Active filtering and loudspeakers for reproducing very low frequencies

This is a summary of a hobby project aimed at making use of the audio frequency range from 16 to 40 Hz. This part of the acoustic spectrum, although present in some recordings, is normally inaudible. Amplifying these frequencies to perceptible levels leads to a new musical experience which appeals to some bass fanatics...

The approach I have taken is sealed speaker design combined with an active crossover and a separate power amplifier. This way the mechanical construction of the speaker is straightforward, while the filtering in the crossover is rather involved.

Speaker designers often aim for a "flat response" down to a certain frequency. This is a practically meaningless specification, for several reasons: i) at the low end, room acoustics will always drastically alter the response, ii) the human ear rapidly becomes insensitive towards very low frequencies, iii) the sound will increasingly be felt, rather than heard, so that any comparison of low and high frequency ranges is subjective†.

Also the efficiency and power handling of any conventional speaker diminishes quickly for ultra low input. Therefore, what is required is a careful choice of energy distribution in a narrow range of frequencies. Custom active crossovers (i.e. frequency filters) provide the necessary flexibility to optimize the use of amplifier power (which is fairly cheap to buy nowadays).

After some early experimentation I decided to use a low pass/band pass in the form of a reconfigurable 10th order Sallen-Key circuit, hand-wired on a drilled board. The idea is to try out different filters to get power only in the desired part of the spectrum, without overloading the speakers by going too low. There is a very convenient online component calculator available at http://beis.de/Elektronik/Filter/Filter.html.

I also looked into digital realizations (DSP), since this allows changing filter characteristics and parameters easily. So far, however, a digital implementation is more expensive than analogue op amp circuits.

Results: The latest setup produces phenomenal depth, revealing content in recordings that is completely absent on normal systems. Although these fundamentals do not contribute to a musical sense of pitch, they add awe-inspiring momentum to both pop and classical music. See below for recordings featuring low bass and a spectral analysis.

At the moment I am using a PA power amp which delivers up to about 1000 watts rms to the sub. This is quite sufficient to work in combination with my main speakers (Linn Keilidh, about 50 watts rms), which really only need help significantly below 40 Hz, and the four Fane drivers seem to handle anything thrown at them at that power, including erroneous signals, plops etc.

 A possible concern with extreme low pass filtering often quoted is the resulting phase response or group delay. However, from listening to the results I found nothing wrong with the timing of the separated bass signal. It blends in seamlessly with the rest of the sound coming from the main speakers. In any case, all information on the attack or onset of transient material is contained in the upper bass range above 40 Hz.

†On the upside, this also means that the well-known rule that power has to be tenfold in order to achieve double the volume, will not hold anymore. Instead, double the power should also double the impact of infrasound. Also this implies a lower limit for frequencies to be reproduced: If a quarter wavelength is much larger than the dimensions of the listener's body the sound wave appears merely as a static change of pressure on the ears, and it is no longer felt. The only remaining effect is shaking furniture, which can easily be achieved without producing a sound wave, e.g. by using bass shakers. The chosen lower limit of 16 Hz for the subwoofer should therefore be low enough.


Further developments:

2004: The first digital prototype. It uses the AL3101 (executes 1k instructions between sampling instants), whose program resides on a separate EEPROM. After considerable efforts turning filter specs into assembler code the unit is now outperforming all analogue versions I ever built. It can easily be adapted to different kinds of music.

There were a few stumbling blocks in the practical implementation of the z transform filter. For example, in order to realize low corner frequencies with fixed point arithmetic it is necessary to reduce the sampling rate of the DSP to get coefficients in a usable range. Also I found out the hard way that writing into the input sample registers ($410, $411) doesn't work, and that the bit order in the EEPROM has to be the opposite of the one documented! But all was well in the end... As you would expect from a digital filter, the measured result matches the theoretical response precisely!

