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

“If you saw a heat wave, would you wave back?”

– Steven Wright

Part 1: The Myth(?)

Once upon a time, back in the “olden days” (as my kids call them), before I worked at Bang & Olufsen, I did a Master’s degree at McGill University as a tonmeister (hence the domain name…). In practice, this means that I was trained to be someone who knew as much about things like room acoustics, microphone techniques, recording practices and electronics as I did about music. (Of course, if I knew nothing about music, then this equation falls apart…) In practice, what it meant was that I spent a LOT of time in recording studios (literally more time than I remember) doing recordings or just listening to them.

Now, let’s think about the design of a typical “good” recording studio control room. Usually, you have a mixing console in the middle of the room, and at least one pair of small studio monitor loudspeakers sitting on the meter bridge. Also, up on the front wall, there’s a large pair of “soffit mounted” loudspeakers built into it. Figure 1, below, shows an example of this.

One story I heard back in the “olden days” was that, if you’re building a recording studio, you should always keep the amplifiers for your big soffit-mounted loudspeakers away from (or at least above) the loudspeakers themselves. You should never NEVER put the amps directly under the loudspeakers. The story went that the reason for this was that hot air rising from the amplifiers would waft past the tweeters, modulating (changing) the speed of sound of the air between the tweeters and the listening position. And, since this modulation was random, then this heat would sometimes cause the right channel to arrive at the listening position earlier than the left, sometimes later. The result (according to the story) would be a constant shifting of the phantom image, moving left and right instead of staying exactly in the middle where it should be. The analogy/metaphor/explanation was that the image location would “shimmer” in the same way that there appears to be water on hot asphalt in the distance on a summer day, or the way you can see heat rising from a hot surface like a barbecue.

Fast-forward about 25 years, and I’m sitting in a meeting at B&O, discussing mechanical design options for high-end loudspeakers. Someone in the room says “one possibility is to put the radiators for the amplifiers on the face of the loudspeaker, just under the midranges and tweeters” and I say “you can’t do that – you’ll screw up the phantom imaging”. Heads turn to look at me, the expressions on the faces obviously say “what on earth are you talking about?” So, I tell the story that I heard back in the olden days…

Quick sidebar: if you don’t already know, almost all Bang & Olufsen loudspeakers are active loudspeakers, which means that the amplifiers and power supply are inside the loudspeaker enclosure. Amplifiers and power supplies are never 100% efficient. In addition to this, because we use DSP to control the loudspeaker, we can push our loudspeaker drivers to their limits without melting their voice coils – this also results in a lot of heat. All of this means that our loudspeakers need a lot of thought into their thermal design – basically, we need to make sure that the heat can get out, which is why we need radiators like the one shown in the photo on the right (which shows the bottom of the back of a BeoLab 20. The vertical stripes are a metal radiator attached to the electronics inside.). We now return you to your regularly scheduled story…

Some of the engineers in the room say “that’s crazy” – and others (the ones I like) say “let’s find out…” So, using the modern tools for finding-things-out, we started by typing things like “loudspeaker amplifier heat phantom image” into Google. This resulted in no information – or at least no useful information. So this meant that we had to do an experiment.

Part 2: The pilot experiment

Okay, so the question is: does heat rising in front of a tweeter have an effect on the sound that it radiates? And, if so, what is/are the effect(s) and what kind of magnitude of effect are we talking about? The easiest way to find this out is to exaggerate the effect. So, we got a tweeter and a hot plate (which lives in the acoustic department exclusively for warming risalamande at the yearly Julefrokost (the ubiquitous Danish “Christmas lunch” literally translated, although it can happen as early as November, it rarely starts at lunchtime, and typically extends well into the evening…) and we set them up as shown in Figure 2.

We put a microphone in front of the tweeter at a distance far enough away that the microphone wasn’t getting heated by the hot plate (about a metre or so…), and we sent a high frequency tone (20 kHz) to the tweeter from a sine wave generator. Then we simply sent the original signal and the output of the microphone to an oscilloscope so that we could look at them in real time.

Figure 3 shows the result when the hot plate was turned off. The original signal and the microphone signal are both clean, as you can see there.

Figure 4 shows the same thing, but the hot plate is now set to “medium”. As you can see there, the output from the tweeter is much more “blurry”. This is because it is moving on the screen over the 30 seconds of the photo exposure. Note that it is moving in both the X-axis (meaning the level was changing over time) and the Y-axis (meaning that the time of travel from the loudspeaker to the microphone was changing over time).

Figure 5 shows the same thing, but the hot plate is now set to “maximum” (hot enough to boil water or to burn risalamande). As you can see there, the output from the tweeter is even more “blurry”for the same reason. It’s also fairly easy to see in that photo that the output from the tweeter is modulating in both axes.

One thing to be clear of here is that we are looking at the effect of modulating the temperature of the air in front of the tweeter. We’re not changing the temperature of the tweeter itself (at least, not with the hot plate – the tweeter heats itself, but that’s another story) or the microphone.

Part 3: The “real” experiment

Okay, so we had some proof that the story that I heard back in the recording studio might be true. At the very least, we found out that it would be easy to measure the effect of heat rising in front of a tweeter. Now we had to get a little more useful data by analysing the signal from the microphone a little better. Looking at the signal on an oscilloscope is good for intuition, but it’s hard to graph the results.

So, this time we changed the setup a little. We used a little studio monitor loudspeaker (with some minor alterations – we taped over the ports to ensure that we weren’t modulating the air around the loudspeaker as a result of airflow through the port, just in case… for the lower frequencies… Since we were only playing sine tones and we’re not really interested in the absolute magnitude response of the loudspeaker, the lack of a port didn’t matter too much to us…) and we recorded the microphone output instead of just looking at the signal on a ‘scope. (We were also careful not to move during the recordings, partly to reduce background noise, but also to avoid creating air currents … just in case…) The total setup (although it’s still pretty simple) is shown in Figure 6.

We also tried measuring the air temperature in front of the loudspeaker, but this was difficult because it was fluctuating so much and so rapidly. So, instead, we put a power meter on the mains feed to the hot plate to get a better idea of how much constant power we were using.

