Nearfield Bass Shootout

[Zilch]

I would suggest that you check your gate time, and windowing, even for swept sine type

measurements. I have commented about this rise in the bass issue in the past.

As I earlier demonstrated, I get essentially the same result using MLS and RTA.

In sinusoidal, the delay is established with each measurement automatically. The frequency for that determination is adjustable; it is set at 1 kHz for these measurements. I'll play with that a bit. It can also be disabled and set manually.

There is an element of irrelevancy in these details with respect to the results comparing the performance of different loudspeakers, which were all measured using the same method under the identical condition.

I have 6 AR 12" woofers, and will compare them all, after confirming that the AR3a box is air tight.

My measurements of the Smaller Advent are consistent with those obtained by Atkinson three years ago:

http://www.stereophile.com/historical/506advent/index4.html

[That doesn't mean we don't both have our heads in dark places, tho.... ]

[genek]

[That doesn't mean we don't both have our heads in dark places, tho.... ]

As long as the results are consistent and it's possible to calibrate them against similar measurements taken by other means (for example, Vilchur's bury-the-box setup) one method ought to be as good as another, yes? Subtracting 4dB from these measurements to convert to the Vilchur numbers seems a relatively small price to pay for avoiding the need to haul speakers and equipment out into the woods and dig holes, provided we know the conversion is valid.

[Zilch]

As long as the results are consistent and it's possible to calibrate them against similar measurements taken by other means (for example, Vilchur's bury-the-box setup) one method ought to be as good as another, yes? Subtracting 4dB from these measurements to convert to the Vilchur numbers seems a relatively small price to pay for avoiding the need to haul speakers and equipment out into the woods and dig holes, provided we know the conversion is valid.

Diggin' holes in the woods might be "suspect," and the spa is in the back yard here.

[it'd be a hazard for the lovely ladies pouring the wine.... ]

[kkantor]

Z-

1- I would strongly encourage you to measure these w/o the crossover in place. Although the argument that, "let's test it the way it is used", seems compelling, the problem is the curve shape obtained when the LP is operating, masks the true Fs, and makes the deep bass response very difficult to interpret. (That's why meaningful subwoofer measurements are so hard to make, even in the test environments.

2- Would you be willing to bring a couple of the units to Berkeley for testing in my lab? I can use a calibrated mic, AP, etc. to see if they agree with your data. Might be a valuable effort, beyond this particular investigation.

3- I still have access to the old "AR" 2pi anechoic chamber up in Benicia, along with original test baffles, so if you want to check the drivers under original conditions, it can be arranged.

-k

Hi Ken!

These are all done with the crossovers operating, the stock speakers measured with the grilles in place. Some of the designs have no lowpass filters. Those that required it have new surrounds.

Someone on another forum asked if the curves tell us how the speakers sound, and the answer is "No," as they don't describe how the bass response is blended with the rest of the particular systems.

I'm just starting on KLH-6, but the others are more comprehensively analyzed in individual threads over on AudioKarma. In some instances, I went on to "Zilchify" them, and the drivers themselves are measured separately. I do have intact samples of all of these, and additional spares, if you want to study any of them....

Edit: An AKer wanted to see how Karma Indignia compared so I added that, as well, with the port closed, black, and also bumped AR3a up 0.25 dB to separate it from Large Advent:

[Zilch]

Let me try with the lowpass bypassed, Ken; then we'll dig deeper into what's up with this. I'd say it warrants another visit, at minimum, to determine if I'm doing something patently stupid here....

[soundminded]

There is also a curve in Villchur's 1957 AES article for the AR Woofer, however

a damping factor of 1 is used which raises Qtc as compared to use with a modern

high damping factor amp. Remember a damping factor of 1 means that the

driving amp has an output impedance equal to the speaker load. The Qtc looks to

be about .9, and I believe that it is about .7 with low impedance drive. The curve

shows little if any peaking, perhaps .5 to 1dB at most even with a damping factor

of 1. There should be no peaking at all with a Qtc of .707 or less since by definition

.707 is a maximally flat response with a monotonic rolloff.

