DIY Axially symmetric oblate spheroid CD waveguides, in solid Oak

[jack_bouska]

I posted some images of my recent waveguide construction on the "Horn system pictures" thread, <http://www.audioheritage.org/vbulletin/showpost.php?p=122818&postcount=49>, and in post #51 "Titanium Dome" followed my post with a request for the & measurements I made on my waveguides.
Rather than clutter up the "Horn system pictures" thread, I have chosen to start a new thread under the DIY section, with more details of the design and images.
The two new waveguides are mounted on a pair of 1" exit TAD 2002 compression driver, and a 2" (49mm actually) exit a pair of JBL 2441 compression driver.
I purchased the TAD new, however the JBL 2441 originally saw duty as part of the sound reinforcement system of the Calgary Saddle dome, home of the 1988 Olympic games <http://www.pengrowthsaddledome.com/foundmain.html>. It may be unusual to use a device which once shared about 1/15 of the coverage duty for a 20,000 seat stadium in my modest sitting lounge, but it should be no surprise to this membership that achieving realistic dynamic range with low distortion does require some extreme measures to achieve our acoustic goals
The full list transducers in the speaker system consist of (refer to picture 4 in this post)
2 x TAD 2002 (4khz - 20khz)
2 x TAD 2441 (1khz-4khz)
4 x JBL 2123 10" cone midrange (250hz - 1khz)
4 x JBL 1401nd 14" cone upper bass (60hz - 250hz)
2 x Altec 3182 18" cone sub bass (7hz-60hz)
The waveguides were designed using information from published papers by Earl Geddes. (reprints can be found at: <http://baseportal.de/cgi-bin/baseportal.pl?htx=/Data/exdreamaudio/download> )

Images and measurments graphs to follow:

Jack Bouska

[jack_bouska]

The first four pictures, in this post illustrate the Oak waveguides during construction, mounting, and in their final location in my listening room. The first images shows the "green" untreated French Oak on the faceplate lathe partway through turning. Note the blue plastic template used to guide the turning operation. I nicknamed the horn flare "the rams head horn" for obvious reasons.
The second image shows how the horns are mounted to a retaining flange which forms part of the brackets which retain the compression drivers. The horns are not bolted directly to the compression drivers. BluTak is used as a flexible gasket to ensure a smooth transition from waveguide throat to driver exit.
The third image shows a front perspective close up of the mid-high section of the loudspeaker.
The fourth image shows a full view of the components, left to right: TX columns contain an Altec 18" in 4 meter folded transmission line cabinet, centre: "stack of loudspeakers" and on the right, the equipment rack with CD, 2x Behringer DCX2496 and the 5kW Tripath power amplifier "plate"
The full system can play peaks well in excess of 130dB, over a power range of 10hz to >20khz
I nicknamed the loudspeaker system "IMPACT STACK"
Jack Bouska

[jack_bouska]