The results

Our analysis was to see how much the phase and the magnitude were changing over time with different frequencies and different settings of the hot plate temperature. This was done by analysing the recordings of the microphone signal for a 30-second period. The results turned out to be different for different frequencies – and surprisingly large in some cases…

Some details for the geeks-amongst-you:

• The recordings were done with a 192 kHz sampling rate so that we had plenty of bandwidth to play with for the next step.
• We took each 30-second recording and band-limited it to a frequency band 2 octaves wide using second-order high pass and low pass filters, with the tone being the centre frequency (geometrically). (In other words, for example, the 16 kHz recording was band-limited from 8 kHz to 32 kHz). The reason for this was to reduce the influence of background noise in the recordings for the level analysis.
• The phase analysis was done based on the output of a single FFT bin which provided its own noise immunity.
• The recordings were done at 5 power consumption settings of the hot plate: 0 W, 75 W, 150 W, 300 W and 700 W. These roughly corresponded to air temperatures in front of the tweeter 25º C, 28º C, 30º C, 34º C, and 44º C. I say “roughly” because the air temperature in front of the tweeter was varying quickly and widely, so this is just a ballpark measurement to get a rough idea of the effect of the hot plate. Due to this uncertainty, the plots below are relative to the power consumption of the hot plate rather than the air temperature.

As you can see above in Figures 8a and 8b, there was almost no effect on a 250 Hz tone, even when we pushed the hot plate up to 700 Watts. There is a very small change in magnitude, however this might be caused by background noise.

As you can see above in Figures 9a and 9b, at 1 kHz the effect is not getting much more noticeable.

Figures 10a and 10b, show the modulation for 4 kHz. Now we’re starting to see some effects…

Figures 11a and 11b, show the modulation for 16 kHz . You can see there that, in a worst-case scenario, we’re getting magnitude changes on the order of +/- 3 dB or so (which would mean, in a stereo system, a worst-case difference between the two loudspeakers’ signals of about 6 dB), and phase changes on the order of about +/- 40 degrees (so a worst-case difference between the two loudspeakers’ signals of about 80 degrees).

If we then look at the peak-to-peak variation in the above graphs and plot that as a function of hot plate power consumption for the different frequencies, we get the results shown in Figures 12 and 13.

So, the conclusion from the measurements was that the effect was considerable at high frequencies and high temperatures, but might be significant at lower values as well… the question was to ask “what is significant?”

Luckily, for the phase modulation part of the question, we had a partial answer from an experiment that we did a long time ago. In a paper called “Audibility of Phase Response Differences in a Stereo Playback System. Part 2: Narrow-Band Stimuli in Headphones and Loudspeakers” (Presented at the 125th AES Convention, October 2008. Paper Number 7559) , Sylvain Choisel and I reported that subjects were able to detect phase response differences in loudspeakers with a threshold of approximately 50 degrees phase difference, regardless of frequency – although we only tested up to 8 kHz… Apart from the 16 kHz measurements in this experiment, none of the frequencies we measured came close to a worst-case difference of 50 degrees – so we’re probably safe on that one. (Although geeks might be interested to see the below for a little more discussion about this issue looking at it from a perspective of time instead of phase.)

The magnitude response differences may be a similar story. Many studies have been done to find out what differences in level between loudspeakers result in changes in phantom image placement – for example, see this site for a good summary. As can be seen in that graph, a 1.5 dB difference (chosen because that’s the worse-case value for the 1 kHz curve in the plot in Figure 12) in level between the two loudspeakers (measured at the listening position) will result in something like a 15% to 20% shift in phantom image location away from centre (that’s 15% to 20% of the distance to one of the loudspeakers from centre) which will probably be noticeable if you’re paying attention, although it might sound more like a “fuzzy” centre image instead of a moving one… A 6 dB difference (roughly the worst-case value for the 16 kHz curve) can result in an approximately 60%  shift in phantom image location. Note, however that we might be jumping to (incorrect) conclusions here, since some of the data in the plots on that PDF file I linked to above are from listening tests with full-range signals. Whether the values will be valid for narrow-band signals, especially at 16 kHz is unknown…

Part 4: Phase vs. Time

Take a look at the side view of our setup, shown below in Figure 14.

This is a simplified version of what is happening in the experiment. The sound wave travels outwards from the tweeter, through the air. However, that air has one area where the temperature is significantly different than the rest of the room.

The speed of sound in air can be calculated as follows:

c = 331.3 + (0.6 * T) m/s

where T is the air temperature in degrees Celsius.

So, for example, if the temperature of the air increases by 10ºC, then the speed of sound increases by 6 m/s. If the temperature increases by 50ºC, then the speed of sound increases by 30 m/s. This will change the time of arrival of the sound at the microphone – the hotter the air, the earlier the sound arrives.

However, this change is a change in time. This converts to a change in phase in the sine wave that we were measuring – but you have to remember that a given change in time is equivalent to a change in phase that increases with frequency. For example, a 1 ms delay change is equivalent to a 45º phase shift at 125 Hz, but a 90º phase shift at 250 Hz, a 180º phase shift at 500 Hz, and a 360º phase shift at 1 kHz, and so on…

So, another way to look at this problem is to consider the change in interchannel delay instead of interchannel phase. If you take a look at this site again, you can see that our perception of the phantom image location in a stereo system is very sensitive to changes in interchannel delay. For example, according to Simonsen, an interchannel delay difference of only 200 µs (that’s 0.0002 seconds!) will result in a 30% change in phantom image location. In other words, if you have a “correct” stereo configuration where your loudspeakers are placed +/- 30º from centre front, then delaying one loudspeaker by 200 µs will move the centre phantom image to 9º off-centre (or 30% of the way to the earlier loudspeaker).

Let’s simplify, just to get an idea of what we’re talking about in our experimental results:

Case 1: If the microphone is 3 m from the tweeter and the air temperature is 25º C for all 3 m of travel, then the speed of sound for the entire trip is 346.3000 m/s and the total travel time is therefore 8.6630 ms.

Case 2: If the microphone is 3 m from the tweeter and the air temperature for the first 50 cm of travel is 44º C and the remaining 2.5 m of travel is 25º C, then the speed of sound for the first 50 cm is 357.7 m/s and for the remaining 2.5 m it’s 346.3 m/s. This means you have a total travel time of 8.6170 ms.