There seems to be some confusion between mechanical damping where the damping factor created by the aerodynamic drag of the stuffing will influence the overall Q of the system and the role the electrical LP filter plays. The crossover frequency of AR3 and AR3a are 3 1/2 octaves above the Fs of the driver in its enclosure, around 42 hz. Even for a first order filter, response is within one db of flat one octave below the corner frequncy which was about 525 or 575 hz. So by 250 hz, the deviation in FR created by the crossover should be negligable and by around 125 hz, it should for all practical intents and purposes be zero. If the LP filter has an effect on the system response at its mechanical resonance frequency, something is very wrong. Only AR9 (and possibly AR90) had a crossover network which affected FR near the in box resonant frequency of the system.

For speakers that are critically damped or overdamped, the electical damping factor of the driving amplifier will not have an appreciable effect on the FR of the system no matter how low that amplifier's damping factor is. That is because nearly all of the potential energy stored in the driver a its maximum excursion will be dissipated by the aerodynamic mechanical drag of the stuffing, not by the electrical shunt of the output stage as the speaker acts as a generator.

BTW, I've given considerable thought to Ken's model and I'm still convinced it is wrong. It is incomplete because the reverse EMF will be generated at frequencies depending on the electrical and mechanical resonance of the system, not by the driving frequency. Therefore an entirely passive model is incomplete. To be correct, the model must include a non linear element that represents the voltage source at those frequencies and the mechanical to electrical conversion efficiency of the driver. Since this is not related to the driving frequency, it will show up by default as intermodulation distortion, not harmonic distortion if it is not damped.

[Carlspeak]

Z-

1- I would strongly encourage you to measure these w/o the crossover in place. Although the argument that, "let's test it the way it is used", seems compelling, the problem is the curve shape obtained when the LP is operating, masks the true Fs, and makes the deep bass response very difficult to interpret. (That's why meaningful subwoofer measurements are so hard to make, even in the test environments.

-k

Does anybody know for sure whether or not Villchure had a LP hooked up to his 3a when he got the curve genek posted?

[genek]

Does anybody know for sure whether or not Villchure had a LP hooked up to his 3a when he got the curve genek posted?

Villchur's treatise on testing says nothing about crossovers being included or excluded, unfortunately, and since the article also does not state which AR model was used to measure the curves in its figures, I don't think we can draw any model-specific conclusions from anything said about them, either.

This is the full page the curve i posted earlier is from. The description refers to the drivers being tested in cabinet (woofer) and on test baffles (mid and tweeter), and again, crossovers are neither said to be included nor excluded.

The only thing I can think of is perhaps to compare the slopes of the rolloffs at each end of each driver's curves to what would be expected from the crossovers...?

[Steve F]

This is the full page the curve i posted earlier is from. The description refers to the drivers being tested in cabinet (woofer) and on test baffles (mid and tweeter), and again, crossovers are neither said to be included nor excluded.

The only thing I can think of is perhaps to compare the slopes of the rolloffs at each end of each driver's curves to what would be expected from the crossovers...?

This is the same Technical Info that I've had since 1972, and I always assumed that the x-overs were in place, since the rolloffs look too smooth and nicely-controlled for just the natural rolloff of the driver.

Also, I thought, why would AR take the pains to point out the x-over frequency if not to show the effect of the circuit on the drivers' response?

This is all just wild supposition on my part. I'd ask anyone out there in Forum land who has access to a raw AR 12" woofer (Ken, Zilch, Carl, etc.) to measure its FR, sans x-o, and see what's what. My guess is that it will "respond" well past the 575 Hz point, with a much more ragged character than what's shown on AR's graphs here.

Steve F.

[Zilch]

This is the same Technical Info that I've had since 1972, and I always assumed that the x-overs were in place, since the rolloffs look too smooth and nicely-controlled for just the natural rolloff of the driver.

I agree. They used the same woofer out to 1 kHz in AR3; that's gotta be the filtered response shown....

[genek]

I agree. They used the same woofer out to 1 kHz in AR3; that's gotta be the filtered response shown....

I don't know if this helps or just confuses things more. Reading through the testing article again, Villchur discusses a midrange driver and says, "the actual indicated power is considered as rolling off at about 7500 cycles. Hence this is the crossover frequency employed for a super-tweeter that is employed with the midrange unit." I think this tells us that the speaker being discussed is an AR-3.

