# B&O Tech: Curves are Better than Corners

#15 in a series of articles about the technology behind Bang & Olufsen loudspeakers

## Interference

Before we start talking about curves and corners, let’s have a quick review on the concept of interference. At its most fundamental level, sound is just a relatively small, relatively fast change in barometric pressure. If the instantaneous pressure is higher than average (which happens to be the same as the pressure inside your head), then your eardrum is pushed into your head. If the instantaneous pressure is lower than average, then your eardrum is pulled out of your head. When your eardrum moves in and out, you hear sound.

One way to create a high pressure is to take a loudspeaker driver and push it outwards. In order to create a low pressure, we pull it inwards, as is shown in the animation below. The red thing is a piston which is basically the way we like to pretend a loudspeaker driver (like a tweeter) behaves. The grey thing is a very, very wide loudspeaker cabinet. The red semicircles show the high pressure zones that expand outwards from the front of the loudspeaker. The green semicircles show the low pressure zones.

If you have two sound sources, their pressure differences (relative to the average pressure) add. So, if you have two high pressures arriving at your eardrum, it will be pushed farther into your head than if only one of them arrived at your ear. Similarly, if you get two low pressures arriving at your eardrum, it will be pulled further out of your head than if only one of them was present. HOWEVER, if you have a high pressure and a low pressure arriving at the same time in the same place (for example, at your eardrum) then they cancel each other and, if they have the same magnitude, your eardrum won’t move at all and you won’t hear anything. (This is how noise-cancelling headphones work. The sound from the headphones is in theory identical to the sound coming to your ears from outside the headphones, except that it’s opposite in polarity, so the sum of the two sounds is nothing.)

Keep all that in mind as you read on…

## Diffraction

It should not come as a surprise that a sound wave will bounce off a hard surface like a flat concrete wall. The question is “why?” The answer to this question can be complicated – but the simple version is that the molecules in a concrete wall are harder to move than the molecules in air – so we have a change in acoustic impedance. This is essentially a measure of how easily the molecules in the substance are moved by a sound wave… sort of… (Let’s leave it at that, since we really don’t need this article to be a thorough discussion of acoustic impedance.)

The interesting thing is that an acoustic wave will be reflected off any change in impedance. So, you don’t have to be going from a low impedance to a high impedance (as in the case of a sound wave trying to move from air into concrete). It will also reflect on a boundary where you change from a high to a low impedance (for example, a sound wave in concrete trying to get out into air – in this case, the sound wave will bounce off the surface of the concrete and move back into it rather than “leak” out into the surrounding air.).

Imagine yourself standing in a long tunnel. You clap your hands, and the sound wave travels down the length of the tunnel until it reaches the end – what happens then? Well, the answer is “two things”. Some of the sound leaks out of the tunnel. However, since the air inside the tunnel has a higher acoustic impedance than the air outside the tunnel (because the sound is freer to go where it wants on the outside), the end of the tunnel is a boundary where there is a change in acoustic impedance. And, as we saw in the last paragraph, this means that we will get a reflection. So, even though the end of the tunnel is open, it reflects your hand clap back into the tunnel. So, some sound leaks out and some reflects. (One way to really experience this is to notice your ears pop when you enter a long tunnel on a fast-moving train. When you first enter the tunnel, your ears pop because of the sudden change in pressure. Some time later, you might notice that your ears pop again. This is because the high-pressure wave front that the train made when it entered the tunnel travelled to the opposite end of the tunnel, bounced back and hit you again.)

If you didn’t know that the second sound was a reflection off the end of the tunnel (for example, you didn’t hear the first hand clap because you were wearing earplugs) you might think that it was a direct sound from someone down at the far end of the tunnel. So, if you’re not the person doing the clapping, but you’re in the tunnel with that person, you get two sounds – the direct sound and the reflection.

There is another, less obvious case where you have a change in acoustic impedance. This is when you have a sound wave travelling along next to the surface of something, and the surface ends. For example, if, in the animation at the top of this page, the surface of the loudspeaker cabinet was not as wide, there would be a corner where the face of the loudspeaker meets its side. At that corner, the acoustic wave front “sees” a change in acoustic impedance. Consequently, there is something like a reflection that starts at the corner. in essence, the corner of the loudspeaker is a boundary that radiates like a second sound source (just like the end of the tunnel in the example above).

So, if we modify the animation at the top of the page to include a narrower cabinet, the result would be something like the animation below.

As you can see there, the corner of the loudspeaker becomes a second source that radiates its own sound waves after the original, direct sound hits it.

This effect is called acoustic diffraction and it has some significant implications on the sound of a loudspeaker. This is directly because of the interference (see above…) between the direct sound from the loudspeaker driver and the secondary sound source caused by the corner.

Remember we saw above in Fig.1 that, when you have two high pressure zones that meet each other, you get more pressure than either one of them alone. Now take a look at the animation above and look for the places where the black curves from the two “sources” intersect. This is where you’ll get an increase in pressure, and therefore more energy than just the direct sound by itself. As you can see in Fig. 3, below, this means that you have an angle off-axis to the front of the loudspeaker where the signal is louder than it is directly on-axis. Of course, this also means that there will be some angles where you hear less (because the secondary wavefront from the corner cancels the direct sound) – these are where the red and green curves (the high and low pressure zones) intersect.

As you can see in Fig 3a, there are different angles where the high pressures add to give you an even higher pressure (notice that the low pressures also add to give you an even lower pressure. The result is that, along those lines, you get constructive interference and therefore the sound is louder than it is elsewhere. I’ve only shown three such angles in this diagram – there are more. You might note as well that the origin of the high pressure lobes is not the centre of the loudspeaker driver (the piston shown in red). It’s somewhere between the primary and secondary sources (in this case, the loudspeaker driver and the corner).

Fig 3b shows two angles where the high and the low pressures overlap, causing destructive interference and therefore cancellation. Therefore, the sound is quieter along those lines than it is elsewhere.

## The real world

What does all of this mean in the real world?

Well, as you’ve probably already guessed, the first conclusion is that building a loudspeaker that has sharp corners is probably a bad idea. For example, if you wanted to build a loudspeaker, and you just put a tweeter on the front and made sharp right angles where the sides meet the front, you will have a problem with diffraction off those corners. As you can see in Figure 3, you will get a boost in the signal at some angles off-axis to the front of the loudspeaker, and some cancellation at other angles. The amount by which the signal will be boosted, the angles where you’ll have the effects, and the frequencies where you’ll have the problems are all dependent on the specific dimensions of the device. For example, the further away the loudspeaker’s corner from the driver, the lower the frequency that will be affected.

Let’s take a real-world example. The very first version prototype of the BeoLab 5 was really just a “normal” three-way loudspeaker that was used to test the ABC algorithm, So, there was a woofer in a cabinet with a microphone for the ABC development, but on top was just a small cabinet with a midrange driver and a tweeter, as you can see in Figures 4 and 5.

Figure 6 shows the “conventional” tweeter cabinet version of one of the BeoLab 5 prototypes which was placed on top of the white woofer cabinet shown in Figure 4 when the Acoustic Lens assembly was removed. As you can see, this is an example of how-not-to-make-a-loudspeaker (if you’re worried about diffraction). We have a tweeter in a flat surface and (some sharp-ish corners at the sides of the loudspeaker face). The result of this is that we have exactly the same problem shown in Figure 3a and 3b, above. We can see this in the measurement of the horizontal directivity of the loudspeaker, shown in Figure 7, below.

It may be a little difficult to read this plot, so I’ll explain a little. The entire plot has been normalised to the on-axis magnitude response of the tweeter. In other words, the measurement doesn’t show the response of the tweeter – it shows how the response changes as you move around the loudspeaker in the horizontal plane.  The X-axis is the frequency of the signal in Hz, ranging from 1.8 kHz to 20 kHz. The Y-axis is the horizontal angle of radiation of the loudspeaker where 0° is directly on-axis, in front the tweeter. The lines in the plot can be thought of as a kind of topographical map with a difference of 0.5 dB per contour. So, if you think of a straight “ridge” in the plot along the 0° line in the middle, the plot generally falls off (in other words, the signal is quieter) as you move around to the side and back of the loudspeaker. You can see that, at the high frequencies, the lines are closer together which means that you lose more level at high frequencies than at low frequencies as you come around to the side of the loudspeaker. This is traditionally called loudspeaker “beaming”. The interesting thing to look at are the four red oval areas. The larger ones are centred around 3.2 kHz and ±40°. The smaller ones are up at about 7.5 kHz and  about ±15°. Because they’re in red, this means that they are louder than the on-axis response, so they are peaks in the topographical map. These peaks are the direct result of diffraction off the edge of the loudspeaker cabinet.  I count 4 red contour lines at the lower frequency peak, which means that we have a beam that is about 2 dB (remember, 0.5 dB per line * 4 lines) louder around 3 kHz at 40° off-axis to the loudspeaker.

This cabinet was built compare the directivity of a normal box-shaped loudspeaker to one with an Acoustic Lens. A close-up of the lens used for this comparison is shown below in Figure 8.

You’ll note in Figure 8 that the Acoustic Lens is slightly different from the final version (hence the “first-generation” qualifier) . This version also suffered from diffraction artefacts caused by the sharp edges where the face of the lens structure meets its side. This was corrected in the second generation version shown below in Figure 9.

Notice that the second-generation lens has curved transitions from face to side to reduce the diffraction problem. This curvature was eventually extended to wrap around the entire structure as can be seen in the photo of the final BeoLab 5 tweeter lens in Figure 10, below.

