16 gauge copper wire to small?

Steven, (and others) I think this may be an (or the) article similar to what you were referring to. DAMPING FACTOR: EFFECTS ON SYSTEM RESPONSE A TECHNICAL ANALYSIS Dick Pierce Professional Audio Development 1 INTRODUCTION 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." [1] 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." Instead of unbridled hyperbole, there have been attempts at a reasoned justification for damping factor. Witness a recent rec.audio.tech post: "Since the amplifier source impedance is indeed much smaller than the speaker impedance, the latter is almost insignificant. In fact, an amplifier with a damping factor of 50 will sink twice the current of one with a damping factor of 25, and therefore dissipate four times the resonant energy." [2] As intuitive as this analysis might seem, it is quite flawed since, as we will see, it simply ignores the one major loss factor in the entire system, throwing it out the window as if the single most important controlling element over cone motion had no real relevance. 2 DAMPING FACTOR: A SUMMARY What is damping factor? Simply stated, it is the ratio between the nominal load impedance (typically 8 ohms) 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 unserstanding by anyone with a reasonable grasp of high-school level math. It has been exhaustively dealt with by Thiele [3], Small [4] and many others decades ago. 3 SYSTEM Q AND DAMPING FACTOR The definitive measurement of such motion is a concept called Q. Technically, it is the ratio of the motional impedance to losses at resonance. Another, completely equivalent view is that Q is the ratio between the amount of energy stored in the system vs the energy dissipated by losses. 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 loud-speaker system's response at cutoff is determined by the system's total Q, designated Qtc, and represents the total resistive losses in the system. Two loss components make up Qtc: the combined mechanical and acoustical losses, designated by Qmc, and the electrical losses, designated by Qec. The total Qtc is related to each of these components as follows:                  Qmc * Qec            Qtc = --------- [Eqation 1]                  Qmc + Qec Qmc is determined by the losses in the driver suspension, absorption losses in the enclosure, leakage losses, and so on. Qec 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 Q, Qec, that is affected by the amplifier source resistance, and thus damping factor. Qec itself is a measure of, simply, the ratio of the energy stored in the moving system to the energy dissipated electrically by the losses in the system, that is, in the resistances in the system. The energy stored in the moving system, the kinetic energy, is dependent upon the amount of mass and the velocity. In the context of a speaker, the Qe is (from Small[4]):                         2 2 Qec = 2 pi Fc Mmc Re / B l   [Eqation 2] where Fc is the resonant frequency of the system, Mmc is the equivalent moving mass of the system, and Re is the DC resistance of the voice coil (and this assumes 0 source impedance or "infinite" damping factor). Further, B represents the magnetic flux density in the gap and l the length of wire in the magnetic field. (We will assume that we are using the same driver for all considerations here, thus, Fc, Mmc B and l remain the same as well.) The effect of source resistance on Qec is simple and straight-forward. From Small again [4]:             Re + Rs Qec' = Qec ---------   [Eqation 3]               Re where Qec' is the new electrical Q with the effect of source resistance, Qec is the electrical Q assuming 0 source resistance (infinite damping factor), Re is the voice coil DC resistance, and Rs is the combined source resistance. The factor        Re + Rs       ---------   [Eqation 4]         Re comes from the fact that Re is built into the original derivation for Qec includes Re in it. The correction simply calculates the incremental increase in Qe with the incremental increase in the total electrical resistance. Reconciling [Eq 4] with [Eq 2], we see that:                              2 2 Qec = 2 pi Fc Mmc (Re+Rs) / B l    [Eqation 6] Thus it becomes obvious that the electrical Q of the speaker or, more generally, the electrical damping of the speaker, is NOT dependent upon the source resistance Rs alone (as the proponents of damping factor erroneously claim), but on the TOTAL series resistance seen by the driver, including the DC resistance of the voice coil, Re. This mistake, as commonly as it is made, the the fatal flaw in the entire damping factor argument. It's very important at this juncture to note two points. First, in nearly every loudspeaker system, and certainly in every loudspeaker system that has any 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 Qec' due to non-zero source resistances, we can then recalculate the total system Q as needed using [Eq 3], above. The effect of the total Q on response at resonance is also fairly straightforward. Again, from Small [4], we find:                       4                     Qtc Gh(max) = sqrt(-------------) [Eqation 7]                     2                Qtc - 0.25 This is valid for Qtc values greater than 0.707. Below that, the system response is overdamped 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. 