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Q: Speaker inductance measurement
I found a formula for calculating speaker inductance but its a little
unclear to me, is this right? \ / \/ M * M  Re * Re / 2Pi  frequency so its the root of (M*MRe*Re), divided by (2*Pi), divided by the frequency? Where (M) is the impedance Magnitude. It says, obtain (M) like this: * Connect an amplifier and frequency generator set to 1000Hz and put a 10 ohm resistor on the output. * Adjust the gain on the amplifier and frequency generator until you get 10 V.A.C. * Remove the resistor and connect the speaker. * Set the frequency at the drivers highest usable frequency. * The voltmeter reading is the driver's impedance magnitude (M) for this frequency. What is the "drivers highest usable frequency" anyway? ZMax? Its my understanding that the inductance should be obtained at 1000Hz, is this what I want? == Posted via Newsfeeds.Com  UnlimitedUncensoredSecure Usenet News== http://www.newsfeeds.com The #1 Newsgroup Service in the World! 120,000+ Newsgroups = East and WestCoast Server Farms  Total Privacy via Encryption = 
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#2




"Nigel Thomson" > wrote in message ... > I found a formula for calculating speaker inductance but its a little > unclear to me, is this right? > > \ / > \/ M * M  Re * Re / 2Pi >  > frequency > > so its the root of (M*MRe*Re), > divided by (2*Pi), > divided by the frequency? > > Where (M) is the impedance Magnitude. > > It says, obtain (M) like this: > > * Connect an amplifier and frequency generator set to 1000Hz and put a > 10 ohm resistor on the output. > > * Adjust the gain on the amplifier and frequency generator until you > get 10 V.A.C. > By doing these steps you have created a (somewhat) calibrated measuring system. You know that 1KHz into a 10 ohm, purely resistive load will yield a voltage reading of 10V. > * Remove the resistor and connect the speaker. Replace a resistive load with a load that is mostly resistance, but some reactance; the speaker. > > * Set the frequency at the drivers highest usable frequency. If you think of the voice coil as a simple coil, it should have a constant value for its inductive reactance in Henries. Voice coils are not simple coils. They are suspended in a strong magnetic fields and they move. But, you are looking for a single target value for the inductive reactance of the coil. So, why not take the measurement where it is likely to have more effect on the whole system? That should be the top end of the portion of the audio spectrum for which this device is going to be used. Try putting in the frequency of the crossover point to the next driver. > > * The voltmeter reading is the driver's impedance magnitude (M) for > this frequency. > That means that M is just a numerical factor, that is a voltage reading that is used to derive the real value in Henries. > What is the "drivers highest usable frequency" anyway? ZMax? > No. Zmax is the maximum linear piston motion of the coil before it leaves the magnetic influence of the pole plate and plug. > Its my understanding that the inductance should be obtained at 1000Hz, > is this what I want? > I don't think you will be able to measure the difference between 1000Hz and 5000Hz. Only 5000Hz will give you a different reading on the meter. Try it! http://www.akrobiz.com/speakers/ ~James. ) > > == Posted via Newsfeeds.Com  UnlimitedUncensoredSecure Usenet News== > http://www.newsfeeds.com The #1 Newsgroup Service in the World! 120,000+ Newsgroups > = East and WestCoast Server Farms  Total Privacy via Encryption = 
#3




Ooops.
Zmax is the maximum impedance at the resonant frequency of the driver. Not where you want to measure the coil's inductive reactance! Xmax is the voice coil throw thingie... ~James. ) 
#4