You may notice that the difference in these two designs was that the original one had sharp corners on the sides. The diffraction effects of these corners were easily visible in the first directivity measurements of the Lens, so the second prototype with the curved transition from front to side was made to eliminate this problem. The directivity measurement of the prototype shown in Figure 9 is seen below in Figure 11.

You’ll see in Figure 11 that there are two significant differences between the directivity of a tweeter in the prototype Acoustic Lens and a conventional cabinet (shown in Figure 7). The first difference is that the beaming effect (seen as a convergence of the contour lines at the high frequencies in Figure 7) does not happen with the lens. The contour lines are much more parallel resulting in a behaviour known as “constant directivity”. This is a way of saying that the loudspeaker has a directivity that is the roughly the same throughout its entire frequency range (rather than beaming in the high end).

The second difference is that the peaks in the 3 kHz and 8 kHz areas, seen in Figure 7, are gone. This is because there are no corners at the edge of the loudspeaker cabinet to cause diffraction. You may note a peak in the magnitude responses off-axis above 15 kHz. We actually don’t know what causes this, however, since it is so high in frequency and only +1 to +1.5 dB, and since this is still only a prototype, it wasn’t really considered to be a significant issue.

## Wrapping up

So, I’ve killed two birds with one stone in this article (or “two flies with one smack” as they say in Denmark). On the one hand,  we’ve seen that, if you’re worried about the directivity and/or the off-axis response of your loudspeaker (I know, the latter is a sub-set of the former…) sticking a tweeter (or a midrange, or a woofer, depending on dimensions and frequency ranges) on the front of a rectangular box is probably a really bad idea. (On the other hand, it’s a pretty easy, and therefore cheap, way to build a speaker, which is why such a design is so popular I guess…) And, on the other hand, we’ve seen one of the characteristics of Acoustic Lenses – being a more constant directivity than a tweeter-on-a-box. The fact that the tweeter mounted in an Acoustic Lens had less diffraction is not because of the Lens geometry in particular, but because of the shaping of its surroundings as part of the development process of BeoLab 5.

There are more stories like this one. For example, if you look carefully at the “plates” of the BeoLab 5 and the prototype in Figure 4 (the part the tweeter and midrange drivers are mounted in), you might notice that the prototype plates are flat, whereas the BeoLab 5 plates curve downwards. This is not because someone thought the curve would look pretty. This was because the circular edge of the prototype plates also caused diffraction, resulting in a higher-level lobe in the vertical plane. Sloping the plates downwards puts their sharp edges in the “shadow” of the plates themselves, reducing the diffraction effects. So, you can see that diffraction and its effects on directivity is one of the other issues that we worry about when we’re building a loudspeaker.

# B&O Tech: Multichannel setup tips and tricks

#14 in a series of articles about the technology behind Bang & Olufsen loudspeakers

Rather than talk about technologies inside B&O equipment, this week I’ll try to go through a couple of strategies on how to properly calibrate the main channels in a surround system – and how to do it improperly, but make it sound better for your friends. I’ll use the example of a BeoPlay V1, a BeoVision 11 or a BeoSystem 4 as the heart of the system – but the basic concepts are the same for any other surround processor.

## Location, location, location

The first step in setting up any surround sound system is the correct placement of your loudspeakers. There are two standard configuration recommendations. The first is from the International Telecommunications Union, in a document called  Recommendation ITU-R BS.775-2 – Multichannel stereophonic sound system with and without accompanying picture (available as a PDF file from the ITU here). The second is called Recommendations for Surround Sound Production from the Producers and Engineers Wing of the Recording Academy of the National Academy of Recording Arts and Sciences (or NARAS – better known as the people that bring you the Grammys). Tha recommendation can be downloaded as a PDF file from here).

The short versions of these two recommendations are as follows:

### ITU-775

The ITU standard configuration is the one people who do research into multichannel audio use for their experiments. It’s also the one we use at Bang & Olufsen when we’re testing our loudspeakers in the Acoustics Department or tuning the parameters in the TrueImage upmixing algorithm.  The nice thing about this configuration is that it matches a surround sound system for someone who sits on a sofa placed against a wall, and has their surround loudspeakers adjacent to the same wall.

In a perfect loudspeaker configuration, all of your loudspeakers are the same distance from the listening position. They have all been calibrated to have the same loudness at the listening position. Also, they are all large, full-range loudspeakers (and therefore, you do not need a subwoofer).

The Centre Front loudspeaker should be in the centre, at the front (we’ll call that 0°). The Left Front and Right Front loudspeakers should be at ±30° relative to that angle. The Left and Right Surround loudspeakers should be located symmetrically at an angle of between ±100° and ±120°.

The ITU-775 document doesn’t specifically state the standard configuration for a 7-channel system, but it does provide a recommendation for a 5-channel system that uses 7 loudspeakers (in cases where you have a larger system and you use two loudspeakers per surround channel). However, the recommendation is still a pretty good recommendation for a 7-channel setup. (This also makes sense, since, if you have 7 loudspeakers, you may occasionally like to use them as a 5-channel system without having to place extra loudspeakers in your room.) If you dig around, you’ll see that this also fits the typical setups used in re-recording studios for doing 7-channel mixes and mastering for Blu-ray releases of films. A good example of this is Tron Legacy, which was produced using a system very much like the one shown below – with matching loudspeakers at 0°, ±30°, ±90° and ±150°. (this also makes sense from a radially symmetry perspective, since, ignoring the centre channel, you have equal loudspeaker spacings of 60°.

### NARAS

The NARAS recommendation is a little different, although the people that wrote it were aware of the ITU recommendation (which came first…), so they made sure that their version didn’t contradict the existing standard. Their version uses the same layout for the front three loudspeakers, but suggests that the surround loudspeakers be a little further back – within the ±110° to ±150° angle, with an “optimal range” of ±135° to ±150°.

Like the ITU standard, the NARAS document also recommends that all loudspeakers be the same type of full-range loudspeakers, all the same distance from the listening position, all level-adjusted to be the same at the listening position.

## The Real World

Both the ITU and the NARAS standards are really designed by and for people who work and live in recording studios or run perceptual experiments involving multichannel audio. This means that they have one chair and no friends – at least when they watch movies and listen to music… However, if you have a sofa and friends, then you will start having some questions – or at least some doubts.

For example, if  you are “normal” (whatever that might mean) but a little careful about your surround sound setup, you probably have something that looks like the drawing below.

What happens if we were to calibrate this system “perfectly” using the centre of the sofa as our reference “sweet spot” as shown in Figure 4? We’d apply a delay to the Centre Front loudspeaker to make the time of arrival of its signals match the Left Front and Right Front loudspeakers (usually done by setting the Speaker Distance). We’d also apply a delay to the surround loudspeakers to do the same. We’d also probably drop the levels of the centre and surround loudspeakers to match the Left Front and Right Front signals (because they’re closer, and therefore louder).

However, let’s think about what happens if you sit on the left side of that sofa? Now, the Left Surround loudspeaker is very close to your left ear – and that has some serious implications on your experience. Firstly, since sound pressure doubles with every halving of distance, (assuming that this diagram is to scale) then sitting on the left side of the sofa means that you’ll get roughly a 6 dB boost (possibly more, if you’re leaning…) in the signal from that one loudspeaker. In addition, since that loudspeaker is so close and arriving at your listening position early, your brain will be able to figure out that the loudspeaker is close because you’re pretty good at localising sources when they’re near your head. The same problem, albeit on a much smaller scale, happens with the centre loudspeaker. If its time-alignment delay is calibrated using the centre position, then, if you’re sitting on the left side of the sofa, then the Left Front loudspeaker’s signal will arrive before the Centre Front. The end result of this is that, if you’re sitting on the side of the sofa, you’ll have too much from one of the surround loudspeakers and the intelligibility of the dialogue will be reduced a little.

So, how should we calibrate the system to make things a little better for your friends? Take a look at Figure 5, below.

What I’m trying to show with this diagram is that both the distance and the level for each loudspeaker should be measured to the closest person in your listening area. So, in this case, the Left Front and Left Surround loudspeakers are calibrated to the left position on the sofa. However, the Centre Front loudspeaker is calibrated at the centre of the sofa. The result of this is that the centre speaker will be delayed – but less than it would have been if you had calibrated it as in Figure 4, because the Left Front loudspeaker is closer to the person on the left side of the sofa than to the person in the centre of the sofa. Also, the Surround loudspeakers will be delayed much more than they would have been using the scheme in Figure 4. However, they’ll still be symmetrical (so the person in the “sweet spot” won’t feel like the surround channels are lopsided, and the friends on the sides of the sofa won’t notice that they’re sitting on top of a loudspeaker… Also, this will result in the centre channel being a bit louder and the surround channels being a little lower in level – both of which are technically incorrect for the person in the sweet spot, but at least it’s a mistake in the right direction – so you’re improving intelligibility of the dialogue

If you do calibrate the system this way, you’ll technically be incorrectly calibrated at the sweet spot, but your friends on the sides of the sofa will be much happier – and you won’t notice too much. Of course, if you have a BeoPlay V1, a BeoVision 11 or a BeoSystem 4, you can make this configuration just one of your nine available Speaker Groups – you can always use another one for a “perfect” calibration for the sweet spot when you’re home alone.

