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Old 30th March 2012, 12:18 AM   #1
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In this thread, I'm going to take a stab at describing how the Danley Paraline and the Sausalito Audio Works lens work.

I'm not 100% certain that I'm correct - but it should be fun to explore it.

First, some pics:

Click the image to open in full size.
VTC Paraline at the throat of a synergy horn (It's the long skinny lens in the center)

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Sausalito Audio Works lens in a Bang & Olufse Beolab 5

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SAW lens in an Audi A8

If anyone curious how these work, they basically take the wavefront off of the driver at the base, and then they reflect it 90 degrees.

IMHO, the primary advantage of the SAW lens and the Paraline is that it allows you to get very very very narrow directivity, without using a looooooooooong waveguide or horn.

For instance, according to the docs, one of the Paralines has the directivity of a horn that's over a meter deep - but the Paraline is about 1" deep!

Stay tuned to see how the magic happens...

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Old 30th March 2012, 12:29 AM   #2
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I'll use it as a cup holder in the Audi...
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Old 30th March 2012, 10:50 AM   #3
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The only basic premise you need to understand about the Paraline is if the dimensions of the acoustic pathway are kept to 1/2 a wavelength or less of the highest frequency of interest, then it will pass through the lens largely unaffected. As long as the wavelength of the highest frequency is significantly larger then its passage way, it will move through the lens like water through a pipe. Exactly like long and low frequency waves in folded bass horns can't acoustically "see" the flat corner bends. It’s simply just a matter of scaling the model to fit the frequency. Sound doesn’t care what frequency it is, it behaves the same way.
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Old 30th March 2012, 12:38 PM   #4
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Quote:
Originally Posted by JLH View Post
The only basic premise you need to understand about the Paraline is if the dimensions of the acoustic pathway are kept to 1/2 a wavelength or less of the highest frequency of interest, then it will pass through the lens largely unaffected. As long as the wavelength of the highest frequency is significantly larger then its passage way, it will move through the lens like water through a pipe. Exactly like long and low frequency waves in folded bass horns can't acoustically "see" the flat corner bends. It’s simply just a matter of scaling the model to fit the frequency. Sound doesn’t care what frequency it is, it behaves the same way.
True, but the information on making a proper reflector is interesting.
There have been a half dozen omnipolar projects on diyaudio which could have been improved with the information from this patent, so thought it would be worthwhile to walk through it.

(BTW, nearly everything you need to know to make one is in the patent, it's wonderfully detailed.)

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Old 30th March 2012, 01:20 PM   #5
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Click the image to open in full size.
As noted in the first post, the 'neat' thing about these inventions is that they give you directivity control that's similar to a long deep horn, but without the brutal space requirements. For instance, one of the Paraline devices has a depth of about an inch, and claims to have the directivity of a horn which is over a meter long. (According to the marketing literature.)

The way that this is achieved is by using a clever reflector. Basically the driver faces upward, and the sound is reflected ninety degrees. The pic above, from the paraline patent, illustrates how this works.

Click the image to open in full size.
If I'm not mistaken, the same math can be used to build your own S.A.W. lens.

Click the image to open in full size.

I took a stab at modeling one of these in Xara, using the dimensions from the patent.

If you'd like to make your own, here's how you could replicate this:
  • First, figure out what vertical coverage you want. The vertical coverage will determine if the driver has a strong forward lobe, or a pattern that's closer to a conventional driver. There are a couple of advantages to using a narrow pattern. First, it raises the on-axis SPL by focusing the energy into a narrower angle. Very much like a horn. Second, and more important, it improves the vertical directivity. (You can see this in the measurements of the B&O speakers.) The vertical directivity is improved because a speaker on a flat baffle will begin to 'beam' as frequency rises. The reflector in this lens assembly equalizes the pathlength, and that improves vertical directivity.

    In my pic above, I used the exact same vertical coverage as the patent - twenty degrees.
  • Second, figure out the angle of the triangle that passes through your driver. It's not clear to me what this signifies - perhaps something to do with the direcitivity of the driver at the apex? I simply used what's in the patent - forty degrees. If I had to hazard a guess, I would think that compression drivers would have a narrower angle than conventional radiators, and ribbons would have the widest angle of all. This is because a compression driver has very narrow directivity at the driver exit, conventional drivers are wider, and ribbons are widest of all.

    Again, just a guess. I used 40 degrees.
  • Third, you need to figure out where the two triangles intersect. From looking at the patent, there is a right triangle that's formed where the center of the driver's diaphragm reflects at 90 degrees off of the reflector.

    You can see it in my pic as a red square in the bottom right. The edges of that square are equal.

    In order for everything to work, the pathlengths have to be equalized quite accurately. If not, you'll get comb filtering and limited bandwidth.

    So if you're going to try and build one of these, I'd measure those two distances quite carefully. If there's a tweeter at the apex, I'll bet that an error on the order of a fraction of an inch would make a measurable difference in the response.
  • Fourth, you need to figure out the height of the triangle that determines the vertical coverage of the device.

    In the pic above, I used a height of 15cm. This height was dictated by the project that I am working on - I am going to build a synergy horn similar to the VTC paraline.

    For your project, the height of the device would largely depend on your crossover point.

    If there is a formula to determine the height of the triangle, I am not aware of what it is.

    Here are some guesses, which might be helpful for you:

    Click the image to open in full size.
    #1 - in the SAW waveguide, the height of the triangle seems to be dictated by the crossover point. For instance, in a horn, the directivity is constrained when the wavelength is equal to or smaller than the diameter of the horn or waveguide. IE, if a horn or waveguide has a mouth that's 8cm in diameter, it will constrain directivity down to 4,250 hz. Looking at the Beolab 5, we see something similar; the directivity is constrained by the aluminum discs above and below the driver.

