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

#### solderdude

##### Major Contributor
In short, there are 2 factors at play:
1: voltage division
2: actual change in damping current.

1: When speakers have considerable varying impedances then due to the voltage division the frequency response is changed. The higher the impedance value changes and the higher the output resistance the higher the effect (change of frequency response)
Depending on the speaker impedance and 'allowed' frequency response variations the damping factor may be higher or lower.
Take into account that the roundtrip resistance of the cable must be added to the output resistance from a voltage division standpoint.
A longer and/or thinner cable thus also has an effect and for this reason, wanting the smallest FR changes and be less dependent on the cable used the output resistance of the amp should be lowest possible to allow for the cable to 'f it up bit while staying within the max. allowed frequency deviations.

The points here thus are:
What max frequency deviation is allowed ? 0.1dB with about all speakers, 0.5dB with about all speakers etc. The more one allows the lower the DF can be.
Cable resistance (roundtrip) the higher the resistance is of the cable, when allowing the same FR deviations mentioned above, the higher the DF should be. Note a factor 10000 and 100 both aren't going to compensate. There is a maximum allowed cable resistance basically.
Speaker impedance the lower the impedance of the speaker are the higher the DF must be to ensure FR deviations remain below the set target. And the higher the impedance variations are relative to the lowest impedance the higher the DF must be to remain below the desired FR variations.

2: Actual damping current change. The actual damping current won't change much when the DF is above say a factor of 10. The damping current is determined by the generated back-EMF and the total resistance path. So DC-resistance of the to be damped driver + DC resistance + impedance of the XO filter in the driver (thus frequency dependent) + roundtrip cable + connectors + output resistance.
It is easy to see that the driver's DC resistance + impedance of the XO filter by far are the greatest contributors when it comes to total resistance path. Varying the cable or output R somewhat won't change the damping current much. Say the DC resistance of a speaker + filter + cable is 8 Ohm and the DF is 1000 the output R = 0.008 Ohm. When the DF is 10 the output R is 0.8 Ohm.
So between a DF of 1000 and DF of 10 the difference in actual damping current = 0.91x smaller in case of a DF of = 0.8dB so very little change in damping current.

This means the voltage division issue is far more important than the damping current.
The maximum allowed frequency variations in as good as all situations for an amplifier, when allowing just 0.1dB variations under those conditions thus requires a high damping factor and short cable runs with low resistance wires.
That's why benchmark comes up with the numbers they use.

Now for headphones (aside from some MA IEMS) the same more or less applies but the lowest required DF is far more relaxed (can be considerably lower in number thus higher in output resistance) because A: membranes aren't as heavy, DC resistance of headphone drivers is much higher than speakers (with some exceptions) and B: impedances do not vary nearly as much relatively to the DC resistance of the driver. Again with the exception of some MA IEMS.
To ensure a low FR change under all circumstances this requires a low output resistance. This is why NwAvGuy set his rules so strict
However, in reality, when owning just one or 2 not or slightly impedance varying headphones that aren't unusally low in impedance the '1/8th rule' can be broken without any ill effects to the frequency response.
To play it safe there is merit to the rule. whether it should be 1/50th or 1/4th depends on what FR variations one allows. 0.1dB or 0.5dB is a substantial difference in rule numbers.

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#### trl

##### Major Contributor
King of Mods
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.

I guess this was already explained, but the answer is still in the same Application Note:

"[...] the effective damping factor can be calculated as follows:
• Amplifier output resistance = 8/370 = 0.0216 Ohms
• Speaker cable resistance = 0.0252 Ohms
• Total source resistance = 0.0216 + 0.0252 = 0.0468
• Effective damping factor = 8/0.0468 = 171"
So AHB2's damping factor was initially 370 referenced on 8-Ohms load, but summing up the 3-meters long cables it decreased to 171.

In my case, by using 6-meters 4mm2 cables (AWG11) I have decreased the initial damping factor of the A-S701 from 240 to only 92, so probably by using shorter and thinker cables the power loss and linearity across audible bandwidth might get improved.

#### solderdude

##### Major Contributor
In my case, by using 6-meters 4mm2 cables (AWG11) I have decreased the initial damping factor of the A-S701 from 240 to only 92, so probably by using shorter and thinker cables the power loss and linearity across audible bandwidth might get improved.
It will improve measurably, the real question is will it improve audibly.

#### trl

##### Major Contributor
King of Mods
It will improve measurably, the real question is will it improve audibly.
Well, in my case REW was showing a pretty flat freq. response, but maybe I'll try sometimes to measure with 1.5mm2 cables instead of 4mm2.

#### ayane

##### Member
My respect for Benchmark is high as always! This article was pretty eye-opening in that I didn't realize it takes a damping factor in the hundreds to achieve reliable output without coloring the frequency response.

That being said, I have doubts regarding the threshold of audibility as it was stated in the article: "The general rule of thumb for A/B and A/B/X tests is that levels should be matched to better than 0.1 dB. If this is not done, the level changes can be detected by many listeners." Citation needed! While I do think an error of 0.1 dB is a great goal to strive for, I don't think a higher error would be much worse, audibly. Even 1 dB is a JND for most people, especially in normal listening environments. I feel like room acoustics would play a larger part in coloring the sound than damping factor. I think this would only be a problem for seasoned listeners with good ears and in optimal listening conditions listening to very specific kinds of music. Feel free to correct me - I'm sure we can and need to do a lot better than 1 dB, but we're greatly overestimating the precision of human audition by suggesting that it takes 0.1 dB to be good enough.

An error of 0.1 dB is a great target because because it's significantly below just-noticeable-difference and it encourages better electronics design, but I don't think it's necessary nor as important as other factors. Targeting below 0.5 dB should suffice for most people.