The difference between Case 1 and Case 2 is 8.6630 – 8.6170 = 0.046 ms or 46 µs, which, according to Simonsen’s results would correspond to something like a 5% shift in centre image location. Audible? Perhaps, but just barely… However, if you’re checking my math, you’ll note that a 46 µs change in time is equivalent to a 264º change in phase at 16 kHz, which was much larger than the roughly 85º we measured in the analysis above (see Figure 13)… So, my simplified example here seems to be exaggerating the effect, which means that a guess (even a calculated guess) of a 46 µs interchannel latency difference is probably an overestimate…

So, we might be able to conclude that the effect of this with respect to change in time of arrival are also inaudible, according to the data…

Part 5: Why is the level changing over time?

You may notice that I’ve avoided an obvious question throughout the above: “Why does the magnitude of the signal change?” If you look at this site, for example, you’ll see that although there is a change in sound absorption with change in air temperature, it is a very small effect. So, why do we measure such a large change in magnitude (or level) correlated with the temperature of the hot plate? There are two possible explanations for this.

The first was already discussed. At low temperature settings, the variation in level is probably simply an artefact of the background noise. All of these measurements were done in the Cube at B&O – which is normally used for a different kind of measurement which is more immune to background noises. This means that the Cube itself doesn’t have to be quiet, so it isn’t soundproofed from the outside world. Extraneous noises such as wind, rain, or someone walking by pushing a cart in the hallway, are easily audible if you’re sitting in the Cube. However, for the measurements in this experiment, those background noises will infect the results.

The second explanation is not related to background noise. As you can see in Figure 12, at higher frequencies, there is a definite increase in level variations caused by increasing temperature of the hot plate. However, the effect is too big to be attributed to absorption changes related to temperature changes. So, what is it? Our best guess is that it’s the result of the changes in thermal currents (in other words, the hot air rising) in front of the tweeter resulting in thermal gradients (differences of temperature in space). This causes differences in speed of sound in space causing refraction of the wavefront. The higher the frequency, the more the tweeter is “beaming” so the effect is more evident than it is at low frequencies where the loudspeaker is more omnidirectional. (Spinning a flashlight generates a more obvious than spinning a naked light bulb.) As the temperature changes in time, the sound beam from the tweeter moves towards and away from the microphone input, which looks like a change in level.

If we had used a cluster of microphones instead, we would very probably have seen the “beam” moving to another microphone as it went quiet at the main mic… Maybe we’ll do that experiment someday and call it “research” – but for now we have the answer we were looking for, so we’ll leave that one for another day…

The conclusion

So, after all that, our end conclusion was, for an active high-end loudspeaker, we should not put radiators directly below the midranges and tweeters – it’s better to put them behind the loudspeaker like we do already in the BeoLab 5 or BeoLab 20, for example. Or perhaps above the tweeter could also be an option – although that might be a challenge for the visual designers…

There’s no guarantee that the artefacts will be audible (in fact, they almost certainly won’t if you’re not paying attention to the phantom image location, or if you aren’t sitting in the sweet spot… but if those were the case, we probably wouldn’t be talking about a high-end loudspeaker…) but the artefacts are certainly measurable – and that’s enough for us to go looking for a better place to put the amplifier radiators.

And now, I guess this also means that when someone types “loudspeaker amplifier heat phantom image” into Google, they’ll get an answer…

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

In the last posting, I talked about a little experiment we did that made us realise that control of a loudspeaker’s directivity (or more simply “beam width”) would be a useful parameter in the hands of a listener. And, in a previous article, I talked a little about why that is probably true. This week, let’s get our hands dirty and talk about how Beam Width Control can be accomplished.

Part 1: What is sound?

Okay – we’re really getting back to basics, but it won’t take long. I promise. In order to get to where we’re headed, we have to have a fairly intuitive grasp of what sound is. At a basic level, sound is a change in air pressure over time. Today’s atmospheric (or barometric) pressure is about 100 kiloPascals (give or take). That pressure can be thought of as a measure of the average distances between the air molecules in the room you’re sitting in. It is also important to note that (unless you’re very unlucky and very uncomfortable) the pressure inside your head is roughly the same as the pressure outside your head (otherwise, you’d probably be talking about going to visit a doctor…). The important thing about this is that this means that the pressure that is exerted on the outside of your eardrum (by the air molecules sitting next to it in your ear canal) is almost identical to the pressure that it exerted on the inside of your eardrum (the part that’s inside your head). Since the two sides are being pressed with the same force, then the eardrum stays where it should.

However, if we momentarily change the air pressure outside your head, then you eardrum will be pushed inwards (if the pressure is higher on the outside of your head) or pulled outwards (if the pressure is lower). This small, momentary change in pressure can be caused by many things, but one of those things is, for example, a woofer getting pushed out of its cabinet (thus making a “high pressure” where the air molecules are squeezed closer together than normal) or pulled into its cabinet (thus making a “low pressure” and pulling the air molecules apart).

So, the woofer pushes out of the cabinet, squeezes the air molecules together which push your eardrum into your head which does a bunch of things that result in you hearing a sound like a kick drum.

Part 2: Frequency and wavelength

Take a loudspeaker into your back yard and play a tone with the same pitch as a “Concert A” (the note you use to tune a violin – or, at least, the note violinists use to start tuning a violin…). This note has a frequency of 440 Hz, which means that your loudspeaker will be moving from its resting position, outwards, back, inwards, and back to the resting position (a full cycle of the tone) 440 times every second. This also means that your eardrum is getting pushed inwards and and pulled outwards 440 times every second.

Now, turn off the loudspeaker and walk 344 m away. When you get there, turn on the tone again. You’ll notice that you don’t hear it right away because sound travels pretty slowly in air. In fact, it will take almost exactly one second from the time you turn on the loudspeaker to the time the sound reaches you, since the speed of sound is 344 m/s (you’re 344 m away, so it takes one second for the sound to get to you).

If, at the instant you start to hear the tone, you were able to freeze time – or at least freeze the air molecules between you and the loudspeaker, you’d see something interesting (at least, I think it’s interesting). The instant you hear the start of the tone (the first cycle), the 441st cycle is starting to be generated by the loudspeaker (because it’s producing 440 cycles per second, and it’s been one second since it started playing the tone). This means that, in your frozen-time-world, there are 440 high and low pressure zones “floating” in the 344 m of air between you and the loudspeaker. Given this information, we can calculate how long the length of one wave is (better known as the “wavelength” of the tone). It’s 344 m divided by 440 cycles per second = 78.2 cm.

