Fall 2010

Building Oblate Spheroid Waveguides
Far and away the most difficult project I've done to date.
Article By Jeff Poth

Difficulty Level

  This article is about some fairly large mid-tweeter horns and what went into them.

Basics of Constant Directivity
This is the short version of the ideas surrounding the Oblate Spheroidal Waveguide (OSWG) and Constant Directivity (CD) horns. CD horns like the OSWG are horns where the beamwidth stays relatively constant with frequency. Directivity is just a different way of saying beamwidth, and CD means a consistent beamwidth or directivity index across the intended coverage bandwidth. CD can be done in a few different ways, for example a truly omnidirectional speaker (where all frequencies are dispersed evenly in all directions) is CD. Dipoles with full dipole cancellation (no or minimal baffle) can also be fairly CD below the dipole peak, which leads to a figure-8 response, with forward and backward lobes. For horns, CD is a limited coverage window with consistent frequency response at multiple locations. In this case the pattern is a 90 degree round (Hemispherical) one, but there are CD devices with other dispersion patterns, such as the oval or near-rectangular patterns produced by some diffraction horns. The defining factor is that as many frequencies as possible have the same dispersion pattern.

Part of the job in a CD two-way horn loudspeaker is matching the dispersion of the woofer to that of the horn, eliminating dramatic changes in the power response/off-axis behavior. In a loudspeaker with a 12" or 15" this usually means a crossover between 1000 and 1500 Hz. Several types of horns can be (fairly) CD, primarily conical/OSWG/Peavey Quadratic Throat and some diffraction horns. What happens with a directivity matched CD two-way loudspeaker is that the woofer is run up until where the beamwidth has tapered to match the horn, where the crossover takes place, and then maintains flat directivity to as high a frequency as possible. This method was pioneered in the days of the groundbreaking JBL 4430, still a highly sought-after monitor today. It utilized a diffraction type horn, the distinctive "Baby Buttcheeks" style.

Very notable amongst this style of loudspeaker are the works of Dr. Earl Geddes. I've been reading the works of Dr. Earl Geddes for some time on his site and the h-ifi forums, most specifically www.diyaudio.com He's a long-term industry guy, having consulted with Peavey, JBL, and others. He offers a line of speakers, some available as kits, some only as completed speakers at  www.gedlee.com  along with quite a lot of other info. Mike Galusha reviewed the "Abbey" kit. Based on long hours of reading and research, I settled on the waveguide design Dr. Geddes used (and defined in his research), the OSWG.

Abbreviations
CD=Constant Directivity
HOM=Higher Order Mode
OB=Open Baffle
OSWG=Oblate Spheroid WaveGuidey

OSWG: Yes, it's SFW
To state it briefly, the OSWG profile is a balance between minimized diffraction and associated "HOM", and as effective a constant directivity behavior as possible. The minimal diffraction is achieved by a short, smooth and precise transition between the compression driver and the horn as well as a mouth roundover. An OSWG does not have any rough edges from which to diffract. Diffraction has historically been used in many horns, and still is used in the top horns for home/studio use from JBL, so the OSWG is not by any means the only way to make a high performance horn, however it does optimize what Geddes describes as the most important criteria, those being low diffraction/Higher Order Modes (HOM) and CD operation over the widest possible bandwidth.

Having been sold on the idea of the OSWG design, I inspected what commercial options were available. Simply put- there are none. There's a 12" version of the OSWG from DDS, but I wanted to go bigger. I decided that the only option was self fabrication. The OSWG is a fairly simple shape, but it takes some doing to build one. The critical part of the OSWG is carefully matching the waveguide flare to your compression driver using a short arc to couple into a conical section (a straight-walled cone), then a second arc as the waveguide ends to couple to a flat front baffle. The mouth termination arc can also be used to continue rounding back to a lip rollover, as I wound up doing. Which of these you choose determines to some extent the behavior of the waveguide near its cutoff. Some prefer free-standing horn geometries (as shown), some want a baffle loaded horn, they each have their own characteristics. The more rounding over and/or baffle exists around the horn, the smoother and deeper the horn will tend to respond, at the cost of size (which screws up the center-center spacing and makes for more "lobing").

