Damping Factor - Interesting article

@bifwynne  Benchmark selected 8 ohm speaker with 13 - 2.6 ohm impedance variation.  One ohm of output impedance would reduce signal to 13/14 and 2.6/3.6 respectively.  Ratio of reduced signals would be 1.286  (28.6% difference) = 2.18dB   It would be much less for my 6ohm speakers that have minimum impedance of 3.6ohm 

@douglas_schroeder  Yes, the difference between DF=20 and DF=2000 seems to be huge, but not for the purpose of damping.  Amplifier with DF=2000 has very low output impedance and will provide steady voltage (ideal voltage source) at all frequencies while speaker impedance vary greatly.   It will affect the sound because of that.  Damping is different story.  When we apply positive voltage speaker membrane moves forward.  When membrane moves forward on its own speaker generates also positive voltage, but now current flows from speaker to amplifier.  Opposite direction of this current produces opposite action on the membrane and membrane stops.  This current depends on back EMF produced by the speaker and impedance in the circuit/loop.  This loop contains speaker internal impedance, impedance of speaker wire and the output impedance of an amp.   Let's assume for a moment that wire is perfect.  Total resistance in the circuit will be resistive portion of the speaker impedance - most likely 6 ohm for 8 ohm speaker and resistance of the amps output.  At DF=20 total resistance in the circuit will be 6 ohm + 8/20 ohm = 6.4 ohm  while for DF=2000 it will be 6 ohm + 8/2000 ohm = 6.004 ohm.   Ratio of braking current in the circuit will be equal to ratio of total resistance - in this case difference of 6.6%.  Is it audible?  Perhaps for trained ears, but it is not as dramatic as DF=20 vs DF=2000.  There will be more sound change from less than perfect driving, than lower damping IMHO.  For DF=200 vs DF=2000 difference in damping will be 0.6%.

@douglas_schroeder I don’t question what you heard at all. My experience is none compare to yours. I merely stated, that the sound difference you heard could likely be because of less stable output voltage while driving and not because of different damping.
As I said, the difference in damping between DF=200 and DF=2000 is only 0.6% but many people believe it is 10x more. The other question is how this high DF was obtained. The easiest way to lower output impedance is to increase feedback. Adding 20dB to feedback lowers output impedance 10 times, but there are consequences of that. One of them is TIM, that produces unpleasant higher order odd harmonics, that make sound bright and unpleasant. Even Benchmark in AHB2, that doesn’t have negative feedback in normal sense (feedback is non-recursive), settled only for DF=350@20Hz. Class D might have inherently low output impedance because output Mosfets always clamp output to low impedance (either GND or VCC), but for the other classes I would even avoid amps with very high DF (like 2000). Something has to give IMHO.

Every amplifier has some feedback. Even emitter resistor is a form of local feedback. The problem with global feedback is, that it corrects with a delay (phase shift from input to output). This delay produces overshoot in time domain (odd harmonics in frequency domain). 40dB feedback means, that amplifier has 100x higher gain without feedback. Since amplifier delays signal from input to output, signal fed back and summed at the input is late. It make very little difference for slow sinewaves, but for fast changing input signals amplifier, for a moment, has 100x higher gain and overshoots. Benchmark is trying to time correct it with separate error amplifier (two sets of output transistors). This overshoot shows in some Stereophile reviews at square wave response.

but the low DF will in many cases be better.

How low?  For electrical damping of 8ohm speaker difference between DF=10 and DF=100 will be like 6.8ohm vs 6.08ohm (assuming 6ohm as resistance of 8ohm coil).  It is about 12% difference in breaking current.

It is possible to make amplifier like that, but I found only car amp that delivers constant power:

https://www.crutchfield.com/S-W0uT7l6IaIv/learn/amplifier-power-labs.html#:~:text=Constant%20Power&text=Normally%2C%20an%20amplifier%20will%20change,impedance%20changes%20happen%20during%20play.

@atmasphere  That's how they describe this car amp:

Speakers and subwoofers change their impedances depending on what frequency note is playing. Normally, an amplifier will change its output power according to what impedance it senses. The Constant Power circuitry Rockford Fosgate developed changes all that, allowing the amp to put out exactly the same power no matter what impedance changes happen during play.

The constant power delivery doesn't necessarily mean it is maximum power (maximum power is delivered only when load impedance is the same as the source impedance).