Jan, I may be confused, but the dualism breaks when you contrast inductors vs. capacitors - electrostatic speakers and electromagnetic ones. If we note that current drive would be inappropriate for electrostatics, it seems apparent that voltage drive is inappropriate for electromagnetics.
However, this only holds true if coil force is directly proportional to coil current, and it was pointed out to me that this is not so.
- keantoken
Yeah, you could be right, as I said I'm not sure. I'll wait for the book.
OTOH suppose this is indeed a better solution, it begs the question why all those 1000's of engineers never got it.
But it is possible; we have a similar situation with opamps - they are all voltage amplifiers (even the CFB ones are used that way) while many people hold that a true current amplifier would have given us much better opamps.
We'll see.
jd
I guess speakers could be modelled with a nonlinear impedance, hence the said better harmonic distortion performance with current drive.
Unfortunatly Esa didn't publish distortion measurements himself.
regards
Unfortunatly Esa didn't publish distortion measurements himself.
regards
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Hi,
Hear, hear.
Absolutely right.
Well, there are several secondary terms in the equations, however I'd say that in the frequency range where the diaphragm movement of the driver is small it holds well enough for government work and beyond.
Ciao T
PS, lets not forget that Sound on Sound measured one specific HiFi Speaker as having 5dB power compression at rated power - with current drive the compression would be 0dB!
Jan, I may be confused, but the dualism breaks when you contrast inductors vs. capacitors - electrostatic speakers and electromagnetic ones. If we note that current drive would be inappropriate for electrostatics, it seems apparent that voltage drive is inappropriate for electromagnetics.
Hear, hear.
Absolutely right.
However, this only holds true if coil force is directly proportional to coil current, and it was pointed out to me that this is not so.
Well, there are several secondary terms in the equations, however I'd say that in the frequency range where the diaphragm movement of the driver is small it holds well enough for government work and beyond.
Ciao T
PS, lets not forget that Sound on Sound measured one specific HiFi Speaker as having 5dB power compression at rated power - with current drive the compression would be 0dB!
Hi,
[snip]PS, lets not forget that Sound on Sound measured one specific HiFi Speaker as having 5dB power compression at rated power - with current drive the compression would be 0dB!
Thorsten, would the compression not result, possible partly, from non-linearity of the magnetic field, i.e. if the voice coil goes to the fringes of the field, the motor efficiency (possibly bad term) becomes less and even with perfect current drive you would get compression, no?
jd
I'm certainly glad to see that some are seeing that the Dualistic view of loudspeaker drive can be very enlightening. It is as much a paradigm changer, as anything else.
Hi,
In the case of the sound on sound test it was only the DCR change with voice coil heating that was taken into account. It was part of an early 2K series comparing "studio monitors" (KRK, Dynaudio) with "HiFi" Speakers (B&W, Warfedale).
As remarked above, in the range where diaphragm deflection is small for any funloving SPL (say above 250Hz) magnet field nonlinearity is minimised.
Here is one reason for fieldcoil speakers - fieldcoils can produce magnetic fields that fully saturate the magent system and extend the linear magnetic field range over permanent magents. Now combine that with current drive and handling mechanical problems (resonances) in a mechanical way.
We may actually be getting somewhere!
Actually, we may end up with the late 1930's "System Eckmiller" German WWII Era monitoring system (used among other applications for the first ever stereophonic recordings of music in 1943 together with AEG Tape machines, TAB Amplifiers and Neumann Condensor Mikes).
I guess time is circular after all and we are caught in a time loop, still trying to solve problems already solved before WWII shifted research to more martial ways.
😀
Nothing new under the sun.
The Eckmiller was driven by Directly Heated Penthodes without feedback and used a series crossover (no EQ) combined with a concentric acoustic system that made the points of incidence of the sound coincident too (unlike Tannoy and Altec) and had a +/-15% impedance from resonance to 16KHz (considered then a sensible upper limit of reproduction).
Talk about prior art. There is enough in this system to dismiss most patents on acoustic systems ever since...
I guess better not loose a major war again! I'm now often traveling on high speed trains running at 160Kmh as well. Without WWII and that revolting austrian Germany would have deployed trains capable of this performance in the early 40's!, not the late 70's (TEE).
Ciao T
Thorsten, would the compression not result, possible partly, from non-linearity of the magnetic field, i.e. if the voice coil goes to the fringes of the field, the motor efficiency (possibly bad term) becomes less and even with perfect current drive you would get compression, no?
