Thursday, June 18, 2009

Filters go bust — time to renew

After a lengthy hiatus — basically I took a break from doing audio and DIY stuff — I've recently (about a week before writing this) finished building a new active filter circuit.

It is soldered on a PCB and replaces an older unit that I'd built up on a veroboard. The veroboard served us well for about 5 years, but finally konked out when the jungle of wire-wrap started breaking and a thick layer of dust made the filters unstable.

Lesson learnt: always remember to put your project in a protective case to keep out the dust and miscellaneous falling objects! Don't just remember it - do it. I put mine on an antistatic sponge with good intentions, but kept procrastinating until it was too late. A consequence of my laziness was that the tweeters were destroyed by loud "clicks" and "pops" towards the end of the filter board's life. This was the ideal opportunity for some refurbishment!

I may have written about the old system before, but just recapping...

The old system:

Speakers:
Accuton C^2 94 midwoofers (18cm),
C^2 23 tweeters (32mm),
Jaycar 12" carbon fibre subwoofer; 4ohm.

Boxes:
15L satellites made from 20mm bubinga (an extremely dense and hard Australian hardwood - I managed to stall a 1200W circular saw while cutting it!!). They needed plenty of pillow stuffing and glued styrofoam to tame the resonances.
A 60L box made with 25mm marine ply and a modest amount of stuffing.

Filters:
From memory...
3rd order high-pass filters at approx 2.7kHz with a low Q (somewhere between Bessel and Butterworth).
The lowpass had a much higher Q to compensate for the apparent "droop" in the C94's sensitivity around 2kHz to 4kHz and to provide a sharper roll-off so that it could attenuate the speaker's 5kHz resonance more effectively.
The midwoofer also had 4dB of baffle-step compensation below around 700Hz.
The subwoofer had a 7th order filter with a somewhat "hacked" response, vaguely resembling a 130Hz Gaussian filter with 12dB of gradual roll-off before undergoing a secondary cut-off at higher frequencies (according to my Multisim simulations anyway). I later added a 6dB step filter to partly compensate for the subwoofer's roll-off below approx 50Hz.

The new system:
Same subwoofer,
Same midwoofers,
New C44-8 high-midrange speakers. These were originally meant for a different system that I never got around to building. Plus they had the same sized frame. In they went!

I added zobel networks for the midwoofers and tweeters. While they probably don't make *much* difference, theoretically, they should improve the amplifier's damping factor at high frequencies. What usually seems to happen is that the speaker produces air resonances inside the box (to be expected), but that stored energy is then turned into electrical signals by the speaker (it is a transducer, after all). Since the amplifier is a strong voltage source, it produces large currents to maintain the correct voltages at its terminals. Thus, there is the potential for unwanted ringing and IM distortion. The zobel networks are basically snubbers that help to reduce these sorts of oscillations.

Filters:
The satellites use linear phase filters with 0.05 degree equiripple and a 2.5kHz cut-off for both low pass and high pass. The calculations for the high pass filter take into account the 1-pole high-pass effect of the DC-blocking capacitors on the amplifier's output.

I chose the "linear phase" filter type in an attempt to reduce the slightly harsh sound of the previous design, which I now attribute to ringing due to high Q factors. People often seem to use Linkwitz Riley filters for all occasions but I saw that option as overkill. Given the number of poles, I simply chose a filter slope that produced negligible overshoot in simulations.

Similarly, I saw the importance of preventing audible ringing from the subwoofer filter. Since it operates at a range where people's hearing is not very sensitive, any "out-of-range" ringing around 100Hz~200Hz may actually be more noticeable than the desired signal below 100Hz! After carefully looking at some different options on TINA (a Texas Instruments sim program), I chose the same Linear Phase 0.05deg type but with 7 poles.

The midwoofers now have adjustable notch filters, which are currently tuned to 4.5kHz, approx 9dB' attenuation and Q ~=12. This seems to match the peak in the C94s' datasheet. The notches use a "simulated inductor" approach, followed by a low pass RC filter at 10kHz to reduce their self-noise.

I've already made a couple of important mods — photos and an update should be coming soon!

Thursday, July 12, 2007

A simple test for comparing the acoustic properties of potential box materials

A common question that speaker DIYers have is: what materials should I use for building a speaker box? MDF (medium density fibre board) is one very popular answer. Plywood is another option. Then there's hardwood, glass, concrete – just about anything with a good combination of high stiffness, high density, and rapid absorption of high frequency kinetic energy.