The woofer curve I posted earlier is for the 3a, and it rolls off lower than the 1kHz point where the earlier one does. I'm thinking this tells us that the crossovers were in place?

[soundminded]

Z-

1- I would strongly encourage you to measure these w/o the crossover in place. Although the argument that, "let's test it the way it is used", seems compelling, the problem is the curve shape obtained when the LP is operating, masks the true Fs, and makes the deep bass response very difficult to interpret. (That's why meaningful subwoofer measurements are so hard to make, even in the test environments.

2- Would you be willing to bring a couple of the units to Berkeley for testing in my lab? I can use a calibrated mic, AP, etc. to see if they agree with your data. Might be a valuable effort, beyond this particular investigation.

3- I still have access to the old "AR" 2pi anechoic chamber up in Benicia, along with original test baffles, so if you want to check the drivers under original conditions, it can be arranged.

-k

"the problem is the curve shape obtained when the LP is operating, masks the true Fs, and makes the deep bass response very difficult to interpret. (That's why meaningful subwoofer measurements are so hard to make, even in the test environments."

Ken, I don't understand the theory behind that reasoning. Could you please explain how it masks the true Fs and why it would make it more difficult to interpret the results?

[speaker dave]

For speakers that are critically damped or overdamped, the electical damping factor of the driving amplifier will not have an appreciable effect on the FR of the system no matter how low that amplifier's damping factor is. That is because nearly all of the potential energy stored in the driver a its maximum excursion will be dissipated by the aerodynamic mechanical drag of the stuffing, not by the electrical shunt of the output stage as the speaker acts as a generator.

This isn't true. Generally the electrical damping dominates, which is to say the electrical Q is lower than the mechanical Q with most all commercial systems. Allthough critical damping (or any desired damping) can be achieved with either predominantly electrical or mechanical means, the advantage of achieving it electrically is that you maximise efficiency for a given curve shape. Low Q with high mechanical damping would equate to less than maximum sensitivity. One way to look at it is to start with an arbitrary system that is somewhat underdamped. To "impove" it one of two choices would be to increase mechanical damping with, say, a lossy blanket behind the woofer. A second choice would be to increase magnet strength: the midrange would go up and the bass at resonance would go down. Both choices can give the same final curve but the second approach raises sensitivity. Most systems have Qm in the 5 to 10 range. A typical system might have a Qm of 10 combined with a Qe of .76 to give a Q total of 0.7 (Reciprocal of the sum of the reciprocals).

By the way, a lot of the mechanical damping can also be built into the surround material. Some lossy rubbers really knock down Qm.

As to the highish apparent Q of Zilch's nearfield measurements, they do bump up a little more than I would have guessed, but not overly so. The Atkinson measurement is very similar, as was my AR2ax measurement (Zilch, did you really mean your comment of 10 dB bump in that measurement?)

As a matter of design, I think this typical bump comes from 2 reasons: First it is the easiest means of equalizing the free field response flat in the lowest octaves. As pointed out, truly flat response in 2 pi would tend to shelve down about 4 dB in 4 pi or anechoic conditions. Crossover EQ to flatten the response is possible but would require an electrical shelf at 200 Hz or so and that is going to mean big and costly components. You can argue that any room puts us near a boundary (at least at very low frequencies) and so flat 2 pi response is the better approach, but the market never punishes us for having too much bass. This leads to the second reason: boxes are never big enough for the chosen woofer. Box size costs money and alienates customers so most designs have woofers that would "rather be" in a little bigger cabinet. The woofers could be optimized for the actual alloted volume but that would require more motor strength and probably more cone mass, again increasing cost.

Vented systems tend to suffer from this, only more so. I remember Don Keele commenting on that at JBL. Especially with the L26, L36, L100 generation, the woofers didn't suit the cabinet sizes and wouldn't have suited them even if converted to acoustic suspension. Idealy a vented system should have about double the box volume of the same woofer in a sealed cabinet. commercially, they seldom get it.

Interesting stuff,

David

[Zilch]

Zilch, did you really mean your comment of 10 dB bump in that measurement?

