Fons A gave a nice exposition of how speakers need damping.
This is how the idea od expressing output impedance as
"damping factor" back in the 1950s and even earlier
(damping factor= 8/output impedance, 8 being the nominal
impedance of a normal speaker, supposedly)
However, I think it is important to think of this issue from the
viewpoint of linear systems. First of all, it will keep your
engineering -oriented gradnchildren from regarding you as a
dinosaur, and second it is MUCH easier to compute that way.
You do not need to know anything at all about how a speaker
works inside. All you need to know about it is its impedance
(in the complex sense: absolute value and phase angle)--and even
audio magazines can measure that, thanks to computer based
measurement systems in particular.
Here is the outline:
1 A speaker is a linear system(well, so one hopes and mostly it
is true to a good approximation at moderate level)
so its input behavior is completely characterized, when it is driven
with a given voltage source, by its complex impedance--as a function of
frequency(and of course on
the output end by its tranfer function). How the impedance arose '
in terms of what the speaker is up to in operation is
irrelevant.
2 By universal agreement, a speaker is a voltage driven device:
Presented with a correct voltage input , it produces a correct output--you
wish! Few speakers actually do, but that is what they are supposed to do.
So the best you can do for them is to present them with the correct input
voltagte
3 amplifiers that work right generate correct voltages. So what you need
for part 2 is to get the voltage actually appearing at the spekaer
terminals to be a constant (frequency inepdendent constant)
multiple of the total voltage generated by the amplifier.
4 the sum of the voltage differences around a circuit is 0.
the amp gets the total right so we are in the position of needing to see
how this total is divided up--inside the amp, through the cables, and
through the speakers.
5 the division occurs entirely according to impedance considerations,
using the same equations except in complex impedance instead of real
valued resistance as for a resistive
voltage divider for DC voltage.
In short, everything is instantly and easily computable once you know the
impedance behavior of the cables, the output impedance of the amplifier
and the impedance of the speaker.
This is one of the beauties of linear systems theory. The complicated
mechanisms by which the impedance is determined inside the "black boxes"
makes no difference at all. All you need are the impedance figures, easily
measured and bingo! You have everything.
Forget antedilluvian "damping factor" . Complex impedance is all you know
and all you need to know. (apologies to Keats)
Robert
PS
Cf
www.regonaudio.com/Why%20Amplifiers%20Don't%20Always%20Sound%20Right.html
for a simplified version of the maths of this
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