B&O Tech: Why select one driver over another? (Part 1)

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

 

Once-upon-a-time, I wrote an article in this series about how a loudspeaker driver is made and (to some extent) how it works. Just recently, a reader asked a question related not only to this topic, but specifically to the BeoLab 90. Teddy wrote:

I am very curious as to why a driver like a Scanspeak Illuminator can reproduce so much more detail of the original signal when the fundamental design principles are just like less expensive drivers. I guess my question is how is a driver with superior detail retrieval designed and constructed? Also, what other benefits do you see when working with high end drivers?

I’m not sure that I can answer this question directly – but, in thinking about an answer, I realised that it might be interesting to talk about one reason why one loudspeaker driver is chosen over another in a given application or project.

A quick background sidebar:  a moving coil dynamic loudspeaker driver is a device that converts an electrical signal into mechanical movement. A voltage is applied to the terminals which causes current to flow through the voice coil (which is wrapped around a tube called a “former” that is attached to the “diaphragm” or “cone” – see Figures 1, 2, 3, and 4, below). That current generates a magnetic field around the wire – and since the coil is sitting in the magnetic field of a permanent magnetic, it wants to move. Depending on the direction of the current, the voice coil will either push outwards or pull inwards resulting in some excursion of the voice coil, former and diaphragm (those parts are all glued together). The whole thing doesn’t fly off because it’s held back by the loudspeaker’s “suspension”. The suspension is comprised of two things – the “surround” (usually a rubber ring that connects the edge of the diaphragm to the top of the basket – the metal frame that supports the whole assembly) and the “spider” (a ring of stretchy fabric that connects the former to the basket). The reason there are two components to the suspension is to ensure that, when the diaphragm moves in and out, it doesn’t rock from side to side. If you want a more complete version of this story, read this article.

A BeoLab 3 woofer, showing some of the components.
Figure 1: A Beolab 3 woofer, showing some of the components.

 

A BeoLab 3 woofer, showing some more of the components.
Figure 2: A Beolab 3 woofer, showing some more of the components.

 

A BeoLab 3 woofer, showing some more of the components.
Figure 3: A BeoLab 3 woofer, showing some more of the components. The spider can also be seen there, but it’s not labeled – it’s the reddish-brown corrugated mesh.

When building any loudspeaker, you have to make some decisions about which driver to use. Lots of factors come into this decision – frequency range, maximum sound pressure level (vs. frequency), directivity (vs. frequency), size, sensitivity, cost, and many more things are weighed in order to make the most appropriate choice for the product. (If you’re making a passive loudspeaker, then the frequency response of the driver is important – but if you’re making an active loudspeaker, particularly one that is DSP-based, this is less of a concern, since it can be fixed (more or less…) in the processing.) One of the more significant issues in this list that an acoustical engineer worries about is the nonlinear distortion characteristics of the driver. (This is a big concern with a DSP-based active loudspeaker because non-linear distortion cannot be fixed in the processing.) If the movement of the driver’s diaphragm isn’t the same shape as the electrical signal that you put into it (for example, if you apply a nice smooth electrical sine wave at the speaker terminals, but the diaphragm moves in a jerky square wave fashion, then the output of the speaker isn’t the same as the input) then the signal has been distorted. There are different types of distortion, so we have to be a little more specific.

Linear distortion is what you have when the change to the signal can be “undone”. For example, if you add bass to a signal, then you’ve distorted it (the output of the bass boost is not the same as the input – but that’s the point). However, if you remove bass from the result, you can (in theory) get back what you started with.

Non-linear distortion is what you have when the change to the signal cannot be undone. If you put in a sine wave and the system clips (“chops off”) the top of it, there’s no way of regaining the nice smooth wave that you started with, because there’s no way of knowing what was there before the signal was chopped off.