So, this means that there are 78.2 cm between each high pressure “bump” in the air. This also means that there is half that distance (39.1 cm) between adjacent high and low pressure zones in the air.

Part 3: Interference

Now let’s take a case where we have two woofers. We’ll put them side by side and we’ll send the same 440 Hz tone to them. So, when one woofer goes out, the other one does as well. This means that each one creates a high pressure in front of it. If you’re exactly the same distance from the two woofers, then those two high pressures add together and you get an even higher pressure at the listening position (assuming that there are no reflecting surfaces nearby). This is called constructive interference. This happens when you have two loudspeaker drivers that are either the same distance from the listening position as in Figure 2 or in exactly the same location (which is not possible), as in Figure 3.

If we change the wiring to the woofers so that they are in opposite polarity, then something different happens. Now, when one woofer goes outwards, the other goes inwards by the same amount. This means that one creates a high pressure in front of it while the other creates a low pressure of the same magnitude. If you’re exactly the same distance from the two woofers, then those two pressures (one high and one low) arrive at the same time and add together, so you get a perfect cancellation at the listening position (assuming that there are no reflecting surfaces nearby). This is called destructive interference. This is shown in Figure 4 and 5.

However, an important thing about what I just said was that you are the same distance from the two woofers. What if you’re not? Let’s say, for example, that you’ve changed your angle to the “front” of the loudspeaker (which has two loudspeaker drivers). This means that you’re closer to one driver than the other. The result is that, although the two drivers are playing the same signal at the same time, your difference in distance causes their individual signals to have different phases at the listening position – possibly even a completely opposite polarity – as is shown in Figure 5.

If you consider Figure 2 and Figure 5 together (they’re really two different views of the same situation, since both loudspeakers are playing the same signal simultaneously) and you include all other listening positions, then you get Figure 6. As you can see there, there is no sound (again, indicated by the greenish colour which means no change in pressure) at the angle shown in Figure 5.

So, Figure 6 shows that, for a position directly in front of the sound sources (to the right of the black dots, in the figure), the result is identical to that in Figure 3 – the two sources add together perfectly if you’re the same distance from them. However, if you start to move away from that line, so that you’re closer to one sound source than the other, then, at some angle, you will get a high pressure from the upper sound source at the same time as you get the previous low pressure from the lower source (because it’s farther away from you, and therefore a bit late in time…) This high+low = nothing, and you hear no sound.

Another, slightly more nuanced way to do this is to not just change the polarity of one of the sound sources, but to alter its phase instead. This is a little like applying a delay to the signal sent to the driver, but it’s a delay that is specific to the frequency that we’re considering. An example of this is shown in Figure 7.

This means that, by changing the phase instead of the polarity of the drivers, I can “steer” the direction of the beam and the “null” (the area where the sound is cancelled out)

It should be noted that, at a different separation of the drivers (more accurately stated: at a different relationship between the wavelength of the signal and the distance between the drivers) , the behaviour would be different. For example, look at Figure 8 which shows the same situation as Figure 6 – the only difference is that the two sound sources are half the distance apart (but the wavelength of the signal has remained the same).

Part 4: Putting it together

So, at a very basic level (so far) we can determine which direction sound is radiated in based on a relationship between

1. the wavelength of the signal it is producing (which is a function of its frequency)
2. the distance between the sound sources (the loudspeaker drivers), and
3. the polarity and/or the phase of the signals sent to the drivers.

All of the examples shown above assume that the two sound sources (the loudspeaker drivers) are playing at the same level, which is not necessarily the case – we can choose to play a given frequency at whatever level we want using a rather simple filter. So, by reducing the level of the “interfering” driver, we can choose how much the directivity of the radiated sound is affected.

In addition to this, all of the examples shown above assume that the sound sources are omnidirectional – that they radiate sound equally at all frequencies – which is not true in real life. In real life, a loudspeaker driver (like a tweeter or a woofer) has some natural directivity pattern. This pattern is different at different frequencies and is influenced by the physical shapes of the driver and the enclosure it’s mounted on.

So, let’s start putting this together.

If I take a loudspeaker driver – say, a midrange unit – and I mount it on the front of a loudspeaker enclosure and measure its directivity pattern  (the geeky term for the width of its sound beam) across its frequency range and beyond I’ll see something like this:

As you can see in that plot, in its low frequency range (the red line on the left), the midrange driver is radiating sound with a wide beam – not completely omnidirectional, but very wide. In its high frequency region (around the right-hand red line) (but still not high enough to be re-routed to the tweeter) the midrange is “beaming” – meaning that the beam is getting too narrow. Our goal is to somehow make the beam widths at these frequency bands (and the ones in between) more alike. So, we want to reduce the width of the beam in the low frequencies and increase the width of the beam in the high frequencies. How can we do this? We’ll use more midrange drivers!

Let’s take two more midrange drivers (one on either side of the “front” or “main” one) and use those to control the beam width. In the lower frequencies, we’ll send a signal to the two side drivers that cancel the energy radiated to the sides of the loudspeaker – this reduces the width of the beam compared to using the front midrange by itself. At higher frequencies, we’ll send a signal to the two side drivers that add to the signal from the front driver to make the width of the beam wider. At a frequency in the middle, we don’t have to do anything, since the width of the beam from the front driver is okay by itself, so at that frequency, we don’t send anything to the adjacent drivers.

“Okay”, I hear you cry, “that’s fine for the beam width looking from the point of view of the front driver, but what happens as I come around towards the rear of the loudspeaker?” Excellent question! As you come around the rear of the loudspeaker, you won’t get much contribution from the front midrange, so the closest “side” midrange driver is the “main” driver in that direction. And, as we saw in the previous paragraph, the signal coming out of that driver is pretty strange (because we intentionally made it strange using the filters – it’s in opposite polarity in its low end, it doesn’t produce anything in its midrange, and it’s quiet, but has a “correct” polarity in its high end). So, we’ll need to put in more midrange drivers to compensate again and clean up the signal heading towards the rear of the loudspeaker. (What we’re doing here is basically the same as we did before, we’re using the “rear” drivers to ensure that all frequencies heading in one rearward direction are equally loud – so we make the “rear” drivers do whatever they have to do at whatever frequency bands they have to do it in to make this true.)

