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From: Chuck Simmons
Organization: You jest.
X-Mailer: Mozilla 4.61 [en] (X11; U; Linux 2.0.33 i586)
Subject: Re: Cancel speaker resistance?
Date: Tue, 17 Sep 2002 13:05:16 GMT
NNTP-Posting-Date: Tue, 17 Sep 2002 06:05:16 PDT
Richard D Pierce wrote:
> In article <3D868192.F61269AB@webaccess.net>,
> Chuck Simmons wrote:
> >> I've studied quite a few impedance curves, and they do strongly tend
> >> to follow a pattern. Peak in the LF range dip, Peak in the middle
> >> range, dip, peak at the high end.
> >> http://www.pcabx.com/product/amplifiers/mag%20left_hi.gif
> >The first two peaks are mechanical. The first peak is the first
> >principle mode of the diaphragm and suspension. Very small speakers
> >don't have the second peak which I suspect is due to the second
> >principle mode of the diaphragm. The third appears to be electrical
> >rather than mechanical because it is present in voice coils not
> >attached to diaphragms. A voice coil with a stiff mass load and a spring
> >suspension has only two peaks corresponding to the spring mass resonance
> >and to the self resonance of the coil and stray capacitance.
> You're right about the first peak at 40 Hz: it's the fundamental
> cone mass/system compliance resonance. The system complisance is
> the combination of the mechanical suspension for the cone and
> the acoustic compliance of the enclosure.
> You're wrong about the second peak, though. This is a two-way
> loudspeaker system, a woofer and tweeter. THe second peak at
> 1800 Hz is a combination of things. First the rise above 200 Hz
> is the beginnings of the lossy inductance in the voice coil.
> That eventually gets shunted by the lower impedance of tweeter
> voice coil. If both drivers present a resistive load above
> mechanical resonance, and a constant-voltage crossover topology
> were used, then the imepdance would be constant. However,
> neither condition is likely to hold, especially in that it is
> most likely NOT a constant-voltage crossover alignment, so you
> have the second peak at 1800 Hz. The third rise in
> impedance above about 6 kHz is primarily the lossy inductance of
> the tweeter voice coil.
It was easy to get fooled because when I use a speaker to test a
transconductance amplifier before attaching it to a much more valuable
VCM, I get similar plots where the first principal mode and the second
principal mode can be seen.
> The self resonance of the coil and stray capacitance never
> really happens, at least not in the audio band, and if it ever
> does, it is a VERY low Q. One of the problems is that the
> first-order models are insufficient to explain the gross second
> order effects that drivers have. FOr example, assuming the plot
> was derived from a real speaker, as opposed to a simulated load,
> you'd find that the tweeter inductance rise is not the xlassic
> doubling of inductive reactance with each octave, rather is
> goes roughly as the square root of frequency. You will also find
> a resistive component that goes as the square root of frequency.
The degree of damping of the coil self resonance seems to be a function
of whether the voice coil is damped. Some are not. Certainly the cheap
speakers I'm willing to sacrifice to amplifier testing (if something
goes wrong I can fry coils) have tended to have little damping on the
electrical modes. Actually, the target VCM usually has a Q of 10 at the
first principal mode and a Q as high as 20 at the coil self resonance.
VCMs have no electrical or mechanical damping in most applications so
they are almost ideal double integrators from current to sensor above
the first principal mode to the coil self resonance. Cheap speakers
deviate from this a little because other modes show up. Of course I
can't do any meaningful measurements on a speaker used for test due to
lack of a sensor. With a VCM I ordinarilly have a sensor with a
sensitivity greater than 1 volt per micrometer.
> This is due to the fact that the inductance is a complex, lossy
> mechanism resulting from frequency-dependent eddy current losses
> in the magnet structure: the higher the frequency, the more
> significant the losses.
I'm not so sure the losses you speak of are in the magnet structure
since there are pure VCMs that don't have a strongly frequency dependent
resistive component. I've actually wondered why I don't measure it. I
suppose part of it has to do with the fact that my transconductance
power amps have a very large output impedance (several thousand ohms at
least) so coil resistance probably gets washed out even when the
amplifier output current is high.
... The times have been,
That, when the brains were out,
the man would die. ... Macbeth
Chuck Simmons firstname.lastname@example.org
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