Initially I wanted to implement a real-time switch between different settings, but haven't done so yet, for two reasons: 1) I am very happy with one particular setting, which is basically a straight Butterworth low pass, 2) Experimenting with cutoff frequencies I realized that higher bass frequencies are great too but can produce structural damage in my fairly old house (plaster cracking up upstairs), so I'll stick with a low setting...

2005: Now there seems to be a big market for subwoofers, with dedicated drivers being made having huge xmax and power handling. These should be better suited to low frequencies than PA drivers. Maybe a new smaller cube with one 15" driver plus three passive radiators for bass reflex would be better. However, I am still sceptical about the robustness of these drivers (foam surrounds, up to ± 35 mm excursion) If anybody wants to let me test these please drop me a line.

2009: If anybody wants to acquire the complete and detailed instructions/code/schematics for building the digital system, these can be bought for a single-user fee. Alternatively, exclusive rights are available. Use the contact form on the parent website www.ztop.freeserve.co.uk.


Appendix 1: details of the speaker cabinet

Here's what I built for an infrasound subwoofer unit using 4 speakers in a cubical sealed enclosure.

The speakers are Fane Colossus 18" (600 W RMS, xmax = 7.2 mm):

  http://www.fane-acoustics.com/downloads/Fane_Colossus_18B600.pdf

These are relatively affordable and can handle a lot of power, although my guess is that any similar drivers will work as well (the more xmax and mechanical/electrical robustness the better). In the sealed enclosure the unit can be driven well below resonance frequency.

The enclosure has inside dimensions of 600 mm cubed. Minimum inside dimensions for the Fane drivers to fit in are 550 mm cubed. The drivers can be mounted from the outside on the front, left, right and top side of the cube. The remaining walls can be covered internally with damping material (e.g. rockwool slabs), although it probably makes no difference below 40 Hz. Also the enclosure doesn't have to be massively rigid for this frequency range.

I tried this first with one, then two and finally with four drivers in the same enclosure. (Note added in 2009: I'm still using the 4 driver system.)


Appendix 2: some theory concerning speakers and enclosures

The SPL (Sound Pressure Level) output of a speaker in a sealed enclosure at any given frequency depends only on the displacement x and the size of the speaker diaphragm. How you achieve this displacement is immaterial; so if electrical input power is sufficiently available, parameters such as resonance frequency and box volume can be ignored.
 
For example, put a 20Hz sine into an 18" driver in a sealed box and increase power until you reach xmax. Obviously, the resulting SPL depends only on xmax and in no way on the resonance frequency. It is the task of active filtering to produce the necessary displacement at the desired frequencies, and to suppress unwanted ones.

Of course more input power and steeper filter curves will be required to achieve this if the box is small or the driver has a higher resonance frequency. Specifically, in the frequency range below resonance the response in a sealed enclosure approaches a slope of 12 dB per octave towards 0 Hz, for the reasons below:

Frequency response of a sealed speaker

There is a myth in the art of speaker design stating that there is some kind of "poor coupling of the speaker diaphragm to the air" which determines the response at low frequencies. This is misleading, because the diaphragm actually doesn't experience any significant resistance from the outside air, and neither is this necessary to produce sound.

That is, the speaker diaphragm simply displaces air, without being impeded by it. In terms of air molecules, the sound pressure produced is proportional to air acceleration. Mathematically, acceleration is the second derivative of displacement. Therefore, translated into the frequency domain, this means a frequency response from diaphragm displacement to SPL which has a slope of +12 dB/octave.

In the extreme low frequency regime, the same applies to the response to electrical input, since the resistance of the diaphragm to displacement (caused by the cone suspension and compression of the enclosed internal air volume) is static, like that of a spring, and therefore the displacement is proportional to the driving force resulting from the applied electrical power.

The behaviour at high frequencies is different. There is only small excursion, so the spring-like restoring force is negligible. Instead, according to Newton's law, the driving force will now be proportional to diaphragm acceleration and therefore SPL itself. Therefore, in theory, the frequency response becomes flat for high frequencies, while the excursion of the diaphragm decreases with a slope of -12dB.

