Vas, as I understand it is the equivalent volume of standardised air that represents the compliance (Cms?) of the speaker in question. I have been told that Vas = Vb((Fb / Fs)² - 1). From this formula I notice right off that for Vas to be positive Fb must be greater than Fs. Since there are no illegal states, Vas can be virtually any real value.
Issue here is Fb. Fs is resonance in open space, Fb is resonance in a closed environment, where the speaker is working against an increased load created by a volume of enclosed air. Because of the additional stiffness created by the enclosed air I visualize the resonant frequency of the speaker to increase, and from data I've seen, that is what happens. But is this necessarily so?
I have speaker in my possession which does quite the opposite, at least as I am measuring. I can place the speaker flat against my floor and measure a markedly reduced resonant frequency. ??????? Same results into 28 liter box.
Now, I am using small signals, output voltage from amplifier is 1 volt. I have checked amp out volts both free air and closed box at both frequencies. The series resistor for watch for current is non-inductive (even if inductive, that would be wrong way). I have noticed that Fb is actual, but have not measured Q in box. There is no dual peak as you might see in a tuned box
I am curious as to what I am doing wrong, or if all is ok with the test setup, what is the physics at play here? I already have boxes under way for this set of speakers, and will use active filters to compensate, if needed, but why the negative Vas???
Issue here is Fb. Fs is resonance in open space, Fb is resonance in a closed environment, where the speaker is working against an increased load created by a volume of enclosed air. Because of the additional stiffness created by the enclosed air I visualize the resonant frequency of the speaker to increase, and from data I've seen, that is what happens. But is this necessarily so?
I have speaker in my possession which does quite the opposite, at least as I am measuring. I can place the speaker flat against my floor and measure a markedly reduced resonant frequency. ??????? Same results into 28 liter box.
Now, I am using small signals, output voltage from amplifier is 1 volt. I have checked amp out volts both free air and closed box at both frequencies. The series resistor for watch for current is non-inductive (even if inductive, that would be wrong way). I have noticed that Fb is actual, but have not measured Q in box. There is no dual peak as you might see in a tuned box
I am curious as to what I am doing wrong, or if all is ok with the test setup, what is the physics at play here? I already have boxes under way for this set of speakers, and will use active filters to compensate, if needed, but why the negative Vas???
Hi,
the T/S parameters are the result of small signal testing, but also in free air with no interfering reflections nor sounds coming to the cone. The cone and Voice Coil act as a microphone and do generate voltages which will seriously affect the measurement results you are trying to take.
Fs is the resonant frequency in free air with no reflections. I have seen it stated that the driver frame must be vertical, i.e. cone pointing horizontally and supported by two completely different methods.
Tightly bolted to an immovable very stiff frame or hanging from a thread from a sky hook, a mighty strong thread for an 18inch driver and I can confirm that the light pendant in the middle of the room did not break loose. I have never compared the solid frame support to the hang by a thread result.
The Fb test must be done in free air. Again no reflections nor wind noise to affect your measured results.
I use the added weight Vas method to avoid having lots of dummy boxes.
Fb takes account of both mass and the compliance of the free air driver and adds on the compliance of the air sealed into the box. This combined compliance must be stiffer than the free air compliance. It cannot be any other way.
This leads to Fb>Fs always.
the T/S parameters are the result of small signal testing, but also in free air with no interfering reflections nor sounds coming to the cone. The cone and Voice Coil act as a microphone and do generate voltages which will seriously affect the measurement results you are trying to take.
Fs is the resonant frequency in free air with no reflections. I have seen it stated that the driver frame must be vertical, i.e. cone pointing horizontally and supported by two completely different methods.
Tightly bolted to an immovable very stiff frame or hanging from a thread from a sky hook, a mighty strong thread for an 18inch driver and I can confirm that the light pendant in the middle of the room did not break loose. I have never compared the solid frame support to the hang by a thread result.
The Fb test must be done in free air. Again no reflections nor wind noise to affect your measured results.
I use the added weight Vas method to avoid having lots of dummy boxes.
Fb takes account of both mass and the compliance of the free air driver and adds on the compliance of the air sealed into the box. This combined compliance must be stiffer than the free air compliance. It cannot be any other way.
This leads to Fb>Fs always.
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AndrewT...Thanks for taking the time to respond back to me. What you have done is reiterated my concern! How did this happen????? Most likely it has to do with my test jig. I have no problem with that. What I want to do is fix my ways, so I can take meaningful measurements.