If, after aligning your system using this method, you still find that the dialogue is a little hard to understand, and the surrounds are a little hot (this is often the case when your sofa and the surround loudspeakers are all situated against the same wall, you should not be afraid to do the following:

• make the centre channel one or two milliseconds early. You can do this by telling your surround processor that it’s about 30 to 60 cm farther away than it really is.
• raise the level of the centre channel 1 or 2 dB
• drop the level of the surrounds as much as necessary – in my experience, it’s not unusual to have to drop them by as much as 6 dB if you’re against the same wall with them. (Note that, if you have a BeoPlay V1, a BeoVision 11 or a BeoSystem 4, you can do this using the “Fader” adjustment in the Sound menus. This will merely control the relative levels of the Front and Surround / Back loudspeakers – so it’s a one-fader solution to doing it manually for each loudspeaker output.)

If your listening area is larger, the technique is the same – you calibrate any given loudspeaker in the system to the closest listening position, and then tweak to taste.

I guess that the big message here is “just because your system is configured ‘correctly’ doesn’t mean that it can’t sound better”. Don’t be more afraid to tweak the adjustments on your calibration than you would be to add cream and sugar to your coffee, or salt and pepper to your meal in a restaurant. As Duke Ellington once said: “If it sounds good, it is good.”

# B&O Tech: But what if my room is Scandinavian?

#13 in a series of articles about the technology behind Bang & Olufsen loudspeakers

The following question recently arrived in my inbox via our customer service department.

“I am an admirer of B&O Hifi products as of over 20 years, but a great mystery for me is how you achieve great sound reproduction in the typically minimalist Scandinavian interior design environmment with polished floors, bare walls and bare glass windows. Effectively such environments are acoustical disasters !?!”

I thought that this was a great question – so it’s the topic of this week’s article.
Of course, you are correct. A room comprised of large flat reflective surfaces with little acoustical absorption has a very different acoustical behaviour from a recording or mastering studio where the final decisions about various aspects of a recording are made. And, consequently, this must have an effect on a listener’s perception of a recording played through a pair (assuming stereo reproduction) of loudspeakers in that room. The initial question to be asked is “what, exactly, are the expected effects of the room’s acoustical behaviour in such a case?” The second is “if the room has too much of an effect, how can I improve the situation (i.e. by adding absorption or changing the physical configuration of the system in the room)?” The third, and possibly final question is “how can we, as a loudspeaker manufacturer compensate (or at least account) for these effects?”
The effect a room’s acoustical behaviour has on a loudspeaker’s sound can, at a simple level, be considered under three general headings:
1. early reflections
2. room modes
3. reverberation

## Early Reflections

Early reflections, from sidewalls and the floor and ceiling, have an influence on both the timbre (tone colour) and the spatial characteristics of a stereo reproduction system. Let’s only think about the timbral effects for this article.
Let’s start by assuming that you have a loudspeaker that has a magnitude response that is perfectly flat – at least from 20 Hz to 20 kHz. We will also assume that it has that response regardless of which direction you measure it in – in other words, it’s a perfectly omnidirectional loudspeaker. The question is, “what effect does the wall reflection have on the measured response of the loudspeaker?”
Very generally speaking, the answer is that you will get a higher level at some frequencies (because the direct sound and the reflection add constructively and reinforce each other) and you will get a lower level at other frequencies (because the direct sound and the reflection work against each other and “cancel each other out”). What is potentially interesting is that the frequencies that add and the frequencies that cancel alternate as you go up the frequency range. So the total result looks like a comb (as in a comb that you use to comb your hair, if, unlike me, you have hair to comb). For example, take a look at Figure 2.
So, you can see in Figure 2 that, at the very low end, the reflection boosts the level of the loudspeaker by a little less than 6 dB (that’s two times the level!) at the listening position. However, as you go up in frequency, the total level drops to about 15 dB less before it starts rising again. As you go up in frequency, the level goes up and down. This alternation actually happens at a regular frequency spacing (i.e. a notch at every 200 Hz) but it doesn’t look regular because the X-axis of my plot is logarithmic (which better represents how we hear differences in frequency).
What happens if we move the wall further away? Well, two things will happen. The first is that the reflection will be quieter, so the peaks and notches won’t be as pronounced. The second is that the spacing of the peaks and notches in frequency will get closer together. For example, take a look at Figure 3.
Similarly, if we move the wall closer, we do the opposite, as in Figure 4.
So, if you have a room with only one wall which is perfectly reflective, and you have a perfectly omnidirectional loudspeaker, then you can see that your best option is to either put the loudspeaker (and yourself) very far or very close to the wall. That way the artefacts caused by the reflection are either too quiet to do any damage, or have an effect that starts at too high a frequency for you to care. Then again, most room have more than one wall, the walls are not perfectly reflective, and the loudspeaker is not perfectly omnidirectional.
So, what happens in the case where the loudspeaker is more directional or you have some fuzzy stuff on your walls? Well, either of these cases will have basically the same effect in most cases since loudspeakers are typically more directional at high frequencies – so you get less high end directed towards the wall. Alternatively, fuzzy stuff tends to soak up high frequencies. So, in either of these two cases, you’ll get less high end in the reflection. Let’s simulate this by putting a low pass filter on the reflection, as shown in Figure 5, 6 and 7 which have identical distances as the simulations in Figures 2, 3, and 4 – for comparison.
What you can see in all three of the previous plots is that, as the high frequency content of the reflection disappears, there is less and less effect on the total. The bottom plot is basically a proof of the age-old rule of thumb that says that, if you put a loudspeaker next to a wall, you’ll get more bass than if it’s farther from the wall. Since there is not much high frequency energy radiated from the rear of most loudspeakers, Figure 7 is a pretty good general representation of what happens when a loudspeaker is placed close to a wall. Of course, the exact behaviour of the directivity of the loudspeaker will be different – but the general shape of the total curve will be pretty similar to what you see there.
So, the end conclusion of all of this is that, in order to reduce undesirable artefacts caused by a wall reflection, you can do any combination of the following:
• move the loudspeaker very close to the wall
• move the loudspeaker farther front the wall
• sit very close to the wall
• sit farther away from the wall
• put absorption on the wall

However, there is one interesting effect that sits on top of all of this – that is the fact that what you’ll see in a measurement with a microphone is not necessarily representative of what you’ll hear. This is because a microphone does not have two ears. Also, the direction the reflection comes from will change how you perceive it. A sidewall reflection sounds different from a floor reflection. This is because you have two ears – one on each side of your head. Your brain uses the sidewall reflections (or, more precisely, how they relate to the direct sound) to determine, in part, how far away a sound source is. Also, since, in the case of sidewall reflections, your two ears get two different delay times on the reflection (usually), you get two different comb-filter patterns, where the peaks in one ear can be used to fill in the notches in the other ear and vice versa. When the reflection comes from the floor or ceiling, your two ears get the same artefacts (since your two ears are the same distance to the floor, probably). Consequently, it’s easily noticeable (and it’s been proven using science!) that a floor or ceiling reflection has a bigger timbral effect on a loudspeaker than a lateral (or sideways) reflection.

## Room modes

Room modes are a completely different beast – although they exist because of reflections. If you pluck a guitar string, you make a deflection in the string that moves outwards until it hits the ends of the string. It then bounces back down the string, bounces again, etc. etc. See the diagrams and animations on this page – they might help. As the wave bounces back and forth, it settles in to a total result where it looks like the string is just bouncing up and down like a skipping rope. The longer the string, the lower the note, because it takes longer for the wave to bounce back and forth on the string. You can also lower the note by lowering the tension of the string, since this will slow down the speed of the wave moving back and forth on it. The last way to lower the note is to make the string heavier (i.e. by making it thicker) – since a heavier string is harder to move, the wave moves slower on it.
The air in a pipe behaves exactly the same way. If you “pluck” the air in the middle of a pipe (say, by clapping our hands, or coughing, or making any noise at all) then the sound wave travels along the pipe until it hits the end. Whether the end of the pipe is capped or not, the wave will bounce back and travel back through the pipe in the opposite direction from whence it came. (Whether the pipe is closed (capped) or open only determines the characteristic of the reflection – there will be a reflection either way.) It might help to look at the animations linked on this page to get an idea of how the air molecules behave in a pipe. As the wave bounces back and forth off he two ends of the pipe, it also settles down (just like the guitar string) into something called a “standing wave”. This is the pipe’s equivalent of the skipping rope behaviour in the guitar string. The result is that the pipe will resonate or ring at a note. The longer the pipe, the lower the note because the speed of the sound wave moving in air in the pipe stays the same, but the longer the pipe, the longer it takes for the wave to bounce back and forth. This is basically how all woodwind instruments work.
What’s interesting is that, when it comes to resonating, a room is basically a pipe. If you “pluck” the air in the room (say, by putting sound out of a loudspeaker) the sound wave will move down the room, bounce off the wall, go back through the room, bounce of the opposite wall, etc. etc. etc. (other things are happening, but we’ll ignore those). This effect is most obvious on a graph by putting some sound in a room and stopping suddenly. Instead of actually stopping, you can see the room “ringing” at a frequency that gradually decays as time goes by. However, it’s important to remember that this ringing is always happening – even while the sound is playing. So, for example, a kick drum “thump” comes out of the speaker which “plucks” the room mode and it rings, while the music continues on. You can see this in Figure 8, below.
Figure 8 shows the concept of the effect of a room mode. The sound coming out of the loudspeaker is shown on the top plot, in black. The response in the room is shown in the middle plot in blue. You can see there that the room keeps “ringing” at a frequency after the sound from the loudspeaker stops. The red plot on the bottom is the difference between the two plots – in other words, the “sound” of the room mode in isolation (note that it’s at a different scale than the top two plots to make things easier to see).

