Building Oblate Spheroid Waveguides
This article is about some fairly large mid-tweeter horns and what went into them.
of Constant Directivity
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.
Yes, it's SFW
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").
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.
Of That For Now! Bring On The Build Pics!
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.
With The Yellow Foam?
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.
You Have A 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.
WAITAMINNIT WHERE'S THE PROFILE?!?!
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.
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.
And Commercial Options