The first two pictures in this post show the waveguide design profile for the 2" throat, and the 1" throat compression drivers respectively. These images can be downloaded, scaled (to match the dimensions listed on the diagrams), and printed to produce templates should anyone wish to construct a copy of these specific waveguides.
Image 1: The 1" exit waveguide is stock Oblate spheroid shape, with a 1/2 round radius at the mouth The 2" exit waveguide is a compound shape, starting with oblate spheroid from mouth to 3/4 horn length, merging (seamlessly) into a tractricx taper for the last 1/4 of the waveguide, to the mouth, finishing in a 1/4 round radius curve to the outside edge.
When I worked up a waveguide design which followed E. Geddes recommendation, to terminate the mouth with a radius edge equal to 1/4 wavelength at lower frequency. limit, this resulted in a radius of over 3" for 1khz, which meant that for a full 1/2 round mouth, I would need an annular ring 6" wide all the way around the mouth.
Image 2: My oblate spheroid mouth is 5" in diameter, which would have made the whole horn 17" in diameter, much too big. Instead, the Tractrics horn mouth termination (which goes from 40deg curving around to 90deg) is only about 1 1/2 inches wide, and I add a 1/4 round radius just to smooth the edge. This makes the whole diameter much more tractable at less than 10" diameter
The last three images show the directivity response of a 2" throat tractrix horn, followed by the 2" waveguide, and finally the 1" waveguide (mounted on the JBL 2441, and TAD 2002 respectively). The measurements were made with a Panasonic mic element, Altec microphone preamp, SoundBlaster Audigy ZS 24/96 pcmcia sound card, IBM laptop and ETF5 software. The measurements were made at low SPL (~88dB) at a distance of 50cm from the mouth.
Image 3: The spl response vs. angle for the Tractrix horn is seen to "fan out" fairly rapidly from about 2.5khz upward, with the curves widening as frequency increases. Only the 90 deg (on axis) curve stays close to flat. (These curves were measured without using any horn compensation) The curves are annotated as angle away from horn axis. This angular coverage is about the same as I would expect from a cone of approximately the same diameter. (not CD)
Images 4-5: Both the 2441 and TAD curves illustrate good examples of constant directivity using the axially symmetric oblate spheroid waveguides invented by Earl Geddes. The spl response curves cluster closely (within a few dB) over the full +/- 40 degree design coverage. The curves are annotated as angle away from the plane of the waveguide mouth (so 90deg is directly on axis). Both these devices have response equalization applied using a Behringer DCX2496 digital crossover.
The spl response curves which are outside this angular coverage (yellow, black and red curves) are seen to drop in amplitude very rapidly with rising frequency, which indicates that the CD waveguide "does what it says on the tin"
Image 4: The 2" throat device on the 2441 is good from about 1khz up to 10khz (where the aluminium diaphragm break-up starts), and the phase plug no longer produces nice planar waves above that frequency.
Image 5: The 1" throat device on the TAD appears to be good from 1khz up to beyond 20khz. No evidence of diaphragm break-up is visible. (Beryllium, the right material for this job)
Jack Bouska

[jack_bouska]

The first four pictures in this post show the uncorrected, and EQ'd-corrected frequency response of the two waveguides, using white noise, averaged over a 4ft x 4ft x 2ft volume at/around the listening position, followed by Fourier transform spectral analysis averaged over about 45 seconds of recorded noise waveform. Use of spatial averaging smoothes through the short period room modes (peaks and nulls), but highlights the response anomalies which are inherent to the device under test. This form of measurement is a balance between the direct arrival energy, and the reverberant sound field in the listening room. (as opposed to the previous ETF5 measurements, which are intentionally restricted to direct arrival only, via close mike placement, and short window on the FFT transform).
The volume of averaging is around the defined listening position, and stays well within the +/- 40deg coverage angles. Both left and right channels are run simultaneously, with uncorrelated white noise between channels. Amplitude is less than 90dB, distance approximately 7-11ft from each channel.
Note that the compression driver/waveguide combinations are not useable without response equalization applied using a Behringer DCX2496 digital crossover) shown annotated on the graphs. The waveguide CD devices do not have the characteristic on axis high frequency boost noted with exponential or tractrix horns.
Image 1: shows the response of the JBL 2441 2" throat drivers on the waveguide, using spatially averaged white noise.
Image 2: shows the response with final EQ applied. I chose to use a parametric EQ (Band pass) centred on 2.62khz with a Q of 0.4, level -8dB cut.
Note the very low level of ripple on both these graphs (around +/- 1db worst case). This is a very good indication of the amount of internal (axial) reflections within the waveguide and coupling throat of the JBL. Poor acoustic impedance matching at the mouth can cause reflections which send energy backwards in the waveguide to be reflected at the phase plug, and generate resonances. These axial modes generally exhibit themselves as the classic "horn honk" and sound similar to the distortion you can hear when speaking through the cardboard tube from kitchen food wrap (or toilet paper tubes). The resonance modes (reflections) are generally visible as ripple in the response of most horns, and a smooth curve is evidence of low levels of reflected energy, and high quality tone. My choice of tractrix mouth instead of 1/2 round radius was apparently a wise one, as borne out by these graphs. The sound is indeed very natural and clear. To quote my audiophile friend on his first listen: " I have never heard horns sound like real music before this!"
Image 3: shows the response of the TAD 2002 1" throat drivers on the waveguide, using spatially averaged white noise.
Image 4: shows the response with final EQ applied. I chose to use a parametric EQ (Band pass) centred on 4.238khz with a Q of 0.5, level -7dB cut, cascaded with a HighPass shelving filter set at 20khz, +15dB, single pole 6dB/oct.
Note the modest increase in the level of ripple on the TAD response (now +/- 2dB). I attribute this to two possibilities: 1) the use of a small 1/2 round radius on the horn mouth which is intended only to operate above 4khz (the crossover frequency for this device) and 2) reflections in the phase plug and throat of the device itself. I have noted these same ripples, at the same frequency locations, on a number of horns, of different taper and length, when used with this same compression driver.
When the crossover is applied, the same graphs show marked reduction of ripple below 4khz (in the crossover band), which indicates that offending reflections (poor mouth termination) can be suppressed by restricting the bandwidth to the range appropriate for the round over at the mouth (1/4 lambda = r)
Image 5: shows the pair of impulse response graphs, using the 90deg measurement from ETF. In the interest of time (I have to go now) I will describe these two graphs in the next post, later this week.
For now the above graphs give a fair overview of the performance of these devices, and I promise more information to follow shortly
Jack Bouska