Non-linear distortion can be generally broken into two general headings: harmonic distortion (sometimes abbreviated THD for Total Harmonic Distortion) and intermodulation distortion (or IMD). Harmonic distortion happens when you put in a signal with one frequency (say, a sinusoidal wave at 1 kHz) and you get out energy at other frequencies (that are multiples of the frequency of the input signal) as well (say, 2kHz, 3 kHz, 4 kHz, and so on…). Intermodulation distortion occurs when you put in more than one frequency (say, 900 Hz and 1000 Hz simultaneously) and you get out other frequencies that are usually mathematically related to the input (typically the sum and difference of multiples of the input frequencies – so, in our example, 1900 Hz (900+1000),  100 Hz (or 1000-900), 2900 Hz (2*1000+900), 1100 Hz (2*1000-900) and lots more…)

Another sidebar: These differences in distortion means that when you say “the signal sounds distorted” – the statement is about as useful as saying “the signal sounds different”. This is even true if you measure the distortion of a system and specify it with a number. See this posting and this posting for a more thorough discussion of this problem…

Back to our loudspeaker: in an ideal world, a loudspeaker driver’s movement would be an exact “replica” (more like an analogy) of the input signal. Sadly, this is never true. Never.

So, we start by accepting the knowledge that a loudspeaker driver is imperfect – and therefore it will impose some harmonic distortion and some intermodulation distortion on the signal. The next question is “why?” and “how can we minimise it?”

In order to talk about that, let’s take a driver and cut it in half. This is shown in Figure 4.

 

Figure X: A cross section of a typical moving coil dynamic loudspeaker driver. The diaphragm is shown at the rest position, with an excursion of 0 mm.
Figure 4: A cross section of a typical moving coil dynamic loudspeaker driver. The diaphragm is shown at the rest position, with an excursion of 0 mm. If you want to see this in 3D, check out this article.

 

There are some moving parts of the loudspeaker driver. These are the diaphragm and dust cap, the former and the voice coil. these are all glued together and move as one part (hopefully…). When they move, the suspension (the surround and the spider) are stretched in one direction or the other. This can be seen in Figure 5.

 

Figure X: The cross-section of a typical moving coil dynamic loudspeaker. The top drawing shows the diaphragm used outwards (a positive excursion). The bottom drawing shows the diaphragm pulled inwards (a negative excursion).
Figure 5: The cross-section of a typical moving coil dynamic loudspeaker. The top drawing shows the diaphragm used outwards (a positive excursion). The bottom drawing shows the diaphragm pulled inwards (a negative excursion).

 

 

Now, let’s pretend that the movement of the diaphragm (and the dust cap, former, and voice coil) is caused by you (instead of being moved by the voice coil) – you’re the one pushing and pulling the moving parts. When the diaphragm is at the rest position, it’s easy to move. However, as you push it further and further out, it becomes harder and harder to move, since the suspension is stretching more and more. (This is just like an elastic band – stretching it a little bit is easy, stretching it a lot is hard.) If you’re pulling the driver inwards, then it’s the same – the father you get from the rest position (the greater the excursion) the harder it is to move.

This behaviour is called the stiffness of the suspension (although it is also called the compliance – which is how not-stiff it is…). We can measure the suspension stiffness and plot it on a graph, relative to how far away the diaphragm is from the rest position (the excursion). An example of this is shown in Figure 6. (Note that Figure 6 is not the actual measurement of a real driver – I just drew a graph to illustrate the concept.)

 

Figure x: An example of a stiffness curve of the driver's suspension. As the excursion of the driver moves away from the rest position (either inwards or outwards) the suspension gets stiffer.
Figure 6: An example of a stiffness curve of the driver’s suspension.

 

There are two things to notice in the graph in Figure 6. The first is that, as the excursion of the diaphragm moves away from the rest position (either inwards or outwards) the suspension gets stiffer (or harder to move). This means that you need less force to move the diaphragm from 0 mm to 1 mm than you do from 5 mm to 6 mm. the second thing is to notice that the curve is not symmetrical. For example, when the diaphragm has moved outwards by 5 mm, the suspension is stiffer than it is if you move it inwards by 5 mm.

Both of these things will be important later.

