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Stephen Mantz on DF


Damping Factor – This amplifier specification has been blown out of all proportion. What it means is the ability of the amplifier to resist a change in it’s output voltage. The formula is DF = Speaker Z/Amplifier output Z (where Z is impedance). So many manufacturers have claimed ridiculous, and often false damping factors. A damping factor of 1000 implies that the output impedance of the amplifier is .004ohm (4ohm load). The only way to attain this figure is to apply masses of negative feedback (or use positive feedback) and too much feedback makes amplifiers sound harsh and clinical. Also damping factor changes with frequency. The lower the frequency the higher the DF number. Typically the DF can be ten times larger at higher frequencies.

Let us take this amplifier whose output impedance is .004 ohms (Zout). The speaker circuit is a series circuit and the following impedances (resistances) are in series with this .004 ohms. Let us assume that this DF measurement was made at the amplifier’s speaker terminal. The first extra contact resistance is the speaker wire to the speaker terminal (WT ohms). Then there is that of the wire itself for two conductors (W). Next is the contact resistance of the wire to the speaker terminal (WS). Next there is the contact resistance of the wire from the speaker terminal to the voice coil (WV) and lastly there is the DC resistance of the voice coil itself (DCR). So what we have is a series circuit with the following resistances in series and adding up. WT+W+WS+WV+DCR+Zout. WT, W, WS, WV and Zout are very small indeed. Certainly less than .1 ohms. Whoa, look what has happened the EFFECTIVE DAMPING FACTOR has been reduced from 1000 to 40 by just taking into account those pesky unavoidable contact resistances. Now for the cruncher, remember that the DCR is also in series and is typically 3.2 ohms for a nominal 4ohm speaker. So we must add 0.1+3.2 = 3.3 ohms and now EFFECTIVE DAMPING FACTOR is now a magnificent 1.212! (4 divided by 3.3). This is the real world. We see that the DCR of the speaker swamps all other resistances in the speaker circuit and the .004 ohms amplifier output impedance is almost meaningless. It has been found that a DF of about 20 is quite sufficient to dampen the voltage spikes from the speaker. An eye opener this one is it not? Good tube amps sound marvelous – low damping factors!

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Audioholics article on DF


Much ballyhoo surrounds the concept of "damping factor." It's been suggested that it accounts for the alleged "dramatic differences" in sound between tube and solid state amplifiers. The claim is made (and partially cloaked in some physical reality) that a low source resistance aids in controlling the motion of the cone at resonance and elsewhere, for example:

"reducing the output impedance of an amplifier and thereby increasing its damping factor will draw more energy from the loudspeaker driver as it is oscillating under its own inertial power."

This is certainly true, to a point. But many of the claims made, especially for the need for triple-digit damping factors, are not based in any reality, be it theoretical, engineering, or acoustical. This same person even suggested:

"a damping factor of 5, ..., grossly changes the time/amplitude envelope of bass notes, for instance. ... the note will start sluggishly and continue to increase in volume for a considerable amount of time, perhaps a second and a half."

Damping Factor: A Summary

What is damping factor? Simply stated, it is the ratio between the nominal load impedance (typically 8W ) and the source impedance of the amplifier. Note that all modern amplifiers (with some extremely rare exceptions) are, essentially, voltage sources, whose output impedance is very low. That means their output voltage is independent, over a wide range, of load impedance.

Many manufacturers trumpet their high damping factors (some claim figures in the hundreds or thousands) as a figure of some importance, hinting strongly that those amplifiers with lower damping factors are decidedly inferior as a result. Historically, this started in the late '60's and early '70's with the widespread availability of solid state output stages in amplifiers, where the effects of high plate resistance and output transformer windings traditionally found in tube amplifiers could be avoided.

Is damping factor important? Maybe. We'll set out to do an analysis of what effect damping factor has on what most proponents claim is the most significant property: controlling the motion of the speaker where it is at its highest, resonance.

The subject of damping factor and its effects on loudspeaker response is not some black art or magic science, or even excessively complex as to prevent its grasp by anyone with a reasonable grasp of high-school level math. It has been exhaustively dealt with by Thiele and Small and many others decades ago.

System Q and Damping Factor

The definitive measurement of such motion is a concept called dfeq8-1.gif . Technically, it is the ratio of the motional impedance to losses at resonance. It is a figure of merit that is intimately connected to the response of the system in both the frequency and the time domains. A loudspeaker system's response at cutoff is determined by the system's total dfeq8-2.gif , designated dfeq8-3.gif , and represents the total resistive losses in the system. Two loss components make up dfeq8-4.gif : the combined mechanical and acoustical losses, designated by dfeq8-5.gif , and the electrical losses, designated by dfeq8-6.gif . The total dfeq8-7.gif is related to each of these components as follows:


dfeq8-9.gif is determined by the losses in the driver suspension, absorption losses in the enclosure, leakage losses, and so on. dfeq8-10.gif is determined by the combination of the electrical resistance from the DC resistance of the voice coil winding, lead resistance, crossover components, and amplifier source resistance. Thus, it is the electrical dfeq8-11.gif , dfeq8-12.gif , that is affected by the amplifier source resistance, and thus damping factor.

The effect of source resistance on dfeq8-13.gif is simple and straightforward. From Small(3):


where dfeq8-15.gif is the new electrical dfeq8-16.gif with the effect of source resistance, dfeq8-17.gif is the electrical dfeq8-11.gif assuming 0W source resistance (infinite damping factor), dfeq8-18.gif is the voice coil DC resistance, and dfeq8-19.gif is the combined source resistance.

