SpeakerBuilding.com - Toccata Grande, Part 1

Toccata Grande, Part 1

By Lars Mytting
20 Jan 1998

Printed from SpeakerBuilding.com, 09 Sep 2010 05:52
URL: http:///content/diy/1011/

Preface

Featuring:

Wood-finish and sand-damping in one step
T-line design
94 dB efficiency
Sturdy driver support
Baffle technique reducing diffraction and improving transients
Cosy talk on sensitivity, driver area, compression, cabinet vibration and other topics
A few disappointments on the way

Summer had been good for them, but the warm July days had passed like a swift river. And, yes... there it came again. Another autumn, another darkness, another set of his wild speaker ideas. She recognised the signs... weird cabinet sketches found on the toilet floor, a huge bill for polypropylene capacitors left in the car, strange technical conversations with his friends. And then she finds him alone in the dark with his computer, his face lit up only up by the rude, yellow colours from the Calsod menu.

Patiently, she starts preparing herself for another autumn without his support. Loneliness, coldness, it would all come now, growing worse for each evening he spends in the basement with that obscure work.

And then that thing. That nasty, huge thing living in the basement... growing bigger and meaner week by week... growing on until it rises and enforces into the living-room around Christmas. A Christmas she hoped that for once would be a clean, humble event with sleds and happy parents. Not this year either. The thing will rise from the basement... his latest, weirdest speaker creation, bigger and uglier and meaner than ever.

Day one considerations

Family life can be very demanding for speaker building. And speaker building can be very demanding for family life. This is one of the reasons why this project took me so long. I wanted to make something experimental, and that requires a lot more time than building just another speaker using well-known techniques. Life is full of two-way speakers, so the aim was to make something else; a large speaker that traded some sound qualities while gaining on other.

This project was never meant to be a easy-assembly kit that would satisfy most tastes. It was intended as a area where I could try out several ideas. The name of the speaker reflects this. "Toccata" was originally the term for a stormy, experimental piece of music used by organ players when trying a new instrument. I can also promise that any organ toccata will be quite fun on the final speaker. "Grande" is simply thrown in to reflect the physical dimensions.

But I must warn the reader that the labour and complexity does not fully justify the final sound quality (my Nightingale speakers perform overall better) -- but the techniques and tricks here can be used in regular speakers with great benefit.

Design goal

When designing a speaker, it is a good idea to start with deciding what compromises the project must be subject to, and define what technical solutions these compromises will dictate. The goal for this speaker was stripped to one single feature, namely good transient response. Another word for it may be "dynamic contrast". A transient is a sound of short duration, and good transient response can only be achieved if the speaker can deliver its output fast and clean, without smearing the original sound, and be completely silent immediately after.

I think this is a crucial quality of a speaker, because the transients embodies a lot of the nerve and realism in sound reproduction. I like systems that really can reproduce the sharp smack from a snare drum, the drama and excitement from heavy notes on a piano, the attack of the human voice.

But no quality in a speaker comes alone. When you improve one thing in your speakers, it is rarely so that just one defined part of the sound gets better. If you can improve the midrange linearity, you will experience that both deep bass notes and small cymbals sound better. Often, we associate these instruments to "belong" to the bass driver and the tweeter, but there is no such analogy in real life. All instruments contain notes which extend far above and beneath their "average" frequency.

Likewise, if you get good transient response, you have also managed the speaker to have low compression, because the drivers must yield the full amount of SPL needed to reproduce the input signal, and a good cabinet, because wall resonances will smear the sound of a otherwise "clean" driver.

No compression -- no depression

Low compression is vital for good transient response. Put simply, compression starts at the point when the input and output of a driver no longer are linear. If the signal corresponds to a output of 99 dB and the speaker output is only 98 dB, compression has occurred. This may happen because the thermal, mechanical or electrical limits of the driver is exceeded.

A general rule is that compression increases greatly with cone excursion. Also, drivers with large voice coil diameters usually have less compression than standard drivers. With standard drivers, compression may occur at low levels, maybe just 3-4 watt. This is something that most speaker driver manufacturers does not like to talk about; but you can have a meaningful discussion of it with professional PA driver manufacturers like ATC and JBL. Also, the happy band of horn speaker enthusiasts is usually able to provide details on this topic. Drivers with low compression gives huge benefit for the dynamic capabilities of a speaker. It will sound more open and free, and the soundstage will be more relaxed at all sound levels -- but the difference will be most noticeable when playing loud.

