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Old 9th October 2010, 09:47 AM   #1
markusA is offline markusA  Sweden
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Default No0b ESL size question

It would seem most people build line-sources i.e. fairly narrow but tall ESL's.
How would it impact the performance if one were to bild something like a 39"x27" panel?

I assume it would improve the low frequency abilites and as long as the area is constant it shouldn't affect the SPL in a negative way.
However, the room reflections would be very different.
I suppose vertical dispersion would become an issue and listening standing up would be "not great".

So, hypothetically speaking... how would the sonic signature change depending on the shape of the panel?
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Old 9th October 2010, 10:25 AM   #2
Calvin is offline Calvin  Germany
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Hi,

the dimensions affect basically two parameters.
1) the distribution character and
2) the acoustic impedance and phase cancellation
The first point is usually optimized for a broadend horizontal distribution and requires a small horizontal dimension
The second point is important for the onset frequency from which value phase cancellation occurs and how well or bad the diaphragm couples to the air. The larger the dimensions the better.
So You have to find a compromise.
Now it has been shown -either by Prof Hunt or Mr. Walker I donīt know at the moment- that a strip-like membrane shape with a height:width relationship of 8:1 works onto a real acoustic impedance not a complex any more over its full working frequency range. This is the ideal which for example the rather small danymic loudspeakers miss and why they need a box to beef up their response. A quadratically shaped membrane of same area would work onto a complex impedance hence the coupling to the air would be inferior and with lower efficiency.
So a strip shaped diaphragm with a ratio of 8.1 works to our favour in that it offers a rather small dimension horizontally and a good coupling to the air at the same. As a further postive sideffect the distribution character changes from a lobe to a cylinder with reduced early reflections from ceiling and ground and a more even SPL-distribution over distance.
And last not to forget...a thin tall strip looks much more sexy than a square shape

jauu
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Old 9th October 2010, 10:59 AM   #3
markusA is offline markusA  Sweden
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Very interesting, the 8:1 ratio concept is new to me.
A 8:1 ratio will make for some very narrow panels. (Or some very tall ones)
I started writing some intricate questions but changed my mind.
In the end I think I can sum it up like this.
Is it worth it, building a "strip" shaped panel? Is it that much better? The low frequencies are likely to suffer?
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Old 9th October 2010, 06:46 PM   #4
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Quote:
Originally Posted by Calvin View Post
Now it has been shown -either by Prof Hunt or Mr. Walker I donīt know at the moment- that a strip-like membrane shape with a height:width relationship of 8:1 works onto a real acoustic impedance not a complex any more over its full working frequency range. This is the ideal which for example the rather small danymic loudspeakers miss and why they need a box to beef up their response. A quadratically shaped membrane of same area would work onto a complex impedance hence the coupling to the air would be inferior and with lower efficiency.
So a strip shaped diaphragm with a ratio of 8.1 works to our favour in that it offers a rather small dimension horizontally and a good coupling to the air at the same. As a further postive sideffect the distribution character changes from a lobe to a cylinder with reduced early reflections from ceiling and ground and a more even SPL-distribution over distance.
And last not to forget...a thin tall strip looks much more sexy than a square shape
I agree that for the same radiating area tall and thin is always more pleasing to the eye than square.
Fortunately, it also tends to be more pleasing to the ear too with its better horizontal dispersion.

I would be very interested to know the source of the idea that an 8:1 ratio is the optimum.
The real part of the radiation impedance does change more gradually with frequency for line sources than square source. But, I would think the optimum would be an infinitely long line source, not 8:1. See the first attachment for comparison of radiation impedance for different ratios of rectangular sources taken from AES.,Vol.38,No.5, 1990May "On the Acoustic Impedance of Baffled Strip Radiators" Note that impedance comparisons are for sources with the same area. So, for the same area a square radiator will be more efficient at radiating low frequencies than a line source in free space. At very low frequencies the efficiency for square and line sources converge.


But, our listening rooms are not free space.
If you can extend your line source floor to ceiling you will get the benefit of mirroring of the line source from the floor and ceiling. In practice, a floor to ceiling line source will have 3db - 6dB more efficiency at low frequencies(below 100Hz) than a square source of equal area. This may not be important for hybrids, but is a substantial advantage for a FR ESL.

So, as Calvin mentioned, line sources provide better horizontal dispersion and generally as good if not better efficiency at low frequencies.


PS
Looking at comparing radiation impedance for square and line sources with equal width instead of equal area, and the line source gains substantially in efficiency over the square source at frequencies below where phase cancellation begins. In fact, gaining 3dB for every octave lower in frequency. Such a comparison was published in AES Vol. 43, No. 7/8, 1995 July/August, "On the Acoustic Impedance of Baffled Strip Radiators". See 2nd attachment for this comparison.
Attached Images
File Type: jpg A1_Rectangular_piston_radiation_impedance.jpg (61.6 KB, 199 views)
File Type: jpg A2_Strip_radiation_impedance.jpg (63.6 KB, 203 views)

Last edited by SY; 11th October 2010 at 02:34 PM. Reason: user request
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Old 9th October 2010, 11:09 PM   #5
markusA is offline markusA  Sweden
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Ok, line sources do seem to have some merits. Otoh Quad's are fairly square so you can probably get a good sounding speaker either way.

In my case, a floor to ceiling panel isn't an option so it'll be something like a 64" tall "strip" panel or a 28"x40" square panel.