#### Wombat

##### Major Contributor
My memory is a bit vague on this but by adding series resistance, 1 to 5 ohms, to the speaker cables of SS amps a reasonable emulation of 'tube sound' is purported. This may be more appropriate for the large woofers of old, e.g. Altec, JBL, Jensen and their overseas equivalents, drivers developed for movie theatre and movie industry soundstage(not HiFi soundstage meaning) use. I have lost the references. Can anyone provide information?

OP

#### MediumRare

##### Major Contributor
Forum Donor
That being said, I have doubts regarding the threshold of audibility as it was stated in the article: "The general rule of thumb for A/B and A/B/X tests is that levels should be matched to better than 0.1 dB. If this is not done, the level changes can be detected by many listeners." Citation needed! While I do think an error of 0.1 dB is a great goal to strive for, I don't think a higher error would be much worse, audibly. Even 1 dB is a JND for most people, especially in normal listening environments. I feel like room acoustics would play a larger part in coloring the sound than damping factor. I think this would only be a problem for seasoned listeners with good ears and in optimal listening conditions listening to very specific kinds of music.
Very easy to test at home if you have an equalizer of any kind. Have a friend change the settings while you are out of the room, then come back and write down what you hear. After 10 trials at different levels (or not) unveil the results.

#### blueone

##### Active Member
Forum Donor
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 example charts I posted have 2 ohm plots.

#### samysound

##### Member
Does the contact resistance added by connection of speaker cable to amp and speakers matter at all? I only see resistance of the speaker wire considered in these equations. Is this because the contact resistance is negligible?

#### blueone

##### Active Member
Forum Donor
so... the whole damping factor thing has always gotten my dander up
I agree. I've never liked damping factor because it's a single value figure of merit. I've always looked for output impedance specifications [edit: or measurements].

#### blueone

##### Active Member
Forum Donor
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.
Interesting. I didn't know that.

#### pjug

##### Senior Member
Forum Donor
I feel like room acoustics would play a larger part in coloring the sound than damping factor. I think this would only be a problem for seasoned listeners with good ears and in optimal listening conditions listening to very specific kinds of music. Feel free to correct me - I'm sure we can and need to do a lot better than 1 dB, but we're greatly overestimating the precision of human audition by suggesting that it takes 0.1 dB to be good enough.
I think this is exactly right. Move your head a foot or so and there is a good chance that the response at the impedance dip frequency changes a lot more than 0.1dB. So if your amp has a very low damping factor and the spreadsheet shows 2dB error, then maybe there is an issue. But if you have 0.2dB or 0.3dB error is this really something to fret over?

#### witwald

##### Member
The example charts I posted have 2 ohm plots.
They certainly do. However, the "gray" curve is mentioned twice in the caption for Figure 1. It's the red curve that corresponds to the resistive 2-ohm load. The gray (black?) curve is the result obtained with the simulated loudspeaker load, and the simulated loudspeaker load doesn't dip below 4 ohms.

As it happens, the damping factor (with the speaker cables included) of the Parasound Halo JC 1+ is approximately 103 at 20 Hz and 1 kHz, decreasing to about 83 at 20 kHz. Looking at the curves for DF = 100 that I computed, the magnitude of the frequency response variations is very similar to the measured modulation in the frequency response of the Parasound amplifier when driving Stereophile's actual simulated loudspeaker load.

#### blueone

##### Active Member
Forum Donor
From Pierce's paper:

"What can be seen from this analysis is that the frequency dependent attenuation due to the amplifier's output resistance is more significant than the effects on system damping."

This is pretty much what Siau is saying. The question is whether the magnitude of the frequency response changes are significant enough to be audible.

#### Speedskater

##### Addicted to Fun and Learning
About a decade ago (maybe longer) there was an internet forum discussion about dummy loads. ArnyK (Arnold B. Krueger RIP) felt that a more complex dummy load was needed than the one John Atkinson was using.

#### blueone

##### Active Member
Forum Donor
They certainly do. However, the "gray" curve is mentioned twice in the caption for Figure 1. It's the red curve that corresponds to the resistive 2-ohm load. The gray (black?) curve is the result obtained with the simulated loudspeaker load, and the simulated loudspeaker load doesn't dip below 4 ohms.
So of the four curves only one is a simulated 2-way speaker load, and the three others are just resistive loads? Interesting.

#### blueone

##### Active Member
Forum Donor
Serves me right for not reading that review. I've never been a fan of Behringer products, so I passed on it. It seems I need to read all of your reviews to get the evolution of your thinking.

#### witwald

##### Member
About a decade ago (maybe longer) there was an internet forum discussion about dummy loads. ArnyK (Arnold B. Krueger RIP) felt that a more complex dummy load was needed than the one John Atkinson was using.
More complex simulated loudspeaker impedance loads can of course be constructed, using a greater number of components. It wouldn't be too hard to model a bass reflex enclosure rather than just a simple sealed enclosure, but some components would be very large in value.

How would we decide on what are more complex simulated load should be? The one that Stereophile uses is quite good, as it includes a reasonable amount of impedance variation, while not being as torturous as some loudspeakers actually are. The Stereophile approach is a middle-of-the-road option, which gives the reader a good idea of what can happen with different amplifiers. It's a lot better than just a simple resistive load, but even the 8-ohm, 4-ohm and 2-ohm loads provide some useful data.

#### witwald

##### Member
Does the contact resistance added by connection of speaker cable to amp and speakers matter at all? I only see resistance of the speaker wire considered in these equations. Is this because the contact resistance is negligible?
The contact resistance should be negligible compared to the resistance of the speaker cable.

#### Pluto

##### Addicted to Fun and Learning
Forum Donor
Low output impedance has no drawbacks
Creating a design of unnecessarily low output impedance is likely to be costly in terms of both money and complexity.