I once experimented with polypropylene and that seemed very promising. I found some published mechanical properties of a variety of plastics and polypropylene was a bit unusual as it had a very low yield strength relative to its ultimate tensile strength. That suggested that it would readily absorb mechanical vibrations and convert the energy into heat, which is exactly what I want a speaker box to do. The classic "tap test" produced a dull thud with no discernable ringing, but that's hardly comprehensive.

So, what to use?

Well, how about a music box? It's perfect! It is:

  • Small and very portable,
  • Reproduces a variety of frequencies upwards of around 1kHz, with lots of harmonic content,
  • Does not require electricity.

Testing a material is as simple as pressing the music box against it and seeing how much of a difference it makes to the sound. Usually the difference is huge – the sound becomes dramatically louder. The apparent tone also varies depending on the size and shape of say, a block of wood.

Generally speaking, a suitable material for building the "box" part of a loudspeaker should be as acoustically inert as possible. We only want the speaker to produce sound, without various box panels vibrating and rattling in consonance.

If you'd like to recommend a good material(s) for building loudspeaker boxes, feel free to share your ideas here!

Monday, June 18, 2007

Mono subwoofer versus stereo woofers

This topic has been done lots of times by different people, but I think it deserves to be revisited as there are a couple of things that often seem to be overlooked.

SPL, maximum loudness and whatnot...

This angle is usually pretty well covered. If you want lots of bass, then you need to work out how much air a speaker can move. As a rough indication, multiply the surface area by the maximum linear displacement, usually referred to as Xmax. However, exactly what constitutes "linear" is debatable. One person's 10mm Xmax might be another's 2mm, depending on the amount of distortion they're willing to accept.

Here's a hypothetical example comparing the displacement volume of dual 25cm (10") woofers with a single 30cm (12") woofer:

A modest 0.5cm Xmax * 330cm2 * 2 woofers = 330cm3

0.7cm * 540cm2 * 1 woofer = 378cm3

However, as they say, "actual performance may vary". There are numerous other criteria to consider so it'll be far more accurate to do a simulation, especially since the peak displacement levels appear to be pretty similar at first glance.

Down-mixing a stereo signal to mono

This is where it gets tricky. Most music sources consist of more than just one channel, so if you're building an active crossover, or at least some kind of gain control, and you want to produce a mono signal for a subwoofer then you're likely to encounter a few unexpected issues. Contrary to popular belief, it's not as simple as taking a stereo signal (from a CD source or whatever) and summing the amplitudes. Why not adjust the gain by 0.707 so that the output powers are summed? Well that doesn't work either.

Well, what exactly is the problem? Take for example a pair of bass speakers placed 1.5m apart:

Initially only one of the speakers is plugged in, then the second one is connected and fed exactly the same signal. What happens then?

Well it depends on the frequency. At some frequencies the average acoustic power delivered to the room will double, while at extremely low frequencies the amplitude will be doubled (almost). The lowest frequency that can undergo strong cancellation is approximately 340/1.5/2 = 113.3Hz, where the 1.5m distance corresponds to a 180 degree phase difference. Below that frequency, the speakers will begin to undergo constructive interference that exceeds the average power doubling that occurs at higher frequencies.

This means that a pair of woofers are acoustically coupled together below a certain corner frequency, which produces a natural 3dB bass boost. The corner frequency is inversely proportional to the physical distance between the woofers. However, a mono subwoofer doesn't have that effect at all.

While there is no right or wrong answer, mono subwoofers aren't hot-swappable with large stereo woofers in full-range loudspeakers. Equalization and level-matching in active crossovers can be a tricky issue that is influenced by the satellite placement.

Thursday, June 7, 2007

New loudspeaker plans... Part B

In an earlier post I started writing up some plans for a loudspeaker that I want to build...

To summarize, it's a 3-way design with a somewhat classic choice of driver sizes: 25cm (10") woofer for the bass, 12cm (4.5") midrange, and a fairly standard 25mm (1") dome tweeter. They will have sealed enclosures so I won't have to deal with issues like temperamental tuning and a peaky bass response. For the woofer I looked at the idea of "pressure loading" (or at least, that's what I'm calling it), whereby the box is small enough so that air resonances only occur at frequencies outside of the speaker's operating range.