There are two audible effects of this. The first is that, if your music contains the frequency that the room wants to resonate at, then that note will sound louder. When you hear people talk of “uneven bass” or a “one-note-bass” effect, one of the first suspects to blame is a room mode.

The second is that, since the mode is ringing along with the music, the overall effect will be muddiness. This is particularly true when one bass note causes the room mode to start ringing, and it keeps ringing when the next bass note is playing.  For example, if your room rings on a C#, and the bass plays a C# followed by a D – then the room will be ringing at C#, conflicting with the D and resulting in mud. This is also true if the kick drum triggers the room mode, so you have a kick drum “plucking” the room ringing on a C# all through the track. If the tune is in the key of F, then this will not be pretty.

If you would like to calculate a prediction of where you’ll have a problem with a room mode, you can just do the following math:

metric version: room mode frequency in Hz = 172 / (room length in metres)

imperial version: room mode frequency in Hz = 558 / (room length in feet)

Your worst modes will be the frequencies calculated using either of the equations above, and multiples of them (i.e. 2 times the result, 3 times the result, and so on).

So, for example, if your room is 5 m wide, your worst-case modes will be at 172 / 5 = 34.4 Hz, as well as 68.8 Hz, 103.2 Hz and so on. Remember that these are just predictions – but they’ll come pretty close. You should also remember that this assumes that you have completely immovable walls and no absorption – if this is not true, then the mode might not be a problem at all. (If you would like to do a more thorough modal analysis of your listening room, check out this page as a good start.)

Sadly, there is not much you can do about room modes. There are ways to manage them, including, but not exclusive to the following strategies:

• make sure that the three dimensions of your listening room are not related to each other with simple ratios
• put up membrane absorbers or slot absorbers that are tuned to the modal frequencies
• place your loudspeaker in a node – a location in a room where it does not couple to a problematic mode (however, note that one mode’s node is another mode’s antinode)
• sit in a node – a location in a room where you do not couple to a problematic mode (see warning above…)
• use room correction DSP software such as ABC in the BeoLab 5

## Reverberation

Reverberation is what you hear when you clap your hands in a big cathedral. It’s the  collection of a lot of reflections bouncing from everywhere as you go through time. When you first clap your hands, you get a couple of reflections that come in separated enough in time that they get their own label – “early reflections”. After that, there are so many reflections coming from so many directions, and so densely packed together in time, that we can’t separate them, so we just call them “reverberation” or “reverb” (although you’ll often hear people call it “echo” which is the wrong word to use for this.

Reverb is what you get when you have a lot of reflective surfaces in your room – but since it’s so irregular in time and space, it just makes a wash of sound rather than a weird comb-filter effect like we saw with a single reflection. So, although it makes things “cloudy” – it’s more like having a fog on your glasses instead of a scratch. Think of it like the soft focus effect that was applied to all attractive alien women on the original Star Trek – you lose the details, but it’s not necessarily a bad thing.

## So what are you gonna do about it?

Fine, this is a short-form version of what a room’s acoustics does to the sound of a loudspeaker, but how do we, as a manufacturer of loudspeakers, ensure that our products can withstand the abuse that your listening room will apply to the sound? Well, there are a number of strategies that we use to do what we can…

1. ABC. The BeoLab 5 has a proprietary system built-in called Adaptive Bass Control or ABC. Pressing a button at the top of the loudspeaker starts a measurement procedure that is performed using a built-in microphone that measures the loudspeaker’s behaviour in two locations. Actually, what it’s doing is looking at the difference in the loudspeaker’s response in those two positions of the microphone to determine the radiation resistance that the loudspeaker “sees” as a result of reflective surfaces in the room. The ABC algorithm then creates a filter that is used to “undo” the effects of some of the low-frequency effects of the room’s acoustics. For example, if the radiation resistance indicates that the loudspeaker is close to a wall (which, as we saw above, will boost the bass) then the filter will reduce the bass symmetrically. That way, the loss in the filter and the gain due to the wall will cancel each other.

2. Position switches. ABC in the BeoLab 5 is a very customised filter that, in part, will adjust the loudspeaker’s response for placement near a wall or in a corner. Almost all of the other BeoLab loudspeakers (and other sound systems such as the BeoPlay A8 and A9, for example), include a manual-adjusted “position switch”. This allows you to use one of three filters that we have customised in the development of the loudspeaker to account for its behaviour according to whether you have placed it away from a reflective surface (“Free”), near one surface (“Wall”) or in a Corner. This is not just a filter that adjusts the bass level. The three filters for “free”, “wall”, and “corner” have been calculated using three dimensional measurements of the acoustical behaviour of the loudspeaker. So, the filters for the BeoLab 3 are completely different from those for the A9, for example, because they have very different directivity characteristics.

3. Sound design in multiple rooms. As I talked about in a previous posting, when we do the sound design of all of our loudspeakers, we tune each of them in at least 4 or 5 rooms with very different acoustical behaviours ranging from a very “dead” living room with lots of absorptive and diffusive surfaces to a larger and very “live” space with a minimalistic decorating, and large flat surfaces (just like the description in the original question). Once we have a single sound design that is based on the common elements those rooms, we test the loudspeakers in more rooms to ensure that they’ll behave well under all conditions.

## Wrap-up

Of course, I haven’t covered everything there is to know about room acoustics here. And, of course, you can’t expect a loudspeaker to sound exactly the same in every room. If that were true, there would be no such thing as a “good”concert hall. A room’s acoustical behaviour affects the sound of all sound sources in the room. On the other hand, humans also have an amazing ability to adapt – in other words you “get used to” the characteristics of your listening room. Back when I was working as a part-time recording engineer in Montreal, I did a lot of recordings in churches. Typically, we (the producer and I) would set up a control room with loudspeakers in a back room, and the musicians would sit out in the church. When we arrived to set up the gear, the first thing was to set up the monitor loudspeakers and a CD player, and we would play CD’s that we knew well while we set up everything else. That way, we would “learn” the characteristics of the control room (since we already knew what was on the discs and the characteristics of the monitor loudspeakers). So, if all of our CD’s sounded like that had too much bass, then we should do a recording with too much bass – it was the fault of the control room.

However,  there is no debate that, due to lots of issues (the first two that come to mind are frequency range and directivity) two different loudspeakers will behave differently from each other in two different rooms. In other words, if you listen to loudspeaker “A” and loudspeaker “B” in a showroom of a shop, you might prefer loudspeaker “A” – but if you took them home, you might prefer loudspeaker “B”. This would not be surprising, since what you hear is not only the loudspeaker but the loudspeaker “filtered” by the listening room. This is exactly why, when you are buying a loudspeaker, you should audition it in your home in order to ensure that you will be happy with your purchase. And THIS is why you can arrange a home demonstration of Bang & Olufsen loudspeakers through your dealer.

# B&O Tech: The Naked Truth II

#12 in a series of articles about the technology behind Bang & Olufsen loudspeakers

As I mentioned in an early posting about two months ago, if I didn’t have time to write enough, I’d cop out and post some photos of development models of some of our loudspeakers. It’s been a busy week. So, here are some photos of the BeoLab 18 and BeoLab 14.

# B&O Tech: How to Make a Loudspeaker Driver (A primer)

#11 in a series of articles about the technology behind Bang & Olufsen loudspeakers

I realised this week that I’ve been throwing around words like ” voice coil”, “suspension”, “surround” and “spider” when I talk about loudspeakers, but many people don’t know what these things are – or how a loudspeaker driver works in general… So, this week, I thought I might back up a couple of steps and talk about some basics. There’s nothing here about Bang & Olufsen loudspeakers specifically – it’s just an introduction to how loudspeaker drivers (like woofers, for example) work.

Back in 1820, a Danish guy named Hans Christian Ørsted was in the middle of giving a lecture when he noticed that, when he switched a circuit on and off, a compass sitting nearby on the desk moved a little. Since he had been poking around with experiments in electricity and magnetism for years, it didn’t take him long to put two and two together and come up with the idea that, when you run electrical current through a wire, you get a magnetic field around it. (Interestingly, not only did Ørsted figure this out (unless you believe that Romagnosi did it), but he also wrote papers on aesthetics – and he was the first person to isolate the element aluminium – and he founded Den Polytekniske Læreanstalt which, today we call the Danish Technical University. So, he had a big influence on B&O in many respects.)

Nowadays, we know that, by putting current through a wire, you produce a magnetic field that has magnetic lines of force that encircle the wire. The direction of the lines of force are dependent on the direction of current, and the extent by which the magnetic lines of force extend away from the wire is dependent on the amount of current.

Depending on whether or not you believe Benjamin Franklin you can use your right or left hand to determine the direction of the lines of force. Figure 1, below, shows a right hand (which indicates that we believe Benjamin Franklin and we say that current runs from the positive terminal of a battery to the negative terminal, which is, in fact, incorrect.). The thumb points in the direction of the current and your other fingers wrap around the wire in the same direction as the magnetic lines of force (which go from North to South on a magnet).

If you take that same wire, keep running current through it, and coil it up like a spring, you can make a slightly more useful magnet that actually has a North pole and a South pole. Again, you can use your right hand to figure out which end is which – you wrap your fingers around the spring in the same direction of the current going through the wire, and your thumb will be pointing towards the North pole of the magnet, as is shown in Figure 2.

Now, if you take two magnets and you put them end-to-end with the North of one facing the North of the other (or South to South), they’ll push each other apart. If you put them North-to-South, they’ll pull each other together.