 

Now let’s consider what’s really doing the pushing and pulling. As I described above, when we apply a voltage to the terminals of the voice coil, a current runs through it and it turns into an electromagnet with a magnetic field around it. If the current goes in one direction, one side of the coil is north and the other is south. If we reverse the current direction, we flip the polarity of the electromagnet. The voice coil is already sitting inside the magnetic field of a permanent magnet, so when it gets its own magnetic field it will try to move in one direction or the other, depending on which end is north and which is south (which are dependent on the direction of the current which is dependent on which loudspeaker terminal has the  positive voltage and which has the negative.)

The bigger the difference in voltage we apply at the terminals, the greater the current through the voice coil, and the stronger the electromagnet. This means that we will be applying more force to move the voice coil (and the former, the diaphragm, and the dust cap) outwards or inwards.

However, there’s a problem in that last statement. We only have the force to move the voice coil if there’s a magnetic field (from the permanent magnet) to push against. If there were no permanent magnet, there would not be anything for the electromagnet (the voice coil) to push against, so it wouldn’t move.

But look again – closely – at Figures 5 and 6. When the voice coil is at rest, it’s sitting in the “gap” which is where the magnetic field is strongest. However, as it moves inwards or outwards, it also moves out of the gap, and therefore out of the magnetic field. This is illustrated below in the three drawings in Figure 7.

 

Figure X:
Figure 7: A cross section of the voice coil (the black circles) on the former (the black vertical line) sitting in the magnetic field (in red) in the gap of the loudspeaker driver (between the two grey rectangles – the top plate and pole piece).

 

Look at the three drawings in Figure 7 which show that, as the coil moves inwards or outwards, part of the coil moves out of the magnetic field (green arrows), so there’s nothing for it to push against. This means that the bigger the excursion of the diaphragm, the less force with which you have to push (or pull) it. This force factor (abbreviated Bl – but we won’t talk about why…) is a product of the strength of the magnetic field, the length of wire in the coil. That value is multiplied by the amount of current flowing through the coil to find the force delivered by the system. However, as we can see above, is also dependent on the position of the voice coil relative to the gap. that change in force factor can be measured for the driver as a function of its excursion. An example of this is shown in Figure 8, below. (Note that Figure 8 is not the actual measurement of a real driver – I just drew a graph to illustrate the concept.)

 

Figure X: An example of an undesirable Bl curve. As soon as the driver moves out of the rest position, you increasingly lose force (and therefore control of its movement).
Figure 8: An example of an undesirable Bl curve. In this example you can see that, as soon as the driver moves out of the rest position, you increasingly lose force factor.

Now, hopefully, you will be asking yourself a very important question. If you look at Figure 6, you can see that, as the excursion of the driver increases, the harder it is to move, so we should have more force factor available to move it. However, Figure 8 shows us that as the excursion of the driver increases we lose force factor… This is something like losing horsepower in your car’s engine every time you go up a hill…

Sadly, although the graphs I drew in Figures 6 and 8 are just invented curves that I drew, they’re not unusual to see… What’s the effect? Basically, it means that you don’t have the ability to push the driver as far out (or in) as you would like, so the peaks (and troughs) in your waveform will be flattened. If either the stiffness or the force factor curves (or both) are asymmetrical, then the flattening will be different on the outwards excursion than the inwards (in other words, the peaks will be squashed differently than the troughs). The total result is that the driver distorts the signals – and you’ll get both harmonic distortion and intermodulation distortion. The less flat the stiffness and/or force factor curves, the more distortion you’ll get. In addition, if you lose force factor with excursion, then when you have an impulsive sound (like a kick drum, for example), you can start moving the diaphragm outwards (because you have force factor at the rest position to do the throwing) but you don’t have the force factor to control its return – so you throw the speaker out, and hope that it comes back instead of pulling it back… This is another form of distortion – but it’s a time-based distortion that might look like “ringing” for example.

But what is it that you want?

In a perfect world, the stiffness of the suspension would be the same, regardless of the excursion of the driver – in other words, it would be a horizontal line instead of the curve in Figure 6. Also, in a perfect world, you would not lose force factor with excursion. In other words, you could always have the same amount of control over the driver, regardless of how far in or out it is.

