From: DPierce@world.std.com (Richard d Pierce)
Subject: Re: How are speaker impedences specified?
Organization: The World Public Access UNIX, Brookline, MA
Date: Wed, 2 Sep 1992 12:14:51 GMT

Bruce G. Bostwick writes:
>
>Bear in mind, too, that the change in impedance with frequency isn't
>even roughly linear.  The voice coil is an inductor with a biased
>core, yes, but the cone is a mechanical component, and so is the air
>in and outside the box, and remember back emf?  That's right, the
>resonances and responses of the speaker, the box, and even the room to
>a tiny extent show up in the circuitry as 'backtalk' to the amp.  This
>means small (and sometimes large) peaks and dips in the impedance
>curve that change, often chaotically, when anything gets moved.
>

Wow, do we have a pile of assertions ripe for the testing or what!?

First, "change in impedance with frequency isn't even roughly linear." 
If we take the statement at face value, then so what? By linear, do you
mean that it can;t be modeled by a first order (linear) equation? If so,
your absolutely right, but, again, so what? At a given drive level, we can
come up with a pretty damned accurate model based on a sufficiently complex
equivalent circuit, and such a model behaves as arbitrarily close to reality
as you care to take the time and effort to make it. It's an excercise I
perform pretty much on a daily basis in my work.

About the voice coiul being an inductor with a "biased core,", in a word,
wrong because of poor understanding of the phenomenon and vast
oversimplificaion. The voice coil (and the magnet) act as transformers. They
essentially transform the motional impedance of the speaker (along with the
absolutely miniscule acoustical impedance) to an electrical equivalent (and,
in doing so, also transform electrical power into mechanical power). Again,
so what?

Now the fun begins. Yeah, what about the cone, and the air both in and outside
box? Are you willing to assert that the air performs non-linearly within the
normal operating range of the loudspeaker. I think not by a long shot. And
back EMF is nothing more than the electrical transformation of the motional
impedance of the system.

Now, the real meat comes in, where the assertion is made that "the resonances,
and responses of the speaker, the box and even the room to a tiny extent show
up in the circuitry as 'backtalk'" (hmmm, reminds me of a recalcitrant student
I once had at a lecture, "But Dr. Bose said..." SMACK!).

Let's look (and I invite you to research this independently) the various
sources of the impedance components in a loudspeaker.

There are "losses". These are the resistive components of the impedance. The
single greatest source of losses is very simple, it's the DC resistance of
the voice coils (and of any resistive attenuator circuits in the crossover).
They acount for typically 95% of the total losses in the passband of the
system (below the passband, they account for ALL the losses, above, the speaker
is essentially reactive and not radiating anyway, by definition).

The second most important set of losses are mechanical. They can be significant
where mechanical velocities are relatively high (such as at the fundamental
resonance of the woofer, where the motional losses might be as much as 10% of
the pure resistive losses), but through most of the passband, they are quite
minimal. 

Then there are the acoustic losses: these are the "losses" into which we 
actually produce sound. They are absolutely insiginificant. I would hazard
to estimate that, in the passband, they account for no more than 1% of the
total losses at best for direct radiator loudspeaker systems (now, as a very
interesting aside, the typical efficiency of a direct radiator system just
so happens to coincide with the ratio of acoustic losses, or more accurately,
the radiation resistance, to all other combined losses!).

The reactive components are due to several things. There is a "reactive"
component on either side of fundamental mechanical resonances. There might
be component due to the fundamental cone breakup mode. There are reactive
components due to crossovers. And there is a reactive component due to
the inductance of the voice coils. Now this latter does not behave like a
pure inductance (and might be the "non-linear" that you refer to but is
not non-linear per se. In fact it behaves very much like a lossy poorly
coupled transformer driving a fairly resistive load).

The real assertion comes when the statement is made that the impedance curve
changes "often chaotically, when anything moves." This is nonsense, plain and
simple. From an empirical standpoint alone, I've measured enough systems to 
find that the amount of coupling between the amplifier and the room is so
small and insignificant as to completely bury any such effects so far down
in the noise that they are undetectable. As to the "chaotic" part, in what
way is it "chaotic". Do you mean that the impedance curve looks lumpy and
irregular. Indeed it does, but it is quite deterministic and hardly chaotic
in any way that I am familiar with the term.

.
-- 
|                Dick Pierce                |
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