In the case of the sound on sound test it was only the DCR change with voice coil heating that was taken into account. It was part of an early 2K series comparing "studio monitors" (KRK, Dynaudio) with "HiFi" Speakers (B&W, Warfedale).
As remarked above, in the range where diaphragm deflection is small for any funloving SPL (say above 250Hz) magnet field nonlinearity is minimised.
Here is one reason for fieldcoil speakers - fieldcoils can produce magnetic fields that fully saturate the magent system and extend the linear magnetic field range over permanent magents. Now combine that with current drive and handling mechanical problems (resonances) in a mechanical way.
We may actually be getting somewhere!
Actually, we may end up with the late 1930's "System Eckmiller" German WWII Era monitoring system (used among other applications for the first ever stereophonic recordings of music in 1943 together with AEG Tape machines, TAB Amplifiers and Neumann Condensor Mikes).
I guess time is circular after all and we are caught in a time loop, still trying to solve problems already solved before WWII shifted research to more martial ways.
😀
Nothing new under the sun.
The Eckmiller was driven by Directly Heated Penthodes without feedback and used a series crossover (no EQ) combined with a concentric acoustic system that made the points of incidence of the sound coincident too (unlike Tannoy and Altec) and had a +/-15% impedance from resonance to 16KHz (considered then a sensible upper limit of reproduction).
Talk about prior art. There is enough in this system to dismiss most patents on acoustic systems ever since...
I guess better not loose a major war again! I'm now often traveling on high speed trains running at 160Kmh as well. Without WWII and that revolting austrian Germany would have deployed trains capable of this performance in the early 40's!, not the late 70's (TEE).
Ciao T
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Hi Janneman,
Only because most people cannot read and those who can refuse to... 🙂
Those who do not know thei history are bound to repeat it...
Attached a single old sheet about the eckmiller driver in german.
Ciao T
Fascinating! But I agree, history repeats itself inexoribly (sp?).
Only because most people cannot read and those who can refuse to... 🙂
Those who do not know thei history are bound to repeat it...
Attached a single old sheet about the eckmiller driver in german.
Ciao T
Attachments
Actually, we may end up with the late 1930's "System Eckmiller" German WWII Era monitoring system (used among other applications for the first ever stereophonic recordings of music in 1943 ...
And Alan Blumlein's stereo 1934 recording of the London Philharmonic Orchestra, among others he made during that era don't count....why?😉
Hi,
I guess because EMI shut down Alan Dower Blumlein in '34 and I never really heard of his (luckily surviving) recordings (which is a shame - he deserves the credit)
So I shall settle merely for the first high fidelity stereo recordings and the first stereophonic tape recordings for Germany, let the British claim stereo even though through an engineer of germanic extraction. 🙂
Shame he died so early.
Ciao T
And Alan Blumlein's stereo 1934 recording of the London Philharmonic Orchestra, among others he made during that era don't count....why?😉
I guess because EMI shut down Alan Dower Blumlein in '34 and I never really heard of his (luckily surviving) recordings (which is a shame - he deserves the credit)
So I shall settle merely for the first high fidelity stereo recordings and the first stereophonic tape recordings for Germany, let the British claim stereo even though through an engineer of germanic extraction. 🙂
Shame he died so early.
Ciao T
Yes, I did.SY said:Did you ask?They (at AES) didn't imply that by some different wording the ad would qualify.
There's only the problem that the systems described at his website don't quite represent current drive, as I have remarked in post #10.Nelson Pass has written extensively about systems optimized for current drive, including much speaker and driver data. These can be found at his website.
??? It is astonishing how some are prone to take personally remarks that are totally impersonal. I cannot undrestand your reaction at all.anatech said:Well, now isn't that insulting? Really, the way you just made that statement is about as close to a public put down as possible without coming right out and making a clear statement. Good lord man, have some respect for some of those around you please!
Your tactics and motives for being here are becoming increasingly clear. This is the Vendor's Bazaar. If you dislike the product offered and dislike the style or anything I say, and you already 'know' so many things and learn nothing new, then you only need to stay away. I'm not in need of your endless counseling and condemnation.anatech said:Your thread attracted my attention, but I was worried that it was merely an ad for your book. In fact, it is beginning to look like it. To be honest with you, using a standard voltage source model amplifier also worked well. Your viewpoint on how we should be driving dynamic loudspeakers is exaggerated from what I have seen so far. The thing is, I'm willing to be open to other ideas on how maybe to improve the performance of a current drive amplifier. It is a fact that you have avoided any clear technical discussions so far, and that makes me wonder if you have really developed this concept much further than I have. Maybe on paper, but I wonder about a working system.
