from a square wave
  • Away from idle (D<0.5 or D>0.5) even harmonics added, as expected from PWM
  • Magnitudes are equal at duty cycle extremes, as expected from an impulse function


If the class-D amplifier is a hysteresis modulator with a passive 2nd order output filter:

Hysteresis Modulator with 2nd Order Output Filter

Features to note in this new plot of the PWM harmonic content versus the duty cycle:

  • The harmonics increase abruptly as clipping is approached, consistent with observation
  • At idle the output is dominated by the fundamental (i.e. a low level sine wave at $$f_{s}$$)
  • Designs with more stable switching frequency at duty cycle extremes are easier to filter


Switching frequency versus duty cycle relationship for a hysteresis modulator:

$$f_{s}=4D\left ( 1-D \right )f_{0}$$

$$f_{s}$$ is the switching frequency at $$D$$
$$f_{0}$$ is the switching frequency at $$D=0.5$$
$$D$$ is the duty cycle $$0\leq D\leq 1$$

The Fountainhead

Friday, June 19th, 2009

New York Skyline

“What is it that I like so much about the house you’re building for me, Howard?”

“A house can have integrity, just as a person,” said Roark, “and just as seldom.”

“In what way?”

“Well, look at it.  Every piece of it is there because the house needs it – and for no other reason.  You see it here from the inside.  The rooms in which you live made the shape.  The relation of masses was determined by the space within.  The ornament was determined by the method of construction, an emphasis on the principle that makes it stand.  You can see each stress, each support that meets it.  Your own eyes go through a structural process when you look at the house, you can follow each step, you see it rise, you know what made it and why it stands.  But you’ve seen buildings with columns that support nothing, with purposeless cornices, with pilasters, mouldings, false arches, false windows.  You’ve seen buildings that look as if they contained a single large hall, they have solid columns and single, solid windows six floors high.  But you enter and find six stories inside.  Or buildings that contain a single hall, but with the facade cut up into floor lines, band courses, tiers of windows.  Do you understand the difference?  Your house is made by its own needs.  Those others are made by the need to impress.  The determining motive of your house is in the house.  The determining motive of the other is in the audience.”


This is the way Howard Roark, the main character of Ayn Rand’s The Fountainhead, describes the house he has designed for friend and supporter Austen Heller.  This novel is rare in its accurate illustration of the way many creative types feel about design – whether architecture, art, or amplifiers.  Non-functional ornamentation can provide transient beauty, but lasting beauty comes only from functionality.  Some of the most beautiful designs in the world are beautiful for two simple reasons:

1) The design serves a purpose better than other designs
2) The embodiment of the design is a function of the purpose

The human body is the best example I am aware of.

Beer and Amplifiers

Friday, June 12th, 2009


Anybody ever notice how “amplifier kits” sound the way that “beer kits” taste?

I recently took up homebrewing and, not knowing any better, I smiled as the nice LHBS man filled up my arms with “beer kit” paraphernalia.  I read the instructions carefully, bottled it up happily, and waited patiently for EIGHT weeks as it aged to “perfection”.  For any of you who have tried a beer kit, you are probably aware that “perfection” is a term to be applied loosely…

After dumping out bottle after bottle of icky beer, I was motivated to try making some beer from scratch.  This took lots of research that involves terms particular to beer making such as “degrees Plato”, “brix”, “original gravity”, “final gravity”, “wort” (pronounced “wert”), etc.  Make no mistake that I still made plenty of errors as I learned the ropes of making beer from scratch, but with a little tenacity I finally made something pretty good.  Please see the recipe below.

This whole experience bears an uncanny resemblance to “amplifier kits”.  This is where you take somebody’s amplifier controller and simply add the right ingredients – output stage, output filter, and power supply are typical – to build a complete amplifier.  It all sounds so simple, like the beer kit, and great results are promised, but these amplifier kits never quite manage to live up to it…

After throwing out the amplifier kit (i.e. “dumping the bad beer”) some are motivated to do research to figure out what is needed to make an amplifier from scratch.  There are many terms particular to amplifier design such as “dead time”, “slew rate”, “THD”, “EMI”, etc.  There are plenty of errors still in store for the would-be amplifier designer, but again with some tenacity it is possible to develop an amplifier that will shame any amplifier kit out there.

“Dry Ice Ale” Recipe

  • 6 lbs Briess 2-row malted barley
  • 2 oz Glacier hop pellets (added during boil)
  • 2 oz Cascade hop pellets (added to secondary)
  • 11g Nottingham ale yeast, proofed
  • Bring 5 gal water to 160F (fill pot with water night before)
  • Add grain and steep 30 min stirring occasionally
  • Remove grain and bring to boil (this is a no-sparge process)
  • Boil 30 min while adding 2 oz Glacier hops continuously
  • Put in ice water bath and stir gently for 20 min
  • Pitch proofed yeast and pour into primary
  • Fill airlock with water and let ferment 1 week
  • Transfer to secondary, add 2 oz Cascade hops
  • Fill airlock with water and let sit 2 weeks
  • Transfer to bottling bucket and add 1/3 cup sugar
  • Fill bottles and let carbonate 1 week
  • Put in cellar and let rest 4 weeks
  • Serve at cellar temperature and enjoy!

