Damping Factorby Ben Blish
April 28th, 2001
Damping Factor is a term audio enthusiasts (and their rabid cousins, the audiophiles) run into time and time again. However, few people actually understand precisely what the term means, what the consequences of a particular damping factor rating might be for the ultimate desired result (sound reproduction!) or what issues affect the application or relevance of damping factor. The idea isn't rocket science, but it's not something you can toss off in a few seconds, either - and so mostly, it stays a mystery. Let's fix that! It'll be a little longwinded, because there are several ways you can look at the issue, but it's interesting if you've got a basic understanding of electric current and voltage, which many people do.
The Technical Basis
One of the things about amplifiers that affects how they can drive a speaker system is the amplifier's output impedance. The lower it is, the better the amplifier can present needed current to the speaker system, assuming that in other ways (such as frequency response) the amplifier performs well.
The better the amplifier can provide varying amounts of current without changing the applied voltage to the speaker system, the more accurately the speaker will reproduce what the amplifier is trying to tell it to do.
The reason that a speaker might require more - or less - current given a particular applied voltage is that the impedance of the speaker system changes depending on what direction the speaker drivers are moving when the voltage is applied, how fast they are moving that way, and where they actually are in the first place. It helps to visualize that the intent of placing a voltage on a speaker system is to put the speaker cone(s) in (a) particular position(s). How difficult that is to do depends on the factors just mentioned (and others, some subtle.)
Another way to look at this is that as the speaker moves, reproducing the music, its actual impedance changes. At one moment, it might appear to be 6 ohms, and a moment later, it might appear to be 40 ohms. Despite this variation, if the amplifier applies five volts to the speaker, it is saying, in effect, "move the driver(s) to this specific physical position, right now, nowhere else and as accurately as possible." That's because the applied voltage waveform is, for all intents and purposes, an exact graph of the desired physical motion of the speaker.
But because the speaker's load impedance will vary widely depending on what it was doing when the five volts was applied, the amount of current that the speaker will draw with the applied five volts will vary widely as well. The amplifier needs to present the applied voltage correctly (five volts in this example) no matter what the speaker impedance is. If it can do that, the speaker's cone movements will produce the most accurate reproduction of the applied voltage changes - in other words, the least distortion will occur because the driver(s) will move to the desired position with the least amount of error in time and space.
Summing up, since music is comprised of a constantly changing set of applied voltages, except when silence is being reproduced, the speaker is always moving in some complex pattern of strokes in and out, and that in turn means that when the amplifier changes the applied voltage, the amount of current consumed by the speaker system in complying with that applied voltage will vary over a wide range. So the amplifier must, to the best of its ability, supply that current and not change the applied voltage as a result. If the voltage changes in the process, the speaker will not reach the originally intended excursion, and distortion is the result.
Deriving Damping FactorsTechnically, the damping factor is the specified load impedance (in use, that'd be the speaker system) divided by the amplifier's output impedance.
To explain this, we're going to avoid the idea of impedance (which has resistive, capacitive and inductive components, some of which vary in effect by frequency, thus varying the actual loading) and use pure resistance to describe the concept. We'll come back to impedance later.
For a perfectly resistive 8 ohm load impedance, an amplifier with a perfectly resistive output impedance of 4 ohms (that's pretty high, by the way) presents a damping factor of eight over four, or two:
Another one: For a perfectly resistive 8 ohm load impedance, an amplifier with an perfectly resistive output impedance of .1 ohms presents a damping factor of eight over point one, or eighty:
From this we can fairly easily see that the damping factor number itself represents a ratio, one that tells you as it becomes larger, that the source (output) impedance of the amplifier is progressively lower. Damping factors can be quite high; for instance, an amplifier with an output impedance of .01 ohms would result in a damping factor of 800 against an 8 ohm load impedance, a very large number as compared to what we usually see power amplifiers rated. And yes, it is possible to achieve that kind of output impedance in a power amplifier. Not easy or necessarily a good idea, mind you, but possible.
We can also see that because damping factor is a ratio that requires the load impedance to compute, it must be stated against some known impedance to be meaningful. When someone says an amplifier's damping factor is 87, that's not enough. They need to say that it is 87 at eight ohms, or 87 at four ohms, or you can't use the number as a basis for any meaningful comparison. Eight ohms is common, but you might run into a rating against four ohms, or sixteen... or ratings for all three. Maybe even one ohm for some of these gee-whiz ultra-stable megawatt car audio amplifiers meant to cause your eardrums to meet in the center of your skull.