Less excursion, please

The way to reduce compression with standard drivers is to reduce their amount of work. Their work corresponds to the sound level, which corresponds to the quantity of air being moved, which corresponds to the product of cone area and excursion. So if we want to reduce compression, we should increase the cone area.

Doubling the cone area will reduce excursion to the half [1]. Four-doubling it will reduce it to 1/4. A average 2-way speaker with one 6.5" driver usually has 120 cm2 cone area. If we are using four 6.5" drivers, or a single driver with a cone area of 480 cm2 (like a 12"), excursion will be 1/4 while achieving the same sound level.

It is especially advisable to have this in mind when choosing crossover frequency, because excursion will be four-doubled for each octave. A 25 mm tweeter must move 0.1 cm3 of air to give 90 dB at 2000 Hz, requiring a excursion of 0.2 mm p-p. For the same SPL at 1000 Hz it must move 0.4 cm3 of air, resulting in excursion of 0.8 mm p-p. For 100 dB the necessary excursion is 0.8 mm at 2000 Hz and 3.2 mm (total damage!) at 1000 Hz.

Common sense and sensitivity

Another natural goal is high sensitivity. Sensitivity corresponds to the sound level you get for the power that is fed into the speaker. Normally, this is measured by the sound level at one metre for 1 watt input [2]. The average 6.5" speaker we mentioned earlier usually has a sensitivity of 85-88 dB. (Very often, manufacturers cheat with the specifications, so that the real sensitivity may be as much as 4-5 dB less than claimed!)

When sensitivity is improved by 3 dB, the output needed from the amplifier is halved. If a 82 dB speaker needs 30 watt to reproduce a certain music signal, a 85 dB speaker will require only 15 watt. And if we could increase sensitivity to 91 dB; the amplifier would just have to deliver 3.75 watt for the same sound level.

The less demand you can put on the amplifier, the better. The amp will use less of its power reserves, making it easier to deliver all the needed output; another step towards our goal of good transient response.

The following example explores the benefits of high sensitivity and low excursion: Say that we want to achieve 100 dB SPL at 150 Hz, corresponding to a air displacement volume of 70 cm3. This is how two typical drivers will manage this: (Sd corresponds to cone area).

Driver 1: 5", Sd 80 cm2, sensitivity 85 dB/1w. The cone must travel 9 mm p-p, and the amp must deliver 32 watt.
Driver 2: 10", Sd 350 cm2, sensitivity 94 dB/1w. The cone must travel 2.1 mm p-p, and the amp must deliver 4 watt.
With driver 2, the amp will have to deliver just 1/8 of the output needed for driver 1, and the driver excursion is only 1/4.

Is it just to load up as many drivers as the baffle can hold then? Sorry, no. Performance of large drivers decrease in the higher frequencies, with poorer radiation and more cone breakup. Big cones require big cabinets. Using multiple small drivers may introduce problems with the radiation pattern. The best midranges are often 4" or 5" big. So ultimately, the final sound quality of a speaker is not only determined by whether the drivers are large or small.

A fistful of drivers

But I guess the previous doctrine would make it strange of me to choose a single 4.5" for this project. The heart of the Toccata speaker is a 10" driver from Seas, whose specifications more or less dictated the rest of the system. Since the goal is to achieve something more than just a slight improvement in sensitivity, I decided to try using two of these woofers.

The star of this show is called Seas CA25FEY/DD, and the drivers have (after regular standards) a giant magnet system. The paper cone is only 26 g, very light for a 10". This gives a average sensitivity of 95 dB for 1 watt input, and the lightweight cone promises good for the lower midrange quality. It is possible to cross the driver in the region of 300-500 Hz without muddling the midrange too much.

But: The big magnet and the light cone gives the driver a low Qts of 0.27, and the other T/S parameters makes it difficult to get deep bass response in both closed and vented boxes. In a standard regular bass reflex (QB3), the -3 dB point is around 50 Hz. This is not too satisfying, since the resonance frequency of the driver is a fair 31 Hz.

The solution I wanted to try was a transmission line enclosure. The low end response of a t-line depends on the resonance frequency of the driver, and the parameters that causes the high rolloff in bass reflex cabinets (Vas and Qts) are less important in a t-line [3]. T-lines also have very flat impedance in the bass area, making a less demanding load for the amplifier -- another nice match with our goal. Neither had I built a t-line before, adding both risk and scientific value to the project.

Seas was so kind to supply me with drivers for the project, and the other drivers are also from their line. For midrange, I chose Seas MT14RCY (H804). This is a 5" midrange driver with TPX cone (a clear plastic material). Its average sensitivity is 89 dB. TPX drivers have a very "free, open and airy" sound quality, if you accept such a unscientific description of low energy storage. A very similar TPX driver is also used with great success in the famous ProAc Response 1S speaker.