It's tough to call where the nearfield bass measurement properly "stitches" to the farfield, as it is progressively less accurate at higher frequencies, and the farfield includes room modes unless it's done MLS, in which case the same applies at lower frequencies.

I see Carl's and my measurements as being effectively the same result; we choose to stitch at different levels, is all. You're more familiar with your AR2ax measurements; how much 2-Pi "boom" would you say they produce? Alas, I don't have any AR2 woofers for a direct comparison, but that could change at any moment. I'm measuring a bunch of AR3a woofers per Ken's recommendation right now, and will report the findings shortly....

[soundminded]

This isn't true. Generally the electrical damping dominates, which is to say the electrical Q is lower than the mechanical Q with most all commercial systems. Allthough critical damping (or any desired damping) can be achieved with either predominantly electrical or mechanical means, the advantage of achieving it electrically is that you maximise efficiency for a given curve shape. Low Q with high mechanical damping would equate to less than maximum sensitivity. One way to look at it is to start with an arbitrary system that is somewhat underdamped. To "impove" it one of two choices would be to increase mechanical damping with, say, a lossy blanket behind the woofer. A second choice would be to increase magnet strength: the midrange would go up and the bass at resonance would go down. Both choices can give the same final curve but the second approach raises sensitivity. Most systems have Qm in the 5 to 10 range. A typical system might have a Qm of 10 combined with a Qe of .76 to give a Q total of 0.7 (Reciprocal of the sum of the reciprocals).

By the way, a lot of the mechanical damping can also be built into the surround material. Some lossy rubbers really knock down Qm.

As to the highish apparent Q of Zilch's nearfield measurements, they do bump up a little more than I would have guessed, but not overly so. The Atkinson measurement is very similar, as was my AR2ax measurement (Zilch, did you really mean your comment of 10 dB bump in that measurement?)

As a matter of design, I think this typical bump comes from 2 reasons: First it is the easiest means of equalizing the free field response flat in the lowest octaves. As pointed out, truly flat response in 2 pi would tend to shelve down about 4 dB in 4 pi or anechoic conditions. Crossover EQ to flatten the response is possible but would require an electrical shelf at 200 Hz or so and that is going to mean big and costly components. You can argue that any room puts us near a boundary (at least at very low frequencies) and so flat 2 pi response is the better approach, but the market never punishes us for having too much bass. This leads to the second reason: boxes are never big enough for the chosen woofer. Box size costs money and alienates customers so most designs have woofers that would "rather be" in a little bigger cabinet. The woofers could be optimized for the actual alloted volume but that would require more motor strength and probably more cone mass, again increasing cost.

Vented systems tend to suffer from this, only more so. I remember Don Keele commenting on that at JBL. Especially with the L26, L36, L100 generation, the woofers didn't suit the cabinet sizes and wouldn't have suited them even if converted to acoustic suspension. Idealy a vented system should have about double the box volume of the same woofer in a sealed cabinet. commercially, they seldom get it.

Interesting stuff,

David

I think you misunderstood what I said. Consider a speaker system that has a system Q of say 0.2 or 0.3 due to being heavily mechanically damped being driven by say Tom's Crown Reference amplifier having a damping factor of 20,000 and a very short piece of heavy gage wire keeping DC resistance near zero. If I understand you correctly, you are saying that adding a series resistor will increase bass output by increasing the electrical Q of the circuit to compensate for a low mechanical Q? I'll have to think about that. BTW, I'm not talking about a compensating filter, just changing the electrical damping of the reverse EMF. It seems to me there wouldn't be much reverse EMF to damp out in that circumstance.

[speaker dave]

I think you misunderstood what I said. Consider a speaker system that has a system Q of say 0.2 or 0.3 due to being heavily mechanically damped being driven by say Tom's Crown Reference amplifier having a damping factor of 20,000 and a very short piece of heavy gage wire keeping DC resistance near zero. If I understand you correctly, you are saying that adding a series resistor will increase bass output by increasing the electrical Q of the circuit to compensate for a low mechanical Q? I'll have to think about that. BTW, I'm not talking about a compensating filter, just changing the electrical damping of the reverse EMF. It seems to me there wouldn't be much reverse EMF to damp out in that circumstance.