In order to flatten the stiffness, we have to look at the behaviour of the surround and the spider (if we’re ignoring the effect of the air behind the driver in the loudspeaker enclosure, which, in a real world, cannot be ignored… but let’s stay out of the real world for the purposes of this discussion). One simple method of flattening the stiffness vs. excursion is to make the driver suspension to allow for a much bigger excursion than you expect, for example. If we look at the measured stiffness of the Scan-Speak Illuminator 12MU/4731T00 (the midrange driver in the BeoLab 90), it looks like the graph in Figure 9. (I traced this using the plot in this article.)

 

Figure x: The stiffness curve of the suspension of the BeoLab 90's midrange driver. The stiffness stays fairly constant until the driver has moved about 5 mm inwards or outwards from the rest position.
Figure 9: The stiffness curve of the suspension of the BeoLab 90’s midrange driver. The stiffness stays fairly constant until the driver has moved about 5 mm inwards or outwards from the rest position.

 

There are two things to notice about this stiffness curve. The first is how flat it is around the rest position. The second is that it’s very symmetrical, particularly around the rest position. (This is the reason the mirror image of the stiffness curve is plotted (in grey) – so that you can see the symmetry of the curve.) So, one reason we chose the Scanspeak Illuminator midrange for the Beolab 90 was for this stiffness curve. The “so what?” of this is that the distortion of the driver is lower than with a typical driver.

 

Next, we look at the force factor or Bl curve. The Illuminator midrange has an unusually flat Bl curve, as can be seen in Figure 10 (also copied from the pdf file lined above). Looking at Figures 9 and 10 together, you can see that, if you stay within an excursion of ± 5 mm or so, both the stiffness and the Bl curves are flat – so the distortion imposed on the audio signal by the driver is very low. Of course, we push the driver further than 5 mm, but even then, the two curves show us that the driver “behaves” better than most…

 

Figure X: The Bl curve of the midrange driver of the Beolab 90. The amount of force (and therefore the control of the driver) stays fairly constant until the excursion of the driver is more than 5 mm away from the rest position.
Figure 10: The Bl force factor curve of the midrange driver of the Beolab 90. The amount of force (and therefore the control of the driver) stays fairly constant until the excursion of the driver is more than 5 mm away from the rest position.

 

How is such a flat Bl curve achieved? Take a look at Figure 11, below.

 

Figure X:
Figure 11: Three different options for the design of a voice coil relative to the magnetic gap and their behaviour with respect to excursion. The top three drawings show a typical design. The middle three show an underhung design. The bottom three show an overhung design. See the text for descriptions of what this means.

 

The top three drawings in Figure 11 show the same situation as was shown in Figure 7. As you can see there, as the voice coil moves, it moves out of the magnetic field and we lose force. However, look at the middle three drawings. In this case, the magnetic field (in red) is much bigger than the coil. So, even though the coil moves inwards and outwards, none of it leaves the magnetic field. This is called an “underhung” design – and the result is a flattened Bl curve. We don’t lose force factor because the coil is always in the gap and therefore doesn’t see a change in the magnetic field.

Another way to achieve the same effect is to make the voice coil much bigger than the magnetic field – an “overhung” design. So, the same amount  of it is always in the gap.

There are advantages and disadvantages to each of these options. In an underhung design, you have a big magnet, and therefore the driver is heavy – so it’s not typically seen in automotive loudspeakers. The overhung design has a heavy voice coil which is harder to move, so you don’t usually see it in drivers for higher-frequency applications… However, if your ONLY concern is the Bl curve, either design will improve your performance.

The Scanspeak Illuminator uses the underhung design, which is is not hard to figure out just by looking at the photos of it in Figures 12 and 13.

 

A Scanspeak Illuminator midrange used in the Beolab 90. It's upside down here, but its easy to see the relatively large size of the magnetic housing in which the voice coil moves.
Figure 12: A Scanspeak Illuminator midrange used in the Beolab 90. It’s upside down here, but its easy to see the relatively large size of the magnetic housing in which the voice coil moves.