For tweeter; I went for the Seas T25. This little sweetheart is full of goodies. Double magnet, silver wire in the voice coil, dome of Seas' best fabric, heavy frame with 6 mm frontplate. Earlier tests have proven it to sound very relaxed and calm while yielding great detail -- again something that makes it a good player on the Toccata Team.

As I should use two midrange drivers, I decided to place them in a MTM-configuration (the tweeter between the midranges). This is sometimes called a d'Appolito configuration, but to achieve a "true d'Appolito" requires a very low crossover frequency. Choosing MTM was a slightly random decision. With a "normal" crossover frequency, you can get a somewhat improved vertical dispersion, but you can also end up with a overall poor radiation pattern. MTM is very popular nowadays, but remember that it is not necessary to use MTM just because you have two midranges! You may be just as good or better served with the mids together. (I guess this would be called MMT or TMM). Many great speakers, like B&W 800, have the drivers placed in MMT.

How many Bel?

But: How can we use midranges with lower sensitivity than the woofers!? The two woofers have a total sensitivity of 98 dB, don't they?

Well, yes, but that is their average sensitivity. Remember that sensitivity figures for drivers are taken as an average, and the exact sensitivity may vary greatly with frequency. The CA25FEY drivers have a steeply rising response, and at 2000 Hz they have a sensitivity of 100 dB! But where we plan to use them -- up to 3-400 Hz, they are at a more normal level of ca. 92 dB pr. driver.

Also, remember that no crossover cuts each driver completely silent after the crossover frequency. If we make a low-order crossover that rolls the woofer of gently -- or if it has significantly higher sensitivity -- it will fill in the otherwise missing output of the midrange.

So -- what do we have? Two 10" and two 5". That gives a total Sd of 910cm2. Later measurements proved the sensitivity to be satisfying, circa 94 dB/1w (or 9,4 Bel -- decibel is one tenth of a Bel, named after Alexander Graham Bell, inventor of the telephone).

Let us compare this with the industry standard 6.5" speaker of 8.6 Bel sensitivity and Sd of 120 cm2. When 120 cm2 is to move 1.5 mm at a given frequency, 910cm2 needs to move just 0.2 mm, because the cone area is 7.6 times bigger [4]. A amp connected to the 6.5" must deliver 10 watt to achieve the reference SPL, but the 9.4 Bel speaker gives the same output with only 1.25 watt invested.

Thus, the Toccata works 7.6 timer easier than the single 6.5", and the amp connected will work 3 times easier.

Modelling the transmission line

As mentioned, this is my first t-line, so you should look elsewhere for expert advice. But I will try to describe some basic principles.

A t-line cabinet consists of a long tunnel, which (ideally) works so that everything except the low frequencies are absorbed in the line. The common design criteria for a t-line are as follows:

1. The length of the line should be 1/4 of the wavelength of the resonance frequency of the driver.

The wavelength of sound is be found by this formula: 343/f

f is the frequency, and 343 is the speed of sound in metres pr. second. If we want to tune a such "quarter wavelength"-cabinet to 40 Hz, the line length should be:

343/40 = 8.575
8.575/4 = 2.14 m
For 50 Hz, the length is ca. 1.7 m, for 25 Hz ca. 3.4 m.

2. The line should be tapered so that it is more narrow at the end. The area at the end should be the same as the Sd of the driver. The area at the beginning of the line should be from 1.25 to 2.5 times the Sd. Many use a chamber behind the driver.

3. Dickason [5] describes the effect of the taperings like this: "Low ratios (around 1.25) give a lean and tight sound quality. Past 1.4-1.5, the emphasis is placed more on the low bass area, and a better sounding midbass".

4. The line is usually folded, so that reasonable dimensions can be achieved.

5. The line is damped with wool or similar material. Density is usually highest at the beginning of the line, with progressively less material towards the end. The damping is highly a question on trial, error and measurement.

6. The impedance of a t-line will be quite flat, with very damped resonance peaks.

7. The frequency response of many t-lines have a lift in the 50-100 Hz region, and a dip in the 150-200 Hz region.

Examples of T-line tuning

Fig. 2. Unfolded T-line model

Example 1:

One 8" driver (Sd 235 cm2), tapering ratio 1.3, tuned to 50 Hz:
a: 305 cm2
b: 1,7 m
c: 235 cm2

Example 2:

One 15" driver (Sd 800 cm2), tapering ratio 2.2, tuned to 25 Hz:
a: 1760 cm2
b: 3,4 m
c: 800 cm2

From example 2 we see that large drivers are quite size-hungry on cabinets, and that the tuning frequency will have great domestic impact.

