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Speaker Off Axis: “Correct” Driver Diameters for Great Off Axis Response

ATC and many other pre-eminent manufacturers of what we call “forward firing cone / dome speakers” believe that for optimal speaker off axis response any given woofer or midrange driver should not be operated above ka=2. The reason is that above ka=2 the driver gets increasingly directional resulting in an off axis suckout at the mid / woofer and tweeter (see our blog post for plenty more on the theory and measurement of speaker directivity). Note that this effect can be entirely mitigated by using waveguides for the tweeter and other loudspeaker design techniques.

 

ka is a dimensionless number that equals circumference (in mm, m, in, ft, etc) divided by wavelength (in the same unit of measure). Circumference can be easily calculated as pi or 3.141 multiplied by the diameter.

 

One point when calculating ka is that the specified diameter of the driver includes the surround which should not be included in these calculations. For example the 150mm / 5.9″ driver in the ATC SCM19 has an actual cone diameter of 4.9″. Further complicating things are drivers that are purposely designed so that the outer edge of the cone decouples from the inner part.  I know at least JBL and ATC and likely a few other manufacturers who are using paper pulp based drivers are trying to get their drivers to behave in this way. Manufacturers who are striving for pistonic response are not going to have drivers that work in this way. As a case in point look carefully at the ATC driver below, from the SCM19. You can see that the cone material is two different colors with a semi-translucent material nearest the surround and there is also a very large soft dome grafted onto the dustcap.
ATC SCM19 Woofer

 

Off axis suckouts (common in many speakers using a largish mid / woofer) look like this:

Ugly, no?

 

This is what a nice off axis looks like (complements to YG Acoustics who uses a waveguide to match tweeter directivity to midwoofer at the crossover):

 

Rather than making you calculate ka one of our nice readers made a graphic for everyone that shows ka=2 for different driver diameters:
driver-beaming

As an example, a 5″ driver should be crossed over at 1700Hz (or lower, depending on crossover slope) to respect ka=2. You can use this chart to do a quick sanity check on how far off ideal the crossover point is for any given design. Note that there are VERY few designs on the market that truly respect the ka=2 rule! And of course clever things like waveguides make the ka=2 rule less of a rule anyway. As ATC point out off axis is not the only design criteria that matters, and good loudspeaker design is a game of balancing the criteria. However just by understanding this point you should see why two way cone / dome designs using 8″ or 10″ woofers and no tweeter waveguide will have by design poor off axis performance. Likewise designers using tweeters with high crossover points and large “pistonic” metal, ceramic or magnesium 6″ drivers.

4 thoughts on “Speaker Off Axis: “Correct” Driver Diameters for Great Off Axis Response”

  1. This is a real spoiler (-: only 1700hz for a 5″ that is bad news for 99% of the speakers out there. Except for the LX521 and a few others.

    I am thinking of buying a pair of ESS Heil AMT. The lowest XO is 700hz but how do I calculate the area of the Heil? so I can find the best XO for the driver

    1. Hey Martin, thanks for your comment. The graph only applied to cone drivers…and is also generic, for best results you’d simply measure or get the off axis response information from the manufacturer’s datasheet.

    2. Only “weakness” of LX521 is it’s not too convincing pursuit of a dipole tweeter. His passion for dipoles is understandable and rear firing tweeter can add “airiness” to the sound but he should have gone for a compression driver/ Geddes’s Oblate Spheroid Wave Guide combo above 1000 Hz.

  2. ATC design their speakers to ka=2, it’s in their marketing materials, along with their reasons for doing so. Most companies do not design to ka=2, so I’m not sure why you chose ATC over any of them to make your point.

    Yes, the SCM19 is crossed at 2.1khz (about 350hz higher than ka=2), but not much higher: ~2.3. Which is almost indistinguishable from 2 in practice.

    Looking at other manufacturers designs, it seems like 90% of them cross their 6-7 inch midwoofers at 2.7-3.1khz and have the directivity problems you presented here. Speakers with ka=3 and worse – you could have picked from any of them.

    Small 2 way speakers capable of both high dynamic range and decent bass output are exceedingly rare. If I were to guess the reasons why ATC chose (yes chose) to not cross their 1 inch dome at 1.7khz, I’d say first, they wanted to ensure the 10 inch baffle didn’t affect (eat) the omnidirectionally radiated sound from the tweeter from 1.4khz down. Next, I’d say they wanted to guarantee the capability of high dynamic range throughout the entire range of the SCM19’s frequency response. Reason being: so that transients (loud, short sounds) of any frequency would be able to be rendered at up to the same level – realistic levels – and without distortion.

    The 1 inch dome in the SCM19 is a great tweeter. It’s their own design and is made in house (like their beautiful woofer you posted a picture of). It’s flat down to 720hz and has linear travel (peak to peak) of 1mm. Unlike the tweeters used by almost all of the other manufacturers (the ones with ka=3 and worse speakers), it could be crossed at 1.7khz

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