That's ok, though. You can easily move everything to a comparable damping factor number. If an amp was rated as having a 100 damping factor against four ohms, then it is 200 against 8 ohms. Why? because the only way you can get a damping factor of 100 at four ohms is with these numbers...
(we got that .04 by computing damping factor / speaker impedance rating)
...so we know the amp is rated for .04 ohms output impedance. Now, we just do this...
...and there you have it. Having worked through the math, you can simply observe that for the common speaker impedance (4, 8 16 ohms) you can double (as rated load impedance goes up) or halve (as rated load impedance goes down) the damping factor and you'll get the right number as long as you don't get confused and go the wrong way. When in doubt, do the math.
So, here we are, thinking we've got a good handle on this. Well... not exactly. It turns out that electrically speaking, there is no distinguishing between the amplifier's output resistance and the series resistance (not impedance, just the resistance) of the speaker system. So an actual amplifier output impedance in use might be a low number (like .1 or .01) added to perhaps 6 ohms (as an average guess at the DC resistance of a particular 8-ohm speaker.) And that affects the control ability of the amplifier. Think about it: If the speaker has a basic resistance of 6 ohms, and the amplifier can apply 10 volts to the speaker, then ohm's law tells us that the most current the amp will ever be called on to deliver, period, end of story, is 10/6=1.666... amperes; if that's not enough to put the speaker drivers into the right position, they're not going to get there. No matter what the output impedance of the amplifier is!
But doesn't this dilute the meaning, and so the actual usefulness, of the damping factor rating? Yes. It does. But it doesn't remove it. If the amplifier has a very low damping factor, that says it has a high output impedance, and that will reduce the amount of current it can deliver even further, and therefore also reduce its ability to control the speaker.
There is another implication lurking here; speakers with lower resistances will support higher current drive. That means that an amplifier can control them better. However, most amplifiers generate more distortion when they produce higher current, so you don't always win this battle!
And then there's the real world...As most of us are aware, speakers are not pure resistive loads. They are anything but, in fact. Sometimes they present a capacitive load, sometimes they present an inductive load, sometimes simply resistive, sometimes a combination of these. Also, the actual resistance of a particular speaker system is almost never the same as the rated impedance. That rating is a general description of the speaker system impedance, and the reason that is so is simply because you just can't make a typical voice-coil based speaker system act like a resistor. After all, speakers are based on the idea of an inductor, a reactive coil of wire wrapped around a magnet - so this isn't anything surprising. Plus, everything else affects the impedance: the speaker wire, the connections, contributions from crossover circuits inside the speaker, corrosion, fuses and circuit breakers, loading by changing a ported cabinet when you plug or unplug a port insert, condition of the speaker assembly (like the foam surrounds of a woofer, or the condition of the ferromagnetic fluid of some tweeters), the cabinet seals, etc. Or in other words, just about everything you can think of or see when you look at or into a speaker.
There are serious consequences. As the frequency(s) of the signal(s) applied to the speaker change, and/or the speaker's physical and/or electrical condition changes, the speaker's load impedance changes too. Sometimes a lot - for instance, you might see an impedance result of anywhere from one to as much as 50 ohms from a particular speaker design within it's normal operating frequency range. Amazing, eh? Sure it is... But absolutely true.
"But if damping factor is a number derived from the speaker impedance, and speaker impedance dances all over the chart, how can damping factor just be a single number?" ...I hear you cry.
That's right. It can't. It's a curve, but its a nasty, wiggly line that looks more like the trail of a worm on LSD than it does like any curve worthy of the name. We typically call things like that "scribbles", not curves. That line will vary depending on the particular speaker you use, the music you play, the volume you play it at, the quality and condition of your connections to the speakers, everything mentioned above and a lot that isn't - even, believe it or not, factors like wind blowing on the cone of a woofer or the ambient humidity and temperature. So in that way, damping factor is indeed a major simplification of what is actually going on and your instincts are right on.
However, we can still draw some general useful conclusions; because the damping factor ultimately is telling us what the output impedance of the amplifier is, it is also telling us an important and easily understood thing: When amplifiers are rated into the same impedance (both into eight ohms, for instance) or when you convert the numbers to the same impedance as I've shown you how to do above, you are now looking at a direct comparison of the output impedance of those amplifiers.