 

 

Figure 13: The drivers of the Beolab 90 in their correct locations and orientations. This is a physical representation of the information given to the visual designers of the loudspeaker.
Figure 13: The drivers of the Beolab 90 in their correct locations and orientations. This is a physical representation of the information given to the visual designers of the loudspeaker.

 

Wrapping up

The stiffness and Bl curves of the Illuminator midrange and the resulting low distortion are just one aspect of the driver that contributed to its choice for the Beolab 90. As I said at the start of the article, there are many, many factors that have to be considered when choosing a driver for a loudspeaker. It is also important to remember that a driver that is a good choice for one loudspeaker does not necessarily mean that it’s a good choice for another loudspeaker. A gearbox that’s perfect for a racing motorcycle is not necessarily going to work well on an 18-wheeler truck. A racing bicycle can go fast partly due to its tires – however, if you put the same tires on a Ferrari, you won’t get very far… Every individual component of any loudspeaker has to be chosen with all of the other components in mind to build an optimal system.

 

 

 

B&O Tech: Intuitive Directivity Plots v.2

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

 

In a past article, I tried to come up with an intuitive way of representing the beam width (or “directivity” – if you’re a geek) of the BeoLab 90. I realised after posting, that there is another way to do this which is used in loudspeaker reviews in some magazines (mostly because it’s the way directivity is plotted by MLSSA). So, I’ve taken the same data as before, and re-plotted it using a “waterfall” function in Matlab. It’s just a different way of looking at the same information – but it might be helpful.

If you’re curious about the details regarding the data itself, this is described here.

 

 

Figure X: BeoLab 90 directivity vs. frequency as a "normal" three-way loudspeaker with the Beam Control disabled. (Note that this is not possible in a production model.)
Figure 1: BeoLab 90 directivity vs. frequency as a “normal” three-way loudspeaker with the Beam Control disabled. (Note that this is not possible in a production model.)

 

Figure X: Directivity vs. frequency of BeoLab 90 in Narrow mode
Figure 2: Directivity vs. frequency of BeoLab 90 in Narrow mode

 

 

Figure X: Directivity vs. frequency of BeoLab 90 in Wide mode. Compare this to the BeoLab 5 plot.
Figure 3: Directivity vs. frequency of BeoLab 90 in Wide mode. Compare this to the BeoLab 5 plot, below. As can be seen here, the low frequency directivity (or beam width) is controlled to be the same as the mid and high frequency bands.

 

Figure X: BeoLab 5 directivity vs. frequency.
Figure 4: BeoLab 5 directivity vs. frequency. As can be seen here, the Acoustic Lens ensures a constant directivity (meaning the same beam width at all frequencies) in the high end. However, the low frequency band is omnidirectional.

 

Figure X: Directivity vs. frequency of BeoLab 90 in Omni mode
Figure 5: Directivity vs. frequency of BeoLab 90 in Omni mode

 

B&O Tech: Product Playlists

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

This is just a list of playlists on the Tidal music streaming service that can be used for testing and demonstrating various Bang & Olufsen products.

If you don’t have a Tidal subscription, you can at least see the list of tracks, artists and albums.

Loudspeakers

Televisions

Music Systems

Headphones

B&O Tech: Intuitive Directivity Plots

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

 

I’ve been writing and presenting a lot of information over the past couple of months about the general topic of loudspeaker directivity or “Beam Width” as we call it in the BeoLab 90. One thing that I’ve noticed is that, every time I have to do this in person, I have to explain how to read our directivity plots. This has made me realise that these are not necessarily intuitive to someone that doesn’t look at these kinds of plots (or topographic maps) every day. So, I’ve been working on finding different ways to show the same data. This posting is a first attempt – there will probably be others in the future…

 

 

 

Figure X: A graphical guide on how to read the circular directivity plots below.
Figure 1: A graphical guide on how to read the circular directivity plots below.