The "Wrong" Way
Are you with me so far dear reader? Some of you have been lost, I'm sure. We'll illustrate with some rough examples. Take your typical 6.5" woofer, 1" tweeter two-way. At low frequencies the output from the 6.5" wraps around the speaker (omni-directional pattern). As the wavelength approaches the cone diameter/baffle dimensions, off-axis response narrows. The narrowing of the dispersion from the woofer itself is due to the sides of the cone being different distances from the listener's ears. The contributions of the outer edge are time delayed relative to the inner edge (the edge closer to the listener) and when those distances are a half wavelength different distances from the listener's ear, they are 180 degrees out of phase with each other and cancel out. At about 2kHz the beamwidth has become fairly narrow, somewhere around a 90 degree beam (plus or minus 45 degrees from a nominal center axis, imagine the cone walls from the midwoofer being extended out into free space). This is your nominal coverage pattern, the edge of which represents a threshold of SPL loss relative to the on-axis radiation, typically -6dB or -12dB is used as a threshold when discussing pattern control. These are only approximate numbers so don't get too hung up on them, cone shape, dustcap/whizzer style, and cone material flexure all play a role (but the dominant effect is cone size for most transducers). So, we have a speaker in which the coverage has gone from an omni-directional pattern to a 90 degree cone- a significant reduction of power into the room (assuming a flat on-axis response). Don't consider this a hard boundary, as there is a gradual reduction in power response, not a hard and fast cutoff. There is still sound outside of the conical coverage area, it's just significantly reduced in amplitude vs. the on-axis (straight out from the dustcap) response.

At 2 kHz the tweeter comes in, and is somewhere between omnidirectional and hemispherical. The size of the baffle will determine how much is hemi vs. omni, as if the baffle is large enough to direct the whole wavefront forward, it will be hemispherical. So you have somewhere between 4 times and 8 times the area being excited by the tweeter as you did by the woofer, again assuming a nominally flat on-axis response. This imbalance wouldn't be a problem if you listened on-axis in an anechoic (reflection free) environment. However, as you move off axis, you will lose midrange between 1000 to 2000 kHz, while retaining the tweeter output and the lower midrange/bass. In other words, the speaker becomes tonally imbalanced the further you move off-axis. To make matters worse, the reflected energy (that which bounces off something in the room before arriving at your ear, as opposed to the direct energy) will likewise be imbalanced as there's less energy exciting less of the room when the beamwidth has narrowed. This throws off the perceived tonal balance further and will often make these types of speakers sound "bright" or "nasal", even at the listening position. A large part (as much as 50%) of what you hear is reflected energy, so when you have sound that is inconsistent in the space it radiates into, it will tend to shift the perceived tonal balance towards those frequencies with the widest dispersion.

The "Right" Way
Now consider a horn that operates with Constant Directivity over its bandwidth. You get a consistent tonal balance on and off axis as well as a consistent balance of reflected energy. Furthermore, there's an overall reduction of reflected energy, as the horn precludes radiation to the rear or sides. There's still energy there, but much less. This allows the sound to be dominated by the direct energy, as opposed to containing a greater amount of reflected. Whether this is or isn't desirable depends on who you talk to. Some believe that reflected energy in the room is a positive thing and desirable for enjoyable listening. While this is a point of discussion, there is an agreement amongst all serious designers I know that the direct and off-axis sound should be matched, and that is the essence of constant directivity. Constant directivity can include Omnidirectional loudspeakers as well as good horns, and bleeding edge minimal baffle dipole designs (Open baffle), but a compression driver and horn can achieve excellent CD behavior along with extremely high sensitivity (a major problem with CD dipoles), low distortion, and excellent dynamics.

Enough Of That For Now! Bring On The Build Pics!
(Are These SFW or NSW?  ;-)  )

First we see the Parts Express 12" waveguides with an "inset throat". I had started with these as a rough experimental device, but they left a problematic lip at the driver/waveguide junction. I looked for something that would allow me to fill the gap and create a rounded profile, transitioning into the horn. I wound up cutting out a section of the top of a two litre bottle (shown). By using putty and compressing it with this, I got the desired throat diameter, as well as a rounded transition into the rest of the horn. A straight edge was used to form the putty to a straight-wall profile following the throat roundover, creating a rough approximation of the OS profile (but with a longer, softer mouth taper and less precision). It is critical to match the diameter of your waveguide's throat to that of the compression driver, as well as the angle (the tube on the compression driver has an expansion characteristic of its own).

I inspected the waveguide, ran some impedance sweeps, and decided to go further with it. I machined a ring for the mounting lip of the waveguide to screw to, with a 45 degree edge on the internal cutout. You can see that there's a ledge routered in as this was necessary to ensure proper centering. Once this was mounted, I began filling it in to create the conical section, as defined by the lip. I tried multiple fillers. The best was a two-part body epoxy paste designed to work alone (doesn't need cloth or a form, you could model with it if it weren't epoxy), but was expensive. All epoxy-based products worked to one extent or another (wood filler with epoxy was the best from an economics vs. performance standpoint).

