# Audibility of Low Damping Factor? - Benchmark Myth-Busting White Paper

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#### Wes

##### Major Contributor
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interesting...

any implications for Class D amps?

#### solderdude

##### Grand Contributor
A speaker cable is in series (both wires) with the speaker system + output resistance.
Passive speakers with XO filters in them also have a series resistance + impedance of the inductances that are in series with the woofer/midrange.

See it this way:
Amp has an ideal output voltage (infinite current and 0 Ohm output resistance and infinite output voltage). It 'sees' its output resistance + total round trip cable resistance + entire speaker in series. The speaker is complex (inductive, resistive and capacitive at various audio frequencies + voicecoil.)

The speaker also generates a signal because it has mass connected to a coil that moves in a magnetic field. The mass requires energy to move and to stop. This is provided by the amp. When the mass isn't stopped by mechanical damping it will generate a voltage.
One can see a speaker as a generator with a resistance.
That resistance is the DC resistance of the speaker. That speaker thus has a voltage. The current (the actual damping current) thus is determined by the total resistance it has which is: speaker resistance + inductor resistance (impedance depending on frequency) + internal speaker wiring + cable wiring + output resistance of the amp.

As the speaker resistance is the largest resistance by far that resistance determines the actual damping current. When a resonance of speaker is near that of the crossover the impedance of the inductance will also play a large role.

#### pjug

##### Major Contributor
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The spreadsheet is pretty handy. Also shows that 8 ohms nominal without a big impedance dip really eases the requirements for damping factor and cable resistance.

#### dc655321

##### Major Contributor
I do have a question on the very last section regarding if the speaker cable should be considered on the amp side or speaker side of the equations.

"Damping Factor" (hate that term) is a property of an amplifier, not the load that it drives.
Since one cannot drive a speaker without an interconnect (cable), and the impedance of the interconnect influences an amp's "damping factor", it makes sense to consider the cable as part of the amplifier's output impedance rather than as part of the load's input impedance.

My \$0.02...

#### scott wurcer

##### Major Contributor
Audio Luminary
Technical Expert
This is disappointing, from Dick's article...

There may be audible differences that are caused by non-zero source resistance. However, this analysis and any mode of measurement and listening demonstrates conclusively that it is not due to the changes in damping the motion of the cone at the point where it's at it's most uncontrolled: system resonances.

He clearly states what he was trying to show, yes there may be audible differences but they are not due to differences in damping the cone motion. The guys at Benchmark disappoint again.

#### sergeauckland

##### Major Contributor
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The resistance of the 'speaker cables is both a part of the load, as seen by the amplifier, and part of the amplifier output impedance, as seen by the back-emf of the loudspeaker.

S

#### amirm

##### Founder/Admin
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Benchmark just issued what seems to me an excellent analysis of this issue with somewhat surprising conclusions.

https://benchmarkmedia.com/blogs/application_notes/audio-myth-damping-factor-isnt-much-of-a-factor

I do have a question on the very last section regarding if the speaker cable should be considered on the amp side or speaker side of the equations.

EEs, please help explain!
It is a correct analysis. We do this all the time with headphone amplifier measurements because it is much more common to have high impedance in headphone amps than speaker amplifiers.

Simply put, if you have a speaker that dips to low impedances (hence the reason I and others publish them), the amplifier output impedance and that of cables becomes more important. The lower the amplifier impedance and that of the speaker cables, the less chances it can change the frequency response of the speaker.

#### blueone

##### Addicted to Fun and Learning
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@John Atkinson

Has been measuring output impedance in his Stereophile amplifier reviews for years (decades?), and he's the only reviewer I've seen who makes an attempt at quantifying the effect of output impedance on frequency response by using a simulated speaker load. For example, one of his recent reviews of a Parasound solid state amplifier:

https://www.stereophile.com/content/parasound-halo-jc-1-monoblock-power-amplifier-measurements-0

You can read the review itself for what all of the plot colors mean, but the charcoal (gray) line is a simulated two ohm load, and you can see that there are minor frequency response aberrations due to the ratio between the low speaker impedance and the amp's output impedance. Of course, this is an amp with a very low output impedance, so the differences are minimal. (And, frankly, John's measurements over the years have been one reason why low output impedance has been an amp buying criteria for me, even though someone as smart as Dick Pierce says it shouldn't be.)

