OK, I'll try.
Damping Factor is a number that relates the output impedance of an amplifier to the impedance of the load that is connected to the amp. In general terms, the Damping Factor number is the speaker’s impedance divided by the output impedance of the amp, calculated at the resonant frequency of the speaker. The higher the DF, the less the load will influence the amp’s output. Above about 10 or 20, differences between Damping Factors become pretty much irrelevant. An important thing to understand about Damping Factor is that it is a somewhat archaic term that doesn’t have a strict formal definition, just a common usage. Amplifiers that use transformers in their output stage tend to have a significantly higher output resistance than contemporary “OTL” (Output TransformerLess) amps. In this case, knowing the DF might be useful in comparing two amps. However, OTL amps generally have much lower output impedance than transformer coupled amps, and so Damping Factor becomes pretty much irrelevant.
Although the Damping Factor is calculated at resonance, it is often applied over the full operating range. In addition to the minor effect of reducing the effective efficiency of a loudspeaker slightly, the output impedance of an amplifier has a significant effect on the overall frequency response, because it interacts with the varying impedance curve of the loudspeaker*. In a typical case, a high amp output impedance will tend to slightly reduce the bass output below the woofer resonant frequency, (“Fs”), strongly boost the bass near Fs, and substantially reduce the upper-bass and lower midrange. What happens above these frequencies is totally dependant on the individual loudspeaker. Lastly, the output impedance has an effect that lends it’s name to the term. A higher impedance reduces the damping of the speaker’s resonant behavior, leading to some overshoot on bass transients.
Note 1: In my tests, the audibility of small changes in damping is somewhat less than the audibility of the frequency boosting that occurs around resonance but, fortunately, improving one improves the other anyway.
Note 2: It is true that there is already another large contributer to the series source resistance seen by the speaker... the voice coil resistance. However, this resistance is already factored into the response of the speaker during its design. Adding additional resistance upsets the delicate balance of resistance, capacitance and inductance of the speaker motor, leading to unexpected response deviations.
As mentioned, Damping Factor is typically determined and stated in a somewhat imprecise manner, but it always involves dividing the speaker’s impedance by the amp’s output impedance. For example, if the “4 Ohm" tap of a tube amp with an average output impedance of 0.2 Ohms is connected to a 4 Ohm, nominal, speaker, one would state the Damping Factor as, “20.” Using a 16 Ohm speaker on the same tap would give a Damping Factor of 80. What makes this imprecise is that there is no standard way to derive either impedance, and no assurance that the DF at resonance applies over a wide range. While an amp’s output impedance varies somewhat, particularly at the frequency extremes, it usually, (but not always!), does remain constant enough for our purposes. The speaker is a different story. Because dynamic speakers have impedance curves that are quite variable, deriving DF involves picking a single, compromise impedance number for the speaker, at the engineer’s discretion. In almost all cases, the single number that is used is the same as the overall advertised impedance of the speaker;: 4, 8, 6, etc. The differences between this “nominal" impedance and the actual impedance is another factor that makes the stated DF such a fuzzy concept.
So, determining the Damping Factor is easy on paper, but is not that easy for a hobbyist without the means to accurately measure the impedances required. It can be done, of course, but, given the dubious definition and utility of the term, it is rarely considered worthwhile.
-k
*- I built a device to allow product reviewers to test how each amplifier is likely to react to a typical speaker, thus highlighting any the real-world tonal differences users might experience between amps. Stereophile uses this device in many of their amp reviews.
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http://www.stereophile.com/reference/60/index.html and
http://bit.ly/ZNzAp5.)
