#20 in a series of articles about the technology behind Bang & Olufsen loudspeakers
This was a presentation I did at a technical press event where we showed the BeoVision Avant for the first time. The video was done by one of the journalists at the event. The associated article (in Danish) is here at http://www.recordere.dk.
#19 in a series of articles about the technology behind Bang & Olufsen loudspeakers
If you take a careful look around the connection panel of almost any Bang & Olufsen loudspeaker, you’ll find a three-position switch that is labelled something like “Free / Wall / Corner” or “F / W / C” or “Pos 1 / Pos 2 / Pos 3”. What does this do and how should you use it?
Let’s pretend that you have a loudspeaker that is perfectly omnidirectional, and it is in a free field (meaning that the sound that radiates from it is free to propagate forever without hitting anything – in other words, it’s floating in infinite space). Let’s then say that we measure the magnitude response of that loudspeaker and we find out that it has a perfectly flat response from 0 Hz to infinity Hz. Remember that the source is perfectly omnidirectional, so the response will be the same regardless of which direction you measure it from. This also means that if you do a lot of magnitude response measurements around the source and average them, it will also be flat, since the average of a whole bunch of the same thing is the same as any one of the things (i.e. the average of 5 & 5 & 5 & 5 & 5 & 5 & 5 is 5).
Now let’s divide the infinite space in half with a very large, perfectly flat wall that extends infinitely – and we’ll put it fairly close to the loudspeaker. Now, if we do a magnitude response measurement at one position, we’ll see a response that is comprised of alternating boosts and cuts as we go up in frequency. This is caused by the interference between the direct sound of the loudspeaker and its reflection off the wall. These two sounds arrive at the measurement microphone at two different times – which means that different frequencies will be separated in phase differently. The higher the frequency, the greater the phase difference between the direct and reflected sounds. And, depending on the phase at any one frequency, the result may either be constructive interference (where the two signals add) or destructive interference (where they cancel each other). If it helps, an easier way to think of this is that the wall is a mirror that results in a reflection of the loudspeaker on the other side of it. The sound that arrives at the microphone is the combination of the two loudspeakers (the real one and the one on the other side of the mirror). If we do an averaged pressure response measurement, the averaging that we have to do results in the fact that we lose the phase information in each of our individual measurements. However, each individual response that we measure has peaks and dips that affects how it adds to the other responses. In the very low frequencies the “two” loudspeakers are very close together relative to the very long wavelengths of low frequencies in air – so they add together almost perfectly. This means that the total output will be doubled at the very low end – 200% of the output (or 6 dB more) than without the wall. At very high frequencies, the outputs of the two loudspeakers add randomly – sometimes increasing, sometimes cancelling the total. The end result of this average is a messy response, but is roughly the same level as 141% (or 3 dB more) than if the wall weren’t there. (Note that the low end is 2 times louder, (because there are two “sources” – the real one and the reflected one. However, the high end is 1.41 times louder. 1,41 is the square root of 2 – the reason for this involves an explanation of power being proportional to the square of the pressure, so doubling the power results in multiplying the pressure by sqrt(2).) Take a look at Figures 2 and 3. You’ll see that the result of placing the theoretical wall near the theoretical loudspeaker is that the low end and the high end are boosted – but the low end is boosted about 3 dB more than the high end. If you compare Figures 2 and 3, you’ll see that the closer the loudspeaker is to the wall, the higher the top frequency of the “low end”.
If you divide space once more, using a second wall that is perpendicular to the first (so now your speaker is on the floor, next to a wall, for example), you are doubling the number of “loudspeakers” again. Now we have one “real” loudspeaker and 3 reflections. Let’s forget about the magnitude response at one location for now and just deal with the power response, since that’s a little less complicated. Now we have 4 times the output (or 12 dB more) in the low frequencies and, 2 times the output (or 6 dB more) in the high frequency ranges. (Notice again that the multiplier for the output in the low end is the number of loudspeakers – either real or reflected – and that the multiplier for the output in the high frequencies is the square root of that number.)
Finally, let’s add one last wall, perpendicular to the other two (i.e. two walls and the floor). This resuts in a total of 8 sources (one real and 7 reflected) which means that the output will be 8 times louder (or 18 dB) in the low end (than if the walls weren’t there) and 2.8 (sqrt(8)) times louder (or 9 dB) in the high end.
