The Magical Number Seven, Plus Two

This DIY loudspeaker system experiments with multiple small wide-range transducers in a multiway configuration. The idea is to join good directional characteristics to coherence and power handling. Another goal is to improve timing by controlling the phase with FIR filters.

 


Wide range

The main speakers are based on seven E.J.Jordan JXR6 HD that I picked them up from a previous linear array system. Arranged as close together as possible, they divides in three groups having the same acoustic center:
- The driver in the middle of the baffle has an effective diameter of 5.6 cm. It is used as a tweeter.
- The up and down ones, wired in series, equivalent to a single 7.9 cm, are for the medium frequencies.
- The four side drivers, two series wired in parallel thus doubling the sound pressure, equivalent to a single 11.2 cm, take the low frequencies.
The whole can be viewed as one coaxial driver.

   

The 20 liter sealed enclosures are made of 30 cm PVC pipes filled with polyurethane foam and a polyester fleece. The build is simple: just a PVC KGU-socket connecting sleeve (which has rubber rings) and two KGM plugs (no glue). The baffle is covered with a 5 mm felt sheet to reduce diffraction and make the drivers flush. Internal standing waves start around 600 Hz.

The graphs below show the magnitude response and group delay measured with a log sweep from 16 to 24000 Hz taking 21.8 s.
The magnitude response stays inside 3 dB from 200 to 20000 Hz.
Group delay rise below 200 Hz reflects the low frequencies roll-off.


Average measure of the six groups of small drivers at 50 cm.


Group delay (blue), minimum group delay (gray), and excess group delay (black).


Subwoofers

The bass extension is provided by two 20 cm SB Acoustics SW26DAC76-4 per channel. With dual rigid aluminum cone and moderate moving mass, these lightweight (neodymium magnet) drivers can be used in rather small sealed enclosures.
The 21 liter enclosures were very easy to build: PVC connecting sleeve and two plugs. They are arranged up and down the main speakers in a way that the acoustic centers match.
Calculated Qtc=0.86 and F3=35 Hz. Internal standing waves start around 600 Hz, well away from the intended operating range.
The magnitude response is very smooth from 50 to 500 Hz.

 
Average measure of the four subwoofers at 5 cm.

 
Group delay (blue), minimum group delay (gray), and excess group delay (black).


Operating

Power is supplied by two Rotel RMB-1565 5-channel Class D amplifiers, one for each stereo channel.
Digital to analog conversion tasks an 8-channel miniDSP U-DAC8 improved by a linear power supply.

Instead of a dedicated DSP, the computer does all the filtering, equalization and phase linearization. I believe it's a better solution because the PC has all the power to compute the FIR filters for phase control. Replacing hardware DSP by computer software is just smarter and can be a lot more economical.
This tutorial may help configuring the PC: Windows PC as a FIR Audio Processor.

The computer is configured with Jonas Thedering's Equalizer APO. The E-APO configuration file looks like this (notice the equal-loudness correction, I don't know how I could live without it before):

# Equal-loudness under 66% volume
LoudnessCorrection: State 1 ReferenceLevel -6 ReferenceOffset 0 Attenuation 0.5
# Conditions
Device: USBStreamer - USBStreamer Multi-channels
Eval: subLevelL = 0
Eval: subLevelR = -1
Eval: lowLevel = -4.5
Eval: midLevel = `lowLevel-2`
Eval: highLevel = `lowLevel`
# Channels (7.1)
#   1   2   3   4   5   6   7   8
#   L   R   C   SUB RL  RR  SL  SR
Copy: 1=L+0.5*C 2=R+0.5*C 3=L+0.5*C 4=R+0.5*C 5=L+0.5*C 6=R+0.5*C 7=L+0.5*SUB 8=R+0.5*SUB
# Low
Channel: 1 2
Convolution: IR_low.wav
Preamp: `lowLevel-6` dB
# Mid
Channel: 3 4
Convolution: IR_mid.wav
Preamp: `midLevel` dB
# High
Channel: 5 6
Convolution: IR_high.wav
Preamp: `highLevel` dB
# Sub Left
Channel: 7
Convolution: IR_sub.wav
Preamp: `subLevelL` dB
# Sub Right
Channel: 8
Convolution: IR_sub.wav
Preamp: `subLevelR` dB

To generate the finite impulse response stereo WAV files I use Thomas Drugeon's rePhase loudspeaker phase linearization, EQ and filtering tool. With the following impulse settings, precision is 2 Hz up to 48 kHz. Including 10 ms for APO processing, total latency is 135 ms.


Crossover

The crossovers consist of linear-phase low/high-pass filters. Having read Application of Digital Crossover Filters to Pair-Wise Symmetric Multi-Way Loudspeakers, I first tried Horbach-Keele filters for control of beamwidth and polar shape. In a four way configuration, a big ratio of 4 is necessary. With the crossover frequencies at the musical notes "la" A2, A4 and A6, good subjective results were obtained in the fields of homogeneity and dispersion. However I felt some harshness presumably due to the difficulty to make clean impulse responses with such steep slopes.

I got a similar but smoother positive effect with the rePhase "Reject low" linear-phase filters. They are asymetrical, with a flat roll-off of the high frequencies and a complementary strong rejection of the low frequencies. The latter feature is valuable for crossing the small drivers with the subs. When I listen to an individual driver (or a group that forms a way), these are for me the best sounding filters. With two octave spans and 20 dB slopes, non-adjacent ways cross at -30 dB, which is low enough to resemble a cut-off.


Equalization

Low frequencies phase and magnitude responses are linearized by inverted second order filters (rePhase compensate mode). The following figures show the equalizations with (red) and without (blue) low/high-pass filters. You may copy the settings to clipboard and load them in rePhase.


rePhase settings for high frequencies.


rePhase settings for medium frequencies.


rePhase settings for low frequencies.


rePhase settings for subwoofers.


Results

For the measures, I used John Mulcahy's REW analysis software.
After equalization, the magnitude response extends from 23 to 18000 Hz without attenuation.


Average measure of the six group of small drivers at 50 cm.


Average measure of the four subwoofers at 5 cm.


Average measures of the small drivers at 50 cm and the subwoofers at 5 cm.


Four measures average of the left and right loudspeakers at the listening position.


Conclusion

The light aluminium transducers make a clear and detailed sound that engages the attention. Exploiting them in such a configuration is obviously beneficial to the homogenity of the musical rendering, so the promise of full spectrum coherence is clearly delivered. One most interesting feature is that the sonic colour remains consistent in a wide field of listening positions. One does not identify the sound from coming from a specific loudspeaker. This feels natural and relaxed at any time, leading to a stronger desire of music.
You guess that I'm very happy but what about the shortcomings? Except for the subwoofers, the cylindrical enclosures diffraction and resonnances are a weakness. After equalization, it's not obvious anymore but the system could be even better with properly designed baffles. This doesn't negate the benefits of the 7+2 drivers configuration and I would advise the curious hobbyist to give it a try.


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December 2018