The Toccata cabinet is tuned to a ratio of 1.5 for a single 10", and the length to 40 Hz. With two drivers, the line is to narrow to correspond with theory, but I did this anyway to add scientific value. To make the line easy to build, the line has just two folds. I found that the Toccata performed best with quite a lot damping material. I guess that this is because the line is so narrow. The t-line tradition prescribes pure wool for damping. I used a combination of wool and a house insulation material called Rockwool of 3 cm thickness.

My opinion is that damping material should sit firmly in place in the cabinet. If not, it may be moved by the internal air pressure, soaking bass energy. Therefore, I stapled the Rockwool to the walls, and filled the space left open with wool. I intensely suggest that you keep one side of the speaker detachable, so that you can add or remove damping material easily. When you are satisfied with the tuning, fasten the side permanently.

Rattle and hum: Resonances

Now, how on Earth do we make a cabinet that suits our monster? The cabinet will be quite big, 125x46x32 cm in total. With this size, wall resonances becomes a factor we must deal seriously with. All materials that vibrate produces sound waves. It is very fair to consider the cabinet walls as a second speaker cone. Since we have dealt a lot with decibels and cone areas the last minutes, let us investigate the cabinet walls with the same methods.

The final Toccata cabinet has two walls of 125x46 cm and a rear wall of 125x32 cm. This gives the astonishing area of 15 500 cm2 -- sixteen times larger than the drivers; equal to twenty 15" drivers! If this area (15 500 cm2) moves 0,0625 mm p-p, they will generate the same sound level as when the speaker cones moves 1 mm! At 270 Hz (a frequency where MDF and chipboard usually have strongest resonances) a movement of only 0,01 mm p-p will generate a sound level of 90 dB!

That is theory. But tests made by Colloms(6) agree, and state that many cabinets at certain frequencies can give higher output than the drivers. And the sound the cabinet produces is distortion and distortion only. Some speaker manufacturers claim they tune their cabinets like a guitar, to the A note of 440 Hz, to the Italian violin maker tradition of the 16th century, or to whatever that appears "musical" in the advertisements.

Let me humbly point out that what they are "tuning" is a board of wood, perhaps 20 mm thick, bolted and glued to a box and coupled to a stand or to the floor. It is interesting that these manufacturers claim to have benefit of modern cone materials like carbon paper, magnesium or polypropylene; since they can make 20 mm chipboard sound so good.

Cabinet questions

Well, the situation looks bad -- together with our two speakers, forty 15" drivers have suddenly showed up in our listening room. The solution was to spend some hours in the basement together with test equipment, trying to find the nature of the resonances of different materials, and to find methods of vibration damping and the effect of decoupling the driver from the materials.

I mounted different drivers in different materials, with different bolts, with different bracing, decoupled them with rubber materials of different viscosity, ran them at high level with different frequencies, and a lot other obscure procedures. All the time I logged the sound output that was transmitted through the material. The proper tool for this is a accelerometer and equipment to record and process the data from it. I had only a oscilloscope and a SPL meter, but I got a good idea of the situation anyway. However, without the proper equipment, it is of no use to quantify the differences I found. Instead, you have to accept this list with a summary of the discoveries I found most vital:

