Damping Factor

[Impious 1,476]

http://www.monsterca...tor_Article.pdf

DAMPING FACTOR

By Richard Clark

At a recent AUTOSOUND 2000 manufacturer sponsored seminar, we were asked to comment on the

subject of amplifier damping factor. I was extremely surprised to find how much importance was attached

to this single specification. Since most folks are a little unclear as to the true meaning of damping factor,

we're presenting the following article.

First of all, let's discuss the items that enter into the damping factor calculation. At the heart of this

calculation is the output impedance of the amplifier. Most all-modern feedback type amps are of the

variety known as constant voltage. This means that they will deliver a constant voltage regardless of their

load - at least in theory. Sooner or later the limits of the amplifier's design will prohibit its constant voltage

characteristics.

It is this constant voltage output characteristic that permits modern car audio amplifiers to deliver more

power into a 2 Ohm load than into a 4 Ohm load. A perfect amplifier should be able to double its power

every time its output load is halved. Remember, Power = E x E divided by R. As an example, examine the

following chart:

8 Ohms = 25 Watts

4 Ohms = 50 Watts

2 Ohms = 100 Watts

1 Ohm = 200 Watts

.5 Ohm = 400 Watts

.25 Ohm = 800 Watts

.0125 Ohm = 1600 Watts

If an amplifier were theoretically perfect, then it would be capable of the type of performance described in

the chart. However, there are many factors that influence this capability. First there is the power supply

section of the amplifier. Even if an amplifier had an unlimited power supply with output transistors that

could handle the current, the design would still not be able to achieve the theoretically perfect output. The

reason being that we do not have access to theoretically perfect components.

Never lose sight of the fact that real components in real amplifiers are subject to real losses. These

losses are a result of junction losses; IR drops in connections and losses in resistances and reactance.

Losses in the output stages essentially form a voltage divider on the output of the amplifier. This drop is

always in series with the load and can be indicated as in Figure N.

In the design of an amplifier, the feedback network is usually wrapped around the section with the most

losses. These losses can be greatly minimized due to the fact that the feedback node is constantly being

corrected. This can be depicted as in Figure O.

Output Impedance Determines Damping Factor

If the output impedance of an amplifier is extremely low, the effect of loading on the output of the amplifier

will be minimal. This means that it will not experience a voltage loss across its own output impedance.

This output impedance does more than determine the effect of loading on the amp. It also determines its

damping factor.

Whenever a signal is fed into a loudspeaker the cone of the speaker will move. Since the cone has mass,

there will be mass in motion. Mass in motion means momentum. When the signal is removed from the

loudspeaker, the momentum of the cone causes the energy stored in the cone to be fed back into the

amplifier. If our perfect amplifier were connected to this speaker, the loudspeaker would be trying to

produce a voltage into 0 Ohms. Remember, a perfect amplifier has an output impedance of 0 Ohms

which is essentially a short circuit.

A voltage cannot be developed across 0 Ohms because it would require an infinite amount of current. It is

this same infinite amount of energy that would now be trying to prevent the speaker cone from moving. If

such were the case, we would certainly have a "tight" sounding speaker with absolutely no hangover.

The good news is that quality amplifiers have very low output impedances. We are very pleased to report

that there are many car audio amplifiers on the market with output impedances on the order of .01 Ohms

or less!

Calculating Damping Factor

Let's clarify a few points before starting our calculations. The frequency of the measurement and the

impedance of the load need to be specified. For example, the use of a 1 KHz signal and a load

impedance of 4 Ohms would be a typical specification.

DEFINITION = A good definition of damping factor would the ratio of the output impedance of the

amplifier to the impedance of the load specified at a given frequency.

An amplifier with an output impedance of 0.5 Ohm will have a damping factor of 8 when connected to a

theoretically perfect 4 Ohm loudspeaker (i.e. purely inductive voice coil.) since 4/.5 = 8.

The following chart assumes such a 4 Ohm speaker:

Output Impedance Damping Factor

4 Ohms 1

2 Ohms 2

1 Ohm 4

.5 Ohm 8

.25 Ohm 16

.125 Ohm 32

.062 Ohm 64

.031 Ohm 128

.0015 Ohm 256

.0007 Ohm 512

.0003 Ohm 1024

.00015 Ohm 2048

.00007 Ohm 4096

.00003 Ohm 8192

Now, for the bad news; it is easy to see how a race to produce such a high damping factor led to a

specification so often quoted by salespeople. The numbers on modern amplifiers (with lots of feedback)

can get very large and they are easy to compare. Sometimes we can get caught up in these big numbers

and we totally miss the point.