What I have done is cookbook, followed procedure outlined, among other places, in ESP website. The free air was done with the speaker facing upwards, resting on the magnet .
I will try suspending in a different fashion. I suspect that it is the free air measurement that is at fault here ( Reflections from the surface that the speaker is resting on), rather than the on the test box.
I'll try it and see.
Thanks again.
What I have done is cookbook, followed procedure outlined, among other places, in ESP website. The free air was done with the speaker facing upwards, resting on the magnet .
I will try suspending in a different fashion. I suspect that it is the free air measurement that is at fault here ( Reflections from the surface that the speaker is resting on), rather than the on the test box.
I'll try it and see.
Thanks again.
I think Resting the speaker on it's magnet is your problem, yes you will get reflections off the floor, but probably more importantly you are working against gravity 🙂 resting on the floor will have even more of an effect if the speaker has a vent in the magnet I suspect...
I've tried both hanging and clamping and preferred clamping. I got more consistent results and smoother impedance curves when clamping, I think the problem with hanging was that the speaker could still move with respect to the air around it (which would be less of a problem the heavier the driver was, I did the comparison with 5" drivers).
Tony.
I've tried both hanging and clamping and preferred clamping. I got more consistent results and smoother impedance curves when clamping, I think the problem with hanging was that the speaker could still move with respect to the air around it (which would be less of a problem the heavier the driver was, I did the comparison with 5" drivers).
Tony.
Andrew is correct that box mounting will always increase total stiffness and always raise resonance. Be aware that laying on the floor will give some extra mass loading. Also make sure that laying it on a surface doesn't close up any rear vents that might change apparent stifness. Suspending by hanging can allow the chassis to move and will perturb the resonance also. Rigidly fastened away from surfaces is the goal. Mounted on an open baffle can be good.
You can also use the added mass technique to calculate effective mass then calculate Cms or Vas from that.
Be forewarned that high accuarcy in T/S numbers is usually elusive.
David S.
(Edit) I see that Tony was a faster typer than me!
You can also use the added mass technique to calculate effective mass then calculate Cms or Vas from that.
Be forewarned that high accuarcy in T/S numbers is usually elusive.
David S.
(Edit) I see that Tony was a faster typer than me!
Regarding the added mass technique. This would be a relative value change, would it not? In other words, if I were to place the speaker in the same position for each measurement, before and after the addition of the mass, then what I am observing is the difference in the 2 values with same environment, not basing my calculations on 2 absolute values from 2 different locations. Understanding the need for accuracy in weighing the mass, this approach might actually improve my accuracy. Certainly worth a try. Don't see how I can do worse than getting a decrease in resonance just because my outdoor temp is also in the negative and I'm too whimpy to put on a coat.
As a side bar, I appreciate how folks are jumping in here. Europe, Australia, Canada. Wow!!!!!!
As a side bar, I appreciate how folks are jumping in here. Europe, Australia, Canada. Wow!!!!!!
minus outside ! Is that C or F or K?
The surround and to some extent the spider will change compliance as the temperature changes.
Very low temperatures will result in very low Vas measurements.
A new surround also results in a low Vas measurement.
The driver needs to be run in at normal operating temperature and tested at the same operating temperature.
The surround and to some extent the spider will change compliance as the temperature changes.
Very low temperatures will result in very low Vas measurements.
A new surround also results in a low Vas measurement.
The driver needs to be run in at normal operating temperature and tested at the same operating temperature.
Actually, Andrew, I was referring to myself, forget the speaker!. Yikes, degree K?... Deg F, and a slight exaggeration. Single digit though. I am somewhat intrigued by the idea of the mass measurement approach. If I can eliminate variables in gathering of data, then I am all for that approach. Kinda like minimizing even order impacts.
The added mass method is approximate and the higher the proportion of the added mass the worse the error becomes.
If your mms is 50gm then don't add 25gms, 50% is far too high.
5gm (10%) should give a reasonable result.
Something you can do is add 5, 10, 15, 20, 25gm and plot the graph of Vas vs added mass. You will see the slope of the line and that the slope gets worse as the mass increases.You can guess at what to expect with 1gm and then do a check measurement to see if you can read at the resolution to detect the frequency change.
