From: Sean Breheny <shb7@cornell.edu>
To: Microcontroller discussion list - Public. <piclist@mit.edu>
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Date: Thu, 19 Mar 2020 00:39:09 -0700
Subject: Re: [EE] Measuring speaker impedance
Thread-Topic: [EE] Measuring speaker impedance
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As James says, there are some problems with this, but I think it could be
done.

What you have to realize, though, is that the whole concept of impedance is
a small-signal one. A speaker only has a well-defined impedance for a fixed
frequency and a small amplitude of signal. Stray capacitance and the
effects of air on the cone will cause the impedance to vary with frequency.
Even at a fixed frequency, the speaker is fundamentally a non-linear device
and so the impedance will change with amplitude and even during each cycle.

However, I suspect that you could make a mathematical model of the speaker,
including some of the non-linear effects, and then apply the audio signal
to both the speaker AND (virtually, in software) to your model. You would
then compare the predicted current (from the model) with the measured,
actual current, and adjust the model parameters until they match within
some tolerance. This setup is known as an "observer" because it ends up
"observing" the hidden parameters of the model based on a history of the
model behavior versus the real system behavior.

Once you had your model,. you could then compute an estimated small-signal
impedance for any given frequency.

One open question is whether all of the relevant model parameters are
observable from the data available to you (applied voltage and measured
current). I suspect that they are as long as the music contains a wide
enough frequency and amplitude content.

This would be a moderately-challenging DSP project. I've done similar
things with electric motors (estimate parameters while the motor is
running). For some parameters, it took only a few days to get things to
work. For others it took months to make it work.

Sean


On Thu, Mar 19, 2020 at 1:17 AM James Cameron <quozl@laptop.org> wrote:

> Problem foreseen is that the impedance you measure will then depend on
> a set of simultaneous frequencies rather than a signal of just one
> frequency, so using the impedance meaningfully is limited.
>
> The other thing is that the starting position of the cone would
> matter; a low frequency signal within the mix of signals could cause
> the cone to be in a position that may beat with the sampling.  So
> despite doing it rapidly you could have the low frequency signal
> imposed on the results.
>
> On Thu, Mar 19, 2020 at 01:02:18AM -0400, Neil wrote:
> > Hi,
> >
> > I'm working on a project for a friend, which will measure speaker
> > impedance over a given frequency range.  I'm thinking I'd use a functio=
n
> > generator sweeping across frequency range, then measure current (prob
> > with a clamp sensor) and voltage across the speaker and do the math fro=
m
> > there.  No prob so far.
> >
> > But can how about doing this dynamically?  IE: play music and
> > dynamically figure out speaker impedance from there.  He believes
> > commercial devices do this.  So far, all I can think of is measuring th=
e
> > voltage and current as before, but dynamically FFT-ing both and
> > (rapidly) doing the math from there.  Does this seem workable?
> >
> > Cheers,
> > -Neil.
> >
> >
> > --
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> --
> James Cameron
> http://quozl.netrek.org/
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