Gratuitous Self Promotion

Saturday, June 6th, 2009

The world’s first review of the HMA-1000 received the elusive Maximum Mojo Award! 


Reviewer Bill Schuchard who calls the amps “The Hephas”:

“The Hephas sound effortless, powerful, and transparent. There is a sense of ease and subtle detail.  The details don’t jump out at you yet you just hear more of what’s going on.  I was consistently hearing things I had never noticed and popping in headphones to verify. The highs are delicate and airy with a huge sense of space. The soundstage is taller and wider and surprisingly deeper than I am used to. Music in the foreground was not only a little closer than I expected but simultaneously the music in the background seemed further away than usual. Typically, I have found amplifiers to sound either forward or recessed but having both shows the delicate balance it struck. I attribute this to the amplifier’s ability to delineate the subtle lower level detail that sets up the space. String instruments not only had an added sense of air about them but some midrange bloom. Getting midrange bloom from a class D amplifier just goes to show that they are not all the same. One main striking aspect of the Hephas is its ability to attack transients. It is lightning fast and makes listening to energetic and uncompressed music so much more enjoyable. Lastly, the bass is interesting in that it’s a tad less controlled than the Bryston 2B SST and slightly richer; almost tube like. When pushed loudly, the bass stayed powerful and controlled all the way up until my woofers started to bottom. At the risk of shredding my GR Research M165X woofers, I had to be a little judicious with the volume knob.”

This is a great parting note from Mr. Schuchard in the review:

“Money speaks larger than words. I purchased the amps and couldn’t be happier with them. If you can’t stomach the price, take a listen and think again. If you can’t afford them, listening is just a tease. The 7 year parts and workmanship warranty and 90 full day ‘no questions asked’ return policy make it easy for one to take the chance on them.”

Bill Schuchard and James Darby of Stereomojo have been wonderful to work with and I couldn’t ask for more from an audiophile publisher.  To say I am surprised and thrilled at receiving the Maximum Mojo Award is an understatement.  As I put it in my first tweet regarding this topic, “Is this how musicians feel after a spectacular performance?”

Barrie Gilbert

Friday, June 5th, 2009

“We aren’t making the best products just because some customer suggested them to us, or even assured us of big orders, but because we have a passion to bring some art, in which we have a large personal investment, to the pinnacle of perfection.” – Barrie Gilbert 


This quote comes from Ch. 18, “It Starts with Tomorrow”, of The Art and Science of Analog Circuit Design.  If you love analog circuits, then this book should be placed right next to your copy of The Art of Electronics, if it isn’t there already.  Please refer to this IEEE article, “The Gears of Genius“, for more on this amazing designer.

There is a section of this chapter that deserves a brief summary – a bit of pseudohistory entitled “History through Dark Glasses”:


“…the first step to a successful product is thorough market research,” reads a young Thomas Edison in his new copy of “Yours is the Market: How to Find Out What People Really Need and Thereby Become Rich and Famous” by Harvard professor Yucan Sellum.  It is essential, says professor Sellum, to listen to the “Voice of the Customer” (VOC).  Young Mr. Edison now goes door-to-door to conduct the needed market research asking if his potential customers see any possible improvements in the way they light their homes.

Door 99

“First, if you can invent a stronger, brighter gas mantle, people will beat a path to your door.  Those durned things are always breaking!  And second, if you can invent a way that causes leaking gas pipes to be self-healing, you’ll quickly find yourself off these streets.”

Door 100

“Now, if you find a way to make our oil-lamps burn twice as bright and and twice as long from one filling, that would be something you could sell.”

Edison returns to his lab, dejected.  He has adhered to professor Sellum’s advice that he must conduct his marketing research “in such a way that…one only elicits those facts which the customer freely wishes to impart to the researcher.”  “Too bad nobody ever asked me if I had any ideas of my own,” sighs Edison as he gazes at his new tungsten lamp powered by a generator spinning in the basement…he then writes:

“Trip Report, 18th November, 1878.  Spent all day doing a VOC in Menlo.  Spoke with 100 people re lighting improvements; got good info. from 83….Action Item: Write Product Development Proposal re Improvements to Gas Mantles and Oil-Lamp Wicks.  Do before Monday exec. council mtng.  Call KJ to consider weaknesses in present methods of mnfng mantles.”


After your masterpiece is created you must listen carefully to your customers and adapt quickly.  However, for that first critical, tenuous, and beautiful spark, you must listen only to the inner dynamo that drives you to create that which has never before existed.