“Okay”, I hear you cry, “that’s fine for the beam width looking from the point of view of the rear of the loudspeaker, but what happens as we go back towards the front of the loudspeaker? Won’t the signals from the rear-facing drivers screw up the signal going forwards?” Excellent question! The answer is “yes”. So, this means that after the signal from the rear-facing midrange drivers is applied (which compensate for the side-facing midrange drivers which compensate for the front facing midrange driver) then we have to go back to the front and find out the effects of the compensation of the compensation on the “original” signal and compensate for that – so we start in a loop where we are compensating for the compensation for the for the compensation for the compensation for the… Well, you get the idea…

The total result is a careful balancing act where some things are known or given:

• the frequency range of the music being played through a given loudspeaker driver (this is limited by the crossover)
• the natural directivity patterns of the loudspeaker drivers on the loudspeaker enclosure within that frequency range
• the locations of the loudspeaker drivers in three-dimensional space
• the orientations of the loudspeaker drivers in three-dimensional space (in other words, which way they’re pointing)

Note that these last two have been calculated and optimised based on a combination of the natural directivity patterns of the loudspeaker drivers and the desired beam widths we want to make available.

As a result each individual loudspeaker driver gets its own customised filter that controls

• the level of the signal at any given frequency
• the phase (which includes delay and polarity – sort of…) of the signal at any given frequency

By controlling the individual output levels and phases of each loudspeaker driver at each frequency it produces, we can change the overall level of the combined signals from all the loudspeaker drivers in a given direction. If we want to be loud at 0º (on-axis) and 20 dB quieter at 90º (to the side), we just apply the filters to all of the drivers to make that happen. If we want the loudspeaker to be only 10 dB down at 90º, then this just means changing to a different set of filters. This can be done independently at different frequencies – with the end goal to make all frequencies behave more similarly, as I talked about in this posting and this posting.

Also, since the filters are merely settings of the DSP (the digital signal processing “brain” of the loudspeaker), we can change the beam width of the loudspeaker merely by loading different filters – one for each loudspeaker driver in the system.

The end result is a loudspeaker that can play many different roles, as was shown in the different plots in this posting. In one mode, the beam width can be set to “narrow” for situations where you have one chair, and no friends and you want the ultimate “sweet spot” experience for an hour or two. In another mode, the beam width can be set to “wide”, resulting in a directivity that is very much like an improved version of the wide dispersion of the BeoLab 5. In yet another mode, the beam width can be set to “omni”, sending sound in all directions, making a kind of “party mode”.

Part 5: The “side” effect: Beam Direction Control

In order to be able to have a Beam Width Control, a loudspeaker must have a number of identical loudspeaker drivers. A collection of tweeters, midranges and woofers, some on the front, some on the sides and some to the rear of the loudspeaker. In addition, each of these drivers must have its own amplifier and DSP channel so that it is independently controllable by the system.

This means that, instead of using the drivers to merely control the width of the beam in the front of the loudspeaker, they can also be used somewhat differently. We could, instead, decide to “rotate” the sound, so that the “main” tweeter and midrange are the ones on the side (or even the rear) of the loudspeaker instead of the ones on the front. This means that, if you’re sitting in a location that is not directly in front of the loudspeakers (say, to the sides, or even behind), it could be possible to improve the sound quality by “rotating” the “on-axis” direction of the loudspeaker towards your listening position. This by-product of Beam Width Control is called Beam Direction Control.

P.S. Apologies for the pun…

For more information on Beam Width Control:

What is “Beam Width Control”?

Shark Fins and the birth of Beam Width Control

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

In the last posting, I described a little experiment that we did where we could easily be accused of asking a stupid question and getting an obvious answer. This posting is a little different, although I’ll also describe a little experiment where we asked a much-less-stupid question and got an answer we weren’t looking for… However, before I describe the experiment itself, we’ll have to start with a little background information.

Let’s say that we wanted to build a “simple” two-way loudspeaker with a tweeter and a woofer in a box like the one shown in Figure 1.

Since we’re Bang & Olufsen, it is implied that this will be a fully active, DSP-based loudspeaker. Let’s also, for the sake of simplicity, say that we used loudspeaker drivers and other components with absolutely no linear distortion artefacts (I can dream, can’t I?). This means that we can apply any kind of filter we like to each of the two loudspeaker drivers to result in whatever response we want (in a given direction in a “free field” (a space with no reflecting surfaces, extending to infinity in all directions) – for more information on this, please read this posting and/or this posting).

Now, it’s fairly reasonable to assume that one portion of a good starting point for a loudspeaker’s acoustic response is to have a flat magnitude response when measured on-axis in a free field. This means that, if you have the loudspeaker in a space that has no reflections, and you are directly in front of it, no frequency will be louder than any other (within some limits, of course…). In fact, this is the way a lot of studio monitor loudspeakers are tuned (which makes sense, since many studio control rooms don’t have a lot of reflections as was discussed here).

The problem is that, if you do make a loudspeaker that is flat-on-axis, you’ll probably have problems in its power response (for a description of what a loudspeaker’s “power response” is, see here). This is dependent on a lot of things like the crossover frequency, the sizes and shapes of the drivers, the phase responses of the crossover filters, the shape of the cabinet, and other things. However, if we were to simplify, we could say that a two-way loudspeaker (say, with a 4th order Linkwitz-Riley crossover, just to pick one type…) that is flat on-axis, will have a dip in its power response at the crossover frequency. This is because, although the two drivers (the tweeter and the woofer) add together nicely in one location (on-axis, directly in front of the loudspeaker) they do not add together nicely anywhere else (because the distances to the two drivers from the listening position are probably not matched, particularly when you go vertical…).

So, one basic problem with building a “simple” two-way loudspeaker is that you have to choose to either have a flat magnitude response on-axis, or a smooth power response (without a dip) – but you can’t have both. (If you want to really dig into this, I’d recommend starting with J. Vanderkooy & S.P. Lipshitz, “Power Response of Loudspeakers with Noncoincident Drivers — The Influence of Crossover Design,” J. Audio Eng. Soc., Vol. 34, No. 4, pp. 236-244 (Apr. 1986).)