Understand this. If your ideas had any commercial promise what-so-ever, there would be corporate interest in what you have to say. It would be spun as "the new, improved way to drive a loudspeaker", championed by the likes of B&O or other companies that could take a different idea and run with it. Lifestyle products would be the early adopters. Think of a Bose system using current drive. They are the hotbed of single driver, extended range products. I'm guessing you haven't been approached by anyone so far.
The one thing I don't believe belongs here, which both ETM and JC are guilty of, is the intellectual snobbery that seems to come easily to them. The air of superiority that these two like to put on is distasteful, as well as unpalatable. Something that certainly does not help the cause in any way.
A falsehood. I have written 19 posts here, most of which contain clear technical discussion about the relevant issues. I am still willing to answer any clearly defined and relevant technical questions as far as I have time; despite that this is not a correct place to go in details. I even attached the plot in post #66 to enhance discussion, but it didn't interest you very much. It's still there. Go on and discuss it!It is a fact that you have avoided any clear technical discussions so far
Actually, this is not true when you consider real world systems. Remember, your amplifier has a finite voltage compliance. It could cause the current amp equivalent to clipping with a voltage amplifier.No, the nonlinearity of inductance distorts the current and hence the sound only on voltage drive.
You are oversimplifying the situation for the purpose of being able to argue your point.
When your claims are proved wrong, you resort to totally absurd comments that don't have any connection to the subject at hand.
You implied that I would have recommended some material that you then found void of real worth. This was a misrepresentation and had to be corrected. Also, any work must be subject to due criticism. There must not be taboos at least in technology.I addressed both yourself and Dave. Also, you had referred to this earlier work - as well as diminished it's completeness. You shouldn't trash other peoples works really. Especially on the same subject as your stuff.
The instantaneous sound pressure radiated by the diaphragm is proportional to the instantaneous acceleration of the same, not to the instantaneous displacement, as I already stated in post #49. This is a quite easily provable and measurable hard fact. Yet the whole loudspeaker industry is stuck in the conception that pressure follows displacement and that this displacement then could be magically controlled by minimizing the output impedance and moving mass.Ahhh, no. Acceleration is one part of the equation while displacement is the other. Displacement allows one to figure out the volume of air displaced, along with the piston area. Acceleration determines how quickly this occurs and may relate to frequency. That's how I would think of the process anyway. You can not eliminate the displacement term, that's the distance that the air mass is accelerated over.
Striving to control the displacement is striving to control the second integral of the signal instead of the signal itself.
The book is not so math-oriented as the preview pages easily lead to understand. The ideas should be understandable at many levels, even without much equations.john curl said:ETM wrote a book that is mostly math, and many of us can sort of follow it. However, if it was presented a little differently, it might be even more understandable, and therefore more defensible.
Actually, one cannot do this way in either mode if the pure driving mode is to be preserved, but the dualism also holds in this.janneman said:You have stated that voltage drive and current drive are complementary views; for example, in current drive you can compensate for resonance peaks by parallel shunting away drive current, while in voltage drive you can do so by series attenuating the drive voltage. There are more examples of this dualism.
If this dualism is the case, one would expect that either method would lead to a similar level of performance, and not that one would be sort of ideal and the other sort of fundamentally flawed. This is not a disagreement with you at this point, as I said, I need to read the book first, but it nags me.
There is dualism with regard to frequency response and impedance issues; but concerning distortion and interference effects, one way is more ideal than the other.
In fact, there is also a THD measurement of the voltage/current conversion, but harmonic distortion in general is not the most important factor, and the various effects can be demonstrated otherwise.Juergen Knoop said:Unfortunatly Esa didn't publish distortion measurements himself.
thanks, must have overlooked that chart. But I don't follow your above reasoning. Whatever harmonic distortion it is an important factor in sound quality or not, measuring acoustical distortion is the best way to show improved linearity with current drive.In fact, there is also a THD measurement of the voltage/current conversion, but harmonic distortion in general is not the most important factor, and the various effects can be demonstrated otherwise.
regards
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Hi ETM,
I also wanted to see if your viewpoint was as extreme as the books title would suggest.