The midrange

Before continuing with the box design for the bass, I need to start thinking about what to do for the midrange speaker. Firstly, I have a feeling that a pressure-loaded box won't be a good idea. Given an estimated cut-off frequency of 3~4kHz, the half-wavelength will be around 3~5cm, which is tiny! The air volume behind the midrange speaker would have to be less than one litre, so let's do some quick estimates and go from there:

Half wavelength at 5kHz:

λ/2 = 340/5000/2 = 34mm

Given a cone area of 50cm2 (I'm using the Seas L12RCY/P for this example) the effective radius is:

r = √(50/π) = 40mm

A cylindrical volume that is slightly wider than the cone would be approximately:

[ π*(34mm + 40mm)2 ]*34mm = 584914mm3 = 584.9cm3 = 0.58L

According to Subwoofer Simulator, when I specify 0.58L as the box volume for a Seas L12RCY/P, the system forms a mechanical high-pass filter with a cut-off at approximately 150Hz. That is decidedly annoying because it's fairly close to the 200~300Hz cut-off that I want. It means that if I want to electrically filter out some of the bass, then the combined filter response will have to be at least 3rd-order and its accuracy will be highly dependent on mechanical and environmental factors such as the speed of sound on a particular day.

Another thing that I'm not sure about is: what happens to the cone when it's cushioned by a relatively small pocket of air? Maybe it will flex and resonate at substantially lower frequencies than predicted in tests that use large air volumes? Maybe the air suspension will be sufficiently affected at low frequencies that it cause inter-modulation distortion when combined with other frequencies?

I think that the midrange needs a relatively large box instead, together with a highly effective means of absorbing resonances.

Anechoic wedges

What better way to describe my idea than to draw it?

What I originally had in mind was a sort of "reverse horn" where the sound waves gradually become more and more concentrated as they radiate away from the speaker. Eventually the energy becomes so concentrated that the surrounding enclosure turns into a heat sink. That idea evolved from a cumbersome spiral-shaped horn into an array of miniature wedges – it's basically still the same thing but in a different format.

Part C: enclosure materials, crossovers, and cohesion between bass and midrange.

Tuesday, June 5, 2007

New loudspeaker in the works... Part A

Well, I'm designing a new pair of loudspeakers. Basically, they'll be a pair of traditional 3-way loudspeakers that use 25cm (10") woofers housed in sealed boxes, 12cm (4.5") midrange speakers, and 25mm dome tweeters. (The original web page that I started about them can be found here.)

I don't intend to build these loudspeakers any earlier than 2008 – partly because I'm a great procrastinator and partly because I don't have anywhere to put them at the moment. So in the meantime I can do the fun part: explore various options, possibilities, and do calculations for the design...



I chose a classic 3-way style because:

  1. It can use relatively benign crossover frequencies around 200~300Hz and 4~5kHz.
  2. The ratio of driver sizes is quite evenly distributed, allowing a predictable off-axis response.
  3. From past experience, a 25cm (10 inch) woofer in a sealed box would have quite well-balanced performance considering the effects of room gain at low frequencies and its ability to reproduce frequencies up to 200~300Hz.
  4. Unlike many other designs such as 2-way and quasi 3-way loudspeakers with large midrange drivers and low crossover points, none of the drivers are pushed to their limits. This means lower distortion and higher power handling.
So if all goes well, the design might even turn out quite elegant due to the lack of any glaring weak points.

Drivers

As a starting point, a suitable woofer may be a Seas L26RFX/P. Midrange units: Seas L12RCY/P, Excel W12CY001, Visaton AL 130 8ohm, or Eton 4-300/25 Hex. The tweeters may be chosen at a later stage.

Box design

Tweeters

Practically all dome tweeters are sold with sealed chambers already built in – either behind the magnet or as a small pocket of air directly behind the dome – so designing a box for them is almost a non-issue. There are some things to remember however: mechanical vibrations and diffraction of the wave-front around nearby box corners. Those effects may produce resonances or adversely affect the off-axis response.

Woofers

The enclosures will be constructed from high grade plywood. One option that I'm interested in is the use of small pressure-loaded boxes.

Pressure-loaded, high Q enclosures:

Although the unequalized bass response may be less than optimal, there could also be several advantages over a classic design where the Qtc is tuned to 0.707:
  • The idea is that if the box is sufficiently small, there won't be any resonant air modes throughout its entire operating range.
  • A small box will be less reliant on the linearity of the speaker's spider and surround – the relatively high spring constant of the air will dominate.
  • Extra space and convenience.
One way to work out whether or not such a design is feasible is to decide what the minimum resonant frequency should be and to calculate corresponding dimensions from that. For example, let's say that the lowest allowable resonant frequency is 500Hz. From that we can work out the wavelength, from the wavelength we can work out the length of a resonant column of air and therefore the maximum dimensions of a box.