So, let’s do something weird. We’ll make a coil of wire, and we’ll put it in a strange-looking permanent magnet that is a bit like a horseshoe magnet that has been wrapped around itself to make a circular plug in the middle which is one pole (say, North) and a ring around it which is the other pole (say, South) as is shown in Figure 3.

Now, if I put current through the wire, I’ll make a magnetic field around it that will either push against or pull towards the magnetic field of the permanent magnet around it. In other words, if it’s free to move, it will.

Now, since a loudspeaker, generally, is a thing that is used to convert electrical energy into acoustical energy; and, since in order to create acoustical energy (i.e. make noises) we need to move air molecules; we can use this strange device we’ve made in Figure 3 to our advantage. However, let’s be a little more methodical about this…

So, let’s build a dynamic moving coil loudspeaker driver, bit by bit. We’ll start by talking about its name. The “dynamic” part means that the basic principle that does the work is electromagnetism (as opposed to electrostatics or some esoteric methods like using plasma, tesla coils, or cats). The “moving coil” part is because, uh, the part of the device that moves in the magnetic field of the permanent magnet is a coil of wire.

What we want to do is to put the wires of the coil inside a magnetic field that is as strong as we can make it (within reason, of course). The easiest way to do this is to make the “gap” the coil sits in as small as possible (and, of course, to use as strong a magnet as we can fit or lift or afford to buy). So, let’s make a small gap for the coil to sit in.

We start by making a “bottom plate” and connect a “pole piece” – this results in a shape that looks like a disc with a cylinder. It’s made out of soft iron because soft iron is a really good magnetic conductor. (In other words, if you stick a magnet on a piece of soft iron, the soft iron basically becomes an extension of the magnet without losing very much magnetic force.) That bottom plate and pole piece assembly is shown in Figure 4, below. I’ve made it red just to keep things clear later. It’s usually not red in real life.

As you can see already, the “plug” in the middle of the magnet in Figure 3 is already visible as part of the pole piece in Figure 4. However, in order to make the strength of the magnetic field greater (in other words, in order to concentrate the magnetic lines of force) we want to make the gap (where the coil is going to sit) narrower. This can be done by making the cylinder on the pole piece a little bigger in diameter – but only where the coil of wire will be. That’s done by putting a ring around it, as is shown by the blue part in Figure 5, below.

Now we add the magnet as you can see in Figure 6.. This looks like a ring that sits on the disc part of the pole piece. The top of the ring is one pole (say, South) and the bottom is the other pole (say, North) of the magnet. However, this means that the North pole of the magnet is extended to the top of the cylinder on the pole piece because (as I said earlier) the soft iron is a good magnetic conductor.

You can see in Figure 6 that the gap between the top of the pole piece and the magnet is pretty big, so let’s make it smaller by putting a “top plate” on the top of the magnet. This is another disc of soft iron, where the hole is just a wee bit bigger than the diameter of the ring around the top of the pole piece as shown in Figure 7. This means that the South pole of the magnet is now the inside edge of the hole in that disc, so we’ve made a circular gap (between the top plate and the ring on the pole piece) that is very small, and therefore has a very concentrated magnetic field.

Unfortunately, we can’t just make a coil of wire and stick it in the gap and hope that it’s going to behave. Instead, we take a roll of cardboard (or something else) – a bit like the cardboard tube in the middle of a roll of toilet tissue – and wrap the coil of wire on that. That cardboard roll that supports the coil is called the “former” – it’s shown in Figure 8.

One little extra piece of information here. Since the voice coil, sitting in a magnetic field is the system that essentially converts electrical energy into movement, we call it the loudspeaker driver’s “motor”. Of course, it isn’t a motor that causes something to spin – but it does cause something to move.

Great. Now we have the coil of wire (the “voice coil”) wrapped around the former, sitting in the magnetic field. So far so good. Now we can put current through the wire and it will want to move in or out of the magnetic (depending on which direction we’re sending the current in). Now, our first problem is that, even if the voice coil and former moved out and in, there is nothing there to push and pull the air molecules in front of it – so it won’t make a lot of noise. So, let’s start putting up a surface that can move some air. We’ll start by putting on a “dust cap” which seals off the end of the former. This is the bump that you see on the front of a woofer in the middle of the cone – so we’re starting to get out to the visible “pretty face” of the loudspeaker driver. The dust cap is shown in Figure 9. Note that the dust cap is not always the same diameter as the former. Note as well that it is usually, but not always convex. Note as well that some drivers don’t have a discrete dust cap (like the BeoLab 3 woofer, for example).

Now we have a problem. We can put current into the coil and get it to move, but there is nothing there to stabilise it. What we need is something to make sure that it doesn’t fall down when you put the loudspeaker on its edge (as most are…). So, we’ll put in a stabiliser. It has to keep the former centred in the magnetic gap, but it also has to be flexible to allow the former to move in and out of the magnet. This part of the loudspeaker is called the “spider” – it looks like a disc that has wiggles in it that can stretch as the former moves in and out. This spider is shown attached to the former in Figure 10. Note that its outside will attached to something else, later.

Welcome to later. Now we need a frame to attach the outside edge of the spider and some other parts of the loudspeaker to – as well as to allow us to attach the whole loudspeaker to a cabinet. This part is called the “basket” – it doesn’t do much other than act as a structural support for everything – a bit like the steel beams in a building. The basket is shown in Figure 11. It may be interesting to note that the basket for an automotive loudspeaker driver is a little different from one for a home loudspeaker because it has to be able to deal with the possibility of a nasty accident. For example, a friend who knows such things once told me that it’s a bad idea to put a woofer intended for a home loudspeaker in a car door because if you’re ever in a side impact collision, it’s not inconceivable that the magnet will rip away from the basket, shoot across the car and cut your legs off. So now I’ve warned you…

Now we can put the rest of the loudspeaker parts on. We attach a “diaphragm” or “cone” which makes the moving surface bigger. That’s the medium-dark green part in Figure 12. If we left it at that, when we moved the loudspeaker in and out of the magnet, it would sag, because the spider isn’t strong enough to keep the whole thing vertical. So, we add a “surround” which is usually made of foam or rubber (or fabric, in the old days). The surround is a flexible ring that is glued to the basket and the edge of the diaphragm. It’s the lightest green thing in Figure 12.

So, now when you put current through the voice coil, it pushes out of (or pulls into) the magnet and moves the former, dust cap and diaphragm with it. This causes the spider and the surround (usually grouped into what we call the “suspension”) to stretch.

If we take the device in Figure 12 and cut it in half, we get a cross section like the one shown in Figure 13.  And, just to prove that I’m not lying, I cut apart a real woofer  – it’s shown in Figure 14. And then, not satisfied that I had done enough damage, I did it again to a BeoLab 3 woofer – those photos are in Figures 15 to 19. Another good example is this picture.

That’s about it for this week. If you want to do a little more digging for yourself, you can look into things like the difference between overhung and underhung voice coils, neodymium vs ferrite, or just watch some relaxing, cool, tangentially-related videos like this one or this one or this one or this one. Or maybe just this.

For the purposes of this explanation, I said that the top of the pole piece is the North pole of the permanent magnet, and the top plate’s inner edge is the South pole. However, there is no fixed convention for this. Manufacturers will almost always ensure that, when you put a positive voltage on the positive terminal of the loudspeaker, the diaphragm will move outwards. However, the north/south-ness of the magnet and the direction the voice coil is wound, and which end of the wire goes to which terminal vary not only from manufacturer to manufacturer, but model to model within one manufacturer’s portfolio.

# B&O Tech: Thermal Compression Compensation

#9 in a series of articles about the technology behind Bang & Olufsen loudspeakers

## Recipe for `Befuddled Speaker Enthusiast´

Makes: One individual with reduced faith in loudspeaker reviews

Total time: approximately 2 hours

Directions

1. Take a woofer and put it in a cabinet
2. Connect an amplifier to it
3. Put it in a sauna
4. Set the room temperature to 20° C and wait until everything in the room is the same temperature
5. Measure the woofer’s on-axis response with a microphone
6. Look at the pretty plot of its magnitude response
7. Turn up the thermostat to 100° C and wait until the woofer warms up
8. Measure the response again
9. Look at the new pretty plot of its magnitude response

## The setup

When you read a magazine review of a loudspeaker, it will include a measurement of its “frequency response” (more accurately called its “magnitude response”) which shows (ignoring a bunch of things) how loud different frequencies are when they come out of the loudspeaker assuming that they all came in at the same level.

However, as we saw in a previous article,  for a Bang & Olufsen loudspeaker, this magnitude response is dependent not only on the loudspeaker, but how loudly you’re playing the signal.

Unfortunately, it gets much worse than this… For example, if we take a woofer (say, the one from the recipe above, for example) we can explain its electromechanical characteristics by breaking it down into different components (both actual and analogical). For example, the suspension (which is comprised of the surround and the spider) can be thought of as a spring. The electrical analogy for this is a capacitor.  If you take all of the moving parts in the loudspeaker driver, they all add up to a mass that has to be moved – the electrical analogy for that mass is an inductor (since an inductor has some electrical “inertia” just like the mass of a bunch of loudspeaker bits). Some of the components are not an electrical analogy – they are real electrical components. For example, the voice coil, since it’s a coil, acts as an inductor. And, since it is a thin bit of wire, it also has some resistance to the flow of electrical current through it, so it’s also a resistor.