I thought we were talking typical speakers: KLH6, Large and small Advent, etc. For those types I maintain that electrical damping dominates mechanical damping and, furthermore, that this is a requirement for best efficiency.

You are right that your new scenario would show less variation with amplifier output impedance. I don't think it is very typical, though.

One comment on damping factor, reverse EMF, etc. I think it is always a little confusing to think in those terms. In the end it is just about interaction between the impedance curve of the speaker and the amplifier output resistance. Low Qm makes a speaker immune to amp impedance variation because it flattens out the woofer Z.

Regards,

David

[speaker dave]

It's tough to call where the nearfield bass measurement properly "stitches" to the farfield, as it is progressively less accurate at higher frequencies, and the farfield includes room modes unless it's done MLS, in which case the same applies at lower frequencies.

I see Carl's and my measurements as being effectively the same result; we choose to stitch at different levels, is all. You're more familiar with your AR2ax measurements; how much 2-Pi "boom" would you say they produce? Alas, I don't have any AR2 woofers for a direct comparison, but that could change at any moment. I'm measuring a bunch of AR3a woofers per Ken's recommendation right now, and will report the findings shortly....

Are you"stitching" here or just deciding where the midband level is? Usually stiching means merging a nearfield woofer curve with a farfield curve of the rest of the system, as Atkiinson did in your Small Advent case.

With a nearfield curve of a woofer you should be able to fit a 2nd order highpass curve to our measurment and then pull off the resonance and Q from that (you know, one of those curve families with Q of 2, 1.4, 1.0, 0.7, 0.5 etc). When you do that you will find that it generally only fits at the corner and a little above (and well below). As soon as the inductance rise of the woofer begins, the nearfield response has to deviate. Also, as soon as the crossover has any effect then the response will deviate. Remember that the farfield response may be flat but this is becasue woofer directivity is compensating for power falloff. A nearfield curve is more representative of a measured power response curve (until cone breakup begins, then I'm not sure what it is).

With that in mind I'd look at my AR2ax nearfield curve from 150-200Hz down only. I'd guess it is more a Q of approx. 1 or 1dB rise.

Looking forward to seeing your AR3 woofer curves.

Make sense?

David

[kkantor]

Does anybody know for sure whether or not Villchure had a LP hooked up to his 3a when he got the curve genek posted?

I'm about 95% sure that no crossovers were used for these measurements.

-k

[kkantor]

"the problem is the curve shape obtained when the LP is operating, masks the true Fs, and makes the deep bass response very difficult to interpret. (That's why meaningful subwoofer measurements are so hard to make, even in the test environments."

Ken, I don't understand the theory behind that reasoning. Could you please explain how it masks the true Fs and why it would make it more difficult to interpret the results?

I just find it personally difficult to visually compare the bass response curves of two different speakers without taking into account the crossover. One speaker may be using a low crossover point and running the woofer at a higher relative level, thus lowering the effective -3 dB point, re: the midband output.

There's also the effect of source impedance on the response curve due to voltage divider effects and, (slightly), electrical Q. But, I wasn't really going there with my comment.

-k

[genek]

I'm about 95% sure that no crossovers were used for these measurements.

Ken, the 3a woofer curve that I posted starts rolling off in the general range of 600Hz. Would this driver do that without a crossover in play?

[Zilch]

Are you"stitching" here or just deciding where the midband level is?

Yes.

Both Carl and I have overlaid the nearfield on the farfield. There's an assumption with respect to the relative levels inherent in doing that.

In my "Shootout" comparisons, you can see where I normalized them, within +/- 0.5 dB. As I mentioned, the validity of doing that is, well, "arguable."

With a nearfield curve of a woofer you should be able to fit a 2nd order highpass curve to our measurment and then pull off the resonance and Q from that (you know, one of those curve families with Q of 2, 1.4, 1.0, 0.7, 0.5 etc).

I'm not getting that. You're converting the 2-Pi nearfield to 4-Pi anechoic first, then?

[Pete B]

Yes.

Both Carl and I have overlaid the nearfield on the farfield. There's an assumption with respect to the relative levels inherent in doing that.