I use a lead sheet shim stuck on with double sided sticky tape. easy to hammer out to 5mil, 5thou, ~0.1mm thick, stick on the double sided tape and rub it on well. Cut with scissors to the weights you require. You might have to go back to your school and ask the science teacher to let you weigh your samples. Remember to remove the backing paper before weighing.
If your mms is 50gm then don't add 25gms, 50% is far too high.
5gm (10%) should give a reasonable result.
Something you can do is add 5, 10, 15, 20, 25gm and plot the graph of Vas vs added mass. You will see the slope of the line and that the slope gets worse as the mass increases.You can guess at what to expect with 1gm and then do a check measurement to see if you can read at the resolution to detect the frequency change.
I use a lead sheet shim stuck on with double sided sticky tape. easy to hammer out to 5mil, 5thou, ~0.1mm thick, stick on the double sided tape and rub it on well. Cut with scissors to the weights you require. You might have to go back to your school and ask the science teacher to let you weigh your samples. Remember to remove the backing paper before weighing.
Excelent idea with the hammered lead Andrew! I always struggled with the added mass, I can't actually remember whether I used large washers sticky taped on the dust cap or rolled up blue tac around the dust cap the last time, both were a bit hit and miss if I recall correctly... I bought myself a little scale accurate to 0.1g twas rather expensive though, probably more than the drivers!
Tony.
Tony.
I've always used the gray modeling clay. Work it into a rope or snake. this also warms it up and makes it more sticky. You can weigh it then form a circle around the dustcap. Whatever you use make sure it is firmly attached so that it doesn't create a secondary resonance.
If you want accuracy you can use multiple techniques and average the results. I've used them all including cutting the woofer apart measuring the pieces and adding calculated air load. If I get 10% variation between approaches I'm happy. 20% I live with🙁 When some calculations depend on area squared (diameter to the 4th) then you can't expect ultimate accuracy!
David
OK, I see. The effect of added mass is not linear. Second order. Away from school way tooooooo long.
Something I've wondered for a while is whether measuring Thiele Small parameters with the driver mounted on a large open baffle (at least for the first measurement where no extra weight and no closed box is used) will give the same result as taking the initial measurement with the driver supported in free space, the method usually advocated ?
Surely the free flow of air around the edge of the driver frame would result in a different loading on the driver (and therefore a change in Fs) than a driver mounted on a large open baffle ?
If there is a difference, how valid is the free space method considering that drivers are always mounted on baffles when used in speakers ? Would a better approach be to always mount the driver on a large open baffle, and then bolt on a 5 sided box to the front of the same baffle to convert it to a sealed box for the second measurement. (or add mass to the cone with the driver still on the baffle in the case of delta mass)
Another thing that has bothered me is that Thiele Small parameters are supposed to be "small signal" parameters and by implication measured at very low signal levels, but none of the articles on measuring Thiele Small parameters I've come across have any advice about what signal levels (relative to the drivers limits) might be appropriate, or even that it matters. (provided that the driver isn't pushed into it's non-linear region)
While recently trying out the impedance measurement mode in LIMP (ARTA) with it's built in Thiele Small calculator, I was at first surprised to see that a previously measured driver (an 8" full range with a very soft cloth surround) was showing a free air resonant frequency of 48Hz - 10Hz higher than the last time I measured it more manually with a swept sine wave oscillator, resistor and multimeter! Calculated Vas was also about half what I was expecting, at about 50 litres. (Previous measurement was around 100 litres)
After a bit of investigating I realised what was going on - I had been using the pink noise mode in LIMP, with the result that the cone excursion was microscopic. I switched to the stepped sine mode and tested it at a few different levels over about a 30dB range.
At very low levels (-30dB or lower relative to 2v RMS, with a series resistor of 33 ohms) the impedance curve was identical to that measured in the noise mode, showing an Fs of 48Hz, however by the time the level was increased to the point where cone movement was just visible the Fs had fallen to and stabilized at 38Hz - the figure I've measured before. Calculated Vas was where it should be ~100 litres.
I'm not sure of the technical term for this mechanical property is, but it's pretty obvious the suspension is stiffer for microscopic movement than it is for significant visible movement. (The xmax of the driver is about +/- 3mm, and I would say the movement was +/-0.5mm at the very most, probably half that, so well within the linear operation of the driver)
Does anyone else take this into account when measuring the impedance curve of a driver, and/or Thiele Small parameters, or does the exact drive level get left up to chance or personal preference ? (Which might be appropriate for one driver but not another)
I tried another driver, this time a Vistaton W300S and there was a difference between microscopic signal levels and "visible movement" levels - it was on the order of about 3Hz, smaller, but still significant.
