Let us assume we possess a linesource ESL. The surface is segmented horizontally and signal processing is applied thus that the radiating surface decreases with increasing frequency. As a result, a uniform cylindrical wavefront is produced at the surface over the full bandwidth of the transducer.
Traditional assumptions dictate that the baffle is rigid and any interaction between the positive and negative phase wavefronts will occur beyond the baffle edge. However, an ESL is a unique case. The surface can be considered virtually massless and thus might also be considered acoustically transparent.
Under such circumstances, will the positive and negative wavefronts interact through the acoustically transparent surface before they reach the edge of the total surface? Assuming they do, how would this affect the response?
Thanks,
Thadman
Traditional assumptions dictate that the baffle is rigid and any interaction between the positive and negative phase wavefronts will occur beyond the baffle edge. However, an ESL is a unique case. The surface can be considered virtually massless and thus might also be considered acoustically transparent.
Under such circumstances, will the positive and negative wavefronts interact through the acoustically transparent surface before they reach the edge of the total surface? Assuming they do, how would this affect the response?
Thanks,
Thadman
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Acoustic crosstalk between drivers happens any time there multiple drivers. ESLs and other open baffles have the advantage both wavefronts from one driver tend to traverse the other drivers at the same time. Since they're out of phase the loading tends to cancel and hence there's less induced movement of the "victim" driver than occurs in box speakers. Unlike dynamic drivers ESLs and magentostats usually have near identical front and rear structures and well aligned acoustic centers, so they're essentially a best case for such cancellation. As you point out the membrane's lighter than a cone but, generally speaking, the acting forces from nearby drivers are in the same order of magnitude as those intended to be applied to the victim driver. The power amp's therefore in a position to damp unwanted displacements from whatever net force remains, though how well it's able to depends on the impedance intervening between the voice coil or stators and the amp.
I've not seen any measurement data on undesired crosstalk between drivers and don't have any myself. But passive radiators are an example of a case where wavefront interaction is deliberately induced within the baffle. Ports and open end transmission lines can be treated as massless drivers in much the same way you propose for ESLs; the difference is the baffle's deliberately configured to induce phase delay and propagation attenuation between the wavefronts. So the virtual "victim" driver becomes an intentional radiator.
I've not seen any measurement data on undesired crosstalk between drivers and don't have any myself. But passive radiators are an example of a case where wavefront interaction is deliberately induced within the baffle. Ports and open end transmission lines can be treated as massless drivers in much the same way you propose for ESLs; the difference is the baffle's deliberately configured to induce phase delay and propagation attenuation between the wavefronts. So the virtual "victim" driver becomes an intentional radiator.
If the diaphragm is massless, could we assume it has a negligible influence on the interaction of the wavefronts? It simply represents a barrier between the wavefronts. If we could make such an assumption, could we ignore the diaphragm and solve for the free response?
Thadman,
a 'massless' foil is acoustically transparent only, if no inner force is acting on it. With the application of an electrical signal, the ESL becomes acoustically rigid. Otherwise it would not be able to transmit sound to the air. The driving force of every segment will be much higher than the 'crosstalk' from adjoining segments. Exception may be a nearby dynamic woofer which can act as a powerful point source on small areas of the ESL foil.
a 'massless' foil is acoustically transparent only, if no inner force is acting on it. With the application of an electrical signal, the ESL becomes acoustically rigid. Otherwise it would not be able to transmit sound to the air. The driving force of every segment will be much higher than the 'crosstalk' from adjoining segments. Exception may be a nearby dynamic woofer which can act as a powerful point source on small areas of the ESL foil.
Rudolf,
Can't FIR filters approach an infinite slope? Assuming we are using a low pass, I don't think it would be unreasonable to suggest that the power sent to that particular segment is negligible above the crossover frequency. We might then assume that only the segments operating below their particular low pass are *acoustically rigid* and the segments operating above their particular low pass are *acoustically transparent*. Under such circumstances, could we assume that the effective baffle is simply the width of the *acoustically rigid* radiating segment since the rest of the baffle is *acoustically transparent*?
If the width of the *acoustically rigid* section was decreased vs frequency, would it not be possible to approach a constant figure-eight response vs frequency for the total system?
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I think that I finally understand. And yes - the *acoustically transparent* part of the ESL should be more transparent than a rigid and massive baffle in the same place. But I am not sure how transparent *transparent* really is. There should still be an impedance mismatch between foil and air. Is that mismatch reversible? Is the power distribution from foil to air the same as from air to foil?
Assuming good enough *transparency* it should very well be possible.
If the area of each segment was restricted thus that the system approximated a point source at all frequencies, couldn't we approach the *optimum* loudspeaker?
The only issue would be maximizing output.
An ESL possesses negligible mass. As a result, impulse response would be fantastic and unparalleled. The film would simply represent a barrier to the air. I would expect its impulse response to be significantly better than any dynamic cone/dome transducer or waveguide.
Since the film is acoustically transparent, diffraction effects would be reduced to negligible levels.
Since the film is being operated above its fundamental resonance, the amplitude of the individual modes would reduce as frequency was increased (modes decrease at a rate defined by 1/J^2, where J=mode number). As a result, the response of the film would approach J=0.
The push-pull alignment inherent to ESLs would also tend to reduce any non-linear distortion to negligible levels.