If you look at the diagram above, you’ll see a very simplified “circuit” that shows the components of a moving coil dynamic loudspeaker. If these components don’t look familiar to you, don’t worry, it’s not important. Some components in the circuit are actual electrical things (like the resistance of the voice coil, shown in red) and others are analogies – electrical representations for a mechanical component in the system (such as a capacitor representing the “spring” of the surround and the spider).

If you know how each of these components behaves, and you know the correct values to put in for a given loudspeaker, and you know how to do the right math, then you can come pretty close to getting a decent prediction of the response of the loudspeaker that you’re modelling with the circuit. However, if you just put in one value for each component, then you’re assuming that they never change – in other words that you’re dealing with a “linear” system.

The problem is that this assumption is incorrect. For example, the Voice Coil Resistance – the amount that the wire in the voice coil resists the flow of current through it when the loudspeaker driver is not moving – changes with temperature. The hotter the wire gets, the higher the resistance goes. (This is a normal behaviour for most resistors.) If the voice coil resistance changes, then the whole system behaves differently, since it isn’t the only component in the circuit. So, as we change the temperature of the voice coil, the total response of the loudspeaker changes.

Sadly, the temperature of the voice coil isn’t only dependent on the room temperature as it seemed to be in our recipe for a Befuddled  Speaker Enthusiast. As soon as you start playing sound with a loudspeaker, it starts heating up. The louder the signal (either because you turned up the volume or because your Metallica album just came on) the hotter it gets. So as you play music, it heats and cools. The speed with which it heats up and cools down is dependent on its “thermal time constant” – a big woofer with a giant magnet will take longer to heat up and cool down (and therefore have a longer thermal time constant) than a little tiny tweeter.

So, now you should have at least three questions that deserve answers:

1. How much does the temperature vary when I play music?
2. How does the response of the loudspeaker change with temperature?
3. How much does the response of the loudspeaker change with temperature?
4. What are you going to do about it?

## 1. Voice coil temperature

As I’ve talked about in a previous article, a loudspeaker driver is, give or take, about 1% efficient. That means that 99% of the power that you push into it (from the amplifier) is not converted into sound. Unfortunately, all of that power is lost as heat – almost all of it at the voice coil of the loudspeaker. So, the louder your music, the hotter your voice coil gets. Of course, if you have a way of cooling it (by using other parts of the loudspeaker as a radiator to your listening room) then it won’t get as hot, and it will cool down faster.

Let’s take a BeoLab 5 as an example (since that’s where we’re headed anyway…). Let’s take some relatively new-ish pop music (which has been mastered to be fairly loud due to a war that has been going on for years) and play it on a B&O player through Power Link (B&O’s version of a line level signal) at maximum volume on a BeoLab 5 whilst monitoring the temperature of the voice coils. What you’ll see if you do this is something like the plot below.

As you can see in the screenshot in Figure 2, the lower woofer (a 15″ driver connected to a 1000 W Ice Power amplifier) varied with a maximum of about 205° C. While it was playing this music at this level, it rarely dropped below 120°C.

This means that the difference in temperature of the woofer was 185°C at a maximum (205°C – 20°C) and rarely below 100°C.

In case you are wondering, this temperature cannot be measured directly, since it would destroy the voice coil if we tried to do so. Instead, what we do is to measure the temperature of the loudspeaker driver magnets, and use that real-time data input in addition to the signal that we’re sending to the drivers to calculate the temperatures of the voice coils based on thermal models of each of them. As you can see in Figure 3, below, the magnet temperatures are very different, and react much more slowly. These measurements were taken at exactly the same time as the ones shown in Figure 2. (Note that, although the mid woofer and woofer voice coils are roughly the same temperature, the mid woofer magnet is hotter than the woofer magnet by about 20°C or so. This just proves that their thermal models are different.)

## 2 & 3. Loudspeaker response changes

So, now the question is “what does this change in temperature do to the response of the driver?” We’ll only deal with one driver – the woofer.

As I mentioned above, the thing that changes most in the model shown in Figure 1 is the loudspeaker driver’s voice coil resistance. For those of you with a background in reading electrical circuits, you may notice that the one shown in Figure 1 has some reactive components in it which will result in a resonance at some frequency. For those of you without a background in reading electrical circuits, what this means is that a loudspeaker driver (like a woofer) has some frequency that it “wants” to ring at – if you thump it with your thumb, that’s the frequency that you will hear ringing – a bit like a bell with a low pitch.

As the voice coil resistance goes up, its resistance increases, and we generally lose sensitivity (i.e. level or loudness) from the woofer. In other words, the hotter it gets, the quieter it gets. However, this only happens at the frequencies where the resistor is not “overridden” by another component – say the mechanical resonance of the woofer or the inductance of the voice coil.

The total result is shown for various temperature differences in Figure 4. Notice that these plots show the change in magnitude response of the driver with CHANGES in temperature. So, the blue curve at the top is the change in magnitude response (which is 0 dB at all frequencies – in other words no change) when the loudspeaker is playing at the same temperature it was measured at (let’s say, 20°C or room temperature). As the temperature of the voice coil increases above that temperature, you can see that you lose output in two frequency bands on either side of a “bump” in the response – this is at the resonant frequency of the loudspeaker driver.

So, the louder you play, the more low end you lose, apart from a peak in the response (which also rings in time) at the resonant frequency of the driver.

In case you’re wondering, the plot shown in Figure 4 is pretty close to the actual response of the 15″ woofer in the BeoLab 5 at different temperatures above room temperature.

## The solution

Interestingly, all of the stuff I said above is true for every loudspeaker. So, if you’re the kind of person who believes that the only proper loudspeaker is one where you have nothing but a loudspeaker driver (in a cabinet of any kind, or not) and an amplifier – and no weird filtering or mucking-about going on, then you’ll have to live with the kind of unpredictable behaviour that you see above. This happens all the time to every dynamic loudspeaker. Since, in a passive loudspeaker, there’s nothing you can do about this (except for trying to keep the drivers cool somehow) you don’t often hear passive loudspeaker manufacturers talking about this little skeleton in their closet…

However, since a BeoLab 5 “knows” the temperature of the voice coil of the woofer, and since it has been programmed with the curves shown above in Figure 4, we can do something about it.

In essence all we need to do is to take Figure 4, flip it upside down and make a filter that “undoes” the effect of temperature on the loudspeaker’s response. In other words, if (because the woofer gets 160°C above “normal”) it drops 3 dB at 20 Hz, the BeoLab 5 knows this and adds 3 dB at 20 Hz. So, built into the BeoLab 5 is a set of filters that are used, depending on the temperature of the woofer’s voice coil. These filters are shown in Figure 5.

It’s important to note three things here.

1. This can be done because we know the behaviour of the woofer at different temperatures (this was measured as part of the development process)
2. This can be done because the loudspeaker “brain” (the DSP) knows the temperature of the voice coil in real time as you’re playing music
3. This filter should only be applied to the woofer. The mid woofer and the other drivers have different behaviours and should not be affected by this correction curve. Therefore, this filtering can only be done because the BeoLab 5 is an active loudspeaker with independent filtering for each loudspeaker driver.

## Some extra information

You should be left with at least one question. I said above that, as the music gets loud, the woofer heats up, so you lose output, so we add a filter that compensates by putting more signal into the driver.

“Waitaminute!” I hear you cry… “The problem is caused by the signal being too loud, so you make it louder!?” Well… yes.

However, there is one more trick up our sleeve. In a previous posting, I mentioned in passing that we also have Thermal Protection in almost all of the loudspeakers in the B&O portfolio. This means that the DSP brain knows the temperature of the drivers and, in a worst-case situation, turns the levels down to protect things from burning up. So, if we go back to the example of a BeoLab 5 playing at full volume, let’s see what’s happening to the signal levels.

These curves in Figure 6 show the gains applied to the four loudspeaker drivers in a BeoLab 5 at the same time as the measurements shown in Figures 2 and 3 were being made. In fact, if you look carefully at Figure 2 around the 23 minute mark, you’ll see that the temperature dropped – which is why the gain in Figure 6 increases (because it can!) in response.

Now, don’t panic. The BeoLab 5 isn’t screwing around with the gains of the drivers all the time. Remember that this test was done at FULL VOLUME – which, for a BeoLAb 5 is VERY LOUD. The gains shown in Figure 6 are a last-ditch effort of the loudspeaker to protect itself from a very mean customer (or the very mean children of a customer who is away for the weekend). This is the equivalent of the airbags deploying in your car. You know that if the airbags are outside the steering wheel (or if the gains in the BeoLab 5 dropped by 15 dB or so) something significant occurred…

Thanks to Gert Munch for his help in cleaning up the mistakes I made in the drafts up to and including the penultimate version of this article.

# B&O Tech: Subwoofer Tweaking for Beginners

#8 in a series of articles about the technology behind Bang & Olufsen loudspeakers

In a previous post, I talked about why a subwoofer might be a smart addition to a sound system – and why a subwoofer brings something different to a Bang & Olufsen loudspeaker configuration than it does for other companies’ loudspeakers.

Usually, in a loudspeaker system that includes a subwoofer, the signal that is sent to that subwoofer is either

1. coming in directly from the medium (say, the Blu-ray disc) from the LFE (Low Frequency Effects) channel OR
2. created by something called a “bass management system” which is basically a mixer (something that adds audio signals) and some frequency division OR
3. all of the above

Let’s assume, for the purposes of this article, that we’re talking about #3. So, let’s start by talking about how a system like that would work. The simple version is that you take an audio input, send it to two different filters, one called a “high pass filter” which lets the high frequencies pass through it and it makes the lower frequencies quieter. The second filter is called a “low pass filter” – you can figure that one out. The output of the high pass filter is sent to your “main” loudspeaker, and the output of the low pass filter is sent to the subwoofer.