This basic problem raised a question in the head of one of our acoustical engineers, Gert Munch. He started to wonder how we could build a loudspeaker that could have a flat magnitude response on-axis and still have a smooth power response that didn’t suffer from a dip at the crossover. One possible solution is to build a loudspeaker with the desired on-axis response, and then somehow create an additional portion of the loudspeaker that could “fill up” the dip in the power response by sending energy into the room without it affecting the on-axis response.

One possible way to do this is to use an extra loudspeaker with a “dipole” characteristic – a two-sided loudspeaker where the same signal is sent to both sides, but in opposite polarity. This means that, when one side of the loudspeaker produces a high pressure, the other side produces a low. When you sit on one side of the loudspeaker or the other, then you hear a signal. However, if you sit “on edge” to the loudspeaker, you hear nothing, since the two sides of the loudspeaker cancel each other out (in theory).

So, Gert’s idea was to add a two-way dipole loudspeaker on the top of a normal two-way loudspeaker and to just use the dipole (which became known as a “shark fin” – shown in Figure 2)  to add energy around the crossover frequency of the “normal” loudspeaker. Since the edge of the dipole was facing forwards, the theory was that none of its sound would have an effect on the on-axis response of the two-way loudspeaker below it.

So, the question to answer was:

“Which sounds better:

• a loudspeaker tuned to be flat on-axis, but with no correction for its power response
• a loudspeaker that was tuned to have a smooth power response (in other words, with a “bump” around the crossover)
• a loudspeaker that was tuned to be flat on-axis and had a power response correction provided by the dipole

?”

Since each of the 6 loudspeaker drivers in our model loudspeaker was independently controllable, this was an easy comparison to do on-the-fly, so we tried it out.

Also, just to be certain, we tried two different orientations of the dipole, both of which had the “null” – the edge of the loudspeaker – facing the listening position. The first orientation is shown in Figures 2 and 3. The second orientation is shown in Figure 4.

So, a bunch of us sat in the listening room for a week or so, listening to the various possible tunings of the loudspeakers, in various positions in the room, with various types of music. We each had an opinion about the whether we liked one configuration more or less than another. However, one thing that was noticeable was that there was an effect not only on the timbral impression of the loudspeakers (the tone colour) – but also on the spatial presentation of the pair. As we switched between the different tunings, phantom images changed in width and distance, and envelopment (when it existed in the recording) also changed.

This was particularly noticeable when the loudspeakers were closer to a reflecting surface, as is shown in Figure 5.

The end result was a bunch of different conclusions:

1. The three different configurations of the loudspeaker (listed above) sounded different. (this was not a big surprise)
2. A two-way loudspeaker tuned to have a smooth power response and a loudspeaker with a flat on-axis response with a shark fin smoothing the power response sounded different – but mostly spatially.
3. Switching between those two loudspeaker configurations listed in Point #2 basically meant that we were switching between two different loudspeakers with the same power response, but different directivities (a fancy word meaning “directional behaviours”).
4. The dipole loudspeaker’s output was audible at the listening position because of the sidewall reflections in the case where the dipole was on top.
5. Switching the dipole on and off had a noticeable effect on the phantom image distance and width… When the dipole was turned on, the sidewall reflections were obviously louder, and the phantom images moved to a distance from the listening position roughly the same as the distance to the loudspeakers themselves. At the same time, the phantom image width increased and became “cloudy” or “fuzzy” and less precise.

All of those little conclusions could be folded into two big ones:

1. The original idea of using a dipole to fill in the power response of the loudspeaker doesn’t work well enough in all situations because we don’t know where the reflective surfaces around the loudspeaker will be in any given configuration.
2. Being able to control the directivity of the loudspeaker (specifically, how much energy is coming from the sidewall reflections) is a very interesting control parameter that we should look into…

So, this is where the concept of the shark fin died, but where the idea of “Beam Width Control” began.

Well… more accurately: it was the beginning of our thinking that being able to change the beam width (or the “directivity”, if you’re a geek) of the loudspeaker would be a useful “handle” in the hands of our customers. The idea that was born was something along the lines of the following: “If a customer could change the beam width of a loudspeaker, then (s)he could change it from being a narrow-directivity loudspeaker for people with one chair and no friends to a wide-directivity loudspeaker for people with a sofa and some friends to an omni-directivity loudspeaker for people throwing a party – all just by the flick of a switch…”

For more information on Beam Width Control:

What is “Beam Width Control”?

Beam Width Control – A Primer

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

“In all affairs it’s a healthy thing now and then to hang a question mark on the things you have long taken for granted.”

-Bertrand Russell

If you were to get your hands on Harry Potter’s invisibility cloak and you were to walk into the acoustics department at Bang & Olufsen and eavesdrop on conversations, you’d sometimes be amazed at some of the questions we ask each other. That’s particularly true when we’re working on a new concept, because, if the concept is new, then it’s also new for us. The good thing is that all of my colleagues (and I) are ready and willing at any time to ask what might be considered to be a stupid (or at least a very basic) question.

One of those questions that we asked each other recently seemed like a basic one – why do we always put the tweeter on the top? It seems like there are very few loudspeakers that don’t do this (of course, there are exceptions – take the BeoLab Penta, for example, which has the tweeter in the middle). However, more often than not, when we (and most other people) make a loudspeaker, we put the loudspeaker drivers in ascending order of frequency – woofers on the bottom, tweeters on the top. Maybe this is because woofers are heavier, and if you stand a BeoLab 5 on its head, it will fall over – but that’s not really the question we were asking…

The REAL question we were asking ourselves at the time was: if we were to build a multi-way loudspeaker – let’s say a 3-way, with a woofer, a midrange and a tweeter, and if the crossovers were such that the bulk of the “interesting” information (say, the vocal range) was coming from the midrange, then why would we not put the midrange at ear height and put the tweeter between it and the woofer? For example, imagine we made BeoLab 20 without an Acoustic Lens on top, would it be better to arrange the drivers like the version on the left of Figure 1 or the version on the right? Which one would sound better?