4 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, once 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 Qtc of 0.707 which leads to a maximally flat response with no peak at system resonance. The mechanical Qmc (i.e. the mechanical contributions to system losses and thus damping) of such a system is typically about 3, we'll take that for our model. Rearranging [Eq 1] to derive the electrical Q of the system:                Qtc * Qmc           Qec = ---------   [Eqation 8]                Qtc - Qmc we find that the electrical Q of the system, with an infinite damping factor, is 0.925. The DC resistance of the voice coil is typical at about 6.5 ohms. Let's generate a table that shows the effects of progressively lower damping factors on the system performance: -------------------------------------------------------- damping   Rs     Qec' Qtc' Gh(max) Decay factor                                time -------------------------------------------------------- inf.      0      0.925 0.707 0.0 dB   0.04 sec 2000      0.004 0.926 0.707 0.0      0.04 1000      0.008 0.926 0.708 0.0      0.04 500       0.016 0.927 0.708 0.0001   0.04 200       0.04   0.931 0.71 0.0004   0.04 100       0.08   0.936 0.714 0.0015   0.04 50        0.16   0.948 0.72 0.0058   0.04 20        0.4    0.982 0.74 0.033    0.041 10        0.8    1.04 0.77 0.11     0.043 5        1.6    1.15 0.83 0.35     0.047 2        4      1.49 0.99 1.24     0.056 1        8      2.06 1.22 2.54     0.069 -------------------------------------------------------- Table 1 The first column is the damping factor using a nominal 8 ohm load. The second is the effective amplifier source resistance that yields that damping factor. The third column is the resulting Qec' caused by the non-zero source resistance, the fourth is the new total system Qtc' 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. 5 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 simply 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. If we select a criteria that 0.1 dB is the absolute best in terms of the audibility of such a peak (and this is probably overly optimistic by at least a factor of 2 to 5), then the data in the table suggests that ANY damping factor over 10 is going to result in inaudible differences between such a damping factor 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. Further, we simply do not observe the "factor-of-four" increase in energy dissipation with a factor of two reduction in source resistance as claimed in [2]. The statement that it's all about energy dissipation is quite correct: remember that what damping is doing is removing energy from a resonant system, and that the measure of damping is Q, the ratio of energy stored to energy dissipated. Look, for example, at the difference in Qt between a damping factor of 50 and 20: the actual difference in the energy dissipated is less than 3%. According to the theory expounded in [2], the difference in energy dissipation should be around a factor of 6! 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 Q 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 Qt figure to better than 5%, and those numbers will swamp any differences in damping factor greater than 20. It is well known that 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. 6 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. We have not looked at the frequency-dependent attenuative effects of the source resistance, but that's not what the strident claims are about. Rather, the people advocating the importance of high damping factors must look elsewhere for a culprit: motion control at resonance simply fails utterly to explain the claimed differences. 7 REFERENCES [1] James Kraft, reply to "Amplifier damping Factor, Another Useless Spec," rec.audio.high-end article 2rcccn$u30@introl.introl.com, 24 May 1994. [2] Steve (aq433@lafn.org), reply to "How can 2 amps sound so different?," rec.audio.tech article 7go6da$b8q$1@nnrp1.dejanews.com, 04 May 1999. [3] A. Neville Thiele, "Loudspeakers in Vented Boxes," Proc. IRE Australia, 1961 Aug., reprinted J. Audio Eng. Soc., 1971 May and June. [4] Richard H. Small, "Closed-Box Loudspeaker Systems," J. Audio Eng. Soc., Part I: "Analysis," 1972 Dec, Part II, "Synthesis," 1973 Jan/Feb. Copyright 1994, 1995, 1998-2001 by Dick Pierce. Permission given for one-time no-charge electronic distribution with subsequent followups. All other rights reserved. | Dick Pierce | | Professional Audio Development | | 1-781/826-4953 Voice and FAX | | DPierce@world.std.com | This document was created with Win2PDF available at http://www.daneprairie.com. The unregistered version of Win2PDF is for evaluation or non-commercial use only.It all reminds me of something that Molière once said to Guy de Maupassant at a café in Vienna: "That's nice. You should write it down."