That’s what happens if you have a good ol’ fashioned monophonic system with only one audio channel, one main loudspeaker and one subwoofer. Most people nowadays, however, have more than one main loudspeaker and lots of channels coming out of their players. So, in cases like that, we have to take the low end (the bass) out of each of the main channels using low pass filters, add the results all together, add the LFE channel to that, and send the total to the subwoofer. A simple version (with some important details left out, since we’re only talking about basic concepts here…) is shown in the diagram below.

Let’s take an audio signal and add it to another audio signal – and, just to keep things simple, we’ll make them both sine waves. This is done by looking at the amplitude of the two signals at a given moment in time, adding those two values, and you get a result. For example:

If you take a look at the example above, there are a couple of things that you can see. The first is that, if you add two sine waves, you get a sine wave. Also, if you add two sine waves of the same frequency, you get a sine wave of the same frequency. Next, if the two sine waves have the same amplitude and are “in phase”- basically meaning that they have the same value at the same time (sort of, but not really like a delay difference of 0) – the result is a sine wave that is in phase with the other two with double the amplitude of the two inputs.

Now, let’s move one of the two signals in time. We’ll make it late by half the length of the sine wave (in time) and see what happens.

Now you can see that, since the bottom plot is the negative of the top plot at any given moment in time (because we’ve delayed it by half a “wave”), when you add them together, you get no output.

Let’s look at one last example, where the two input signals have some phase difference that is not quite so simple. This is shown in the figure below.

Again, you can see that, when you add two sine waves of the same frequency, you get another sine wave of the same frequency. You can also see that the phase (remember – phase is something like delay) of the result is not the same as the phase of either of the two inputs. Finally, you can see that the amplitude (the maximum value) of the result is neither 0 nor 2 – it’s something in between.

So, the moral of this story is that, if you have two sine waves then the result (what you hear) is (at least partly) dependent on how the two signals add – and that result might mean that you get something twice as loud as either input – or it could mean that you get nothing – or you get something in between.

## The real world

The three plots shown above illustrate some simple examples of what happens when you have two sound sources that are added together to produce a result. For the purposes of this article, the two sources are two loudspeakers – the “main” loudspeaker and the subwoofer, and the result is the sum of those two signals at your listening position. Let’s go back to thinking about what frequency ranges are produced by these two loudspeakers. The plot below shows the magnitude responses of the filters in a BeoVision 11’s internal bass management system at its default crossover frequency of 120 Hz. The red curve shows the response of the low pass filter whose output is sent to the subwoofer output. The black curve shows the response of the high pass filter whose output is sent to a main loudspeaker.

Take a look at the response of the signal that is processed by the low pass filter. You’ll notice that, although the “crossover frequency” is set to 120 Hz, there is still signal coming out of the filter (and therefore out of the subwoofer) above that frequency – it’s just getting quieter as you go further up and away from the crossover.

You might also notice that, at the crossover frequency, the level of the signal coming out of the low pass filter is identical to the level of the signal coming out of the high pass signal. That’s (more or less) what makes it the crossover frequency. As you move down from that frequency, you gradually get more out of the low pass (the sub) than the high pass (the main). As you move up in frequency, the opposite happens. However, there is a region around the crossover where both loudspeakers are contributing roughly equally (within reason) to the signal that you get at the listening position. So, the “truth” is a little more like the plot below:

I’ve chosen -20 dB as the point where I can start ignoring a signal, but that’s a pretty arbitrary decision on my part. I could have set my threshold higher or lower and still argued that I was right. So, if you disagree with my choice of -20 dB as the threshold of “I don’t care any more” then I agree with you. :-)

By now, you should start to worry a little. You should be asking something like “hmmmm… you’re telling me that there is a big band of frequencies (say, roughly between 1 and 2 octaves) right around where human voice fundamental frequencies sit (well, at least my voice sits there – but I sing bass…) where a bass management system will send the signal out of two loudspeakers!? AND, to add insult to injury, you told me (in the previous section) that if the phases and amplitudes of those signals from those loudspeakers aren’t perfectly aligned, the result at the listening position won’t be the same as the input of the whole system?” If you ARE asking something like that, then you’re in good shape. As has been said by many other people in the past: the first step in fixing a problem is admitting you have one.

So, let’s ask a different question: what parts of the audio signal chain could affect either the amplitude or the phase of the signals coming out of the loudspeakers? Brace yourself… This list includes, but is not exclusive to:

1. The characteristics of the filters in the bass management system
2. The characteristics of the filtering in the loudspeakers
3. The physical principal of the loudspeaker (i.e. sealed cabinets will be different from ported loudspeakers which are different from passive radiators)
4. Diffraction (although this might be a small issue)
5. Latencies (total delay) of the loudspeakers (for example, digital loudspeakers have a bigger delay than analogue ones typically)
6. Distances of the loudspeakers to the listening position
7. The characteristics of the room itself
8. And more!

All of these issues (including the ones that fall under the “And more” category) have some effect on the phase (and amplitude) of the signal that you hear at the listening position. And, since some of these (like the distances and the room characteristics) are impossible for us (as a manufacturer) to predict, we have to give you, the end user, some way of adjusting your signals so that you can compensate for misbehaviour in your final system.

Now, although this is a “technical” article, I think that it would be too technical to start looking at the specifics of the phase responses of sealed cabinet vs ported loudspeakers, for example, since the details will be messed up by the listening room anyway. So, instead of getting into too many details, let’s just say that “you can’t expect your system to work perfectly without tweaking it” (see the reasons above) and just talk about some strategies for setting up your system so that it behaves as well as it can (without going out and hiring an acoustical consultant).

## BeoLab 19 Controls

The BeoLab 19 has a number of controls that have not been available on previous B&O subwoofers. As a result they may cause a little confusion and playing with them without knowing what to expect or listen for could result in your system not performing as well as it could. On the other hand, it could be that these controls could help you improve your system if you’re finding that it’s not really behaving.  Let’s take each control, one by one, and explain what it does, and talk about strategy afterwards.

### Gain

The gain knob (on the left in the diagram above) is basically just a volume knob that controls how loud the subwoofer is overall. Let’s say, for example, that you have a perfectly configured system, then the outputs of the subwoofer and the main loudspeaker mate perfectly and result in a perfectly flat response below, through and above the crossover region. (this never happens in real life – but we can pretend). The diagram below shows an example of this, where the top plot shows the outputs of the subwoofer and main loudspeaker and the bottom plot shows the total result at the listening position.

If you do nothing but change the gain of the subwoofer, (using the Gain knob on the BeoLab 19, for example) then the result would be something like the plot below.

You can see in the plot above that all you do is to boost a region of low frequencies without doing anything strange through the crossover region. So, if you like bass, this might be a nice tweak for you. However, in theory, your goal is to get a response like the one in the first plot, where the outputs of the subwoofer and main loudspeakers have the same level (at the listening position).

### LP Filter

One possible configuration of the BeoLab 19 is to connect it in parallel with your main loudspeakers and to not use and external bass management system.

If you do this, then you are relying on the fact that the main loudspeakers have a high pass filter built-in, and you will align the low pass filter inside the BeoLab 19 to have approximately the same frequency so that the total result is a smooth-ish crossover region. In order for the low pass filter to work, you will have to turn it ON using the switch. (Note that, if you’re using an external bass management system as in the BeoVision 11, for example, then you should turn the low pass filter OFF, thus removing it from the signal path of the subwoofer.)

In theory, the goal here is to match the cutoff frequencies so the two loudspeakers behave nicely together across the crossover region. For example, if the natural low frequency cutoff is about 50 Hz, and you set the LPF in the subwoofer to 50 Hz, then you get the result below

What would happen if you set the LPF incorrectly – let’s say that you make it higher than the correct value, since you would think that, by overlapping the sub with the main speaker, you’ll get more output and impress the neighbours. Well, the result would be the plot below.

As you can see, although the sub is now delivering more signal (because it’s going all the way up to 120 Hz instead of 50 Hz in the previous plot), you actually get a reduction in the total output of the system. This may be initially counterintuitive, but it’s true in our example, since (as you may remember from something I said earlier in this article) the phase of the subwoofer is, in part, determined by the characteristics of the filtering in the loudspeaker. By changing the low pass filter frequency, we change the phase of the subwoofer in the crossover region and result in a cancellation with the main loudspeaker instead of a summing. In essence, both the sub and the main loudspeaker are now working very hard to cancel each other (especially around 80 Hz or so) and you hear very little at the listening position.

On the other hand, I have assumed here that the main loudspeaker’s high pass filter is a very specific type. A different main loudspeaker with a low frequency cutoff of 50 Hz would have had a completely different behaviour as you can see below.

So, the moral of the story here is that setting the low pass filter frequency will have some effect on your total response. However, you should not jump to the conclusion that you can predict what the frequency should be – you will have to fiddle with the knob whilst listening to or measuring the total output of the system. You should also not jump to the conclusion that increasing the frequency range that is covered by the subwoofer in a parallel configuration will result in more output from your system. Overlap is not necessarily a good thing – sometimes, more is less…

### Phase

Go back up and take a look at the two sine wave in the plots in Figure 4. One way to describe these two waves is to say that the middle one is half a wave later than the upper one – in other words, they are 180º out of phase. Another way to describe them is to say that the middle one is the inverse of the upper one – they have the same instantaneous value at any time, except that they are the negative of each other (in other words, signal 2 = signal 1 * -1).