Effective Damping Factor (EDF)

In the case of damping factor, I believe that it could be compared to the old saying of not being able to

see the forest because of all the trees. The only thing that really matters is Effective Damping Factor

(EDF). Effective Damping Factor more accurately describes the interaction between a real amplifier and a

real speaker. Unfortunately real speakers have a real problem with EDF. This is due primarily to the DC

resistance of the voice coil. When we calculate the EDF of an amplifier and speaker, it is absolutely

necessary that we include this DC resistance into the formula. Figure P illustrates the inclusion of the

speaker's impedance into the EDF.

The actual impedance of the speaker may be 4 Ohms. If we measure the voice coil of this speaker, we

will probably find that it has a DC resistance of about 3 Ohms. When calculating the EDF effect on this

speaker, we must add the 3 Ohms of DC resistance as if it were a resistor between the output of the amp

and the voice coil of the speaker. Remember the resistive part of the speaker is the part where the signal

is turned into heat. No work is actually done in this resistance.

The inductive element of the voice coil is the only part that does work to create sound. This is one reason

speakers are so inefficient. Most of the voice coil is a resistive element that can do no work. Someday if

we develop room temperature superconductors and can afford to use them for voice coils, we are going

to see some really efficient speakers.

From the damping factor chart it is obvious that the most damping we can expect from our amp/speaker

combination is only about two. An amplifier with a damping factor exceeding 10 times this amount is no

longer going to play a significant role in this overall calculation. This would yield a practical limit on

amplifier damping requirements to about twenty.

There are times when the actual damping factor can exceed this number; one such case would be that of

a dynamic loudspeaker in resonance. As we have learned, at resonance a loudspeaker's impedance is at

a maximum level. At resonance, the DC element stays the same and only the reactance increases. This

means that the ratio gets larger and the DC element becomes a smaller percentage of the total.

For example, if the speaker impedance at resonance increased to 40 Ohms and the DC resistance was

still 3 Ohms and the amplifier were .1 Ohms, and then the actual damping could be 40/3.1, or 13. This is

certainly much better than 2, but quite a bit short of the 100, 200, or 500 claimed by salesmen who

unknowingly think this factor so important. Fortunately for most loudspeakers this extra damping happens

where they need it the most. This is because at resonance, speakers typically are very uncontrolled and

have the least mechanical damping. It is also this factor that enables us to be able to connect speakers in

series and not have to worry about losing damping. The actual impedance of the loudspeakers in series is

doubled, but the ratio to the amplifier must also be increased by a factor of 2 to 1. The result is no change

in performance.

It is quite possible that this information may be in stark contrast to current marketing trends. However this

does not change the fact that this information is accurate. The best way to achieve total control over

speaker movement is with a servo system. Only armed with a quality servo system can effective damping

characteristics be achieved. A servo essentially puts the loudspeaker in the corrective feedback loop of

the amplifier. This topic will be the subject of a future article.

[Impious 1,476]

Stephen Mantz on DF

http://zedaudiocorp....l-GREYSCALE.pdf

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!

[Impious 1,476]

Audioholics article on DF

http://www.audioholi...system-response

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 . 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 , designated , and represents the total resistive losses in the system. Two loss components make up : the combined mechanical and acoustical losses, designated by , and the electrical losses, designated by . The total is related to each of these components as follows:

is determined by the losses in the driver suspension, absorption losses in the enclosure, leakage losses, and so on. 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 , , that is affected by the amplifier source resistance, and thus damping factor.

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

where is the new electrical with the effect of source resistance, is the electrical assuming 0W source resistance (infinite damping factor), is the voice coil DC resistance, and 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 due to non-zero source resistances, we can then recalculate the total system as needed using eq. 2, above.

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

This is valid for 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 of 0.707 which leads to a maximally flat response with no peak at system resonance. The mechanical of such a system is typically about 3, we'll take that for our model. Rearranging Eq. 1 to derive the electrical of the system, we find that the electrical 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 caused by the non-zero source resistance, the fourth is the new total system 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.

Analysis

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 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 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 is the gain or loss due to attenuation, is the amplifier source resistance, and 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.

Conclusions

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.

[Aaron Clinton 2,372]

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

[j-roadtatts 1,129]

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

You and Me both.

Yes I am Young Bull.

[edouble101 314]