Once we had a cone, we now had to re-introduce a lip. I used a Styrofoam ring from the hobby store, and some casting cloth- this is plaster powder on cloth. I shaped the Styrofoam roughly with sandpaper, and wrapped it in casting cloth for strength, then affixed to the horn assembly.

More filling more filling more filling.Then sanding.Then filling. And so it went until I was ready to start spraying them with the appliance epoxy surface coat. This was chosen as it would prevent any damage to the filler materials and hold the assembly together nicely. Unfortunately, it was still far too rough following the spray- so more sanding, then spraying...

And sanding and spraying...

Here's one after one of the spray coats and a sanding. You can see the elevated portions got knocked down leaving a cool tigerstripe look. This was not to last J.

After a while longer working on them, I cut a couple circles, then drilled holes in the middle and truncated one side. Also cut bevels on all edges and epoxied it to the back of the assembly. This is to be used as a mounting point for the waveguide.

What's With The Yellow Foam?
"Don't eat that yellow snow." -- Frank Zappa
The foam is a particular type, called "Reticulated foam". Essentially, it's a web of plastic, lacking the walls of the cell structure that are present in varying degrees in other foams. Acoustic foam is generally "open cell" which means that there is at least one wall missing from each cell, but there are still cell walls in place. This makes it a fairly effective absorber but also forms a barrier and can reflect energy too. Closed cell foam is used in a variety of applications but is generally not useful to us in audio. The recommended pore density is about 30 to 40 ppi.

Dr. Geddes has a patent on the use of the foam to mostly (80%) fill the horn, as you can see in his products. As used here is not covered by his patent, as there was prior art for the use of foam in horns. The ideas were different, but there was still foam there.

The foam as used here is to damp "HOM", Higher Order Modes. This is best described as the energy that's reflected within a horn. Per Geddes, this is a significant source of disturbance within the horn and is a major detractor from sound quality. These are unavoidably generated by the use of an obstacle to control dispersion (read: horn) but can be minimized and suppressed. Imagine if you will, a 6ft tube of concrete pipe. Standing inside it and speaking, the sound is free to exit, and yet you still have echoes. This is the sound bouncing around the interior. These are HOMs and the portion of the sound that leaves the pipe directly is the direct wave. The situation with a compression driver and horn isn't so dire, but every obstacle and even the driver itself generate some of these that aren't traveling directly out of the waveguide. Obstacles scatter sound in all directions. This is also the reason you see extensive use of roundovers in many fine speakers- the dome tweeters so prevalent in today's "mainstream" hifi will reflect sound from the enclosure edges, and rounding over reduces the nasties introduced. You see felt covered baffles for this very reason. Horns bypass it but need to have a roundover at the mouth (the large end) in order to avoid similar problems. The aesthetically pleasing LeCleach profile takes this to an extreme, as do some of the others, like spherical horns.

The foam shown here is a trimmed aquarium filter foam of the appropriate reticulated style. I tried shaping the foam with a hot wire cutter, and also by just trimming with scissors. Either worked but the scissors seemed more effective. Treat it like Michelangelo and remove everything that's not a foam plug. I fairly quickly managed a pressure-fit plug of foam, and fitted it. By using low-loss foam like the reticulated style, the direct sound only is marginally affected. The sound (HOM) bouncing around within the horn (the throat in particular, which is the most tube-like part) would encounter the foam multiple times, making it relatively lossy, while only slightly affecting the direct path sound that only encounters the foam one time.    Short version: the foam removes harshness from the horn sound.

So, You Have A Horn...
Yet Where Does The Sound Come From?
This particular horn is driven by a JBL 2426h compression driver. This is a driver with a Titanium diaphragm and their diamond edge suspension. As with all compression drivers, the motor is extremely powerful, and combined with this horn, it gives us very high sensitivity that is on the order of 100dB/W/m after compensation. A CD horn has a frequency response something like a lump, with a first order (6dB/octave) rolloff above some given frequency defined by the rolloff of the horn/driver combination and a steep, usually second order, rolloff below. By adding a single pole correction filter (read: series capacitor) you can adjust this to achieve maximally flat response within the band where the response is falling. The falling frequency response is counteracted by the rising response of the capacitor filter. Most (all?) compression drivers behave this way, and the characteristics of sound are dominated by the waveguide/horn.

