December 29, 2010

Oblate spheroid waveguides

An oblate spheroid is the Rolex of waveguides and horns. It is the ideal choice for high frequency compression drivers where sound quality and constant directivity are the main goals. If those aren't your goals, they should be! When using loaded compression drivers, you have a few strong advantages:
  • ability to achieve controlled directivity
  • ability to choose coverage angle to match the polar response of the midrange driver
  • very high efficiency and output
All horns in this application make at least one big compromise. The first is to use diffraction to achieve controlled directivity. This results in poor sound quality due to a much larger amount of higher order modes (HOMs), which according to Geddes is the main cause of sound quality issues with horns. The second is directivity. The popular tractrix profile is considered one of the better sounding HF horns, but the response narrows with increasing frequency.

This begs the question "why still use HF horns?" There are some who are tolerant of horn coloration and who are less concerned with directivity. The latter is one of the most overlooked issues in audio.

What about conical?

Conical waveguides are similar, but differ most at the throat which is the most critical area. A compression driver like the B&C DE250 has a conical exit tube with a 6 degree taper. When loaded into a conical waveguide, a sharp transition of 6 to 45 degrees is formed. This causes diffraction at the throat and more HOMs. The oblate spheroid waveguide has a gradual transition after which the two are the same. It takes a little more effort to add the transition and some maths is involved, but the oblate spheroid is clearly better.

How to derive the contour

Spreadsheets have been made and Hornresp can also export a text file which contains the co-ordinates of the profile. There are four variables involved:
  • throat area (match to the compression driver exit tube, typically 1")
  • mouth area (match to the mid driver)
  • coverage angle
  • compression driver exit tube angle
 These together determine the contour and axial length, along with the bandwidth. The exit tube of the compression driver determines the high frequency limit - usually just under 20k for a 1" exit. Larger compression drivers have less high frequency extension.

Matching mid drivers

A smaller mouth has less low frequency extension. Normally the waveguide mouth and mid driver should match in size. Some examples

15" mid + 15" (diameter) waveguide - 900 Hz crossover
12" mid + 12" (diameter) waveguide - 1200 Hz crossover
10" mid + 10" (diameter) waveguide - 1500 Hz crossover
8" mid + 8" (diameter) waveguide - 1800 Hz crossover
6" mid + 6" (diameter) waveguide - 2000 Hz crossover

This should work with a 90 degree oblate spheroid waveguide, where both will have matching directivity at the crossover, then the response will widen until it is omni directional at bass frequencies. The high frequency response will have near constant directivity in the waveguide bandwidth. As a result, we want to use the waveguide for as much of the range as we can. Size matters.

How much effort?

To design and build speakers like this isn't trivial. For most there are some easier and preferable options. For a fully sorted state of the art version, I suggest Geddes kits where the Abbey is probably the sweet spot.

Gedlee kits >

A cheaper and less refined version is the Econowave. It uses stock waveguides which are cheap and easy to get hold of. There are many drivers that have already been used where the crossover design has already been done.

Introducing the Econowave >

Also similar are Pi speaker kits.

If you are like me and insist on designing and building your own, then expect a challenge! Building a decent waveguide is a lot more difficult than simply building a box. Designing the crossover is time consuming and requires many measurements. In my case, I enjoy the learning process, the challenge involved and my ultimate goal is to create a unique custom made speaker that combines style and performance like a highly tuned sports car.

Read about my 6" prototype >

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