If the radiating area was restricted thus that spherical wavefronts were produced at the front and rear of the surface, we could achieve constant directivity at all frequencies (LF-->MF-->HF).
Is there anything I'm missing here?
Basically you're reinventing Final Sound's ESLs. They went bust, what, a couple months ago? Final had a well thought out design but clearly it wasn't that extraordinary. Any ESL is going to be subject to the usual ESL limitations of limited excursion and capacitive loading. So you're looking at line sources with the usual source integration issues (limited vertical dispersion and crossing to dynamic subwoofers) that entails. Not point sources and spherical wavefronts.
With respect to crosstalk the idea of acoustically rigid and transparent as a function of crossover band only applies to passive crossovers. With an active crossover---as implied by the mention of FIR---the power amp has control over the full spectrum, at least to the extent it can sense and correct membrane displacements within its GBP. Also, there are plenty of membrane modes which will radiate sound in the near field but create no net current absorbable by the power amp. So in this sense transparency probably has more to do with how incident waves strike the victim membrane than the crossover. As I pointed out earlier, 'stats are something of a best case for this.
Diffraction occurs from all surfaces, so you'll need to take into account the stators as well as whatever boundary conditions apply at the edges of the membrane. Per unit area, electro and magnetostat films have about a tenth the mass of a soft dome tweeter. Is that neglible? I would bet not but you'd have to A/B against plasma drivers to find out. If you look at 'stat CSDs they're usually cleaner than dynamic drivers. But not perfect.
All drivers are subject to a phase modulation distortion floor. Good drivers approach that floor regardless of implementation (though it's less of an issue for AMTs) and so the best way to reduce distortion is to trade increased Sd for reduced excursion. I've not seen a rigorous comparison of electrostats against dynamic driver line arrays with similar Sd but the data I've come across suggests the two are comparable. So it's probably unlikely electrostats have any great advantage in this regard; if you think about it, magnetostats and dynamic drivers are usually push/pull as well.
Music's power spectral density generally decreases as 1/f, not 1/f^2, so a modal decay of J^2 probably isn't a useful model. There's significant variability from one musical passage to another---sometimes the PSD is just 1, for example---and modal analysis only gets you so far due to the loss of time information.
If you want a point source speaker I'd suggest magnetostats over electrostats. See Bohlender Grabaener's Neo drivers as a starting point (also the Radias if you're interested in line source alternatives to electrostats). If both horizontally and vertically limited directivity is acceptable another option would be a Quad type design.
Why couldn't you segment the film into circular segments? In this way, it would be possible to produce a spherical wavefront. The stator spacing could be allowed to vary for each segment, increasing sensitivity where significant displacement is not required.
As long as the ESL is able to operate down to the modal region I do not see integration as an issue. Are you aware of Dr. Geddes approach to the modal region? He uses multiple distributed subs. Proximity isn't as important since ray acoustics do not apply.
The mass of the film is small with respect to the mass of the air. As a result, the air will contribute significant damping to the individual modes. I do not believe such damping is significant for dynamic drivers due to their increased mass. It's not perfect, but it should offer a significantly improved response over dynamic drivers and waveguides.
I'm not sure how the spectral density is significant with regards to the modal response of the film. I think the optimum loudspeaker would assume a constant power vs frequency since the source material is ill defined. The equation specifies that the amplitude of the individual modes decreases by 1/J^2 with increasing frequency. It does not specify the decay. The decay should be highly dependent upon the mechanical impedance (film <--> air).
Instead of the diaphragm operating as the capacitor and anti-phase AC current applied to the stators, could we instead operate the stators as the capacitor and apply AC current to the diaphragm? Has this been done before?
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If the HF segment is considered rigid enough to move air, why wouldn't the other parts of the panel also be rigid?
The polarizing force should be uniform over the entire diaphragm. A different frequency would (most of the time) result in a different instantaneous combination of polarizing and modulating voltage, and therefore a different instantaneous offset from zero, but other segments should be just as "rigid" as the HF segment.
(For circular segmentation, see Quad.)
The polarizing force should be uniform over the entire diaphragm. A different frequency would (most of the time) result in a different instantaneous combination of polarizing and modulating voltage, and therefore a different instantaneous offset from zero, but other segments should be just as "rigid" as the HF segment.
(For circular segmentation, see Quad.)
As Paul mentioned, that's what Quad does. Hence my suggestion to look into their designs above. Ring radiators create toriodal wavefronts, not spherical ones. Provided the radiator's acoustically small spherical's a reasonable approximation in the far field. But for bass rings listening distances are not necessarily far field.
I'm aware of multiple subs (though they're not gedlee specific). My personal experience runs counter to the assertion ray acoustics are irrelevant in the modal region. But if multisubs works for you by all means go with it.
Because power amp drives the film according to the music. If you could go over your thinking around modes in more detail that would probably help resolve the disconnect in our thinking. In particular, can you link the approach and equations you're using? I'm not following the reasoning around mass matching and damping as the volume of air under consideration is unclear.
Power handling tends to follow size while bandwidth is inversely proportional to size. So a flat PSD causes an f^2 kind of problem; the tweeters blow well before the woofers take much load. How much this is an issue depends on SPL requirements, amplifier and crossover implementation, and tolerances for clipping distortion; there's no well defined optimum.
Yup.
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