Given a sound velocity of approximately 340m/s (it varies), the wavelength is:

λ = 340 / 500 = 0.68m

But, what fraction of the wavelength is relevant? A quarter? Half? A whole wavelength? And why? This is where a bit of nodal analysis comes in handy. (A refresher: nodes are regions of minimum velocity and maximum pressure oscillation, while anti-nodes are regions of maximum displacement and minimum pressure variation). A loudspeaker can be likened to a musical instrument where the speaker driver is like a resonator or an actuator of some sort, such as a reed, while the box forms a resonant column of air, similar to a stopped organ pipe.


My initial line of thinking was that there'll be an audible resonance when the length of an air column is one quarter of a wavelength. However, I looked around on the web and people's measurements suggested that the system would behave as though both ends are fixed, not just one end. At first I wasn't quite sure why that was the case.

I tried to visualize in my mind what happens and then I realised that when the speaker cone is at an anti-node, it directly controls the displacement of the air. It's not really a resonance at all if the cone directly controls the region of maximum displacement.

When it's at a node, there is no such control. It means that there's at least one anti-node floating inside the box, which could reach an enormous displacement amplitude if there's very little damping. The node next to the speaker cone therefore produces a large opposing force and that is what I want to avoid.

For a 500Hz frequency limit, the maximum allowable length is therefore:

L = λ/2 = 0.34m

Rough estimate for a cube shaped box:

V = 3.4dm3 = 39.3L

A slightly more accurate estimate would be to calculate the distance from the centre of one box face (where the speaker is positioned) to a corner on the opposite side:

B = √(A2/2)
C = √(A2/2 + A2) = √(1.5*A2) = 0.34m
A = √(0.342/1.5) = 0.278m

V = 2.78dm3 = 21.4L

The resulting volume is a bit on the small side, however a cube isn't exactly the most efficient possible shape. How about a hemisphere? Using the formula for the volume of a sphere:

V = 4/3πr3

where r = 0.34m or 3.4dm, the volume of a hemisphere is:

Vh = 2/3πr3 = 82.3L

Obviously the calculations are just estimates that ignore lots of real-life variables, but they're accurate enough to give some ballpark values that could be used in a process of elimination. A box somewhere between 20L and 80L, with no resonances up to 500Hz certainly sounds appealing. The trick will be to devise an effective shape that doesn't clash with other requirements such as minimizing the distance between the woofer and the midrange driver.

Check back soon for Part B where I'll look at some other options: over-sized boxes, anechoic wedges, "reverse horns" and similar possibilities for the midrange enclosures.

Sunday, May 27, 2007

Simulation programs

Loudspeaker simulation/modelling programs are indispensable! One of the most important pieces of advice I could possibly give regarding loudspeaker simulators is: get one!

Calculators and formulae for working out box volumes are better than nothing, but they don't give you a 'feel' for what happens when you alter various parameters. For example: a Javascript based calculator might recommend an "optimum" box volume of 50L for a certain speaker, whereas a simulator might suggest that there's very little practical difference in the performance between 50L and 35L.

I've found programs such as Subwoofer Simulator and WinISD to be extremely useful, and not just for building a loudspeaker and getting the project "over and done with" more quickly. They help to create a better understanding of the mechanisms involved so you can make better decisions, choose more appropriate speakers for the job, consider variables that you might have overlooked and more. How does the cone excursion vary according to frequency? What's the maximum power that can be applied before the Xmax is exceeded?

Saturday, May 26, 2007

Acoustic labyrinth

As the name implies, a labyrinth design is intended to channel the speaker's back-wave through a series of tunnels/tubes/openings and so-forth (like a labyrinth) until practically all of the acoustic energy is absorbed. Very little sound is reflected back to the speaker and thus the system behaves like an infinite baffle.

It sounds nice in theory, but it's usually far from ideal in practice. At best, a knowledge of horn design principles can be used to design a box that absorbs energy in an effective manner. For example, one practical approach might be a spiral shaped column of air (think: sea-shell design). In the same way that horn loading increases a loudspeaker's efficiency, the same principle can be used to concentrate acoustic energy onto damping materials, thus making them more effective at absorbing energy. Anechoic chambers rely on this principle by using thin triangular wedges on the interior walls.