 

Figure 1, above, shows the idea. We have a loudspeaker, pointing to the right of the screen (towards the word “front”). We measure the magnitude response (more commonly called the “frequency response”) of the loudspeaker on-axis, directly in front of it. Then we rotate the angle of the listening position around the loudspeaker, towards the side. As we do, we measure how much the level changes (usually it gets quieter, but sometimes, at some frequencies and some angles, it gets louder) as a function of angle and frequency. As the angle to the listening position increases, some frequencies will get quiet very quickly, some will not get quiet at all – even when we reach the back of the loudspeaker.

The plot above shows one way to look at this. The inner rings are the low frequencies (in the case of the plots on this webpage, the inner-most ring is 50 Hz) and the further outwards you go, the higher in frequency. The distance between the rings is logarithmic (in other words, by octave) so it makes more sense musically.

 

If you’re used to looking at the contour plots that I typically show on this site, then take a look at Figure 2 which shows exactly the same data. In this case, it’s plotted as a contour plot (like a topographic map) showing the -3 dB, -6 dB, -9 dB, and -12 dB contours relative to the on-axis response.

 

BeoLab 90: Beam Width Control: Off

Figures 2 and 3 show the directivity of the BeoLab 90 if you were to disable the Beam Width Control function entirely and just use the front woofer, midrange and tweeter by themselves (and therefore turn off the 15 other loudspeaker drivers in the system. It’s important to note that this is not possible in a production model loudspeaker – we did it as part of the initial measurements of the loudspeaker during the development process.

 

Figure X: BeoLab 90 directivity vs. frequency as a "normal" three-way loudspeaker with the Beam Control disabled. (Note that this is not possible in a production model.)
Figure 2: BeoLab 90 directivity vs. frequency as a “normal” three-way loudspeaker with the Beam Control disabled. (Note that this is not possible in a production model.)

 

 

 

 

Figure X: BeoLab 90 directivity vs. frequency as a "normal" three-way loudspeaker with the Beam Control disabled. (Note that this is not possible in a production model.)
Figure 3: BeoLab 90 directivity vs. frequency as a “normal” three-way loudspeaker with the Beam Control disabled. (Note that this is not possible in a production model.)

 

 

BeoLab 90: Narrow Beam

As I’ve discussed in other postings, our goal with BeoLab 90’s directivity was two-fold: The first was to have a constant directivity – meaning that it should be the same at all frequencies. The second was that the directivity should be narrow in order to reduce the influence of sidewall reflections. Of course, it should not be too narrow – you don’t want a loudspeaker that you can hear in your left ear, but not your right or “headphones at a distance” as I read on one website.

So, we played around with different target directivity functions during the development process, trying to find a beam width that was not too wide and not too narrow. Figures 4 and 5 aren’t drawings of the actual target for BeoLab 90 – but they’re illustrative of the concept.

 

Figure X: An example of a possible target for the Directivity vs. frequency of a loudspeaker with a narrow beam width and constant directivity.
Figure 4: An example of a possible target for the Directivity vs. frequency of a loudspeaker with a narrow beam width and constant directivity.

 

 

Figure X: An example of a possible target for the Directivity vs. frequency of a loudspeaker with a narrow beam width and constant directivity.
Figure 5: An example of a possible target for the Directivity vs. frequency of a loudspeaker with a narrow beam width and constant directivity.

 

The actual directivity of the narrow beam width in BeoLab 90 is plotted in Figures 6 and 7.

 

Figure X: Directivity vs. frequency of BeoLab 90 in Narrow mode
Figure 6: Directivity vs. frequency of BeoLab 90 in Narrow mode

 

 

 

 

 

Figure X: Directivity vs. frequency of BeoLab 90 in Narrow mode
Figure 7: Directivity vs. frequency of BeoLab 90 in Narrow mode

It might also be interesting to compare this to one of BeoLab 90’s competitors from another manufacturer, shown in Figure 8.