It's very important at this point to note two points. First, in nearly every loudspeaker system, and certainly in every loudspeaker system that has nay pretenses of high-fidelity, the majority of the losses are electrical in nature, usually by a factor of 3 to 1 or greater. Secondly, of those electrical losses, the largest part, by far, is the DC resistance of the voice coil.

Now, once we know the new dfeq8-20.gif due to non-zero source resistances, we can then recalculate the total system dfeq8-21.gif as needed using eq. 2, above.

The effect of the total dfeq8-22.gif on response at resonance is also fairly straightforward. Again, from Small, we find:


This is valid for dfeq8-24.gif values greater than 0.707. Below that, the system response is over-damped and there is no response peak.

We can also calculated how long it takes for the system to damp itself out under these various conditions. The scope of this article precludes a detailed description of the method, but the figures we'll look at later on are based on both simulations and measurements of real systems, and the resulting decay times are based on well-established principles of the audibility of reverberation times at the frequencies of interest.

Practical Effects of Damping Factor on System Response

With this information in hand, we can now set out to examine what the exact effect of source resistance and damping factor are on real loudspeaker systems. Let's take an example of a closed-box, acoustic suspension system, one that has been optimized for an amplifier with an infinite damping factor. This system, let's say, has a system resonance of 40 Hz and a system dfeq8-25.gif of 0.707 which leads to a maximally flat response with no peak at system resonance. The mechanical dfeq8-26.gif of such a system is typically about 3, we'll take that for our model. Rearranging Eq. 1 to derive the electrical dfeq8-27.gif of the system, we find that the electrical dfeq8-28.gif of the system, with an infinite damping factor, is 0.925. The DC resistance of the voice coil is typical at about 6.5 W . From this data and the equations above, let's generate a table that shows the effects of progressively lower damping factors on the system performance

[see table in article]

The first column is the damping factor using a nominal 8W load. The second is the effective amplifier source resistance that yields that damping factor. The third column is the resulting dfeq8-29.gif caused by the non-zero source resistance, the fourth is the new total system dfeq8-30.gif that results. The fifth column is the resulting peak that is the direct result of the loss of damping control because of the non-zero source resistance, and the last column is the decay time to below audibility in seconds.


Several things are apparent from this table. First and foremost, any notion of severe overhang or extended "time amplitude envelopes) resulting from low damping factors simple does not exist. We see, at most, a doubling of decay time (this doubling is true no matter what criteria is selected for decay time). The figure we see here of 70 milliseconds is well over an order of magnitude lower than that suggested by one person, and this represents what I think we all agree is an absolute worst-case scenario of a damping factor of 1.

Secondly, the effects of this loss of damping on system frequency response is non-existent in most cases, and minimal in all but the worst case scenario. Using the criteria that 0.1 dB is the smallest audible peak, the data in the table suggests that any damping factor over 10 is going to result in inaudible differences between that and one equal to infinity. It's highly doubtful that a response peak of 1/3 dB is going to be identifiable reliably, thus extending the limit another factor of two lower to a damping factor of 5.

All this is well and good, but the argument suggesting that these minute changes may be audible suffers from even more fatal flaws. The differences that we see in dfeq8-16.gif figures up to the point where the damping factor is less than 10 are far less than the variations seen in normal driver-to-driver parameters in single-lot productions. Even those manufacturers who deliberately sort and match drivers are not likely to match a dfeq8-24.gif figure to better than 5%, and those numbers will swamp any differences in damping factor greater than 20.

Further, the performance of drivers and systems is dependent upon temperature, humidity and barometric pressure, and those environmental variables will introduce performance changes on the order of those presented by damping factors of 20 or less. And we have completely ignored the effects presented by the crossover and lead resistances, which will be a constant in any of these figures, and further diminish the effects of non-zero source resistance.

Frequency-Dependent Attenuation

The analysis thus far deals with one very specific and narrow aspect of the effects of non-zero source resistance: damping or the dissipation and control of energy stored in the mechanical resonance of loudspeakers. This is not to suggest that there is no effect due to amplifier output resistance.

Another mechanism that most certainly can have measurable and audible effects are response errors due to the frequency dependent impedance load presented by the speaker. The higher the output resistance of the source, the greater the magnitude of the response deviations. The attenuation can be approximated given the source resistance and impedance vs. frequency:


where dfeq8-33.gif is the gain or loss due to attenuation, dfeq8-34.gif is the amplifier source resistance, and dfeq8-35.gif is the frequency dependent loudspeaker impedance.

As a means of comparison, let's reexamine the effects of non-zero source resistance on a typical speaker whose impedance varies from a low of 6 ohms to a high of 40 ohms.

[see table in article]

As before, the first column shows the nominal 8 ohm damping factor, the second shows the corresponding output resistance of the amplifier. The second and third columns show the minimum and maximum attenuation due to the amplifier's source resistance, and the last column illustrates the resulting deviation in the frequency response caused by the output resistance.

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. More importantly, these effects should not be confused with damping effects, as they represent two different mechanisms.

However, these data do not support the assertion often made for the advantages of extremely high damping factors. Even given, again, the very conservative argument that ±0.1 dB deviation in frequency response is audible, that still suggests that damping factors in excess of 50 will not lead to audible improvements, all else being equal. And, as before, these deviations must be considered in the context of normal response variations due to manufacturing tolerances and environmental changes.


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. Even considering the substantially larger response variations resulting from the non-flat impedance vs. frequency function of most loudspeakers, the magnitude of the problem simply is not what is claimed.

Rather, the people advocating the importance of high damping factors must look elsewhere for a culprit: motion control at resonance, or damping, simply fails to explain the claimed differences.

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Thats awesome. I need to take my time and read that a few times. :)

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Thats awesome. I need to take my time and read that a few times. smile.gif

You and Me both.

Yes I am Young Bull.smile.gif

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