some of the equations didn't come out exactly correct, but I can send them to anybody in text format, if inteested, so you can get them the way the original author intended. (and , yes, I did try to correct them )It all reminds me of something that Molière once said to Guy de Maupassant at a café in Vienna: "That's nice. You should write it down."

Steve- I'm not saying that Dan is wrong. He's infinitely more knowledgable than I about the intracicies of some things, driver design especially. I do believe, and can support with tests, that wire gauge does have an effect on the sound of a driver. Specifically, I think it has an influence on the relationship between an amplifier's output impedence and the driver's reactance, and a change in the total system Q, which is indeed dependent on the output of the impedence of the amplifier. NB, for the putposes of this discussion, I'm not going to make anyone's brain hurt (including mine) by discussing negative output impedences in amplifiers, mainly because every car amp I've ever seen has had a relatively high (0.01R or so) and definitely positive Zo. haemphyst posted the Dick Pierce paper I was going to look for, and altho the equations didn't come across totally intact, it's pretty easy to see that the Q of the system becomes progressively less damped as the DF drops. I disagree with Dick that DF doens't influence the motion of the cone at it's least damped point. As far as his assmption that driver tolerance will swamp DF irregulartities, I've found that many drivers that differ in their specifications, sometimes wildly, will match very nicely when placed into the same box, because the tolerances act to cancel each other. A number of years back, I had a set of 4 Peioneer 10" woofers I wanted to use. I measured the T/S parameters of each very carefully, and came out with Qtc and Qms differences exceeding 40%, but when I loaded the paramaters itno my modelling programs, they agreed that the drivers would perform within 1dB of each other in the exact same box. A change in the porting of less than 5Hz brought them all into a less than 5% window. I've had the same experience with a lot of other drivers, from Vifa mids to Shivas. I also disagree with Dick that a diffference of 1/3dB is inaudible, when it's been shown coutless times that although it is not perceived as a difference in loudness, a change of volume of 0.3dB is perceived as a definite change in the "sound" of a system, and that when critical AB or ABX tests are performed, matching is required within 0.1dB, preferrably less if possible. Finally, I honestly believe that the changes in effective Q are the main source of DF complaints. I know for a fact that there is a perceptable difference when changing DF by an order of magnitude (~10 to >100). For Steve's benefit, it was when I moved my dual Dhiva subs from an old Phase Linear 700 II to a Crown K2, both driving the speakers through seperate runs of 6AWG. The first thing my sister noticed was that "the kick drum sounds a lot tighter", which is, as I have found in my years of recording, directly related to the dampening of said drum, either directly or at the reproduction device, AKA the speaker. A high Q (>1) as has been known for a long time, has a typically loose or boomy sound, and does not excel at providing flat frequency reproduction. When combined with the truly wonky way that a small space (a car) influences the behavior of a subwoofer or woofer, things get magnified in a somewhat unpredictable way. My biggest beef with DF is that people say 18 is fine for a 30' round trip on 4 or 2 ohm drivers that are expected to play loudly. Not only will you lose a very real portion of your power in the wire, but the DF will be so low with a 2 ohm load that the Q will be totally shot to hell. Comments are welcome for now. I'll post more when I'm not on a working vacation. -daveThis is not a sig. This is a duck. Quack.

Is it just me or did anyone else feel like this is flying way over their head. I like to think of myself as somewhat knowledgable but all this has just flown way over my head. I bookmarked this so I can read it a few times to get a handle on it, but im not holding my breath :)double-secret reverse-osmosis speaker-cone-induced high-level interference distortion, Its a killer

Steven- It's late so I'm keeping this short, but I'm going to look into it a little further as I get some time this week. Regarding the wildly varying impedence of drivers as they move through the magnetic field of the motor (which I freely admit is not figurd into any of these calculations), we also have to think about back EMF and it's effect upon the system Q as the driver is forced to change directions abruptly, as well as the effect that has upon the output of the amplifier. Given the normal motion of a subwoofer (the easiest to use here because of the low frequencies involved) the driver spends a comparatively large time in linear travel than it does changing directions. As the driver is traveling, it is bring moved through the field of the motor not unlike a projectile in a rail gun. The changes in BL will influence the way the motor reacts to the input signal, which will either magnify or contradict any changes in Qts induced by cable effects. I have a hunch that it magnifies it more often than it counteracts it. As the coil is driven through the field, if I recall my magentic mechnics correctly, the induced EMF will be practically zero, since it will be int he same direction as the input signal, and will end up being absorbed by the amplifier's power supply, and Zcoil will be pretty much ignorable. Only at the transitions in direction will the EMF counterr the input signal, and that's where Qt makes it's most audible point, and where additional cable resistance will allow more back-EMF buildup, increasing Qt and causing the audible effects. Of course, these are sleep deprived mignight ramblings, so I reserve the right to change my mind when I get some rest and have a chance to pull out a textbook. -daveThis is not a sig. This is a duck. Quack.

LOL, I think people should stick to the real question at hand. That being current handling, and not so much if the *golden ears* can tell a difference. A person is in a moving vehicle, while in transit there is eminating road noise, and noise(s) related to the vehicles mechanicals. The sub in question is normally in the trunk, sealed off from the interior cabin. I would offer to the average Joe, that you will not hear the difference that so many people keep referencing to. Stick to the basics 101, will the guage of wire be enough for the current being transferred?? If yes, then use it . . . If no, or if, the future requirements or needs change, then having installed a 12 guage wire to the said device will simply address that need later. End of story. Regards EVIL Teken . . .

Amen Brother, Testify :)double-secret reverse-osmosis speaker-cone-induced high-level interference distortion, Its a killer

Point taken Rat/Teken. The rule I go by is use the fattest pipe that is practical. If that's18, fine. If it's 16 or 14, that's fine too. 12 or 10? go for it. Subs get fatter pipes than tweets, mainly because of the higher currents. Mids go somewhere in between. Over 1kW? Better use fatter than 12AWG. Remember, power losses in wire go with the square of the voltage drop. Overall tho, make yourselves happy. Steven and I will probably continue this via private email -daveThis is not a sig. This is a duck. Quack.