Nigel Thomson wrote: > I found a formula for calculating speaker inductance but its a little > unclear to me, is this right? > > \ / > \/ M * M  Re * Re / 2Pi >  > frequency > > so its the root of (M*MRe*Re), > divided by (2*Pi), > divided by the frequency? First, a suggestion: don't try to "draw" equations, write them out using understandable notation. That way, what you're sayinng isn't so dependent upon your ability to draw or someone's ability to "read" a picture. Using that principle, your equation restated might look like: L = sqrt(M^2  Re^2)/(2 pi F) Let's reverse that to understand where it came from. The impedance of a series inductor and resistor at any given frequency the vector sum of the resistance and the inductive reactance (wL, where w is radian frequency, 2 pi F). As a vector sum, the Pythagorean equation rules: Zt = sqrt(R^2 + wL^2) or Zt = sqrt(R^2 + (2 pi F L)^2) Square both sides and expand terms: Zt^2 = R^2 + 4 pi^2 F^2 L^2 Subtract R_2 from both sides: Zt^2  R^2 = 4 pi^2 F^2 L^2 Divide both sides by the frequency terms: (Zt^2  R^2)/(4 pi^2 F^2) = L^2 And take the square root of both sides: sqrt(Zt^2  R^2)/(2 pi F) = L Or, rearranged: L = sqrt(Zt^2  R^2)/(2 pi F) which matches your equation, and illustrates how it was obtained. > It says, obtain (M) like this: Look for a recent posty of mine describing a simple, reliable way of measuring impedance magnitude. > What is the "drivers highest usable frequency" anyway? ZMax? > > Its my understanding that the inductance should be obtained at 1000Hz, > is this what I want? All of what you say is based on the assumption that the voice coil inductance is essentially a perfect resistor in series with a perfect inductor, and the physical reality if FAR from that. By "perfect," I mean that the resitive part of the model remains constant with both current and frequency, as does the inductive part, and the only variable is the inductive reactance, which is directly proportional to frequency. However, what actually happens in a driver far from that perfect model. We can largely ignore the effects of the motional impedance in most cases, as the peak in the motional impedance, occuring at the driver's fundamental mechanical resonance, is far enough separated in frequency so as to have negligable influence. Additonally, since the velocity of the voice coil goes as the reciprocal of frequency above resonance, the raw effects of simple voice coil motion simply becomes insignificant at higher frequencies, contrary to the implications made by another respondant. Instead, what has a SUBSTANTIAL confounding influence is that the voice coil is immersed in a large amount of (relatively) poor electrically conductive material, notably the pole piece and front plate of the magnet structure. This material is typically made of lowcarbon steel. The generation of timevariant magnetic fields by the signal passing through the voice coil generates secondary eddy currents in these metallic structures, and these metals are lossy. The degree of coupling is frequency dependent as well. The result is that when, in fact, you analyze the rising impedance of the voice coil, you find that it does NOT behave as a simple series resistorinductor model. INstead, you find, curiously, that the VALUE of the resistive part increases with frequency, and the VALUE of the inductive part DECRESES with frequency. This can be readily observed in the deviation from the ideal model. In the ideal model, the impedance rise should approach and, eventually, reach a rate where the impedance doubles with each octave. Further, you'll find that the phase angle of the impedance will approach 90 degrees. In actually measuring the impedance over frequency, you will instead that it does neother of these. You find that instead of the impedance doubling with each octave, that it increases only by about 40% or so each octave. And you'll find that the impedance, sintead of approaching 90 degrees, only approaches and never exceeds about 45 degrees. Analyzing the impedance characteristics reveals a curious thing: that the resistive part is NOT constant, equal to Re, but there is a second resistive part in addition taht's negligable at low frequencies and significant at higher frequencies, and increases roughly as the square root of frequency. Equally curious is the fact that the INDUCTANACE is high at low frequencies and decreases as frequency goes up, roughly as the inverse square root of frequency, rather than staying constant. This means that once you get to a certain frequency, and that's only about an octave above the resistive portion of the mid range impedance trough, the inductuive REACTANCE, rather than doubling with each octave, climbs at a slower rate, but the resistive component, which should remain constant with frequency, increases itself at about the square root of the frequency. For example, a typical 8" woofer might be "rated" by the manu facturer as having an inductance at 1 kHz of .8 mH and a DC resistance of 6.5 ohms. That would indicate that at 1 kHz, the driver's impedance is sqrt(6.5^2 + (2 pi 1e3 .0008)^2) or about 8.2 ohms. In fact, many manufacturers simply measure the impedance at 1 kHz and "assume" the equation you stated is correct and thus derive the impedance from that. If the simple model were true, then we would expect that the impedance at, say 2 kHz would be sqrt(6.5^2 + (2 pi 2e3 .0008)^2) or 12 ohms, at 4 kHz about 21 ohms, and so forth. In fact, when we actually MEASURE the impedance, we find that at 2 kHz, the imepdance is only about 10 Ohms, and at 4 kHz it's about 16 ohms. What went wrong? Well, the issue is that instead of storing the energy in a magnetic field, it's because the generated eddy current flowing through the metallic front plate and pole piece is dissipating the energy by slightly heating these elements through simple ohmic losses. The basic principle is that you CANNOT assume the voice coil model at high frequencies is a simple series inductance resistance: it's more complex that that and not in any subtle way. The assumption is sufficiently at variance with the actual physical reality such that the predicted vs real impedance is WAY off, often by a factor of two or more within the audio band. One of the consequences is that if you attempt to calculate the values for a complex conjugate circuit correcting for driver inductance based on the simple model, the values you derive will most assuredly NOT be correct, and be off by a substantial amount, enough to screw up the response of your network based on such assumptions. For more details, you might want to check a number of articles on the topic, the most notable of which is Vanderkooy, "A Model of Loudspeaker Impedance Incorporating Eddy Currents in the Pole Structure" (J. Audio Eng. Soc., vol 37, no 3, pp 119128, 1983 March). The fact that the coil moves and is suspended in a strong magnetic field, as suggested by another poster, is largely irrelevant to the problem, as Vaderkooy clearly demonstrates in his article. He performed experiements, for example, using a demagnetized structure and with the voice coil locked firmly in place and found no substantial differences in the high frequency impedance function of the driver., Rather, as I describe above, the major source of deviation from ideal behavior is the presence of the conductive metalic structure surrounding the voice coil and the effects of generated eddy currents in that structure. Without, then, the ability to precisely measure the true characteristics of the impedance, notable, the actuall resistive and inductive portions of the impedance at the frequency of interest, the best you can do is measure the actual impedance at the frequency of interest. If it's significantly up the impedance curve, assume the phase angle is near 45 degrees and then dervice both the resistive and inductive portions from that and proceed accordingly. In the transition region between the midrange torugh and the point where the impedance is steadily climbing in frequency, assume the phase angle is somweherte in between 0 and 45 degrees and proceed from there. Ideally, the best procedure is to measure both the imepdance magnitude AND phase (as I allude to in my impedometer article) and, with those in hand, you CAN derive accurate values for the resistive and inductive portions of the impedance. 
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