So, intuitively, you can see that shifting the phase of a signal by 180º is the same as flipping it upside down. This could mean that, for example, all other things being ignored, that when a kick drum tells your subwoofer to push outwards, shifting the phase by 180º will result in your subwoofer sucking inwards instead. However, this is only true if all other things are being ignored. As soon as your subwoofer has a high pass filter (i.e. a low frequency limit) and a low pass filter (a high frequency limit) and it’s a loudspeaker driver in a cabinet in a room, all bets are off. All of those aspects (and more!) will have some effect on the phase of the system, so you can’t predict whether the kick drum will cause the woofer to put out or suck inwards.

So, instead of worrying about the “absolute phase” of the subwoofer, it’s more interesting to worry, once again, how it matches up with the main loudspeaker. Let’s take exactly the same responses from the plots shown in Figure 14 above (which didn’t add together so well for some reason) and shift the phase of the sub by 180º using the Phase switch. The result is shown below in Figure 15.

As you can see, the big dip in the total response of the system (seen in Figure 14) has been corrected, and we now have more output (actually, a little too much) below that. So, the result is that the total system response is much better than it was without flipping the phase switch.

Of course, if we flipped the phase switch in a system that was behaving nicely, then bad things might happen. Let’s flip the phase on the system shown in Figure 9, for example. That total result would look like the one in Figure 16, below.

As you can see, you get the same amount of low bass in Figures 9 and 16. However, there is a nasty dip at the crossover frequency of 120 Hz when the two loudspeakers are cancelling each other.

So, the moral of the story here is that, if you have a problem in the crossover region between the main loudspeaker and the subwoofer, flipping the phase of one of the two might help the situation – although it might make things worse…

### Pos (aka Position)

Almost every loudspeaker in the Bang & Olufsen portfolio has a switch that lets you change the characteristics of the loudspeaker to compensate for the differences in its response as a result of its placement in a room. Generally speaking, the closer you put a loudspeaker to a wall, the more bass you’ll get out of it. If you put it closer to two walls (i.e. in a corner) you’ll get even more bass. However, that is a very general characterisation – the reality is that you’ll get a little more at some frequencies and a little less in other frequencies – and that behaviour is dependent on the diameters of the loudspeaker drivers, the crossover frequencies, and the  physical shape of the loudspeaker.

So, without getting into the details of exactly what is being changed in a BeoLab 19 (or BeoLab 2 or BeoLab 11 – or any other loudspeaker for that matter), let’s say that you should put the position switch in whatever setting best corresponds to the location of the loudspeaker in your room. However, if you want, you could cheat a little and fiddle with the switch to see if you like another setting more.

For example, if your loudspeaker is in the corner, and you put it in “free” mode, you’ll get LOTS of bass – too much bass. But if you like bass, this is one way to get it. Of course, there are other implications to this decision, but if you like bass enough, that might be reason enough to change to the “incorrect” the switch setting.

### Wired / Wireless

The BeoLab 19 has the ability to receive its input via the analogue or digital input OR via the wireless receiver module that is built into it. This switch merely tells the loudspeaker whether it should “listen” to the wired input (either analogue or digital) or the wireless one. (Note that the BeoLab 2 and the BeoLab 11 do not have wireless receivers.)

### L / R/ L+R

Most subwoofers (including the BeoLab 2 and the BeoLab 11) are built with the assumption that you will use them either:

• as a stand-alone subwoofer in a multichannel (i.e. 5.1 or 7.1) system where it gets the “.1” output from the source (that may, or may not have bass management) and so you just send one audio channel into it OR
• in a 2.1 setup where you want the left and right channels coming into the subwoofer where they are added together produce a mono bass signal internally

Consequently, most subwoofers either have 1 input (assuming that they are to be connected to the “subwoofer out” on something like an AVR) or a 2-channel stereo input (assuming that they should “see” left and right) that is summed to mono. BeoLab 2 and 11 are built based on the second assumption.

BeoLab 19 allows you to use the subwoofer in either of these configurations. So, in either “L” or “R” mode, it is only “listening to” the Left or Right audio channel on the Power Link input. In “L+R” mode, the input of the subwoofer is taking both audio input channels and summing them to make a mono input to the subwoofer. Note that, if you send exactly the same signal on the Left and Right audio channels on the Power Link cable, and then you switch the BeoLab 19 from either L or R to L+R, you’ll find that you get a doubling in the output level. This is because a signal plus itself is twice as loud. Since this is what BeoLab 2 and 11 do all the time, if you simply replace a BeoLab 2 or 11 with a BeoLab 19, you should put the 19 in “L+R” mode – otherwise you’ll lose some bass in your system.

However, if you want to use a single Power Link cable to run to the Subwoofer and to another loudspeaker (say, a centre channel, for example), then you should put the BeoLab 19 in either L or R mode (and the other loudspeaker in the opposite mode) so that you can access both loudspeakers independently. This is also the case if you want to run two BeoLab 19’s on the same Power Link cable and use the 2-channel LFE output option in a BeoVision 11. In this case, you se one BeoLab 19 to “L”, the other to “R” and set the Speaker Roles in the BeoVision 11 to “Sub Left” and “Sub Right” (or “Sub Front” and “Sub Back”) appropriately.

Note that, if you are in Wireless mode, the “L/R/L+R” switch does nothing.

## How to do it (Finally!)

### Method for an Externally Bass Managed Configuration

If your main loudspeakers and your subwoofer are connected to a system that has a bass management system, then you should use it. There are a number of reasons for this:

• the main loudspeakers may behave better (for example, with respect to distortion or port noise) if they are not being pushed by a lot of bass
• a bass management system will work for a multichannel loudspeaker system
• a bass management system (for example, in a BeoVision 11) will be capable of making some “intelligent” decisions with respect to your entire system
• a good bass management system (for example, in a BeoVision 11) will allow you to make fine adjustments to accommodate your configuration and room

So, your procedure here (assuming that you have a BeoVision 11 and a BeoLab 19 and some main loudspeakers) is as follows:

1. Turn off the LP Filter on the BeoLab 19, set the Phase to 0, set the Gain to 0, and set the other switches to whatever is best for your particular configuration.
2. Put the correct loudspeaker models into the Speaker Connections menu on the BV11.
This will compensate for differences in the latencies and sensitivities of the loudspeakers, in addition to making some intelligent decisions about where to route the bass.
3. Set your Speaker Distances correctly
This will ensure that you do not have phase differences in the loudspeakers at the listening position as a result of problems caused by the speed of sound and mis-matched distances.
4. Set your Speaker Levels correctly
On a BeoVision 11, this is done by making sure that, at the same volume level, all loudspeakers produce the same level in “dB SPL, C-weighted, Slow” on an SPL meter like this one, or this one, or this one, for example.
5. Turn on a piece of music that has a constant bass level
The opening of Freddy Mercury’s “Living on my Own” or Santanta’s “You Are My Kind” are a possible tunes. Claire Martin singing “Black Coffee” is also a good candidate. If you want to look like a professional, then I suppose that you could use pink noise or this track instead of music.
6. Sit in the listening position and listen to the total behaviour of the system. Pay particular attention to “unevenness in the bass”. In other words, listen to the bass and pay attention to whether some notes are quieter or louder than others.
7. In theory, if you performed Step 4 correctly, then you shouldn’t have to play with the Speaker Level in the TV or the Gain on the subwoofer.
8. If there is a general area somewhere in the middle of the bass where lots of notes are too quiet, try flipping the phase on the subwoofer.
9. If some individual frequencies (or notes) are quiet then playing with the allpass filter on the TV might help.
10. If some individual frequencies (or notes) are louder than others, this is probably caused by the room, and you might be able to deal with it by moving the subwoofer. If, when you put the sub in the corner, you make this problem worse, it is almost certainly the room acoustics that you’re dealing with, so moving the sub is your best bet.

### Method for a Parallel Connection Configuration

Since, in a configuration where the sub and the loudspeaker are connected in parallel, the behaviour of the transition between the BL19 and the main loudspeakers (let’s say that there are only two of them for this example) in the system is not only dependent on the loudspeaker models themselves, but also the distances to the 3 loudspeakers and the behaviour of the room, the best thing to do is to do a bunch of acoustical measurements, interpret the results and then make adjustments to the system, evaluating the measurements repeatedly as you go along. If you can’t do this, then you can tune it by ear. Unfortunately, this will take more time, and might require an extra person to help, but it will probably result in better results than doing nothing. Here is how I would do it:
1. Turn the LPF frequency as low as you can go
2. Turn on a piece of music that has a constant bass level
3. The opening of Freddy Mercury’s “Living on my Own” or Santanta’s “You Are My Kind” are a possible tunes. Claire Martin singing “Black Coffee” is also a good candidate. If you want to look like a professional, then I suppose that you could use pink noise or this track instead of music.
4. Sit in the listening position and ask someone to turn the LPF as low as it will go.
You should notice that there is a “hole” in the level of the bass between the subwoofer and the main loudspeaker. Turn up the LPF frequency and pay attention whether the “hole” fills up or gets worse. If it gets worse, flip the phase switch and start Step 4 again.
5. If the hole did not get worse, then keep turning up the LPF frequency until it sounds like there the hole is filled up.
6. One you’re done playing with the LPF frequency, try moving the Gain to adjust the bass to the level that you like.