This nonlinear response (lump) makes the filter design a little more complex. In addition to creating a filter to limit low frequency content in the input signal (traditional high-pass filter), you also need to incorporate equalization for the high end rolloff (CD compensation), and typically also level-matching capability like an L-Pad or some resistance. This is beyond the scope of this article, but I will be publishing an article covering much of this in the near future. The compression driver is a significant variable and my own crossover would not work for other compression drivers, which would need steeper cutoffs and different impedance and level compensation, as well as requiring matching to a different midbass section.

You can use Jeff Bagby's PCD software to model and design your crossover. I have found it to be very effective for predicting real world performance, given sufficient information in- like your own response measurements. I will cover this in more detail when I finish my article on crossovers for these pages. My own solution incorporated a few impedance correction notch filters, and I coaxed it into a fairly simple alignment. I use the JBL 2226h 15" woofer to its natural celing of about 1500Hz, and the horn above, though it is significantly active between 1 kHz and 1500 Hz. A 5uF capacitor provides the Constant Directivity correction, as well as setting the high pass filter in conjunction with the natural horn/driver rolloff. This simple crossover high-pass/low-pass arrangement would not be possible with other components, however. The JBL drivers are very well behaved- the compression driver can be used to 500 Hz in level limited applications, and the 2226h has a well behaved top end. I also damped the cone of the 2226h to further suppress the top end behavior. Most larger woofers have unlistenable top ends, and even the stock 2226h is somewhat harsh if you don't tweak it a bit.

HEY WAITAMINNIT WHERE'S THE PROFILE?!?!
And is it me, or does this pic look like female gentailia?

This is a rough sketch giving the basic content. No doubt I'm going to get an Earlfull (like it doc?) about the accuracy of this drawing, but it's rough for a reason- the practicalities of assembly and mouth termination create some variance in what people will be able to (or want to) assemble, and the critical components are represented. Anyone undertaking an assembly of this magnitude will need to spend some time reviewing more precise discussion of the Oblate Spheroid Waveguide profile. Dr. Geddes site www.gedlee.com should give you a very good starting point, and plenty of information is readily available. This is not a project for those unwilling to research or needing spoonfeeding beyond what's here.

Sound And Application
This project took me a very long time to achieve, about a year of off-and on work, and on the order of 80 hours work. They cost about $180 to assemble total, between the significant number of fillers (the preferred 2-part body filler is about $20 a tub) and the sprayable epoxy used for the finish and sealant. Given so much input, I was apprehensive about firing them up, as anything short of excellence would have been a major disappointment.

They are indeed excellent. Frequently highly dynamic speakers have significant limitations- many horns sound "honky", many high efficiency speakers like lowthers tend to have a limited range of output before they cease to be able to play cleanly. These are not level limited in any way, being the same type of gear you would use for maximum output in a professional application to fill a stadium. At home levels, there are no realistic limits to how much SPL you can achieve. They are very sensitive and one could use low-powered amplifiers, though they're not quite as sensitive as some of the more extreme systems like Edgarhorns. I'd say that for most users, a 300B SET amplifier would be an incredible match for a system with these mated to a very high efficiency (pro style) 12" or 15".

They are, as said, extremely dynamic (par for the course with horns), but also very refined. Part of this is because they interact with the room in a much more consistent fashion than does a "normal" speaker. This gives them a smooth, consistent tonal balance all through the upper octaves. They pass the "listening from another room test. This is due to the consistent room response. The clarity and image specificity are also impressive, the lack of room reflections gives a very clean and intelligible response. Most loudspeakers suffer badly on dialogue comprehension vs. headphones, but I get better results with these than with some phones.

The assembly does have a natural rolloff over 10 kHz. I have made supertweeters to resolve this problem but have not implemented them as the consistent pattern up to 10 kHz provides sufficient top end. It is not "dull" but doesn't have the last little bit of air. Apart from this minor issue, they make world-class treble response. When one considers that the >10 kHz response is merely suppressed and not eliminated, but also has minimal program material, this small compromise is not of major importance.  

Not Much More
These horns have been the most difficult project I've done, and have been well worth it. I can recommend this sort of horn without reservation, but only advanced DIYers need apply. You will need to create a crossover and overall system design, and make a number of fabrication decisions.

Thanks And Commercial Options
Thank you to Dr. Geddes, Dr. Toole, Wayne Parham, Sean Olive, and all those who have promoted our understanding of loudspeakers, horns, and room interaction. Particular thanks to Dr. Geddes for the excellent waveguide design. www.gedlee.com and www.audiokinesis.com offer completed Oblate Spheroid designs, and www.pispeakers.com offers horn loudspeakers with some of the same principles of design (and quality) but not strictly OSWG based. Only Dr. Geddes offers an OSWG design with a waveguide as large as this one, the imposing "Summa".