So, the first lesson to be learned here, for now, is that, in a theoretical world, where loudspeakers are perfectly omnidirectional and walls go forever, the more walls you have the bigger the bass boost. (Of course, you’ll also get a boost in the high end, but it will be smaller than the low-end boost, and you’ll probably compensate for that with the volume knob when the vocals and snare drum come in…) There is a second, nearly-as-important lesson. Look carefully, for example, at Figures 7 and 8. Starting in the low end, you can see the bass boost resulting from the collective reflections off the two walls. As you go up in frequency, you can see that the boost drops. However, before it levels out (albeit messily) at the high end, you can see that there is a deep drop in the level (i.e. in Figure 8, it’s at 100 Hz). This is because, for the particular wall distances we’re looking at, there is more cancellation of signals going on than there is constructive interference. So, the average is lower than if the walls weren’t there. This will be important later…
We can then take it one step further and consider that the very pretty graph shown in Figure 1 is extremely theoretical. A free field is an imaginary space – the reality is that a “free standing” loudspeaker is not really in a free field. For starters, it has to stand on something (unless you’re hanging it from the ceiling) – so the floor is not very far away – probably 1 m or so. Secondly, unless you live in a VERY large house, even when the loudspeaker is placed far from a wall, it’s probably not going to tens of metres away from any way. We can set a limit of something like 1 m on this – meaning, if you’re more than 1 m from any wall, we’ll call that “free”. This means that, in a real space, where the loudspeaker is at least 1 m from any surface, the response you get as a result of those three adjacent walls is roughly like the graph shown in Figure 8. The implications of this previous paragraph, in the real world, are important. What this means is that, when we do the sound design for a loudspeaker, we have to choose its position in a room rather carefully. Typically, it’s in a “free” position, which means, in a real world, about 1 m from each of the two adjacent walls (this isn’t measured exactly – everything in this article should be considered to be approximate). (Of course, loudspeakers that are, in all likelihood destined for a wall bracket are tuned on a wall instead.) So, the “free” position isn’t the same as the theoretical free field in Figure 1. It’s more like the not-very-close-to-a-surface case shown in Figure 8. The behaviour of the loudspeaker in this location is then the “reference” – the goal is then to ensure that, if a customer places the same loudspeaker against one wall or in a corner of two walls, the loudspeaker will sound the same as it does in the reference position. We do this by looking at the difference between the averaged response of the loudspeaker in the “wall” or “corner” location and the reference “free” position. For example, if we were making perfectly omnidirectional loudspeakers, and we say that 30 cm from a wall is close enough to call the loudspeaker in a “wall” position, then we would subtract the response curve shown in Figure 8 (the reference “Free” response) from the response shown in Figure 4. This difference, shown in Figure 9, below, is the “eq curve” applied to a loudspeaker that is placed closer to a wall. So, you can see that we get a large bump in the low end (in this case, with these dimensions) around 100 Hz, and dips below and above this peak (at 20 Hz and around 400 Hz).
If we were making perfectly omnidirectional loudspeakers, and we compare a “corner” position 30 cm from three perpendicular wall, then we would subtract the response curve shown in Figure 8 (the reference “Free” response) from the response shown in Figure 7. This difference, shown in Figure 10, is the “eq curve” applied to a loudspeaker that is placed closer to a wall. So, you can see that we get a larger bump in the low end (in this case, with these dimensions), still around 100 Hz, and a dip above this peak (at around 300 Hz).