After answering that question, there’s a second question would follow closely behind: how close together do the drivers with adjacent frequency bands (i.e. the woofer and the midrange or the tweeter and the midrange) have to be in order for them to sound like one thing? Of course, these two questions are inter-related. If your midrange and tweeter are so far apart that they sound like different sound sources, then you would probably be more interested in where the voice was coming from than where the cymbals were coming from…

Of course, step one in answering the second question could be to calculate/simulate the response of the loudspeaker, based on distance between drivers, the crossover frequency (and therefore the wavelengths of the frequency band we’re interested in), the slopes of the crossover filters, and so on. It would also be pretty easy to make a prototype model out of MDF, put the loudspeaker drivers in there, do the vertical directivity measurements of the system in the Cube, and see how well the theory matches reality.

However, the question we were really interested in was “but how would it sound?” – just to get a rough idea before going any further. And I have to stress here that we were really talking about getting a rough idea. What I’m about to describe to you is a little undertaking that we put together in a day – just to find out what would happen. This was not a big, scientifically-valid experiment using a large number of subjects and intensive statistics to evaluate the results. It was a couple of guys having a chat over coffee one morning when one of them said “I wonder what would happen if we put the midrange on top…” and then, off they went to a listening room to find out.

One thing we have learned in doing both “quick-n-dirty” listening comparisons and “real, scientifically valid listening tests” is that the placement of a loudspeaker in a room, has a huge effect on how the loudspeaker sounds. So, when we’re comparing two loudspeakers, we try to put them as close together as possible. So, we tried different versions of this. In the first, we took two pairs of loudspeakers, and put the left loudspeakers in each pair side-by-side, with one pair upside down and the other right-side up, as shown in Figure 2.

We then switched between the right-side up pair and the upside down pair, listening for a change in vertical position of the image. Note that we tried two arrangements of this – one where both right-side up loudspeakers were to the left of the upside-down loudspeakers. The other where the “right-side up” loudspeakers were the “outside” pair, as shown in Figure 3.

There are advantages and disadvantages of both of these arrangements – but in both cases, there is a lateral shift in the stereo image. When switching between pairs, either you get a left-right shift in image, or a change in width… It turned out that this change was more distracting than the vertical arrangement of the drivers, so we changed configuration to the one shown in Figure 4, below.

Now, instead of switching between loudspeakers, we pretended that one of them was a tweeter and other was a mid-woofer, and switched which was which, on the fly. Our “virtual” crossover was close-ish to the real crossover in the loudspeakers (our crossover was at 3.5 kHz, if you’re curious), so you could say that we were sort-of changing between using the upper tweeter + the lower woofer and using the upper woofer + lower tweeter, the “acoustical centres” of which are roughly at the same height. (remember – this was a quick-n-dirty experiment…)

After having listened to these three configurations of loudspeakers, we decided that the vertical arrangement of the drivers was not important with the vertical separation we were using.

This brought us to the second part of the question… If the tweeter and the midrange were further apart, would we have a preference? So, we kept our virtual crossover, using one loudspeaker as the “tweeter” and the other as the “mid-woofer”, and we moved the loudspeakers further apart, one example of which is shown in Figure 7. (One thing to note here is that when I say “further apart” I’m talking about the separation in the vertical angles of the sources – not necessarily their actual distance from each other. For example, if the loudspeakers were 1 m apart vertically, and you were level with one of the loudspeakers, but the listening position was a kilometre away, then the vertical angular separation (0.057 degrees) would be much smaller than if you were 1 m away (45 degrees)…)

The answer we arrived at at the end was that, when the vertical separation of the drivers gets extreme (perhaps I should use the word “silly” instead), we preferred the configuration where the “mid-woofer” was at ear-height. However, this was basically a choice of which version we disliked less (“preference” is a loaded word…). When the drivers get far enough apart, of course, they no longer “hang together” as a single device without some extra signal processing tricks.

So, we went to lunch having made the decision that, as long as the tweeters and the midranges are close enough to each other vertically, we really didn’t have a preference as to which was on top, so, if anyone asked, we would let the visual designers decide. (Remember that “close enough” is not only determined by this little experiment – it is also determined by the wavelengths of the crossover frequencies and whether or not there are more drivers to consider. For example, in the example in Figure 1, it might be that we don’t care about the relative placement of the tweeter and midrange in isolation – but perhaps putting the tweeter between the midrange and woofer will make them too far apart to have a nice vertical directivity behaviour across the lower crossover…)

Addendum

This isn’t the first time we asked ourselves such a question. Although I was not yet working at B&O at the time, my colleagues tell me that, back in the days when they were developing the BeoLab 3500 and the BeoLab 7-1 (both of which are “stereo” loudspeakers – essentially two multi-way loudspeakers in a single device) , they questioned the driver arrangement as well. Should the tweeters or the midranges / woofers be on the outside? You can see in the photos of the 3500 on this page that they decided to put the lower-frequency bands wider because the overall impression with stereo signals was wider than if the tweeters were on the outside.

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

Introduction:
Why do I need to compensate for my room?

Take a look at Figure 1. You’ll see a pair of headphones (BeoPlay H6‘s, if you’re curious…) sitting under a lamp that is lighting them directly. (That lamp is the only light source in the room. I can’t prove it, so you’ll have to trust me on this one…) You can see the headphones because the light is shining on them, right? Well… sort of.

What happens if we put something between the lamp and the headphones? Take a look at Figure 2, which was taken with the same camera, the same lens, the same shutter speed, the same F-stop, and the same ISO (in other words, I’m not playing any tricks on you – I promise…).

Notice that you can still see the headphones, even though there is no direct light shining on them. This probably does not come as a surprise, since there is a mirror next to them – so there is enough light bouncing off the mirror to reflect enough light back to the headphones so that we can still see them. In fact, there’s enough light from the mirror that we can see the shadow caused by the reflected lamp (which is also visible in Figure 1, if you’re paying attention…).

If you don’t believe me, look around the room you’re sitting in right now. You can probably see everything in it – even the things that do not have light shining directly on them (for example, the wall behind an open door, or the floor beneath your feet if you lift them a little…)

Exactly the same is true for sound. Let’s turn the lamp into a loudspeaker and the headphones on the floor into you, in the listening position and send a “click” sound (what we geeks call an “impulse”) out of the loudspeaker. What arrives at the listening position? This is illustrated in Figure 3, which is what we call an “impulse response” – how a room responds to an impulse (a click coming from a loudspeaker).