Instantaneous acceleration must track the input signal by a constant. If not, the driver introduces an aberration (distortion) in the force or acceleration it applies to the air (or water if you're designing a hydrophone). The acceleration creates a displacement, which is another way of saying that the speaker cone travels over some distance. If your integral is such a small value that the distance tends to zero, you have proved that distance and displacement are irrelevant. But, at the same time so is your point. The force (acceleration) that doesn't travel any distance is of no use other than a mental construct. Remember that force x distance = work. No distance = no work. Cute concept, but not useful.
-Chris (I don't even know what you're arguing about now 🙂 )
Well, imagine if someone had answered you in that way. It wasn't pretty.It is astonishing how some are prone to take personally remarks that are totally impersonal. I cannot undrestand your reaction at all.
Just in case there are any misunderstandings then, I only wanted to talk with the author to see where your look at these things from. It helps to understand the viewpoint of a person who is trying to get their message out.Your tactics and motives for being here are becoming increasingly clear.
I also wanted to see if your viewpoint was as extreme as the books title would suggest.
It's in my nature to help, and to draw attention to areas that could use some polish. I'm not perfect, but I don't fail to see both sides of a situation. You complained that your book was not well received by the AES. I have no love for that organization either, but I didn't know how stuck in the sand you and the AES were. You are both pretty darn stuck if you ask me. Yeah, I know. You didn't ask.I'm not in need of your endless counseling and condemnation.
I said I was interested in the topic. I said I had some experience with the material. I'm not so arrogant as to think I know everything, so I ask when I'm not sure on something, or if some material contradicts what I've seen before. You would do at least the same.If you dislike the product offered and dislike the style or anything I say, and you already 'know' so many things and learn nothing new, then you only need to stay away.
Okay, I guess this is open to interpretation on at least two sides. I'm just going to see where you go in that case.I have written 19 posts here, most of which contain clear technical discussion about the relevant issues.
Okay, so I guess you are saying your amplifiers have no voltage limits then? Allow me to clarify what I was saying as it's clear only a simulator is unlimited. When we are detecting safe limits for a conventional power amplifier, we most often are worried about what electrical quantity? If you answered "current flow", you'd be correct. As we in agreement as far as a simple system is concerned? Fancy second breakdown curves are not considered to avoid a silly argument. Now, in a current amplifier, we aren't normally worried about running out of voltage as the amp would simply clip and place a limit on the available current flow. However, this would generate high distortion along with high levels of harmonics that might overpower a tweeter in a multi driver system on a single amp. So, you would wish to avoid this situation - yes? In other words, you have to deal with a voltage limit. Another aspect is the total power dissipated by the output devices. This is the same issue no matter if the amp is current or voltage drive. Current x voltage = heat, no matter what the device is doing. Therefore, for this aspect, a current drive amplifier is on the same level as a voltage drive amplifier. My comments were an attempt to show you that both amplifier types faced similar real world problems. That's in answer to your total dismissal of the current technology that is most often used to energize loudspeaker systems. If you were not so totally blind to anything that differs from what you see is an improved concept, you could then come across as a balanced and reasonable person. Again, just a reference to how inflexible you seem to be.When your claims are proved wrong, you resort to totally absurd comments that don't have any connection to the subject at hand.
No, that's not what I said at all. I said I read the material for one.You implied that I would have recommended some material that you then found void of real worth.
Well, that is true in near field for sure. This same concept has been used with those impossibly small sub woofer systems like the Sunfire sub. They decided to throw out Thiel and Small all together and treat the woofer surface as a movable surface. The idea being that with enough amplifier power, you could treat a speaker more like a piston. It works. One of the hallmarks of a driver suitable for this is that it is incredibly stiff. You can usually stand on a cone (before assembly in to a driver unit) without damaging it or modifying it's shape. I actually was standing on one, it may have been an Epos unit. I was also lucky enough to talk to the designer for some time on it. However, none of this has anything to do with the type of amplifier you drive the speaker with.The instantaneous sound pressure radiated by the diaphragm is proportional to the instantaneous acceleration of the same ...
Do you mean a plural of the word, Tabu? I would agree with you there. It took a couple readings to figure out what you were saying.There must not be tabus at least in technology.