Note that this analysis is a simplification, because it does not include the dynamics of the motor system (complex impedance). However, away from resonance, it is not too far off to assume a static relationship between applied voltage (in units of dB) and the force produced by the voice coil. The point for sealed subwoofer applications is that there is always a basic response curve which is no worse than 12 dB/octave below resonance. Active equalization can then easily designed around this fact.

Comparison with other types of enclosure:

Vented systems, horns and transmission lines can in principle 1) produce more SPL than sealed enclosures, 2) require less power to get the same SPL, and 3) produce less harmonic distortion. This makes them preferable to sealed designs if a lower limit to the frequency response is acceptable. However, for the bass range concerned they will have to be unfeasibly large (even a quarter wavelength of a 20 Hz tone is 4 metres...) A sealed enclosure, on the other hand, does not require tuning and its dimensions can be kept smaller than a quarter wavelength.

Another effective solution (where possible) is to use building walls as an 'inverted enclosure' or 'infinite baffle'. For example, you can pump sound into the listening room using drivers whose rears face into an adjacent room or cellar below.

Also passive radiators are a good idea for sealed boxes. Their mass can be increased so that even in a small enclosure they will move with a phase shift with respect to the main driver. This "bass reflex" effect causes the passive radiators to contribute to the push of air from the main driver, rather than cancelling it.

Another issue is power dissipation: once you reach the kilowatt range drivers will heat up considerably under sustained input. Therefore sealed systems are probably restricted to home entertainment, which does not require full output for more than short periods at a time. However, one way to overcome this problem would be to install the drivers the other way with magnets outside the box.
Rotary woofer: Recently, a new type of subwoofer driver has been invented that is basically a fan running at constant speed, in which the angle of the blades is set by the input signal, thus producing air velocity proportional to the signal. This way, the response has a slope of only 6 dB/octave, instead of the usual 12 dB/octave for air displacement type drivers. Since there is no significant restoring force on the blades, the rotary woofer also requires far less power than normal drivers. It works up to a certain frequency - apparently about 25 Hz - see www.rotarywoofer.com. Maybe its use in the reproduction of music will be limited, but this system will probably be the ultimate answer for enthusiasts seeking true infrasound below 20 Hz.
 


Appendix 3:  some recordings with low frequency content

Pop:

Phil Collins - True Colours

Michael Jackson  - Earth Song

Frank Zappa - Yo' Mama

BAP - Jupp

Nena - Wunder geschehen (new version)

 Marillion - Blind Curve

 Madonna - Oh Father

Celine Dion - All by myself; My Heart Will Go On

Earth, Wind & Fire - Let's groove (brilliant bass drum...)

Lipps Inc. - Funky Town

Donald Fagen - Tomorrow's Girls

Van Halen - Unchained

 Eurythmics - Angel

 Alanis Morisette - Hand in my pocket

Sanctuary Rig - Dawn of a new day (ii)

Genesis - Squonk

Yes - State of Play

Mike and the Mechanics - Silent Running



Classical/Organ:

Daniel Roth - "Improvisations", Motette CD 10751, Tracks 6, 7, 9

Sydney Opera House Organ Extravaganza, ABC Classics 465 649-2

Naji Hakim - "Canticum", EMI Classics 7243 5 72272 2 3, Tracks 5, 8

Jean Guillou - "The great organ of St. Eustache, Paris", Dorian DOR-90134

Catharine Crozier - "Organ works by Ned Rorem",  Delos DE 3076, Tracks 11, 16

Kevin Bowyer - "Organ Xplosion", Vol. 1, NPC007 or FRC8103, Tracks 1, 4, 11

Erich Kunzel - "Ein Straussfest", Telarc CD 80098, Track 12 (no bass boost needed for this disk...)



Frequency analysis, each showing the best bit in the song:


 
  


Suggested subwoofer crossover for the above material:


 

 
(Stand 1.10.9)