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Old 14th February 2010, 07:17 PM   #1
Rudolf is offline Rudolf  Germany
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Default On the directivity of dipole tweeters

There have been some attempts lately to make dipole tweeters work up to high frequencies with constant directivity. How high can we go, if the tweeter housing is already almost as small as its radiating area?

I would like to demonstrate the issues involved with an idealized 1 inch circular tweeter. I am using some Boxsim simulations to show things detached from specific driver peculiarities like FR and dome breakup modes.

Letís start with the mathematical dipole model Ė first for a dipole distance of 2,5 cm to keep things within 20 kHz:

Click the image to open in full size.

This is equivalent to this Linkwitz figure.

A 1íí tweeter would have a physical diameter of at least 2,5 cm. This would lead to a dipole distance of 1,25 cm. As a 2-point source this would sim like this:

Click the image to open in full size.

Of course a tweeter is no 2-point source. Letís first move to a dipole point source on a 25x25 mm square baffle (Boxsim canít do circular baffles).

Click the image to open in full size.

We can see that the dipole peaks are slightly lower in frequency because a 25x25 mm baffle is more like a 28 mm disc than 25 mm. More important by far is the change in directivity that is introduced by the baffle. The dipole 8 gets sort of slimmer.

Since a real tweeter is not a point source on a baffle, we make the cone/dome/foil as wide as the baffle. Note that our model is working as a dipole membrane in a housing with no depth now. Any real world tweeter would have to be larger:

Click the image to open in full size.

Note how the dipole 8 gets even slimmer than before and how the dipole peaks move to even lower frequencies. Strangely the 60 deg peak is at a lower frequency than the on-axis peak. Same for 30 deg. How come? The next diagram shows why by overlaying the last two diagrams:

Click the image to open in full size.

The wider source starts to beam Ė lower in frequency at wider angles. From a certain frequency up the directivity of the tweeter is no longer controlled by the dipole function but by the tweeter diameter. The next diagram shows this relationship at the first dipole peak:

Click the image to open in full size.

A monopole tweeter would have a main beam to the front of almost the same contour as the figure 8 of the dipole. This would be true for any driver whose radiating area is as large as its baffle Ė regardless of size. Any attempt to manipulate the radiation at the sides of the baffle is quite fruitless for frequencies above the first dipole peak Ė they donít show up any longer at the sides.

The only cure is to move the first dipole peak up by making the tweeter smaller. Above the first dipole peak all compact drivers will move from the (constant) directivity of the dipole 8 to the frequency dependent directivity of a beaming driver.

Thatís how I see it.
Attached Images
File Type: gif dipol 25_1.gif (7.8 KB, 2158 views)
File Type: gif dipol 25_2.gif (7.0 KB, 2157 views)
File Type: gif dipol 25_3.gif (7.1 KB, 2136 views)
File Type: gif dipol 25_4.gif (7.1 KB, 2138 views)
File Type: gif dipol 25_5.gif (8.7 KB, 2131 views)
File Type: gif dipol 25_7.gif (7.3 KB, 2132 views)
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Old 14th February 2010, 08:37 PM   #2
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Thanks, Rudolf.
If we plugged my Mundorf 2340 into that it would look worse...
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Old 14th February 2010, 10:37 PM   #3
keyser is offline keyser  Netherlands
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I've been doing similar simulations with Tolvan Edge. A point source on a 2 mm wide circular baffle looks nice. It would need a couple of centimeters excursion though. Perfect dipole treble seems impossible in the real world. Drivers such as the Mundorf and the Neo3W seem good practical dipole tweeters.
I think the only way to extend constant directivity without these issues would have to be waveguided tweeters.
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Old 15th February 2010, 08:39 AM   #4
Rudolf is offline Rudolf  Germany
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Quote:
Originally Posted by keyser View Post
Perfect dipole treble seems impossible in the real world.
That's exactly what I believe too.
Quote:
Drivers such as the Mundorf and the Neo3W seem good practical dipole tweeters.
Agreed again. And I don't see a practical way to 'tune' them to even better performance with diy means.
Quote:
I think the only way to extend constant directivity without these issues would have to be waveguided tweeters.
But there are two caveats:
1. Different manners to produce directivity lead to different expansions of the directivity function WRT angle. Would dipole directivity merge seamlessly with WG directivity?
2. If you want a WG to stretch 3 octaves, it needs to be rather deep. Put two of them back to back to get some sort of figure 8 pattern - and they will get de-correlated quite easily.
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Old 15th February 2010, 09:13 AM   #5
keyser is offline keyser  Netherlands
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Quote:
Originally Posted by Rudolf View Post
That's exactly what I believe too.

Agreed again. And I don't see a practical way to 'tune' them to even better performance with diy means.

But there are two caveats:
1. Different manners to produce directivity lead to different expansions of the directivity function WRT angle. Would dipole directivity merge seamlessly with WG directivity?
2. If you want a WG to stretch 3 octaves, it needs to be rather deep. Put two of them back to back to get some sort of figure 8 pattern - and they will get de-correlated quite easily.
I've only been contemplating the idea of using WG's to extend controlled directivity to higher frequencies only recently. There are indeed practical problems, of which I am not sure they can be overcome. I've never worked with waveguides, but I think there are possibilities. I might try it for a next project. However, the Neo3W in an unbaffled configuration doesn't leave me wanting. I've rarely heard the highs this detailed - yet clean, without harshness.
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Old 21st February 2010, 11:24 PM   #6
Rudolf is offline Rudolf  Germany
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Default Dipole tweeters in the real world

In post #1 I talked about a 1 inch dipole tweeter on a 1 inch circular baffle and with no depth. This is certainly a theoretical concept only. How near to that can we get with real world tweeters? Before we start I would like to refresh your knowledge of ‘dipole distance’. This is the distance from the middle of the rear dipole source to the plane of the front dipole source:

Click the image to open in full size.