Since the point of Thiele Small parameters is to help simulate the bass response, and bass inevitably requires more than microscopic cone movement, I presume the measurement taken at the higher signal level (but still at less than 1/5th of Xmax or so) is the valid one to use ?
I guess if you were to graph apparent Fs vs drive level you could quickly determine where the "knee" in Fs was, and work out from that the optimum drive level to get accurate measurements.
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the air loadings are very different.
Some of the mass that is resonating is the air mass. Change the air loading and you change the air mass and get the wrong result.
you're reading the bad texts.
1k0, 500mW resistor is sometimes recommended as the measurement resistor for a "normal" impedance driver.
That automatically defines the maximum power delivered to the DUT.
DBMandrake, Hi, I'm the noob here, but I have read that it is best to keep the output voltage from the power amp at < 1v. Less than 1watt. This is using a series resistor of 6-10 ohms, so that the vc is going to see between 0.4 and 0.8 volts. If you set up a audio oscillator direct without a power amp between, then I see about a 1k ohm series resistor. This will severely reduce the emf across the vc, if you were to keep the output at 1 volt.
I am not quite as excited about the 1k ohm series resistor, as the delta v as we sweep across resonance is not nearly as pronounced as when you have the 10 ohm series resistor (vc is going to swing, what, say from 5 ohm to 40 ohm) Depending on what you use for a meter, this can disappear into meter resolution. Another problem is if you use an audio oscillator directly, you now have the output impedance of the oscillator to contend with, and the low z of the 10 ohm resistor loads the heck out of the oscillator. Be aware, I speak in general terms here, you will find exceptions. The 1k resistor is to try to give a constant voltage source "feel" to what you are doing. Using a smaller value will allow for changing source voltage which of course will mess up your measurements.
Try to stay with a dc coupled power amp to drive your test setup, it will minimize the source as a potential error component.
I say this having just been through seeing myself get -Vas values. I did verify the source as being constant though. Thinking I got that part right, at least.
I am not quite as excited about the 1k ohm series resistor, as the delta v as we sweep across resonance is not nearly as pronounced as when you have the 10 ohm series resistor (vc is going to swing, what, say from 5 ohm to 40 ohm) Depending on what you use for a meter, this can disappear into meter resolution. Another problem is if you use an audio oscillator directly, you now have the output impedance of the oscillator to contend with, and the low z of the 10 ohm resistor loads the heck out of the oscillator. Be aware, I speak in general terms here, you will find exceptions. The 1k resistor is to try to give a constant voltage source "feel" to what you are doing. Using a smaller value will allow for changing source voltage which of course will mess up your measurements.
Try to stay with a dc coupled power amp to drive your test setup, it will minimize the source as a potential error component.
I say this having just been through seeing myself get -Vas values. I did verify the source as being constant though. Thinking I got that part right, at least.
Small signal generally means small enough that it has no impact on the factors being measured. That is, if reduction in drive makes no difference you must be in the small signal range, so your methodology of trying various levels and seeing the threshold of change is the right approach.
Frankly, I am a bit surprised that you are seeing effects by sub-milimeter excursions. For drive I have typically used 600 or 1k series resistence and as much voltage as I could get. The high series resistence prevented much voltage getting through (except a little more at resonance). The sweep level is typically quiet, just audible.
Spiders are nonlinear, generally with an S shaped stiffness. I have seen a couple with an "oilcan" characteristic that toggled near the zero crossing but the majority are linear enough near zero excursion.
Although you will use the woofer at much higher drive, you want to test it at low drive. In the end the BL and mass figures are most key. Shifts in suspension stiffness with drive are much less important since vented boxes are generally insensitive to compliance changes.
Highly non-linear BL can be a problem, but if a system is that nonlinear then distortion will be obvious as well as the parameter related response variation.
David S.
Except I made the assumption that the signal level above which the Fs starts to stabilize is the correct one, rather than the other way around.
I was as surprised as you, I didn't even consider the possibility at first and it took me an hour of going over my measurement set up trying to find out where the discrepancy was coming from - it was my first time using LIMP so I wasn't sure if I was using it correctly or not.