We mentioned that speakers are not purely resistive. That means, in electronic terms, that they are often (almost always, in fact) reactive. And that word in this context can be taken to mean about what it sounds like; the amplifier attempts to apply a signal to the speaker, and bingo, the speaker reacts, sucking more current than it needed a moment ago, or actually trying to feed current back into the amplifier. Or, it might resist a change in applied current, and as a direct consequence, not do what it is being told to at the moment. Yes, we're talking about behaviors that introduce nothing other than distortion, that evil and annoying nemesis of all of us. Ideally, the speaker should do what it is told, and nothing else. But they never do.
It helps when an amplifier has a high damping factor (in other words, a low output impedance) because the degree to which it is affected, itself, by these annoying speaker behaviors is reduced along with its output impedance. If the speaker needs more current (its overall impedance drops) then a lower amplifier output impedance will allow that current to be drawn out of the amplifier without causing much of a change in the applied voltage - and that means less distortion.
And so...Like most specifications, damping factor does not tell you an amplifier is "good". It can't; no more than a tuner with a great image rejection specification is guaranteed to be a "good tuner". There is a lot more to good amplifier performance than output impedance. Frequency response, mentioned previously, is a good example; suppose the amplifier had a damping factor of 10,000 at 8 ohms, a stunning number (because it implies a very, very low output impedance)... but could only reproduce frequencies between 300 Hz and 1 KHz? Your music would sound pretty awful. Another is distortion: Suppose the amplifier distorts the music? What good is it then to have the speaker do more (even just slightly more) precisely what the amplifier says? Not much! So don't let damping factor go to your head, so to speak - it's one of many specs, one where higher numbers are better because they tell you that the amplifier has a lower output impedance, which is good. Read all the specs, try to learn what they all mean, and then you'll be able to get a good picture of amplifier performance.
The bottom line is, a really low damping factor can tell you an amp isn't going to be all that great with a highly reactive speaker (the larger a speaker driver is physically, and the more power it is designed to handle, the more likely it is to be highly reactive.) What's really low? Well, if we're talking about 8 ohm speakers, a damping factor below about 30 indicates it's going to have noticeably poorer control of a highly reactive load as compared to an amplifier with a damping factor of 100. How much? It works out to about 10% worse (because you have to factor in the speaker resistance.) As the damping factor goes lower, it gets worse yet. You can hear a 10% difference in speaker control. Trust me!
Bonus InformationA very high damping factor can tell you something else, and almost always does unless the manufacturer specifically tells you otherwise: Since it tells you that the amplifier has very, very low output impedance, it also tells you that the amplifier design probably has a lot of negative feedback. And a lot of people worry about that, because it means that the amplifier, unless designed very carefully indeed, will probably exhibit more phase shift than an amplifier that has less negative feedback - and that means it will distort the sound. The more phase shift, the more distortion. But don't worry about it too much... if you saw the phase shift curves of most speaker systems, you'd probably have a heart attack right on the spot.
Some PerspectiveI know some of you are thinking glumly, if speakers are so nasty about reproducing music, what difference does it make if an amplifier has some slight flaws? After all, all "hi-fi" amplifiers are really pretty good, right?
Well, yes. Right. But look at it this way. Speakers (and tape heads, and phono cartridges) do indeed color music more than any other component in a typical stereo system other than something like tone controls, which are meant to. The room you set up the system in will too, as will the physical layout you choose and the stuff hanging on the walls. Given a particular set of speakers, you eventually will find you like that color (even if its a super high end set that has almost none.) That in turn would lead you to get a set of them if it's within your means. The less crud the rest of your system adds to the signal, the more you'll hear just those speakers.
In the old days, when hi-fi shops were easy to find, you could walk in and a good place would let you switch different speaker systems in and out, amps in and out, etc. You could always hear the difference in the speakers. It's a lot more difficult to hear differences between most decent or better amplifiers. You can, but you'd better have some pretty exceptional ears when you're auditioning the best that good manufacturers can put together.
Hey, enjoy your music. Don't sweat it. Play with the knobs, and if you like what you're hearing, the specs are probably pretty good. Or your ears don't care. Maybe someday you'll hear something better, or you'll use specs to put something together you know is better. Maybe not. But if you like what you're hearing, you're on the right path. I can guarantee you one thing: There are an awful lot of people out there spending money on specs they will never be able to hear as differences in the music in a million years. Just don't expect them to ever admit it. I have to really work not to laugh my head off when someone tells me they spent several hundred dollars - or even over a thousand - on speaker cables and they "sound better" than a nice heavy gauge twisted pair of stranded copper wires they could have had for about five bucks...