If you intend to transfer energy into the air, you generally do this through displacement. You move a volume of air, there is no way around this. If you were to take a screen and accelerate it, there would be darned little acoustic energy created - right? You can accelerate air all you want, but to do this without any displacement wouldn't buy you anything - assuming it were possible to do this in the first place. The entire concept of displacement is part of acceleration, you can not separate the two. To accelerate anything implies movement. If that thing is physical, it will have dimensions, and therefore cover an area. If you move that area, or displace it, the moving area will cover a volume of whatever is surrounding it. Real world now. An isolated mathematical idea has no value unless you tie it into what actually occurs. There is a guy named Stanley Lipshitz who enjoys arguing in a very similar fashion to how you do. I figure the two of you would get along famously. BTW, he's well entrenched in the AES and various committees. I don't believe he would have been consulted on your book under consideration, so he may be a "friendly". You should really look the man up. He works out of the University of Waterloo here in Ontario, at least he did last time I looked.Yet the whole loudspeaker industry is stuck in the conception that pressure follows displacement
What you are actually talking about is the idea of matching the impedance of the "air exciter" (for lack of a better term) to the impedance of the medium you wish to excite. Horn type enclosures are an attempt to make an acoustic transformer to make the match closer to unity. It also transfers more energy to the air per unit energy in. In other words, the efficiency of the air - loudspeaker system goes up. Just like in electronic power transfer theory. This would also hold true for anything you attempt to do, a more efficient coupling between a loudspeaker and the air has exactly zero to do with how you go about energizing that speaker. I don't even know why you brought this up since it applies equally to each system.... this displacement then could be magically controlled by minimizing the output impedance and moving mass.
Now, as far as controlling the second integral, that is exactly what must happen to produce low distortion sound. After all, the heating of the voice coil reduces the displacement, and that is distortion (compression, or amplitude distortion). Another would be an uneven magnetic field that decreases the motor strength near each extreme of the displacement of the voice coil. Again, we have a reduced displacement as a result, which is again amplitude distortion.Striving to control the displacement is striving to control the second integral of the signal instead of the signal itself.
Instantaneous acceleration must track the input signal by a constant. If not, the driver introduces an aberration (distortion) in the force or acceleration it applies to the air (or water if you're designing a hydrophone). The acceleration creates a displacement, which is another way of saying that the speaker cone travels over some distance. If your integral is such a small value that the distance tends to zero, you have proved that distance and displacement are irrelevant. But, at the same time so is your point. The force (acceleration) that doesn't travel any distance is of no use other than a mental construct. Remember that force x distance = work. No distance = no work. Cute concept, but not useful.
-Chris (I don't even know what you're arguing about now 🙂 )
If you put a correctly designed copper ring or cap into the voicecoil gap it does not matter any more if the amp has current or voltage drive. The remaining issue is heating of the voicecoild but that can be solved with mechanical design too.
Distortion of the current that is send back to the amp due to mechanical unlinearity and design of the magnet system can be solved mechanical too. Turning the world up side down to cutrrent drive is impossible anyway because the market has already decided on voltage drive. So it is much more productive to find solutions that work with voltage drive.
Distortion of the current that is send back to the amp due to mechanical unlinearity and design of the magnet system can be solved mechanical too. Turning the world up side down to cutrrent drive is impossible anyway because the market has already decided on voltage drive. So it is much more productive to find solutions that work with voltage drive.
ETM, I have received your book as yet, but I hope to comment more when I get it. Keep up the good work.
I can well imagine, and it won't move me a jot if someone said his book has a certain target audience.anatech said:Well, imagine if someone had answered you in that way. It wasn't pretty.
This is personal assault and something one would not expect from a moderator. An apologize would be in order.anatech said:You are both pretty darn stuck
If you were not so totally blind to anything that differs from what you see is an improved concept, you could then come across as a balanced and reasonable person.
Again, a totally irrelevant comment that has nothing to do with the subject, that was the distortion caused by the nonlinearity of driver inductance.Okay, so I guess you are saying your amplifiers have no voltage limits then? Allow me to clarify what I was saying as it's clear only a simulator is unlimited. When we are detecting safe limits for a conventional power amplifier, we most often are worried about what electrical quantity? If you answered "current flow", you'd be correct. As we in agreement as far as a simple system is concerned? Fancy second breakdown curves are not considered to avoid a silly argument. Now, in a current amplifier, we aren't normally worried about running out of voltage as the amp would simply clip and place a limit on the available current flow. However, this would generate high distortion along with high levels of harmonics that might overpower a tweeter in a multi driver system on a single amp. So, you would wish to avoid this situation - yes? In other words, you have to deal with a voltage limit. Another aspect is the total power dissipated by the output devices. This is the same issue no matter if the amp is current or voltage drive. Current x voltage = heat, no matter what the device is doing. Therefore, for this aspect, a current drive amplifier is on the same level as a voltage drive amplifier. My comments were an attempt to show you that both amplifier types faced similar real world problems. That's in answer to your total dismissal of the current technology that is most often used to energize loudspeaker systems. If you were not so totally blind to anything that differs from what you see is an improved concept, you could then come across as a balanced and reasonable person. Again, just a reference to how inflexible you seem to be.