Contrast the simulated measurements of the Parasound amp with that of those of a Pass First Watt amp (note the difference in the y-axis scale):

first-watt-sit-3-power-amplifier-measurements

While I believe that John Siau might be ever-so-slightly ( ) over-emphasizing the case for low output impedance, my question is: why not design for lowest output impedance? Low output impedance has no drawbacks I can think of, while output impedance higher than about 0.2 ohms might make an audible difference in frequency response with some speakers.

#### solderdude

##### Grand Contributor
I have been measuring the effect of output R for headphones for a long time. Not just electrically but also in sound output.
Impedance differences in the headphone business are infinitely greater than with speakers. Due to the lightweight drivers and often closed well damped circumstances most headphones rely mostly on 'mechanical' damping and less so on electrical. There are plenty headphones that have impedances that barely rise around their resonances.

#### mhardy6647

##### Master Contributor
so... the whole damping factor thing has always gotten my dander up

Mostly because (and as mentioned in the Benchmark link), most loudspeakers don't present a frequency invariant impedance load to an amplifier. Trying to capture this aspect of loudspeaker/amplifier interaction with one number is (I am grasping for a word that adequately conveys my dudgeon) foolhardy.

The way I look at it, an amplifier with a high(ish) output impedance "feels" (ahem, interacts with) its load more than one with a very low output impedance. The result (again, the way I look at it) is one of those places where the subjectivists and the objectivists cross paths -- there really is "synergy" between some amplifiers and some loudspeaker loads!

OP

#### MediumRare

##### Major Contributor
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So here is my confusion: if you assign the cable impedance to the amp side of the equation, the damping factor goes down dramatically. If you assign it to the total load the amp faces (added to the speaker) the damping factor is essentially unchanged. So which way models best the effects on FR at low v high impedance sections of the audio spectrum?

#### DonH56

##### Master Contributor
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So here is my confusion: if you assign the cable impedance to the amp side of the equation, the damping factor goes down dramatically. If you assign it to the total load the amp faces (added to the speaker) the damping factor is essentially unchanged. So which way models best the effects on FR at low v high impedance sections of the audio spectrum?

The damping factor applies to the amplifier but what the speaker cares about is the effective driving (source) impedance it sees. So, if you are looking for why speaker response varies, look at the driving impedance from the speaker's point of view.

Another way to think about it: If the amplifier has 0-ohm output (infinite damping factor), and you stick 100 ohms in series with it to the speakers, it looks like a 100-ohm source to the speaker and frequency response will vary with any impedance variations within the speaker.

Except for a few special cases (like the old Kenwood Sigma-Drive and a couple of other amps) the cable's impedance is not in the amplifier's feedback loop and thus is not compensated. Any impedance added after the amplifier's output effectively reduces the damping factor seen at the load (speaker).

Example:
Amp has DF = 100 into 8 ohms, or an output impedance of 8/100 = 0.08 ohms​
Add 0.1 ohms of speaker cable, then the speaker "sees" 0.18 ohms driving-point impedance, for an effective damping factor of 44.44.​
Damping factor is generally defined just for the amplifier and a given (usually resistive) load, but if you want to apply the concept to the speaker, that is what I would do. I personally prefer to know the actual output impedance, preferably over frequency since it tends to rise with frequency.

HTH - Don

OP

#### MediumRare

##### Major Contributor
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The damping factor applies to the amplifier but what the speaker cares about is the effective driving (source) impedance it sees. So, if you are looking for why speaker response varies, look at the driving impedance from the speaker's point of view.
Great explanation, Don. So the speaker is more sensitive to the load it faces than the amp is. Makes a lot of sense. If I understand correctly, the drivers’ continuing motion is the problem here so having the lowest possible impedance facing it reduces the uncontrolled movement.

#### DonH56

##### Master Contributor
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The load the amplifier sees is the cables plus the speaker. The driving source the speaker sees is the cables plus the amp.