Figure X: Directivity vs. frequency of a competitor's loudspeaker. This should be compared with the BeoLab 90 's "Narrow" plot
Figure 8: Directivity vs. frequency of a competitor’s loudspeaker. This should be compared with the BeoLab 90 ‘s “Narrow” plot

 

BeoLab 90: Wide Beam

Again, we can look at a candidate for a target (but not the target) for the wide beam mode. This is shown in Figures 8 and 9.

 

Figure X: An example of a possible target for the Directivity vs. frequency of a loudspeaker with a wide beam width and constant directivity.
Figure 9: An example of a possible target for the Directivity vs. frequency of a loudspeaker with a wide beam width and constant directivity.

 

 

Figure X: An example of a possible target for the Directivity vs. frequency of a loudspeaker with a wide beam width and constant directivity.
Figure 10: An example of a possible target for the Directivity vs. frequency of a loudspeaker with a wide beam width and constant directivity.

 

 

The actual directivity of the wide beam is shown in Figures 10 and 11.

Figure X: Directivity vs. frequency of BeoLab 90 in Wide mode. Compare this to the BeoLab 5 plot.
Figure 11: Directivity vs. frequency of BeoLab 90 in Wide mode. Compare this to the BeoLab 5 plot.

 

 

Figure X: Directivity vs. frequency of BeoLab 90 in Wide mode. Compare this to the BeoLab 5 plot.
Figure 12: Directivity vs. frequency of BeoLab 90 in Wide mode. Compare this to the BeoLab 5 plot.

 

In addition, it might be interesting to compare those plots to the BeoLab 5 directivity, which had similar targets of a constant and wide directivity.

 

 

Figure X: BeoLab 5 directivity vs. frequency.
Figure 13: BeoLab 5 directivity vs. frequency.

 

 

Figure X: BeoLab 5 directivity vs. frequency.
Figure 14: BeoLab 5 directivity vs. frequency.

 

 

BeoLab 90: Omni Beam

The directivity of BeoLab 90’s Omni mode is shown below in Figures 15 and 16. The lobing caused by the distances between the tweeters is visible in the contour plot, however, as you can see in Figure 16, there is certainly energy being directed in all directions across the entire frequency spectrum. However, the high-frequency lobing, in addition to the beaming in the lower midrange area would indicate that this mode is not appropriate for critical listening…

Figure X: Directivity vs. frequency of BeoLab 90 in Omni mode
Figure 15: Directivity vs. frequency of BeoLab 90 in Omni mode

 

Figure X: Directivity vs. frequency of BeoLab 90 in Omni mode
Figure 16: Directivity vs. frequency of BeoLab 90 in Omni mode

 

 

Some details

The plots above were done in the horizontal plane with a smoothing of 1/12 octave (by semitone).

The measurements on the loudspeakers were done in 73 increments of 5º from -180º to 180º (in other words, we’re actually measuring both sides of the loudspeaker – we don’t just measure one side and assume the directivity is symmetrical.

 

 

 

B&O Tech: Uni-Phase Loudspeakers

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

Warning: In this page, I use a bunch of equations that might look very unfamiliar. These are called “s-domain expressions”, used in Laplace analysis. If these do not make any sense, don’t worry – it’s not really important that they do – so you can just skip over any math that looks ugly without guilt or concern. The reasons I used it here were twofold: firstly, these are taken from the equations in Bækgaard’s paper (mentioned below), and secondly, it’s the easiest way to show that something is missing (the “MissingPortion” in the intuitive equations below) in a two-way loudspeaker with one type of crossover.

When you build a two-way loudspeaker (one with a tweeter and a woofer), you have to divide the energy in the audio signal before sending it to the two drivers using a circuit called a crossover. This filters the signal sent to a tweeter using a high-pass filter (which only allows the high frequencies to pass through it) and the signal sent to the woofer using a low-pass filter (which allows the low frequencies to pass). The result is a signal that crosses over from the woofer to the tweeter as the frequency increases – hence the name. However, this is not necessarily the end of the solution, since high-pass and low-pass filters have some characteristics that we need to worry about.