So, this means that, for these perfectly omnidirectional loudspeakers, considering only these dimensions, the equalisation filters we would have to apply to the loudspeaker to compensate for a “wall” or “corner” position would have to be the inverse of the curves in Figures 9 and 10. In other words, we would just flip them upside down to undo the change in the loudspeaker’s timbre as a result of its placement. However, in real life, loudspeakers are not omnidirectional at all frequencies. In real life, they don’t even have the same directional characteristics (omnidirectional or not…) as themselves at all frequencies. Due to their physical shape, the size of the loudspeaker drivers and the choice of crossover frequencies (amongst other things…) a typical loudspeaker will radiate different frequencies at different levels in different directions – even if it has been equalised to be perfectly flat on-axis in a free field. In addition, additional (perhaps unwanted) moving “parts” such as air flow in and out of a port, a slave driver or even a moving panel in the loudspeaker cabinet (see this article for a discussion about this) will not only affect the magnitude of a signal in a given direction, but also its phase relative to the on-axis response. So, what impact does reality have on the rule-of-thumb lessons learned above? Let’s take an only-slightly-more realistic example of a loudspeaker that is omnidirectional in the low frequency bands and very directional in the mid and upper frequency bands. Now, the energy in the low end will radiate forwards and backwards, reflecting off the wall (or walls) and still resulting in a boost. However, since the high frequency bands are not omnidirectional, you won’t get a boost from the reflections in the power response of the loudspeaker in the room. Consequently, the bass boost caused by the presence of the walls will be exaggerated due to the difference in directivity of the loudspeaker in different frequency bands. Of course, the actual directivity of a loudspeaker is considerably more complicated and messy than a simple description like “omni in the low end and beaming in the high end” – but we won’t delve very far into the details of that in this article. Let’s just stop at “real life is complicated”. The end result of this is that, if we do the same math as I used to do the plots shown above, but we include the actual directivity measurements of the actual loudspeaker, then we can calculate the final equalisation curves that we need to make the wall and corner positions sound more like the free position. An example of these curves are shown below in Figure 11. Note that these curves are applied to the “free” setting which, in the case of this loudspeaker, is the reference position in which it was tuned during the sound design process. The two things to note here are the dip at around 100 Hz which counteracts the boost that we see in the theoretical curves in Figures 9 and 10. There is also a slight boost around 200 Hz which compensates for the dip that can be seen in Figures 9 and 10. The very low end is untouched, since there is very little difference in the extreme low end of the loudspeaker. This is because, in a normal room, you can’t get far enough away for the walls to “not exist” at 20 Hz – the wavelength of the very low end is just too big.
So, as you can see, the “Free / Wall / Corner” position switch, supplied on almost all Bang & Olufsen loudspeakers, is not merely a simple shelving filter with a 3 dB or 6 dB difference on the low end. It’s a rather complicated filter that is customised for each loudspeaker that we make, since it is dependent on the specific directional characteristics of that loudspeaker.
#18 in a series of articles about the technology behind Bang & Olufsen loudspeakers
Another busy week – so another set of photos…
#17 in a series of articles about the technology behind Bang & Olufsen loudspeakers
This week, instead of talking about what is inside the loudspeakers, let’s talk about what I listen for when sound is coming out of them. Specifically, let’s talk about one spatial aspect of the mix – where instruments and voices are located in two-dimensional space. (This will be a short posting this week, because it includes homework…)
Step 1: Go out and buy a copy of Jennifer Warnes’s album called “Famous Blue Raincoat: The Songs of Leonard Cohen” and play track 2 – “Bird on a Wire”.
Step 2: Close your eyes and really concentrate on where the various voices and instruments are located in space relative to your loudspeakers. If you hear what I hear, you’ll hear something like what I’ve tried to represent on the map shown in the figure below.
I’ve used some colour coding, just to help keep things straight:
Note that Jennifer sings her own backup vocals, so the “voice”, and the two “bk” (for backup – not Burger King) positions are all her. It also sounds like she’s singing in the “choir” on the left – but it’s hard for me to hear exactly where she is.
Whenever I’m listening to a pair of loudspeakers (or a car audio system, or the behaviour of an upmix algorithm) to determine the spatial properties, I use this map (which I normally keep in my head – not on paper…) to determine how things are behaving. The two big questions I’m trying to answer when considering a map like this revolve around the loudspeakers’ ability to deliver the (1) accuracy and (2) the precision I’m looking for. (Although many marketing claims will use these words interchangeably, they do not mean the same thing.)
The question of accuracy is one of whether the instruments are located in the correct places, both in terms of left and right, but also in terms of distance. For example, the tune starts with a hit on the centre tom-tom, followed immediately by the bigger tom-tom on the left of the mix. If I have to point at that second, deeper-pitched tom-tom – which direction am I pointing in? Is it far enough left-of-centre, but not hard over in the left loudspeaker? (This will be determined by how well the loudspeakers’ signals are matched at the listening position, as well as the location of the listening position.) Secondly, how far away does it sound, relative to other sound sources in the mix? (This will be influenced primarily by the mix itself.) Finally, how far away does it sound from the listening position in the room? (This will be influenced not only by the mix, but by the directivity of the loudspeakers and the strength of sidewall reflections in the listening room. I talked about that in another blog posting once-upon-a-time.)
The question of precision can be thought of as a question of the size of the image. Is it a pin-point in space (both left/right and in distance)? Or is a cloud – a fuzzy location with indistinct edges? Typically, this characteristic is determined by the mix (for example, whether the panning was done using amplitude or delay differences between the two audio channels), but also by the loudspeaker matching across the frequency range and their directivity. For example, one of the experiments that we did here at B&O some years ago showed that a difference as small as 3 degrees in the phase response matching of a pair of loudspeakers could cause a centrally-located phantom image to lose precision and start to become fuzzy.