All materials have one or more frequencies where they enter resonance and start vibrating. The intensity, decay time and frequency range of the vibration depends on size, weight, density and stiffness.
The higher mass of the material, the higher SPL is needed to excite vibration. A extremely heavy and rigid cabinet is universally the best cabinet.
MDF and chipboard resonate at averagely 150-400 Hz, with the strongest resonances usually at 250-300 Hz. Nearly all speakers suffers heavily from cabinet distortion in this frequency range.
MDF have shorter decay time than chipboard, and the vibration peak is more damped. Still, MDF have substantial vibration, and is far from the optimum cabinet material. You can easily find the resonance frequencies of a speaker cabinet with a sinus generator(7) (or test-CD) and a amplifier. Play a sinus tone at loud level and change the frequency slowly. Hold your hand on the cabinet side to find the frequencies where it vibrates. When you hit the resonance frequency, the sound will also change, and you will hear the distortion generated by the cabinet. Maybe you recognise some irritating sounds that you thought belonged to a weak part of the system! You can also check the resonance properties of a given material by mounting a driver to it and run the previous procedure.
The most effective means of reducing vibration decay time is to brace the cabinet. A single-piece cabinet, like a concrete tube, (see http://www.speakerbuilding.com/content/1019/) will usually have less vibration than a cabinet that is assembled of separate parts.
Vibration is easily transmitted to other materials by mechanical coupling.
Using materials of different resonance frequencies may reduce some of the output of the vibrations. The layers should have as little mechanical coupling between each other as possible, or the cavity should contain a material whose damping properties corresponds to the resonance frequency of the inner wall.
Sand is a good agent of dissipating vibrations of a wide frequency range into heat.
Air will also dissipate vibrations, because no mechanical coupling is the best decoupling. This can be done by making a second box outside the cabinet with as little mechanical coupling to the inner cabinet as possible. The outer wall must have properties so that it does not "let out" the sound from the inner wall. This is a exciting method that may be investigated further.
Decoupling the drivers with elastic materials like thick gaskets or rubber strings is difficult. I had great hopes for this method, and a interesting idea would be to decouple midranges that are crossed below the resonance frequency of the cabinet. But practical tests showed that the decoupling had to be very soft to work. With soft coupling, the driver would wobble and partly cancel its own output. With stiff material the vibrations would be coupled, achieving nothing. A 5" midrange with a 10 gram cone generates at 104 dB SPL a oscillating force of 44 Newton(8) -- equal to 4,5 kg. The weight of the driver and the decoupling must withstand these forces, or the driver will wobble. A 25 mm tweeter at 106 dB will have a acceleration of 7000 g (6 g is regarded lethal for humans!), but assuming the dome weighs a typical 0,35 gram, it will generate just 24 Newton, and the weight ratio of the dome and the rest of the driver is so large that a softer decoupling can be used -- but the only effect would be to isolate the tweeter from vibrations in the cabinet. Another problem is that the frequencies where it is interesting to decouple drivers from the cabinet (200-500 Hz) often corresponds to the lower crossover frequency in 3-way systems!
It is possible to get very low cabinet vibration by using separate cabinets with different resonance frequencies for bass and midrange/tweeter. The crossover frequency should be the median of the two resonance frequencies of the cabinets.
A pure bass cabinet should be extremely stiff and rigid with high resonance frequency. The walls must not flex when excited with the large air pressure caused by the big air displacement in the bass region.
The midrange cabinet should be "thick, lazy and dizzy", with a low resonance frequency. A solution may be to use two thin walls with a thick sand layer and no bracing. Flexing walls is far less critical than for bass drivers. Making the midrange a dipole may be another solution.
Fastening the driver magnet to the cabinet has a very good effect on the sound quality of both woofers and midranges. The driver will stay very firmly in place this way, and yield a far more detailed midrange, and a tighter, harder bass. The best condition for a driver is that only the cone is to move -- and nothing, nothing, nothing else. Fastening drivers this way will do more for precise sound reproduction than any cable investment.
Using bolts instead of screws to fasten drivers may give a slight reduction in cabinet vibration. I believe this is because the vibration from the cone is transmitted to a smaller area instead of directly into the wood.
Make your woodwork strong. If a wall joint is not well fit, the forces inside the cabinet will attack it and excite a resonance. Use every chance you find to brace as many sides of the speaker to each other.
Bracing should run parallel with the largest (longest) side of the cabinet -- so that the largest area is divided. A floor-standing cabinet should have a brace from floor to bottom; not a horizontal shelf. Then continue bracing with the next largest area, and so on.
A common, but not optimum formula for sand damping is to use two walls of MDF of the same thickness, bolted and glued together over spacers that form a cavity where a layer of sand can be filled. This will couple vibrations from the inner wall to the outer, which has the same resonance frequency, and the potential of the sand is not fully utilised.
The viscosity of the sand can be far better employed to absorb vibrations if the outer wall is very thin, and with as little contact with the inner wall as possible. The sand layer should be as thick as possible. The only job of the outer wall is to keep the sand from leaking out. There is no need to make it rigid, because if the inner wall is properly constructed, it will withstand all the internal air pressure. The outer wall can be veneered board, and you can therefore get a nice wood finish in one step.
Tests showed that even a very modest layer of 9 mm sand towards a outer wall of 6 mm will dissipate heavy vibration. A 6 mm outer wall were more than enough to keep 9 mm sand safely in place in a big cabinet. Even better would be a 3 mm wall and a sand layer of 15-20 mm, but some evenly distributed fastening points is then necessary to prevent the outer wall from cracking up!

Figures

Fig. 1. Picture of the Toccata loudspeaker
The Toccata loudspeaker

Fig. 2. Unfolded T-line model
Unfolded T-line model