I tried a few values between 33 ohms and 1K with LIMP. Because it uses dual channel measurement to measure the voltage on both sides of the series resistor it can work out the true impedance without needing the series resistor to be high enough to approximate a current source - an approach that can still introduce several percent error even with 1K when only measuring the voltage across the driver.
My sound card output is about 35 ohms, so on a sensitive driver I can drive it to the point where there is a mm or so excursion at resonance via the 33 ohm resistor. (Or drive it much lower...)
I don't think it's a case of non-linearity around the zero point, but rather a threshold decrease in stiffness beyond a certain (quite small) amount of excursion, with a slow recovery.
What I forgot to mention last time is that I also discovered that if I manually moved the drivers across their full excursion several times ("exercised" the suspension in other words) and then very quickly measured them at a very low signal level (ARTA in pink noise mode can plot the entire impedance curve in real time in under a second) the results corresponded exactly with the stepped tone based measurement taken at a higher signal level that was enough to cause about 1mm of excursion.
What was also interesting is that if you watched the continuous real time impedance curve measurement, over a period of about 10-15 seconds it would gradually change back to the "small signal" result. So whatever the effect is, the change in stiffness has a recovery time of ~10 seconds rather than being something that is changing on a cycle by cycle basis purely on the excursion of that cycle.
(Maybe "Thixotropy" or possibly "shear thinning" effects in the suspension surround and/or spider ?)
Here are some measurements taken with LIMP showing the change. 0dB = 2v RMS at the input to the series resistor.
[special=:
Visaton W300S. -20dB pink noise mode (100ohm series resistor)
Fs = 30.52 Hz
Re = 6.80 ohms[dc]
Le = 284.11 uH
L2 = 1402.64 uH
R2 = 29.70 ohms
Qt = 0.37
Qes = 0.44
Qms = 2.19
Mms = 59.64 grams
Rms = 5.226318 kg/s
Cms = 0.000456 m/N
Vas = 154.32 liters
Sd= 490.87 cm^2
Bl = 13.258449 Tm
ETA = 0.95 %
Lp(2.83V/1m) = 92.60 dB
Added Mass Method:
Added mass = 10.00 grams
Diameter= 25.00 cm
Visaton W300S. -20dB pink noise mode (100ohm resistor) immediately after "exercising" suspension manually
Fs = 27.98 Hz
Re = 6.80 ohms[dc]
Le = 285.36 uH
L2 = 1384.55 uH
R2 = 29.49 ohms
Qt = 0.34
Qes = 0.41
Qms = 2.01
Mms = 60.47 grams
Rms = 5.278939 kg/s
Cms = 0.000535 m/N
Vas = 181.01 liters
Sd= 490.87 cm^2
Bl = 13.271551 Tm
ETA = 0.93 %
Lp(2.83V/1m) = 92.49 dB
Added Mass Method:
Added mass = 10.00 grams
Diameter= 25.00 cm
Visaton W300S. 0dB RMS, 33 ohm series resistor, stepped tone mode, no manual exercising of suspension (approx 1mm peak-peak excursion at resonance)
Fs = 27.92 Hz
Re = 6.80 ohms[dc]
Le = 283.33 uH
L2 = 1419.29 uH
R2 = 30.12 ohms
Qt = 0.35
Qes = 0.42
Qms = 1.92
Mms = 60.20 grams
Rms = 5.514250 kg/s
Cms = 0.000540 m/N
Vas = 182.65 liters
Sd= 490.87 cm^2
Bl = 13.010550 Tm
ETA = 0.90 %
Lp(2.83V/1m) = 92.36 dB
Added Mass Method:
Added mass = 10.00 grams
Diameter= 25.00 cm
]%[/special]
The Vas is a lot lower than Visaton's quoted parameters, and Fs higher. It seems that the suspension is a lot stiffer than claimed, although as you say the difference in a bass reflex alignment is relatively benign.
The difference between the extremely small signal and moderate signal characterstics is even more pronounced on the 8" driver.