    The dimensions of the paraline are simpler to calculate; it's plain ol' horn math and I'll get to that in a future post.


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Old 30th March 2012, 02:52 PM   #6
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Great job.
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Old 30th March 2012, 03:14 PM   #7
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Your drawings look a lot like the microwave horns that have been around for a while. Was this considered a new invention for Sausilito?

I also looks like there are two areas with very different path lengths. The back half of the tweeter dome sees the convex surface, as you have drawn in your cross section. The front half sees the upper concave reflector that appears to be a longer path length. As with all of these reflectors, there is also interference with the direct path from the tweeter. This path is shorter so there usually is significant vertical nulling from those 2 (or 3) paths.

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Old 30th March 2012, 04:44 PM   #8
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Originally Posted by Patrick Bateman View Post
It's not clear to me what this signifies - perhaps something to do with the direcitivity of the driver at the apex?

In the pic above, I used a height of 15cm. This height was dictated by the project that I am working on - I am going to build a synergy horn similar to the VTC paraline.

For your project, the height of the device would largely depend on your crossover point.

If there is a formula to determine the height of the triangle, I am not aware of what it is.

In the SAW waveguide, the height of the triangle seems to be dictated by the crossover point. For instance, in a horn, the directivity is constrained when the wavelength is equal to or smaller than the diameter of the horn or waveguide. IE, if a horn or waveguide has a mouth that's 8cm in diameter, it will constrain directivity down to 4,250 hz. Looking at the Beolab 5, we see something similar; the directivity is constrained by the aluminum discs above and below the driver.
The length of the initial horn throat prior to the Paraline curve portion of the horn is also crossover frequency dependent. Too short, and the initial horn portion will not have pattern control, which will result in diffraction in the Paraline transition, resulting in multiple reflections off the latter horn section sidewalls , resulting in severe frequency dependent comb filtering.

The diagram below shows the high frequency green lines as “good”, and the lower frequency orange and red lines as “bad”.

For the design to work properly, the initial horn exit diameter must be at least a wavelength of the low frequency crossover desired, about six inches or more for a 2000 Hz crossover.

The design is good, but as in all horn designs, size does matter, shrink this concept from a 45 inch wide horn exit (as in the DSL JH-90) down to a 22.5” horn exit and the crossover point must be raised an octave to keep pattern control and avoid peaks and dips.

Art
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Old 31st March 2012, 08:10 PM   #9
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Originally Posted by weltersys View Post
The length of the initial horn throat prior to the Paraline curve portion of the horn is also crossover frequency dependent. Too short, and the initial horn portion will not have pattern control, which will result in diffraction in the Paraline transition, resulting in multiple reflections off the latter horn section sidewalls , resulting in severe frequency dependent comb filtering.

The diagram below shows the high frequency green lines as “good”, and the lower frequency orange and red lines as “bad”.

<snip>

Art
Art,

Thanks for taking the time to type this up. I've studied this for a few hours and it's really helped me understand what's going on in the paraline.

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Old 31st March 2012, 08:27 PM   #10
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As noted above, I spent a few hours studying the paraline patent, and there are some interesting innovations in here which aren't obvious.

First, the paraline appears to be a way to reduce the depth of a narrow angle horn. For instance, if you make a horn with a coverage angle of 20 degrees, it is going to be VERY deep. This is basic geometry; with a narrow coverage angle it will have a small mouth but a very long depth. Similar to a length of pipe, but slowly expanding.

But there are a couple of things happening in the Paraline which aren't immediately obvious.

The first is that it's delaying part of the wavefront.

Click the image to open in full size.
Click the image to open in full size.
I think this is easiest to understand if you look at the wavefront of a horn with a wide coverage angle. Car audio horns are a good example of this. They have a wavefront that's about 45 degrees horizontally, but less than half that vertically. Due to the horizontal angle, the edges of the wavefront lag the apex of the wavefront.

That probably doesn't sound like a big deal; but it makes it very difficult to get the midrange in-phase with the tweeter at the crossover point in more than one location.

In the pic above, I've done my best to illustrate the problem. See how the wavefront at the edge of the horn is a few miiliseconds BEHIND the wave at the center if you're off axis? The green box, labeled 'maximum error', is there to show how much delay is acceptable before the phase gets screwed up. It signifies one quarter wavelength at a crossover frequency of 2000hz. (4.25cm)

In other words, you'll have excellent frequency response, phase response and imaging, but only if you're on axis.

As I see it, there are a three solutions to the problem. The first is to listen to both speakers on-axis. The second is to delay the part of the wavefront that's at the edge of the horn. Which is exactly what the Paraline does. The last is to use a very narrow coverage angle, so that the difference in delay between the edges of the horn and the center of the horn is minimized. Which might explain why the Synergy horns use a narrower angle than the Unity horns.

For instance, let's say you're using one of these devices, with a mouth that's 30cm across. And you're crossing over to a midrange with a diaphragm that's 20cm across. The directivity of the midrange and the horn are dramatically different at the crossover point. And this means that you can get the response in-phase at one angle, but not at *all* angles.

In other words, if you optimize the phase-response on-axis, it will suffer off-axis, because the wavefront of the horn is dramatically different than the wavefront of the midrange.

Click the image to open in full size.

The Paraline's most interesting feature, IMHO, is that it can 'bend' the wavefront. There's a time delay imposed by the path through the Paraline, but that time delay varies by a few centimeters. Basically the wave at the center of the horn is 'pulled back' by the Paraline.

This time delay creates some very interesting advantages, particularly when you're using lots of drivers.


Last edited by Patrick Bateman; 31st March 2012 at 08:37 PM.
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