The top plot in Figure 1 shows the signal that is sent to the input of the loudspeaker. The bottom plot is the signal at the input of the microphone placed at the listening room. If we zoom in on the bottom plot, the result is Figure 4. This makes it much easier to see the direct sound and the reflections as separate components.

If we zoom in even further to the beginning of the plot in Figure 4, we can see individual reflections in the room’s response, as is shown in Figure 5.

Let’s take the total impulse response and separate the direct sound from the rest. This is shown in Figure 6.

We can then calculate the magnitude responses of the two separate components individually to see what their relative contributions are – shown in Figure 7.

Now, before you get carried away, I have to say up-front that this plot is a little misleading for many reasons – but I’ll only mention two…

The first is that it shows that the direct sound is quieter than the reflected sound in almost all frequency bands, but as you can see in Figure 6, the reflected energy is never actually louder than the direct sound. However, the reflected energy lasts for much longer than the direct sound, which is why the analysis “sees” it as containing more energy – but you don’t hear the decay in the room’s response at the same time when you play a click out of the loudspeaker. Then again, you usually don’t listen to a click – you listen to music, so you’re listening to the end of the room decay on the music that happened a second ago while you’re listening to the middle of the decay on the music that happened a half-second ago while you’re listening to the direct sound of the music that happened just now… So, at any given time, if you’re playing music (assuming that this music was constantly loud – like Metallica, for example…), you’re hearing a lot of energy from the room smearing music from the recent past, compared to the amount of energy in the direct sound which is the most recent thing to come out of the loudspeaker.

The second is in the apparent magnitude response of the direct sound. It appears from the red curve in Figure 7 that this loudspeaker has a response that lacks low frequency energy. This is not actually true – the loudspeaker that I used for this measurement actually has a flat on-axis magnitude response within about 1 dB from well below 20 Hz to well above 20 kHz. However, in order to see that actual response of the loudspeaker, I would have to use a much longer slice of time than the little red spike shown in Figure 6. In other words, the weirdness in the magnitude response is an artefact of the time-slicing of the impulse response. The details of this are complicated, so I won’t bother explaining it in this article – you’ll just have to trust me when I say that that isn’t really the actual response of the loudspeaker in free space…

The “punch line” for all of this is that the room has a significant influence on the perceived sound of the loudspeaker (something I talked about in more detail in this article). The more reflective the surfaces in the room, the more influence it has on the sound. (Also, the more omnidirectional the loudspeaker, the more energy it sends in more directions in the room, which also will mean that the room has more influence on the total sound at the listening position… but there’s more information about that in the article on Beam Width Control.)

So, if the room has a significant influence on the sound of the loudspeaker at the listening position, then it’s smart to want to do something about it. In a best case (and very generally speaking…), we would want to measure the effects that the room has on the overall sound of the loudspeaker and “undo” them. The problem is that we can’t actually undo them without changing the room itself. However, we can make some compensation for some aspects of the effects of the room. For example, one of the obvious things in the blue curve in Figure 7 is that the listening room I did the measurement in  has a nasty resonance in the low end (specifically, it’s at about 57 Hz which is the second axial mode for the depth of the room which is about 6 m). It would certainly help the overall sound of the loudspeaker to put in a notch filter at that frequency – in a best case, we should measure the phase response of the room’s resonance and insert a filter that has the opposite phase response. But that’s just the beginning with one mode – there are lots more things to fix…

A short history

Almost all Bang & Olufsen loudspeakers have a switch that allows you to change its magnitude response to compensate for the position of the loudspeaker in the room. This is typically called a Free/Wall/Corner switch, since it’s designed to offset the changes to the timbre of the loudspeaker caused by the closest boundaries. There’s a whole article about this effect and how we make a filter to compensate for it at this link.

In 2002, Bang & Olufsen took this a step further when it introduced the BeoLab 5 which included ABC – Automatic Bass Calibration. This was a system that uses a microphone to measure the effects of the listening room’s acoustical behaviour on the sound of the loudspeaker, and then creates a filter that compensates for those effects in the low frequency band. As a simple example, if your room tends to increase the apparent bass level, then the BeoLab 5’s reduce their bass level by the same amount. This system works very well, but it has some drawbacks. Specifically, ABC is designed to improve the response of the loudspeaker averaged over all locations in the room. However this follows the philosophy first stated Spock said in Star Trek II: The Wrath of Kahn when he said “the needs of the many outweigh the needs of the few, or the one.” In other words, in order to make the averaged response of the loudspeaker better in all locations in the room, it could be that the response at one location in the room (say, the “sweet spot” for example…) gets worse (whatever that might mean…). This philosophy behind ABC makes sense in BeoLab 5, since it is designed as a loudspeaker that has a wide horizontal directivity – meaning it is designed as a loudspeaker for “social” listening, not as a loudspeaker for someone with one chair and no friends… Therefore an improved average room response would “win” in importance over an improved sweet spot.

Active Room Compensation

We are currently working on a taking this concept to a new level with Active Room Compensation. Using an external microphone, we can measure the effects of the room’s acoustical behaviour in different zones in the room and subsequently optimise compensation filters for different situations. For example, in order to duplicate the behaviour of BeoLab 5’s ABC, we just need to use the microphone to measure a number of widely-space locations around the room, thus giving us a total average for the space. However, if we want to create a room compensation filter for a single location – the sweet spot, for example – then we can restrict the locations of the microphone measurements to that area within the room. If we want to have a compensation filter that is pretty good for the whole room, but has emphasis on the sweet spot, we just have to make more measurements in the sweet spot than in the rest of the room. The weighting of importance of different locations in the room can be determined by the number of microphone measurements we do in each location. Of course, this isn’s as simple a procedure as pressing one button, as in ABC on the BeoLab 5, but it has the advantage in the ability to create a compensation filter for a specific location instead of for the whole listening space.

As part of this work, we are developing a new concept in acoustical room compensation: multichannel processing. This means that the loudspeakers not only “see” each other as having an effect on the room – but they help each other to control the room’s acoustical influence. So, if you play music in the left loudspeaker only, then some sound will also come out of the right loudspeaker. This is because both the left and right loudspeakers are working together to control the room (which is being “activated” by sound only from the left loudspeaker.