Now, I'm perfectly happy with your explanations and the "strip" design is probably easier to build. The only reason I'm thinking about the square design as an option is because it would fit beautifully on top of dynamic bass. (Maybe a TH or a FLH?)
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Old 10th October 2010, 07:06 AM   #6
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Quote:Otoh Quad's are fairly square so you can probably get a good sounding speaker either way.

Quads are rectangular in overall shape but they are a three way design using a narrow treble line source tweeter flanked by two wider mid range sections and two bass panel sections. They would not sound any good if they were a single full range panel of the same size.
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Old 10th October 2010, 08:19 AM   #7
markusA is offline markusA  Sweden
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Ah, I missed that.
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Old 21st February 2011, 03:14 PM   #8
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Quote:
Originally Posted by Calvin View Post
Now it has been shown -either by Prof Hunt or Mr. Walker I donīt know at the moment- that a strip-like membrane shape with a height:width relationship of 8:1 works onto a real acoustic impedance not a complex any more over its full working frequency range.
Quote:
Originally Posted by bolserst View Post
I would be very interested to know the source of the idea that an 8:1 ratio is the optimum.
The real part of the radiation impedance does change more gradually with frequency for line sources than square source. But, I would think the optimum would be an infinitely long line source, not 8:1.
Calvin’s statement about a rectangular ESL with an 8:1 ratio having a real acoustic radiation impedance over its full working frequency range puzzled me greatly.
But, I think I stumbled on the source for Calvin’s statement. And, once the context of the statement is understood, it makes sense.

From "Telstar Shaped Electrostatic Speaker", by R. J. Matthys, Audio, vol. 48, May 1964:
“The diameter of a single electrostatic diaphragm (round or square) is about 1/24 of the wavelength of sound at the diaphragm’s resonant frequency. Since the air load on a diaphragm is reactive and not resistive when the diameter is less than one-third of the wavelength, a single electrostatic diaphragm will see a reactive air load in the frequency range between the fundamental diaphragm resonance and about eight times this resonant frequency.
Walker has shown that an electrostatic speaker reacts differently to a reactive load than does a moving coil loudspeaker…The best solution is to add speakers of the same size in parallel until the diameter of the speaker array is one-third the wavelength of sound at the fundamental resonant frequency of the diaphragm. This solution solves the reactive air load problem by making the air load resistive at all frequencies above the fundamental diaphragm resonance. Another way of accomplishing the same thing is to make the diaphragm rectangular, with the length of each diaphragm equal to eight times the width.

Attachment (1) shows that for ka>1 (ie diameter > 1/3 wavelength) radiation impedance is resistive and constant.
What Matthys said was that it would be possible to combine multiple smaller ESL panels into an array such that the resulting size would make the radiation impedance on each of the ESL panels resistive over their full working range even if this isn't the case when one panel is operated alone. If, as he states for his small ESL panels, the diameter is 1/24 wavelength at their fundamental resonance, an array of 64 panels arranged as in Attachment (2) would provide the desired resistive radiation over the full working range of the ESL panels.

Alternatively, Matthys states(highlighted in red above) that using rectangular shapes ESL strips with ratio of length to width of 8:1 could also be used to achieve the same result.
See Attachment (3).

Note that it is only the array of 8:1 ESL panels that achieves the resistive radiation over the full working range.
One 8:1 ESL panel operated by itself does not.
With just one 8:1 ESL panel, the radiation impedance turns reactive as soon as the wavelength gets longer than the width of the ESL panel, and you get a falling response with reducing frequency below this point. This is the dipole cancellation that we are all familiar with.
Attached Images
File Type: jpg A2_Strip_radiation_impedance.jpg (63.6 KB, 153 views)
File Type: jpg array_1.jpg (32.0 KB, 151 views)
File Type: jpg array_2.jpg (21.9 KB, 150 views)

Last edited by bolserst; 21st February 2011 at 03:19 PM.
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Old 21st February 2011, 05:17 PM   #9
markusA is offline markusA  Sweden
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Is there a practical way of calculating the diaphragm's resonant frequency?
If not it seems like a catch 22 situation to me?
You have to know the resonance frequeency to determine the width of the panels but you won't know the resonance frequency until you build a panel...
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Old 21st February 2011, 08:02 PM   #10
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Quote:
Originally Posted by markusA View Post
Is there a practical way of calculating the diaphragm's resonant frequency?
If not it seems like a catch 22 situation to me?
You have to know the resonance frequeency to determine the width of the panels but you won't know the resonance frequency until you build a panel...
It seems a simple matter, resonance being a function of just two terms: diaphragm stiffness and airload mass.
But, there are a lot of inter-related items that impact these two terms.

1) Diaphragm stiffness is determined by:
- film thickness and the tension you apply to the film. This might be derived from heat shrinking, or stretching with weights or an inner-tube stretching table.
- the diaphragm bias voltage induces a negative stiffness term that subtracts from the mechanical stiffness of the tensioned diaphragm. It is mainly a function of bias voltage gradient in the gap and diaphragm area, but is also a weak function of the D/S spacing. Increasing bias voltage reduces stiffness and lowers resonance

2) The effective moving mass at resonance is determined by:
- the shape and size of the diaphragm. For the same area, a square has a larger airload than a rectangle
- any baffle extension added to the sides of the diaphragm adds to the mass and lowers resonance
- placing multiple panels next to each other increases the mass load and lowers resonance

With all these variables in play it is difficult to calculate in advance what the resonant frequency will be of an ESL in a final configuration. You can either follow a well trodden path and build panels with dimensions and film thickness used by others, or build a few test panels of your own to gather enough data to get you where you want to go.
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