[special=
Coral Flat 8 Mk 2. -20dB noise measurement, 100 ohm:
Fs = 46.43 Hz
Re = 7.40 ohms[dc]
Le = 172.92 uH
L2 = 482.81 uH
R2 = 18.39 ohms
Qt = 0.44
Qes = 0.47
Qms = 7.05
Mms = 10.72 grams
Rms = 0.443579 kg/s
Cms = 0.001096 m/N
Vas = 68.70 liters
Sd= 211.24 cm^2
Bl = 7.038980 Tm
ETA = 1.42 %
Lp(2.83V/1m) = 93.95 dB
Added Mass Method:
Added mass = 9.00 grams
Diameter= 16.40 cm
Coral Flat 8 Mk 2. -20dB, 100 ohm stepped tone measurement:
Fs = 46.50 Hz
Re = 7.40 ohms[dc]
Le = 161.91 uH
L2 = 484.82 uH
R2 = 20.61 ohms
Qt = 0.48
Qes = 0.51
Qms = 8.03
Mms = 11.90 grams
Rms = 0.432960 kg/s
Cms = 0.000985 m/N
Vas = 61.70 liters
Sd= 211.24 cm^2
Bl = 7.109678 Tm
ETA = 1.17 %
Lp(2.83V/1m) = 93.13 dB
Added Mass Method:
Added mass = 9.00 grams
Diameter= 16.40 cm
Coral Flat 8 Mk 2. 0dB, 100 ohm stepped tone measurement: (approx 1mm peak-peak excursion at resonance)
Fs = 37.35 Hz
Re = 7.40 ohms[dc]
Le = 162.36 uH
L2 = 492.87 uH
R2 = 22.00 ohms
Qt = 0.40
Qes = 0.43
Qms = 4.75
Mms = 11.16 grams
Rms = 0.551711 kg/s
Cms = 0.001627 m/N
Vas = 101.99 liters
Sd= 211.24 cm^2
Bl = 6.689461 Tm
ETA = 1.18 %
Lp(2.83V/1m) = 93.16 dB
Added Mass Method:
Added mass = 9.00 grams
Diameter= 16.40 cm
]%[/special]
What's interesting in these figures in particular is not only has Fs shifted a lot but Qms is radically different. 4.75 vs 8.03. Vas is different by a factor of two to one.
Are there any conclusions that can be drawn from these measurements ?
I wouldn't say either driver is unusually non-linear, in fact subjectively both are excellent, so I'm guessing that it's variations in compliance at play here rather than any significant non-linearity in the motor ?
So which is the correct condition to measure under ?
Are there assumptions built into the equations used to calculate simulated responses that assume free space measurement was used, or infinite baffle ?
Well, all very interesting!
Most spiders exhibit a lot of creep phenomenon. That is if you stretch them to a certain displacement the force required to hold that shift relaxes after some seconds. Release them and the pop back not quite to zero and then creep slowly back to the center spot. They are taking a set to static inputs.
You are saying somewhat the opposite, that this exercising is breaking them free from some central point stiffness and that they later take a set back into the stiffer set point. I don't think I have ever seen this short of some older ferrofluid tweeters that needed a little exercise to limber them up between uses (I'm starting to know how that feels).
Are the spider and surrounds of any exotic material? Are the spiders especially heavy duty with lots of resin impregnation?
In the end I don't think you are having trouble with your testing methodology as much as you have stumbled across an unusual driver. Our usual assumption is that nonlinearities diminish with level, below some threshold they are inconsequential. That is what the notion of "small signal" comes from. Your driver doesn't seem to respond that way.
It isn't rubbing is it? That gives rise to stick friction and crossover-notch-like dead zones at small drive.
Don't wory about Qms. It will tend to track with fs (fs/Qt should be constant) so if fs is not as expected Qms will also be off.
David S.
Most spiders exhibit a lot of creep phenomenon. That is if you stretch them to a certain displacement the force required to hold that shift relaxes after some seconds. Release them and the pop back not quite to zero and then creep slowly back to the center spot. They are taking a set to static inputs.
You are saying somewhat the opposite, that this exercising is breaking them free from some central point stiffness and that they later take a set back into the stiffer set point. I don't think I have ever seen this short of some older ferrofluid tweeters that needed a little exercise to limber them up between uses (I'm starting to know how that feels).
Are the spider and surrounds of any exotic material? Are the spiders especially heavy duty with lots of resin impregnation?
In the end I don't think you are having trouble with your testing methodology as much as you have stumbled across an unusual driver. Our usual assumption is that nonlinearities diminish with level, below some threshold they are inconsequential. That is what the notion of "small signal" comes from. Your driver doesn't seem to respond that way.
It isn't rubbing is it? That gives rise to stick friction and crossover-notch-like dead zones at small drive.
Don't wory about Qms. It will tend to track with fs (fs/Qt should be constant) so if fs is not as expected Qms will also be off.
David S.
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