The dipole distance (red line) is shown for two dome tweeters back-to back in a tube (left), for a planar tweeter like the B&G Neo 3 (middle) and a small baffle with two vertically offset tweeters (right – more about that later). Note that the dipole distance will not vary around the perimeter for the tube, but it will vary for the rectangular constructions.

I have built two dome tweeter dipoles in the back-to-back fashion:

Click the image to open in full size.

The bigger one is two Monacor DT-25N back to back in a tube of 3.3 cm radius and 4.4 cm depth (including the front plates of the tweeters). This adds up to a dipole distance of 7.7 cm, which would correspond as wavelength to a frequency of 4450 Hz. Let’s look at some measurements from 0 deg to 90 deg horizontal with a high pass filter at 2.5 kHz to protect the drivers. Shown are 0, 15, 30, 45, 60, 75 and 90 deg:

Click the image to open in full size.

We see nice constant directivity from 1 kHz to almost 4 kHz. At 4.5 kHz - the wavelength of the dipole distance - the wave from the rear tweeter will need just a wavelength to reach around to the front - so no phase difference (or 360 deg) on axis to the wave from the front tweeter. Since both waves are 180 deg out of phase at the source, they will reduce each other. Hence we see a dip in the on axis frequency response. Above that dip the dipole CD gets lost and beaming takes over. You see that in the spreading of the off-axis-SPLs with rising frequency above 4.5 kHz.

You may have noticed that those DT-25N are really small tweeters. Two Seas Millenium tweeters mounted back to back (as used in Linkwitz’ Orion) would have a dipole distance of 13.7 cm. This corresponds to 2500 Hz. You simply can’t have dipole CD with them anywhere within their recommend frequency range.

The smallest tweeters I could find where the Dayton ND20FA. You see a back-to-back dipole with them beside the Monacors in the picture. The dipole distance of the Dayton tweeter dipole is 5.6 cm ( 6125 Hz). I have measured their horizontal response too:

Click the image to open in full size.

You see how the on-axis-dip has moved up to near 6 kHz. Below nice CD down from 4.5 kHz, above 6.5 kHz beaming (which does not show very well because some low pass got in the way above 10 kHz). This is as good as it gets with back-to-back tweeters.

I have borrowed a diagram from cuibono for the BG Neo3PDR planar tweeter:

Click the image to open in full size.

Its dipole length of 4.1 cm (8575Hz) and some makes it probably the best CD dipole tweeter available today. As shown, the frequency range is in conjunction with a TB W4-1320sj, fully EQ'd and crossed at 1.7 kHz. The lines represent 0, 30, 45 and 60deg off axis. Of course you can see the CD area and the beaming area very well.

I have asked myself if it would be possible to undercut the dipole length of 4.1 cm. Voila:

Click the image to open in full size.

I placed two Dayton ND20FA-6 back to back, but vertically offset, on a small baffle (8 x 4.4 x 1.4 cm). This results in a dipole distance of 3.6 cm at minimum (9527 Hz). See the horizontal response (0, 15, 30, 45, 60, 75, 90 deg), measured at 45 cm distance:

Click the image to open in full size.

Not too shabby, either, with that dip at 8 kHz.

You may think that the vertical response will be very bad, concerning the vertical offset of 3.4 cm between the driver centers. That’s what I did too. But measurements along the vertical axis show a benign response. Green line is the power response:

Click the image to open in full size.

Click the image to open in full size.

Time to do some decent bafflets for those ND 20FA. Here in Germany four of them cost as much as one Neo3 .
Attached Images
File Type: gif Monacor DT25N backback.gif (22.3 KB, 1851 views)
File Type: gif DaytonND20 backback.gif (26.8 KB, 2061 views)
File Type: gif DaytonND20 vertplus.gif (30.5 KB, 1842 views)
File Type: gif DaytonND20 vertminus.gif (34.0 KB, 1852 views)
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Last edited by Rudolf; 21st February 2010 at 11:32 PM.
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Old 21st February 2010, 11:55 PM   #7
Paul W is offline Paul W  United States
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Nice work Rudolf!

Vifa OX20SC00-04 might also be interesting to try.
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Old 22nd February 2010, 12:57 AM   #8
cuibono is offline cuibono  United States
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All very interesting - I'll keep watching this thread. Those vertical polars aren't too bad...
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Old 22nd February 2010, 12:47 PM   #9
Rudolf is offline Rudolf  Germany
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Quote:
Originally Posted by Paul W View Post
Vifa OX20SC00-04 might also be interesting to try.
Wow! That Vifa is really small - but sadly seems to be unobtainium here around
Next candidate for a step up in quality for me would be the Monacor DT-25TI with the face plate cut off.

Click the image to open in full size.
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Old 22nd February 2010, 12:57 PM   #10
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very interesting thread---nice Boxsim simulations!

mow i need to learn more German so i can try an do some interesting sims too as i only use as much as i understand in german language
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