In my "Shootout" comparisons, you can see where I normalized them, within +/- 0.5 dB. As I mentioned, the validity of doing that is, well, "arguable."

I'm not getting that. You're converting the 2-Pi nearfield to 4-Pi anechoic first, then?

Properly functioning sealed box systems are essentially a second order high pass filter

in the piston range and ignoring HF effects due to VC or crossover inductance. There

are a few well known properties of such systems. It is best to disconnect the crossover

since it makes any measurement more innacurate.

First, the fundamental characteristics of Fc and Qtc can be measured by the electrical

input impedance. The voice coil inductance introduces an error term but it is usually not

too significant around Fc, the crossover would make this worse as Ken also pointed out.

If you use a woofer tester with the driver in the box you will measure Fc, and Qtc rather

than Fs and Qts, and you can determine the shape of the low frequency rolloff from these

parameters. There is no doubt about this, it is essentially the breakthrough

made by Thiele of T&S theory.

Measuring the amplitude response near field and it should also match the expected 2nd

order high pass response.

Measuring the amplitude response 2pi anechoic should also provide an excellent match

to the 2nd order HP funtion.

These characteristics have been proven by the pioneers in speaker design, there is no

doubt about these facts.

If you do not get agreement below about 200 Hz then either your test speaker is broken,

or there is something wrong with your measurements.

[Zilch]

Ken, the 3a woofer curve that I posted starts rolling off in the general range of 600Hz. Would this driver do that without a crossover in play?

Ken knows a secret.

It is best to disconnect the crossover since it makes any measurement more innacurate.

Thanks, Pete. I'm working through this here....

[speaker dave]

Yes.

Both Carl and I have overlaid the nearfield on the farfield. There's an assumption with respect to the relative levels inherent in doing that.

In my "Shootout" comparisons, you can see where I normalized them, within +/- 0.5 dB. As I mentioned, the validity of doing that is, well, "arguable."

I'm not getting that. You're converting the 2-Pi nearfield to 4-Pi anechoic first, then?

Yes, you've overlaid without stitching (splicing). Those that stitch curves together have to guess where the nearfield curves and the farfield curves are both roughly accurate (their regions of accuracy may not overlap!) and then shift level so that the curves can line up. Its not a totally satisfactory approach but in the absence of a good anechoic chamber it is better than nothing.

I'm not converting from 2pi to 4pi (not sure I understand your comment) but here is some more on the actual difference. Apologies to those who already know this stuff.

I've scrounged some images from the web of the original Olson measurements where he measured the actual effects of a variety of cabinet shapes. He actually used a small microphone and measured it unbaffled then placed it on various cabinets under test, so the curves show the gain from baffling and the wiggles inherent in the number and location of the surrounding edges. An arbitrary test speaker would be meaured by the microphone, both with and without the baffling. The curves would be subtracted for their difference, so the response of the loudspeaker would be irrelevant. The end result, although measured by adding baffling to a microphone, would be the same if applied to a speaker (reciprocity).

This isn't exactly the 2pi to 4pi conversion as 2pi (infinite baffle) curve would be a straight line at the +6dB level rather than the starting basis of a straight line at 0db, but the shapes of the curve differences are the same. (Sorry if I'm confusing anyone.)

Note a couple of things: smooth shapes are better, the sphere gives the smoothest transition. Anything with rounded edges or beveled edges is better than sharp edges. Symmetry on the mounting face is bad, so mounting on center of the end of a cylinder or the center of a square face is very bad. These curves have to be scaled for the size of the cabinet. Twice as big would move the wiggles down to half the frequency.

Important! All of the curves have an up-slope in the 100-200Hz region (I think these cabinets are a little smaller than a typical bookshelf speaker so think: 50-100Hz region). This would inherently correct the downslope of most of the woofer curves that you have measured.

From my experience cabinet curve K is the most typical curve, with 4-5dB of shelving and the broad bump in the lower midrange. You'll see this shape in a lot of bookshelf woofers.