[jack_bouska]

The last image in the preceding post (#4 above) showed the pair of impulse response graphs for the compression drivers on waveguides (JBL top, TAD bottom). The amplitude scale is linear (+/- 32k, 16 bit wave file), and the time scale is in samples @ 48khz sample rate. The display window is 120 samples long, or 2.5ms. The energy on both devices is seen to decay by 99% in the first 1/2 millisecond, and further attenuate to approximately 99.9% within the first full millisecond. Both wave shapes exhibit a classic high-pass differentiation filter shape (prominent peak-trough), followed by an exponentially decaying tail of band limited lower frequencies. The impulse response of both devices also display a 2nd negative pulse following the first trough. I suspect this is a function of the digital EQ applied via the Behringer DCX2496 crossover, and I intend to investigate by running some "raw" measurements, driving the compression drivers directly from the soundcard/amp with no equalization applied.

The first image in this post shows the ETF5 cumulative spectral display, in linear scale format. The spectral plot serves two useful diagnostic purposes: first it illustrates the decay in energy with time, (similar to a waterfall), by using four overlapped FFT graphs (each 2.6ms long), with start times of 0,1,2,3ms respectively. Second, the linear scale spectral graph can be used to identify/analyze internal mouth-throat-phase plug resonances (axial modes), which cause response ripples due to comb filtering of the reverberation pattern.

The 2441 graph (top) shows that between 1.5khz and 10khz, the energy from 1-3ms is on average about 20db lower than the first arrival, which implies very little energy storage within the device or diaphragm. Much of the measured energy beyond 1ms is likely reflected from surfaces near the microphone (floor, walls, furniture), while some of it is related to the unavoidable effect of abrupt horn mouth termination, and the acoustic impedance contrast associated with the rapid change in coverage angle from +/- 40deg to full space (+/- 180deg). At the rim of the waveguide (or any ordinary horn), the acoustic impedance contrast generates diffractions, sending some energy backwards within the waveguide from the mouth towards the throat. This is reflected again from the position of the phase plug (another cause of acoustic impedance contrast within the compression driver itself), and the affair sets up a series of decaying "normal mode" reverberation, with reverberation time (period) roughly equal to the length of the horn (plus compression driver coupling throat), divided by speed of sound. (~ 35cm/ms)

In their article: "Round The Horn" Philip Newell and Keith Holland, (Speaker Builder, 8/94) suggest that much of the classic "horn honk" is attributable to these mouth-throat resonances. For a practical demonstration of how important good mouth termination is for neutral tonality, simply take your favourite magazine, roll it up into a conical shape "megaphone" hold it up to your mouth and clearly utter the phrase: "this is the sound of horn honk". (and you will be speaking the truth). Horn honk can be easily detected by your ears as acoustic resonance and emphasis of some frequencies, along with recognition of the delayed energy caused by the trapped waves. Bad horns have a great deal, and good horns have almost no detectable evidence. The axially symmetric horn tested by Keith Holland was documented as sounding like a quad electrostatic by the listening panel.