You might note that I used the term “two-dimensional space” in the beginning of this posting. In my head, the two dimensions are (1) angle to the source and (2) distance to the source. I don’t think in X-Y cartesian terms, but Polar terms.
An important thing to mention before I wrap up is that this aspect of a loudspeaker’s performance (accuracy and precision of phantom imaging) is only one quality of many. Of course, if you’re not sitting in the sweet spot, none of this can be heard, so it doesn’t matter. Also, if your loudspeakers are not positioned “correctly” (±30 degrees of centre and equidistant from the listening position) then none of this can be heard, so it doesn’t matter. And so on and so on. The point I’m trying to make here is that phantom image representation is only one of the many things to listen for, not only in a recording but also when evaluating loudspeakers.
#16 in a series of articles about the technology behind Bang & Olufsen loudspeakers
Take a balloon and blow it up. It will look something like the drawing in the centre of Figure 1.
If you put your hands on the top and bottom of the ballon and compress them, you’ll make the balloon shorter, but you’ll also make it wider (as is shown on the left side of Figure 1). This is because the air inside the balloon is under a higher pressure when you squeeze your hands together, and that pressure pushes harder on the parts of the balloon that aren’t being held in by your hands.
If, instead, you grab the top and bottom of the balloon and stretch them further apart, you’ll make the balloon narrower (as is shown on the right side of Figure 1). This is because you’ve created more space inside the balloon, thus lowering the internal pressure pushing out on its walls. The lower the pressure, the less the air pushes outwards, so the balloon collapses.
What we’ve described here is basically the same as what happens to a sealed loudspeaker cabinet (if you’re not careful when you do its mechanical design). However, instead of your hands squeezing a balloon (a sealed “cabinet” of air), we use the signal from a power amplifier to pull the woofer into the cabinet. This increases the pressure inside the cabinet, since it’s sealed and there’s nowhere for the air to go. As a result, the trapped air tries to push outwards on the sides of the cabinet. If the walls of the cabinet are thin, then the cabinet itself will act like the balloon and expand.
Similarly, if you put a positive signal on the power amplifier, you’ll move the woofer out of the cabinet, reducing the air pressure inside it and “sucking” the sidewalls of the loudspeaker in (if they are so thin that they can move).
Generally speaking, you want a loudspeaker to behave as a piston in a baffle (like this). This means (in this case) that you want the woofer to move in and out of a loudspeaker cabinet and you don’t want the cabinet itself to move at all. (We’ll talk later about why this is a bad thing.)
There are a number of different ways to do this. One way is to make your loudspeaker cabinet out of something very, very, very stiff (and probably, as a result, very, very, very heavy). For example, we make our prototypes out of 22 mm or 25 mm thick MDF (and sometimes we use two sheets of it, glued back to back, to make sure that things are stiff enough). Most of our loudspeakers like the BeoLab 9, for this week’s example, have enclosures that are made of plastic, so we use some different methods to achieve the stiffness and rigidity we need to ensure that our enclosures are not singing along with the drivers.
The first step in ensuring that the walls of the loudspeaker cabinet are stiff enough is to make them thick enough. How thick is “enough” depends on the loudspeaker itself. A subwoofer with a small enclosure volume will have to withstand more internal air pressure than a midrange in a larger enclosure. Of course, we can’t simply make the walls of the cabinet out of overly thick plastic, since that would not only be an unnecessary waste of materials, it would increase the weight of the loudspeaker (a consideration for shipping) and the cooling time of the plastic when it’s in production (a consideration for the production line timing and costs).
A second way to make the sidewalls stiffer is to use ribs – usually on the inside of the cabinet. These are moulded as part of the sidewall itself – they aren’t just glued on to the inside surface of the cabinet. If you take a look at Figure 3, you can see the ribs on the inside of the sidewalls of the BeoLab 9. These run diagonally and vertically in the case of this loudspeaker – but they’re not just randomly placed inside the loudspeaker. They have been strategically placed using simulations in the early development stages, and measurements of the early prototypes. These measurements are done using very small accelerometers glued to the sides of the loudspeakers and monitoring their outputs while playing signals through the loudspeaker drivers. (In case you’re wondering, the depth of the ribs is about 22 – 25 mm, depending on where you measure.)
A third tactic is to use a plastic that is stiffened by adding things to it. The usual method is to use fibre-reinforced plastic. The fibres in the plastic help give it a structural strength that you can’t get from just plastic alone.