Cone movement or back-emf is one issue; others include the impedance over frequency due to the crossover and driver parameters. A lot of speakers exhibit 2x to 4x or more impedance variation over frequency. For example, an 8-ohm speaker may have a low point below 4 ohms at one frequency, and a high of 16 ohms at another frequency. If the amp plus cable impedance was zero ohms this would not matter. When it is some value higher than zero it creates a voltage divider with the load, so the voltage at the speaker will vary with impedance which in turn varies with frequency. That can change the sound. The usually extremes are to compare a tube amplifier that might have an output impedance of a few ohms to a SS amp with impedance in the tens of milli-ohms range. The tube amplifier's "sound" will change much more than the SS amp due to the changing speaker impedance when the amplifier's output impedance is so high (or damping factor so low) because the amplitude will change with frequency (lower with lower speaker impedance).

An amp with 1-ohm output impedance putting out 1 V into 8 ohms will put out only 0.9 V into 4 ohms, a change of -0.915 dB. A SS amp with 0.01 ohm output impedance (10 milli-ohms, damping factor of 800) will change only -0.011 dB.

HTH - Don

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#### amirm

##### Founder/Admin
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@John Atkinson

Has been measuring output impedance in his Stereophile amplifier reviews for years (decades?), and he's the only reviewer I've seen who makes an attempt at quantifying the effect of output impedance on frequency response by using a simulated speaker load. For example, one of his recent reviews of a Parasound solid state amplifier:
He is not the only one. I did that too. Indeed I built the same load he did and ran it on a few amps. Net result was that the frequency response variations were very small as to not be worth continuing to test with it. JA uses much magnified scale to show variations.

#### amirm

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#### witwald

##### Senior Member
The Stereophile simulated loudspeaker load, which was mentioned earlier in this thread, has a minimum impedance of about 4.0 ohms at around 5 kHz. The circuit has been published, including details of the component values, and nominally represents a two-way closed box loudspeaker system (with a low-frequency resonance at about 70 Hz). Using those component values, it has been possible to compute this circuit's impedance as a function of frequency, and the results match the published measurements to an excellent degree. Some small differences are apparent, and these are probably due to component value differences between the theoretical circuit and the as-built circuit.

The plot below shows the computed frequency response functions of amplifiers with various values of damping factor (DF) when loaded by the Stereophile loudspeaker simulator circuit. The damping factors studied include values of 10, 15, 25, 50, and 100. The source impecance (Rg) is also indicated, and the impedance of the loudspeaker simulator circuit is also plotted. It is clearly evident that the variations in amplifier frequency response closely follow the variations in the impedance of the simulated loudspeaker load.

Once the damping factor is greater than 100, then the frequency response variations are going to be quite small, and can probably be neglected. However, at low damping factors, such as 10 or 15, which are in the realm of what tube amplifiers have, then the frequency response errors are much greater, and they are likely to be audible. One thing to keep in mind is that, when an amplifier has a low damping factor, it's frequency response will be affected differently by different loudspeakers.

For frequencies above about 200 Hz, it would be quite feasible to design a conjugate impedance network that could be used to equalise the impedance of the simulated loudspeaker circuit (or that of a real loudspeaker), and make its impedance much flatter. This combination would appear more like a constant resistive load to the amplifier. This would result in that portion of the loudspeaker sound pressure output becoming much less sensitive to the frequency response variations caused by amplifier damping factor. Conjugate impedance networks are already used in equalizing the impedance of individual loudspeaker drivers to remove their rise in impedance due to voice-coil inductance. These simple networks are usually known as Zobel networks, and they make crossover network design simpler in some circumstances.

#### samsa

##### Senior Member
While I believe that John Siau might be ever-so-slightly ( ) over-emphasizing the case for low output impedance, my question is: why not design for lowest output impedance? Low output impedance has no drawbacks I can think of, while output impedance higher than about 0.2 ohms might make an audible difference in frequency response with some speakers.

One of the advantages of Class-D is that you can design for very low output impedance. The Hypex NC252MP has an output impedance <3.5 mΩ over the entire audio band (<1.5 mΩ below 1 kHz). Compare that to the 21.6 mΩ output impedance of the Benchmark ABH2.

For the ABH2, the output impedance of the amplifier is comparable to that of 10 feet of good quality speaker cable. For the Hypex module, it's an order-of-magnitude smaller, and can be neglected relative to the effect of the cable.

Net result was that the frequency response variations were very small as to not be worth continuing to test with it. JA uses much magnified scale to show variations.

@John_Siau advocates keeping the variation in frequency response to ~0.1 dB (the accepted level-matching threshold of ABX testing). So, yeah you do need to magnify the scale, for that to be visible.

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