Damping Factor - Interesting article

BTW:  I really like how Ayre amps, and especially headphone amps sound.

here is a thought: own better speaker with a smooth impedance modulus,

You know, this can be done artificially for peaky impedance speakers, but it's expensive and wastes a lot of heat.  Low order crossovers (1st) and series crossovers also avoid these issues.

An amplifier that doubles in power as the impedance is squared will keep the most consistent anechoic output.

Buddy, you went the wrong way. I know of no amp that doubles power as impedance goes from 4 to 16 Ohms. That is certainly not an ideal voltage source anymore.


You are also conflating dispersion with relative differences in amp output
vs. impedance.


The feedback loop of Class D amps looks so different from linear amps I’m not at all sure we should be judging by the same criteria, assuming 35db is even correct. Last I looked there were at least 3 different ways in which Class D amps used feedback.


It is not unreasonable to imagine an amp with a 300 DF at 20 Hz but 50 at 20 kHz. At 20 Hz the amp’s output Z is ~ 0.03 Ohms, but at 20 kHz ~ 0.16 Ohms. With a normal dynamic speaker, these are not really significant, but ~ 0.16 Ohms is significant when compared to the 0.5 or less an ESL may present. Some quick math, and you’ll see about 1/4 of the amp’s output voltage is gone.


Of course, this is all hypothetical and math-y. Listening alone will tell you if you’d like it.


Best,
E

Another dimension of DF not often discussed is having high DF, and high current through the treble.  While conventional speakers tend to have their low points in the mid-bass, where most amps have the highest DF, ESL's are essentially capacitors, and have their lowest impedance in the peak frequency.

Having an amp that can do high current and low output impedance at 20 kHz can restore the treble.  This is a reason why a lot of tube amps can sound dull with ESLs.

Of course, no one cares more about this than Roger Sanders, and his Coda based amps are optimized for low DF and high current across the spectrum.

https://www.sanderssoundsystems.com/

My understanding is that low damping factor generally calls for high amounts of global negative feedbac

Doesn’t have to be global.  Local feedback can also be used to lower distortion and increase DF.  Also, a high output impedance (low DF) can be offset by having more output devices.

Still, yes, it is easy and cheap to achieve low damping factors with high amounts of global feedback.

One last thing:

Damping factor theory is basically series network analysis. There’s nothing here very complicated. You just string up your amp’s output impedance and put it in series with the load, then analyze the difference in output vs. F.

Amp (+) --> Output Z --> Load Z --> Amp (-)

A little work with a spreadsheet and a speaker impedance graph and you too could model this at home! Any EE learns to do this probably in the first semester of electronics. If you want to learn more search for "AC Circuit Analysis"

There is one thing I’d like to say though: While network analysis like this is straightforward, the effects I’ve heard from speaker cables has led me to believe that amps are more susceptible to cable and speaker impedance than we would model this way. I don’t think the model as outlined above fully accounts for what I’ve heard in all instances. This does not mean speaker cables are worth $30,000. It just means I think there’s untapped research to be done there.

Best,

E

I just looked at the speaker load Stereophile uses:

https://www.stereophile.com/reference/60/index.html


That is a very easy to drive load compared to a lot of the speakers they review today, or are typical. I wrote to them in the hopes they update it. This speaker is a much more typical load:

https://www.stereophile.com/content/bowers-amp-wilkins-804-diamond-loudspeaker

I am 100% sure they will ignore me.

It's' my impression (with no formal data) that speakers have tended towards harder-to-drive as SS amplifiers got bigger, beefier and more expensive.  Even the DIY speakers I make have a tough time staying above 3 Ohms to get decent sensitivity out of them.

The Focal is an interesting speaker to chose, since I've analyzed at least one model in depth, and let me tell you, it deliberately dropped the impedance.  No doubt in my mind that having a low impedance was a crossover design goal. Since then I've seen they have a remarkably similar profile in many of their speakers, and it does make a difference.  It makes a speaker seem more "discerning" of amplifiers. "My Focal must be better because I can hear the difference in amps." is the message.


Still, people don't want to chat about that, there are many other high end speakers which brush with low impedance. From B&W to your average ESL. 


The Stereophile simulated speaker load is more forgiving than some, but you can still see the impedance dependent effects there if you look at a tube amp review. The principle is the same, if not as large.

Best,
E

Yep. This is why Stereophile tests with a simulated speaker load. Look at any amp review, and compare tube amps to SS in the measurements.

For a counter point though, look at Nelson Pass. He wrote at least one article where he showed that with some speakers, low damping factor, not high,  is ideal.


Best,E