A fourth possibility is to create a laminate material where you build up the enclosure using layers of different materials (or layers of the same material with different structural composition). This increases stiffness in the same way that a sheet of plywood is stiffer than a sheet of wood.
So, in the case of the BeoLab 9 (as with many of our other loudspeakers), three of these tactics were used. The plastic is thick enough, it has strengthening ribs on the inside, and it is a laminate (if you slice it open, you’ll see that it is a layer of foamed plastic, sandwiched between “skin” layers of solid plastic).
However, when they (I wasn’t part of the BeoLab 9 development team – I was still working in the Automotive Department at the time) got to the last stages of the development, it became obvious that there was a problem. There was an audible resonance caused by the woofer. Some digging around resulted in the finding out that the sides of the cabinet were moving too much. In essence, the problem was almost exactly as I described with the balloon in Figure 1.
As I tried to show in Figure 4, when the woofer moved inwards, it pushed the sidewalls of the loudspeaker outwards (shown with the blue lines). When the woofer moved outwards, it sucked the sidewalls inwards (the red lines). (I’m over-simplifying here, but not enough to start a fight.)
However, as I said, this was discovered rather late in the development process. The problem had to be fixed, but the question was how to do it without starting from scratch and creating new moulding tools for making the plastic enclosure. The solution was to use the sidewalls to reinforce each other. Since the movement of the opposite sides was in opposite directions (i.e. the left and right sides of the loudspeaker either wanted to move apart or together at any given moment) they could be braced by connecting them with a bridge. Take a look again at Figure 3. You’ll see a metal rod that goes straight across the middle of the woofer enclosure. You can see it just above the back of the woofer in Figure 5 as well.
That piece became known in the acoustics department as the “dog bone” because its final version had the basic shape of a cartoon dog bone. The end result is that the rod is included in the BeoLab 9 construction to prevent the sidewalls of the woofer cabinet from moving when you’re playing loudly.
Here’s another photo showing the internal PCB with the amplifier and filters – not because it’s relevant to this discussion, but just because it might be interesting…
So, we’ve seen how we get rid of parts of the loudspeaker moving when they shouldn’t. The question is “why is it a big deal?” Well, it’s a little like Sir Robert Helpmann’s comment about the difficulties in choreographing a nude ballet – the problem is that some parts of the body keep moving when the other parts have stopped.
In theory, a loudspeaker should behave the same at all frequencies (that statement can mean a lot of different things – and I am happy to argue that it is both true and false, depending. So don’t try to start a fight with me on that one, and please don’t mis-quote me and say that I’m contradicting Siegfried Linkwitz or anyone else by taking that statement out of context on a hi-fi forum somewhere else…) As I mentioned in a previous posting, we like to pretend that a loudspeaker is just a moving piston in an infinite baffle, since that behaves pretty well. Of course, no one actually believes that this model is true – but it’s a comforting ideal.
Take a look at the shape of the blue and red versions of the loudspeaker cross-section in Figure 4, above. You might notice that, when the woofer goes outwards, the cabinet goes inwards. When the woofer goes inwards, the cabinet goes outwards. (this is an oversimplification of the truth, but let’s go with it for now). This means that, from the point of view of the air pressure radiating from the entire loudspeaker, the woofer goes positive and the cabinet goes negative at the same time. So, the sound pressure radiating off the cabinet cancels the sound pressure radiating off the woofer as can be seen in an example of two opposite-polarity sources causing destructive interference as in the animation below. (Note the intersection of the red and green curves where you will hear no sound at all…)
Not only that, but the cabinet as a sound source has a very different directivity than the woofer by itself. So, the result is… complicated. The truth is even more complicated, since the cabinet will not behave as nicely as this – it will resonate better at some frequencies than others, making some notes “bloom” – they’ll appear to be louder (or quieter, depending on where you are and how the room interacts with the loudspeaker) and they might even appear to come from a different direction.
So, the moral of the story here is that you want all parts of the loudspeaker to not be moving when the parts that are supposed to be moving are doing so.
And, before you go and listen to your loudspeakers and look for “blooming” and blaming it on panel resonances or vibrating cabinets, don’t forget that your room modes are more likely a primary source of mis-behaviour when it comes to some bass notes sounding different from the others. However, if you have problems with your room acoustics, we can’t fix that with ribs and dogbones – unless you also bring in a large dog. (I know, I know – the linked paper is about humans – but it does make a mention of animals in the abstract…)
#15 in a series of articles about the technology behind Bang & Olufsen loudspeakers
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…
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.
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.
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.
#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.
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:
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°.
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.
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:
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.”