These resonances take the form of delayed signals, which are added back into the acoustic output (with alternating polarity). The delay+addition of signal creates a comb filtering effect, which on a log scale amplitude plot appears as a sinusoidal ripple in the (otherwise smooth) response. The period of this sinusoidal pattern is related to the time constant of the reverberation according to the equations: time period = 1 / frequency (as measured peak to peak on a linear frequency scale spectral graph)
Inspecting the first image of this post shows the most pronounced ripple to have a peak to peak span of about 400-500hz, which relates to 1/400 = .0025s = 2.5ms or around 87cm, which corresponds to the distance from the horn to the floor, and back to the microphone. Intra-waveguide reflections would need to be less than the 20cm (x2) length along the waveguide axis. (40cm / 35cm/ms = 1.14ms, and 1/(.00114) = 877Hz) This corresponds to ripples with duration of 900hz or longer. Evidence of these periods are difficult to discern on the blue spectral graph, but are noticeable on the later spectral lines, with some periodic notches noticed at 1-2khz. This would imply some reverberation between the throat and mouth of the wooden waveguide section (10cm) or more likely, between the phase plug and the transition to the wooden waveguide section (~6-8cm). The exit point from the compression drivers to the waveguide acts as a circular diffraction aperture, such that the near planar wave front emerging from the compression driver effectively diffracts into a spherical wave front, to ultimately fill the conical expansion of the oblate spheroid contour.

This ripple (900-2khz period) is very low amplitude, perhaps 1-2dB out of the total 40dB on the vertical axis. This effect is not audible by me, as I rate the waveguides as having near-zero horn honk characteristic.
Incidentally, the intra-phase plug resonances would generate ripple with a 10kHz period on these graphs, and indeed there does appear to be some visible on these graphs, however I would need to do more work to determine if this is truly a phase plug problem, or if it has been induced by my heavy handed equalization scheme.

The second image in this post shows the measured phase response of the waveguides, (blue line) compared with the calculated minimum phase for a filter with the same frequency response (using Hilbert transform). Ignore the vertical lines on the top plot, where the measured phase slightly exceeds the +/- 180deg vertical scale (phase wrapping).

The third image shows the 1/3 octave smoothed, on-axis, frequency response of the waveguides, with a gating of ~10ms. The close mike position, coupled with the short window, mean that these graphs correspond to the direct arrival "anechoic" frequency response (although some pesky reflections do affect the response accuracy). Full equalization has been applied, with the lower frequency of the crossover set to 350hz

The fourth image of this post contains the waterfall plots for the waveguides, and are included mainly as "eye candy". Apart from the obvious quality of the rapid energy decay with time, also note that the devices are relatively resonance free (apart from the common bump and ridge at 1khz). The ridges down at the noise floor are largely influenced by early reflections from floor and surrounding objects. However one important feature of note is visible on the JBL 2441 graphs at approximately 10khz. A dip in the frequency response (T=0) rapidly turns into a non-decaying ridge along the time axis. This is a clear indication of a diaphragm break-up mode, and is audible when the 2441+waveguide is run full band (1-20kHz). For frequencies below 10kHz the performance is exemplary, and rivals (or perhaps even betters) the performance of the TAD with it's modern phase plug and exotic Beryllium diaphragm. (Note, the JBL 2441 has 1dB more sensitivity, than the TAD 2002, and can handle 9dB more power input-watts).

The fifth image in this post (and the last in this series) shows the ETF 1/3 octave smoothed (direct arrival weighted) frequency response, compared to the spatially averaged, white noise excitation, spectral estimate (reverberant field weighted). The frequency response is wide and smooth, but more importantly, the direct arrival response closely matches the reverberant field response, which is a direct consequence of employing the constant directivity oblate spheroid waveguides. This allows me to choose a single set of response EQ curves which are appropriate for both the on-axis direct arrival wave front, and also appropriate for the reverberant portion of the wave field in the room. The CD waveguides permit the generation of a smooth 360deg (solid angle) power response, when the speakers are placed in the corners of my listening room.
Jack Bouska

[Titanium Dome]

Jack

That's a plethora of information. Thank you.

You've clearly been working and thinking hard on these units.

I see some room treatments there. Comments?