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| Elliott Sound Products | Practical DIY Waveguides - Part 2 |
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Please Note: A number of people have told me that this series of articles contains errors. I do not dispute this, but I will point out that it is a contributed article, and I never had access to most of the references cited. Some formulae appear to be incorrect (or may lack clarity). I have not been able to contact the original author, so I don't have the resources to make corrections. The general principles are sound, and it's probable that anyone intending to build their own can do so without needing to make all the calculations shown.
I apologise for the inconvenience of presenting an 'incomplete' article, but I've decided that it's better to keep the article (with caveats) than to remove it. There is still some very useful information in the three articles, and (IMO) this outweighs the fact that it contains errors and omissions. I apologise in advance for any inconvenience this may cause, but I do hope that readers will find the information useful (at least in terms of general principles).
This is a combination of a waveguide and a 125mm (5 inch) mid woofer that typically constitutes the mid and upper range of a three way or a small satellite. The mid driver in this case is a nondescript unit salvaged from a Sharp discount store system.
In this we want to compensate for as much as possible of the 20mm acoustic offset between the drivers, match the cone drivers off axis output in the 3kHz region out to 45°, and get a centre distance between drivers of 114mm or less.
The mid driver has a 134mm frame diameter, meaning the tweeter centre can be no more than 47mm from its edge.
Figure 4 - On Axis, 15° ,30°, and 45° Off Axis Response of Mid Driver
From this, a 90° waveguide above 3kHz seems to be indicated. A two section unit has a width of 78mm and an overall depth of 12mm. Mounting the mid-driver on the baffle front allows around 16mm of offset compensation.
d = [ Tan ( a / 2 ) ( 0.7 w - t ) / 2 ] = 8.3mm
dt = d + ( w - 0.7w ) / 2r ( 1 - cos [ a / 2 ] ) = 12.2mm
r = [( w - 0.7w ) /2 ] / cos( a / 2 ) = 16.5mm
Figure 5 - 3kHz Waveguide Drawing
Two versions of this wave guide were made - one for use with the tweeter including the phase plate, and the other without the phase plate. The phase plate is the small device that can be seen suspended in front of the tweeter dome. It is used to correct a slight downward trend in the drivers amplitude response with increasing frequency, at the expense of introducing a few anomalies. Overall the driver has better performance without it but the on axis frequency response is not so flat.
The tweeter's front plate includes the phase plate and a vestigial 45 degree horn 3mm deep. With the phase plate the throat is 38mm in diameter, and without it the diameter is 34mm. The conical section is then 3mm longer, because the original front plate of the tweeter was modified by cutting out its centre with a 50mm hole saw.
Figure 6 - Unmounted Wave Guide & Waveguide With Mid Driver on 370 x 370mm Baffle
The cover plate you can see on the baffle covers up a hole that is used to mount the raw tweeter for initial frequency response and offset measurements.
Figure 7 - Waveguide & Mid Driver, (Green), On Axis with Phase Plate (Red), Phase Plate Removed (Blue)
The acoustic offset between the drivers is shown below ...
Figure 8 - Acoustic offset, Waveguide (Blue), Mid (Red), Input Reference (Black)
The above was measured with the microphone mid way between the driver centres. The top trace is the reference (electrical) amplifier output. The time delay between the start of the electrical signal and that from the microphone is due to microphone distance from the drivers. From this one can see that the acoustic offset between the two drivers is nearly completely cancelled.
When the tweeter has its phase plate removed, it has additional falling high frequency output. When this is equalised adequately it results in an overall efficiency a bit too low for the mid driver, so for this article the driver with phase plate was chosen. The tweeter was then equalised to flatten its output and give an efficiency compatible with the mid driver. The values are shown in the circuit below.
Figure 9 - Tweeter Equalisation Circuit
This is a simple equaliser, giving a 6dB/octave rise above the frequency determined by the values of C1 and the tweeter's impedance. The maximum rise is limited by R1, which is selected to ensure that the tweeter gets the correct level at frequencies below those limited by C1. As shown, the 3dB boost frequency is theoretically just under 20kHz, but this assumes the impedance is 8 ohms. It will be typically somewhat higher than this, so it is easier to obtain the needed values by experimentation and measurement than to try to use a maths formula.
Figure 10 - Waveguide on Axis With Above Equaliser
The crossover shown is designed for bi-amping, and only has high and low pass sections. The remaining section (low-mid, typically at around 300Hz) is done actively, as shown and described in Biamping - Not Quite Magic, but Close. The values shown are those that give the flattest on axis response.
Figure 11 - Mid to High Crossover, Incorporating Equaliser
The Zobel network (R3 and C4) ideally needs to be selected to suit the actual driver used, but as shown it should work well with a fairly wide range of drivers having similar (typical?) parameters. This network ensures that the midrange driver's inductance (or semi-inductance if you prefer) does not cause the load on the crossover filter to change as frequency increases.
Figure 12 - Mid with Crossover (Blue), Waveguide with Crossover (Green) & Combined Output (Red)
Figure 13 - On Axis (Black), 15° (Blue), 30° (Green) and 45° (Red) Off Axis, Both Drivers Plus Crossover
Figure 14 - Pulse Response of Drivers and Crossover On Axis
The pulse response of the two drivers and crossover shows good settling with little ringing.
Although the ability of a loudspeaker to reproduce accurate square waves is not found to be of much in importance by most research, it is however a property shown by speakers with acoustically aligned drivers. This is illustrated in Figure 15, measured on axis halfway between the driver centres. Figure 16 is the same, but 15° off axis.
Figure 15 - Squarewave Response, On Axis
Figure 16 - Squarewave Response, 15° Off Axis
The method of designing waveguides outlined allows DIY people to produce constant directivity characteristics in loudspeaker systems above some chosen frequency. They are also a simple way of compensating for acoustic offset as well as increasing excursion limited power handling and reducing distortion.
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