Pete B is correct that theory says that the woofer of an acoustic suspension system represents a 2nd order high-pass. Measurements of the impedance curve will give Fc and Qtc, which should also agree with a curve fit to a second order curve of the right f and Q. The theory only pertains to the 2 pi case or even power response in 2pi. Crossover rolloffs, woofer inductance rolloffs, driver directional effects, and cabinet diffraction effects aren't covered by T/S theory and must be added on top of the basic second order curve if you want a more complete model. This is why I think your curves are best considered only below 150-200 Hz (where the difference between 2pi and 4pi is just a couple of dB of upslope).

Regards,

David

[soundminded]

I thought we were talking typical speakers: KLH6, Large and small Advent, etc. For those types I maintain that electrical damping dominates mechanical damping and, furthermore, that this is a requirement for best efficiency.

You are right that your new scenario would show less variation with amplifier output impedance. I don't think it is very typical, though.

One comment on damping factor, reverse EMF, etc. I think it is always a little confusing to think in those terms. In the end it is just about interaction between the impedance curve of the speaker and the amplifier output resistance. Low Qm makes a speaker immune to amp impedance variation because it flattens out the woofer Z.

Regards,

David

"One comment on damping factor, reverse EMF, etc. I think it is always a little confusing to think in those terms..."

That depends on how you look at it. If you think strictly in terms of Qe, Qm, Qt, Vas, you're probably right. If you think in terms of Newton's second law of motion which the T-S parameters are based on and the second law of thermodynamics, you realize that all of the energy pumped into a speaker will ultimately be turned into heat. How that happens depends on several factors. A small percentage will be first turned into sound, the useful work output that will eventually dissipate as heat in the surfaces the sound waves encounter. The rest will either be dissipated directly through frictional mechanical losses in the driver itself and in the enclosure, mostly through aerodynamic drag in the case of an AS speaker system or through electrical resistance heating. The kinetic energy is greatest when the cone is passing throught its zero crossing point and the moving mass has its highest velocity. At that point potential energy is zero. At its extreme excursion on each cycle, it's potential energy is greatest because the restoring force is at its maximum and its velocity and therefore its kinetic energy is zero because it is stopped to reverse direction. If the system Q is high as in the case of a ported speaker which effectively has a resonant air column, a frequency at which the resistance to air flow is very low, the mass of the cone is high, and the frictional losses in the speaker suspension itself is low, electrical damping will be the overriding factor. The driver wants to continue vibrating at the resonant frequency no matter what the driving frequency. In this case, small changes to the series (DC) resistance of the electrical circuit whether it's due to the internal amplifier output impedence or the DC resistance of the speaker wires can have a substantial effect at the rate of dissipation. In the case of a highly mechanically damped speaker, it is the frictional losses that will be most responsible for energy dissipation.

The principle is directly analagous to dynamic electrical braking of rotary motors for say cranes. When the motor is stopped, the voltage source is removed and the armature windings are connected to a shunt, a low resistance bar of copper that quickly converts the rotary momentum into heat from the reverse emf. This saves the life of any mechanical brakes that may also be used to slow the motor. Reverse EMF is a critical factor in motors including linear motors because it limits the current that flows through them. Without reverse EMF, the motor current is only limited by the DC resistance and for an AC motor the reactive inductance of the windings. This is the locked rotor current and would be analogous to the current draw in a speaker if you physically restrained the voice coil from moving. It's often about ten times the full speed running amperage. The critical role the stuffing plays in an AS speaker cannot be overemphasized. The size, shape, density, and amount of fibers is critical. The frictional loss is velocity related, exactly what you want. The finer and more fibers you have, the greater the surface area and the more effective the loss. The tradeoff is that as the volume increases, the amount of air you displace for a given surface area increases too. This increases the K in the equation which is the displacement related force or springiness of the air trapped inside. You can see one major advantage of the AS design over the ported design by realizing that for an AS design, K is independent of frequency because it depends only on the gas laws, P1*V1=P2*V2. In a ported design K is highly dependent on frequency, being very low at the resonant frequency and its multiples and very high at the midpoints between them. This is why it is very much harder to design a ported speaker with a flat bass output that does not have a high Q. About the best you can do is try to match the Q of the air column with the resonance frequency and Q of the driver so that they compliment or compensate for each other.