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THE TERM "DAMPING FACTOR" (DF) is supposed to mean some sort of relation between the internal impedance of an amplifier and the impedance of the nominal load. If we use this as a definition, and then define "nominal load" as what ideally would be connected,, then an amplifier with 0.8 ohms internal impedance with an 8-ohm load rating would have a "damping factor" of DF=8/0.8=10. If the actual connected load were 16 or 32 ohms, the so-called damping factor would be 20 or 40.
There is a fallacy in this concept. The actual load on an amplifier, the loudspeaker, consists of the ohmic or d.c. resistance of the voice coil plus some "impedance," part of which is "motional," that is, due to motion of the coil in its magnetic field. The true damping effect is the absorption of unwanted motion or overshoot by the resistance in the circuit which includes acoustic damping and the d.c. resistance of the voice coil. Typically an 8-ohm loudspeaker might have 6 ohms resistance. The minimum impedance of an amplifier might approach zero, (except for special feedback systems which have fallen into disrepute due to instability and other objectionable manifestations. When the impedance becomes less than zero by positive feedback, one has a potential oscillator) but the 6 ohms in the voice coil is still there. Thus the true damping factor of the amplifier could hardly exceed 8 + 6 = 1.33 even if the DF of the amplifier were "infinite" (internal impedance equal to zero). Practically, many loudspeakers are tested on a "constant-voltage basis" and to achieve performance equal to the tests would call for an amplifier to have a flat response relative to a reasonable range of load impedances, that is to say the amplifier would desirably have a low internal impedance. Most amplifiers worthy of connecting to good loudspeakers exhibit an internal impedance of a fraction of one ohm.
We ran a response curve on one of our horn-loaded loudspeakers using a McIntosh MC 30 (a tube amplifier which has been discontinued) and another curve using a one-of-a-kind solid-state amplifier of very low internal impedance. The curves differed by less than one decibel over the 2020,000 Hz range.
Generally speaking we like the new solid-state amplifiers with their low internal impedance because they exhibit low distortion and are "constant-voltage sources"-that is, with a constant-voltage input we get a constant-voltage output even with wide variations of load impedance which all speakers exhibit. But as far as "damping" is concerned, this should be a function of the "speaker, not the amplifier. We are proponents of horn loading as this makes the "damping" take the form of useful output (sound), the efficiency is high and the speaker distortion low. But as far as the amplifier contributing to the damping, this is apt to be a delusion.
If the speaker resistance is 6 ohms, what matters if the amplifier impedance is 0.6 or 0.06 or 0.006 ohms? The resistance in the circuit to produce electrical damping is still 6 ohms, plus whatever tiny bit the amplifier puts in series with the 6 ohms.
So forget "damping factor" as such. Get any good amplifier that exhibits low amplifier distortion (harmonic and modulation) and has a low internal impedance-anything under 0.2 ohms should offer substantially a "constant voltage source"-and if you have to find this internal impedance by using the maker's "damping factor," just remember that any number over about 20 would be good and anything over 100 is sales propaganda except inasmuch as the feedback to produce low internal impedance may contribute to reduced distortion. After all, low distortion should be the criterion, not "damping factor." I hope I haven't stepped on any amplifier maker's toes. Among amplifiers we have used are McIntosh and Marantz, both tube and solid-state.
Finally, recall the words of the sage, J. Figby Blotz, who wrote, "The aural differences between $200 and $500 amplifiers is almost negligible; the comparison between speakers exhibiting the same price ratio is startling."
Additional and Remotely Related Notes
We have run sound-pressure frequency-response curves on several loudspeakers driven by different amplifiers with speakers connected to different nominal-impedance taps. The response curves differed by less than 1/2 dB over the 20-20,000 Hz range. The Marantz Model 9 was fed to a KLIPSCHORN and curves run using 1-ohm and 16-ohm taps, adjusting input to produce 4 volts at 1000 Hz. The two curves superpose "exactly" or well within the resolution of our X-Y recorder.
Another curve was run using a low internal-impedance solid-state amplifier which curve compares within 1/2 dB of the curves run using the Marantz Model 9.
It was said "Forget damping factor as such." However this number may be used to compute the internal impedance of the amplifier.
R_amp = Z/DF
where R_amp is the internal impedance of the amplifier, Z is the nominal load impedance and DF is the stated damping factor. This is valid only at the frequency for which the damping factor is stated, usually 1000 Hz.
From the value of Ramp one can get an approximation for the change in amplifier voltage for different load impedances. Usually the lower Ramp the better the amplifier because of the larger feedback which tends to reduce distortion, provided that the high feedback does not induce instability under certain load conditions.
The load impedance (impedance of the speaker) consists of a dissipative part (the actual ohmic resistance of the voice coil), and a complex impedance consisting of various electrical and acoustic reactances and the radiation resistance, the latter contributing to the acoustic damping. Really this is the most significant part of the damping system; the higher the radiation resistance the more energy is absorbed by the air and the better (more natural) the damping. This is not a conflict; the lower the dissipative resistance the better; the higher the radiation resistance the better.
In typical horn-type loudspeakers, the radiation resistance is usually close to the maximum attainable and the natural damping nearly optimum. In direct-radiator speakers the radiation resistance is a very small fraction of the total system resistance, the efficiency is low, and dependence is on amplifier damping. Even when viscous semi-fluids are applied to speaker outer suspensions (surrounds) and enclosures completely stuffed with fiberglass, amplifier damping is significant, but actually the amplifier damping factors higher than about 5 or 10 fail to contribute much because there is always the ohmic resistance of the voice coil in series with the low amplifier internal impedance.
Back in 1934, when an "all time high" in audio may have been achieved, Wente and Thuras of The Bell Telephone Laboratories concluded that the loudspeaker should have an impedance about 2.25 times the amplifier impedance-a damping factor of only 2.25, corresponding to an amplifier impedance of about 7 ohms for driving a 16-ohm speaker. This does not mean that modern amplifiers with 0.7 or 0.07 ohms are wrong but rather that speaker designers are working on designs that work better out of a constant voltage source.
"Damping factor" is more significant in terms of amplifier internal impedance and the implication of lower distortion than it is relative to damping of transients in the loudspeaker.
Amplifiers with recommended loads of 4 or 8 ohms may be operated with higher impedance loads with a probable reduction in distortion. While the amplifier power output may be reduced one decibel, it may be that the acoustic power will be increased by several dB because of the higher efficiency.
Specifically in the case of Klipsch speakers, the nominal impedance is 16 ohms, arrived at by taking the square root of the product of the impedances at the first peak and first trough. (We may be the only ones using this computed impedance) . However, our Klipschorn exhibits about 9 ohms impedance at 400 Hz and presents an ideal load to an amplifier of "nominally 8 ohms" and would cause a slightly reduced amplifier distortion if connected to a 4 ohm amplifier. For years we have recommended the use of the 4-ohm tap on certain tube amplifiers as a simple and effective way of achieving a bridged center speaker for stereo from two amplifiers.
Maybe this is a complicated way to say "use the 4- or 8-ohm amplifiers with our speakers" and don't worry about the "impedance mismatch." It usually (if not generally) is permissible to connect a higher-impedance load to a given amplifier, but it is generally ill advised to connect a lower-impedance load. Simply stated, it is permissible to connect a 16-ohm load to a 4-ohm amplifier but not acceptable practice to connect a 4-ohm load to a 16-ohm amplifier-or a one ohm load to a 4-ohm amplifier.
(adapted from Audio magazine, Mar. 1970)
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