Again, absurd commentary that is not related to what I said.Well, that is true in near field for sure. This same concept has been used with those impossibly small sub woofer systems like the Sunfire sub. They decided to throw out Thiel and Small all together and treat the woofer surface as a movable surface. The idea being that with enough amplifier power, you could treat a speaker more like a piston. It works. One of the hallmarks of a driver suitable for this is that it is incredibly stiff. You can usually stand on a cone (before assembly in to a driver unit) without damaging it or modifying it's shape. I actually was standing on one, it may have been an Epos unit. I was also lucky enough to talk to the designer for some time on it. However, none of this has anything to do with the type of amplifier you drive the speaker with.
Again, totally irrelevant verbiage. I have never said that acceleration can occur without displacement.If you intend to transfer energy into the air, you generally do this through displacement. You move a volume of air, there is no way around this. If you were to take a screen and accelerate it, there would be darned little acoustic energy created - right? You can accelerate air all you want, but to do this without any displacement wouldn't buy you anything - assuming it were possible to do this in the first place. The entire concept of displacement is part of acceleration, you can not separate the two. To accelerate anything implies movement. If that thing is physical, it will have dimensions, and therefore cover an area. If you move that area, or displace it, the moving area will cover a volume of whatever is surrounding it. Real world now. An isolated mathematical idea has no value unless you tie it into what actually occurs. There is a guy named Stanley Lipshitz who enjoys arguing in a very similar fashion to how you do. I figure the two of you would get along famously. BTW, he's well entrenched in the AES and various committees. I don't believe he would have been consulted on your book under consideration, so he may be a "friendly". You should really look the man up. He works out of the University of Waterloo here in Ontario, at least he did last time I looked.
No, I'm not talking about such things. Output impedance is a property of amplifiers.What you are actually talking about is the idea of matching the impedance of the "air exciter" (for lack of a better term) to the impedance of the medium you wish to excite. Horn type enclosures are an attempt to make an acoustic transformer to make the match closer to unity. It also transfers more energy to the air per unit energy in. In other words, the efficiency of the air - loudspeaker system goes up. Just like in electronic power transfer theory. This would also hold true for anything you attempt to do, a more efficient coupling between a loudspeaker and the air has exactly zero to do with how you go about energizing that speaker. I don't even know why you brought this up since it applies equally to each system.
The nonidealities of the voice coil and magnetic system have nothing to do with the fundamental principle that I stated.Now, as far as controlling the second integral, that is exactly what must happen to produce low distortion sound. After all, the heating of the voice coil reduces the displacement, and that is distortion (compression, or amplitude distortion). Another would be an uneven magnetic field that decreases the motor strength near each extreme of the displacement of the voice coil. Again, we have a reduced displacement as a result, which is again amplitude distortion.
Rubbish again. I have never denied the existence of displacement.Instantaneous acceleration must track the input signal by a constant. If not, the driver introduces an aberration (distortion) in the force or acceleration it applies to the air (or water if you're designing a hydrophone). The acceleration creates a displacement, which is another way of saying that the speaker cone travels over some distance. If your integral is such a small value that the distance tends to zero, you have proved that distance and displacement are irrelevant. But, at the same time so is your point. The force (acceleration) that doesn't travel any distance is of no use other than a mental construct. Remember that force x distance = work. No distance = no work. Cute concept, but not useful.
It is for this reason that I think it would be easier to discuss this in differential equation form, (hopefully, DOT notation) where we can get a feeling as to the changes that occur, when we use either voltage or current drive. It would also be easier to then 'play' with the constants of compliance, damping and mass, respectively and get a solid feel as to what we can do to optimize each condition.
What's the hangup with dot notation? That's only time derivatives. A differential equation is a differential equation.
Dot notation is easier to write, and I find it easier to conceptualize the tradeoffs in speaker variables. This is most probably why Rice and Kellogg used it, and why J. Manger also used it. It is only a serious suggestion to the book's author, as his generalized equation on page 338 (I believe) is difficult to relate directly to the specific loudspeaker tradeoffs by those who are not comfortable with differential equations.
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