The last section ended with a link to Scan Speak's calculation program, which can simulate the reproduction of a woofer in a cabinet. This time we use some more advanced software that unfortunately shows us some unpleasant truths about loudspeakers.

9 litres. That's the volume that's most ideal for a 4 ohm Scan Speak 15WU woofer. Here it behaves most ideally in terms of the balance between step response, efficiency and deep bass characteristics, I think. Add to that the volume that speaker units, bass reflex tubes and braces etc. take up inside the cabinet, so the real cabinet volume probably needs to be around 10.5 to 11 litres to fit. Thanks to everyone who has contributed calculations and comments to the blog. It is instructive and I hope it continues. A larger cabinet gives basically nothing but a degraded step response, while a smaller cabinet gives poorer depth characteristics. That's why the choice fell on 9 liters for the version of the Speaker Q113 I call "Revolution". I would add that the simulations in today's post, are not the final vote. They are just used to show something else interesting.

I'll just turn up the volume

Today, we're looking at the bass response of a Scan Speak 15 WU in a 9-litre cabinet and doing a few simulations that you can't normally do in regular software. I think you'll find it interesting. I want to emphasize that the issues I'm addressing now apply to all dynamic loudspeakers, regardless of construction method, size, provenance, etc. I will show you what happens to the bass response when you turn up the volume.

Keep an eye on the bass response

The simulation of Scan Speak 15 WU has now been moved to the LEAP 5 program. Remember that this is a simulation, not a measurement. I would ask you to keep an eye on the speaker response below 200 Hz, i.e. the bass response. The first three illustrations are relatively simple simulations, made from Scan Speak's own specifications of the speaker unit's Qts, Fs and Vas. Three different cabinet sizes have been calculated, of 9, 12 and 15 litres respectively (red, green and blue). The measurement paper shows 1 dB per measurement line.

The speaker sits in an infinite wall in an infinite space

Simulations of this kind are, usually, made as a 2pi setup. The speaker unit sits virtually on an infinitely large plate with the cabinet volume behind it. Speaker manufacturers measure their units using a similar method. The best that can be said about the method is that it is a measurement standard everyone agrees on. The results are quite a way from what you get with a speaker in a cabinet and in a living room. It's worth knowing. More on that later. There is no simulated crossover on the speaker and the "measurement distance" to the speaker is 1 meter.

1. illustration. Look at the curves. At the bottom, we add 1W, but at the top the speaker gets 50W. See how the curve changes below 100 Hz. (Click for larger image. Use the browser's back button to return to this blog post)

1. illustration. The simulated bass response

The bottom curve shows the frequency response of the speaker with 1W (or 2.83 V) of power applied. The voice coil temperature is 25 degrees. Below about 70 Hz you can see the difference between a cabinet volume of 9.12 and 15 litres. In fact, no noticeable difference, although the larger cabinet plays a few dB higher in the deepest bass in this case. From 200 Hz and down, you notice that the curve looks like "a soft shoulder" or something like that. Herein lies some of the point of the day! The top curve of the 1st illustration shows the speaker's frequency response with 50W applied. The speaker now plays louder and therefore the curve is higher on the meter. LEAP 5 calculates that the speaker's voice coil is now 85 degrees hot. For this reason alone, the bass response of the speaker below 200 Hz has changed. You see that the "soft hanging shoulder" is almost straightened. It is not wrong to conclude that a frequency response measured at 1W has little to do with reality when the speaker is supplied with 50 W. There is more.

2. illustration. The speaker is supplied with 150W and the voice coil is 200 degrees hot. The same speaker now measures completely different.

2. illustration. Full power

Scan Speak states on their datasheet that 15 WU can withstand 150 W in a 100 hour test, and now we simulate what the frequency response of the speaker looks like under those conditions. The speaker's voice coil is now 200 degrees hot and the speaker plays 105 dB at 1 meter. That's pretty good for such a small speaker, by the way. And notice the frequency response below 200 Hz! The soft shoulder has been completely corrected and there's even a slight overshoot. In other words: The speaker has different bass response depending on how loud it plays. It also has different bass response, depending on how hot the voice coil is. One thing is certain: a simulation showing the speaker's frequency response with a 25-degree voice coil and a voltage of 2.83V is not an accurate picture of the speaker's bass response in the real world.

3. illustration. Stroke length. At low frequencies the motor system can move the diaphragm up to +/- 9 mm. That's wild

3. illustration. How much the voice coil moves

The ability of the voice coil and motor system to move the diaphragm can be partially calculated by subtracting the height of the magnetic gap from the voice coil height. This calculation gives +/- 6 mm for the 15 WU. However, a voice coil can move further than the actual magnetic field implies, because there may be plenty of magnetic force left, just outside the magnetic gap itself. Here, speaker unit manufacturers have not really agreed on a common standard, but Scan Speak calculates the linear stroke length out to the point where 85% of the motor system's force factor remains. That point, according to Scan Speak, is 3 mm either side of the force field, adding 6 mm to the stroke length. That brings the total stroke to an insane +/- 9 mm! At this point, we don't know anything about how the speaker sounds, but we can see that the unit's limitation lies in the mechanical construction and not the electrical.

4. illustration. In LEAP 5, the virtual speaker is designed and placed in a cabinet with a surprising result.

5. illustration. The cabinet dimensions have more influence on the bass response than common simulations show. 5 dB dip at 190 Hz!

4th and 5th illustration. Surprising diffraction analysis

So far, the speaker's bass response is simulated from a traditional 2pi setup that doesn't resemble the real world much. Therefore, we now draw a symbolic cabinet (4th illustration) and move the woofer out of the infinite wall. See in the 5th illustration what this has brought about! Around 190 Hz a wide dip with a depth of 5 dB has occurred, which is related to the cabinet dimensions only. Normally, a speaker builder would work to make the simulations look good, and then rush to build a cabinet. The challenge is that you can rarely make measurements below 300 Hz, so you have to believe your simulations. The example shows that simulations based on an infinite wall do not tell the whole story of the speaker's bass response. The dimensions of the cabinet must be taken into account so that you can better trust what you simulate. Now, some problems disappear and others arise when the speaker is placed in a real room, but this simple example shows that you have to orient yourself in many directions to go forward.

Conclusion so far

It is convenient for manufacturers of loudspeaker devices to provide technical specifications based on a measurement standard. This gives a chance to compare the loudspeaker units. Just be aware that the specifications change a lot when the input exceeds 2.83 Volts. This happens with normal music listening and nobody can know exactly where the specifications move to. You can simulate the speaker's bass response in a computer program, but what are you simulating in reality? Many programs simulate from an input of 2.83 volts, assuming the woofer sits in an infinite wall in an infinite room. This creates a pleasant opportunity to play with a virtual speaker, but there is a blind spot in the method, because what speaker works under those conditions? None. This is clearly seen when our experimental speaker is simulated with a random cabinet ... in an infinite room, on an infinite wall. A dip of 5 dB at 190 Hz, due in part to the shape of the cabinet, is no small matter.
It's about substituting knowledge for chance, to pave the way for better sound, even if that acquired knowledge can be uncomfortable and annoying, as here.
More next time, when we simulate a cabinet based on the specs we ourselves derived from the 15 WU and look at what adding it does to the speaker.