One of those issues is that of the phase response of the filters. Although there are many different types of high-pass and low-pass filters, let’s take a simple example of the filters used in a second-order Butterworth two-way crossover – a very typical choice for passive loudspeaker designers.

In a typical (second-order Butterworth) two-way crossover, the two bands are 180° out of phase as can be seen in the phase responses calculated using Equations 1 and 2 and plotted in Figure 1.

uniphase_equations_01
Figure 1: The Low Pass (black) and High Pass (blue) components of a two-way loudspeaker with a 2nd-order Butterworth crossover network (assuming that both drivers had perfectly flat magnitude responses). Notice that the phase responses are 180º apart at all frequencies.

This phase difference isn’t a big problem at frequencies that are far away from the crossover frequency (where the two components have the same magnitude) because the quieter one isn’t loud enough to cancel the louder one very much. However, the closer you get to the crossover frequency, the more their magnitudes are alike, and so the more they cancel each other. In fact, at the crossover frequency itself, their magnitudes are identical, and, because they are 180° apart in phase, their sum is completely cancelled, resulting in no output at all. (Keep in mind here that, for the purposes of this posting, I’m living in a perfect world where loudspeaker drivers are perfectly linear, there are no time-of-arrival differences between the two drivers at the listening position, and things like diffraction and reflections do not exist…) The total result would therefore look like the responses shown in Figure 2.

Figure 2: The total result of adding the two components in Figure 1, if the polarity of one of the two is not inverted.

To avoid complete cancellation at the crossover frequency where the two signals have identical magnitude, the polarity of the upper frequency band is typically inverted. (This is expressed as the negative sign at the beginning of the right-hand side of Equation 3). However, this solution results in a total sum that has a “bump” in its magnitude response as well as an allpass characteristic (meaning that the phase response of the total output is not a straight line).

Figure 3: The total result of adding the two components in Figure 1, if the polarity of one of the two (in this case, the high pass component).

At the listening position, on-axis to the loudspeaker, in this perfect world, these two frequency responses for the low frequency and high frequency sections (expressed in Equations 1 and 2) are combined using Equation 3.

uniphase_equations_02

In May 1977, Erik Bækgaard (pronounced something like BECK-gore), a manager of electronic engineering at B&O, published a paper in the Journal of the Audio Engineering Society where he described a solution to this problem associated with second-order Butterworth crossovers. Take a look at that last equation… Since we want the output to equal the input, we want F_Total(s) = 1. Therefore we can calculate what is missing from the s-plane equation to make that happen.

In other words, what we want is:

uniphase_equations_03

Bækgaard’s solution to this problem was to insert that component missing in Equation 5.

uniphase_equations_04

The frequency response of that resulting “MissingPortion” is a first-order bandpass filter with a phase response that is exactly between the phase responses of the high pass and low pass components, as can be seen in Figure 4, below. By adding that missing link to the system, the phase response of the entire system is corrected, so Bækgaard called the additional loudspeaker driver a  “phase link” driver. So now, if we add the high pass, low pass and phase link components, we get the following:

uniphase_equations_05

… which means that the output of the system equals the input – exactly what we wanted!

The Low Pass (black), High Pass (blue), and Phase Link (red) components of a Uni-Phase loudspeaker.

Physically speaking, the solution to the problem was to add a third section in the crossover and an extra loudspeaker driver to fill in the missing phase component, linking the upper and lower frequency sections and avoiding the necessity for polarity inversion. This corrected the phase response of the entire system, eliminated the all pass characteristic and flattened the on-axis magnitude response, as can be seen in Figure 5.

The result was an entire range of loudspeakers, dubbed the “Uni-Phase” series, that was produced from 1976 to 1987. As is shown in Bækgaard’s paper, his system also improved the loudspeakers’ responses in the time domain, not only on-axis, but also off-axis in the vertical plane.

Figure 5: The total result if the three components shown in Figure 4 are added. Notice that the bump in the magnitude response from Figure 3 disappears, and the phase response becomes flat.

Figure 6, below, shows an example of one of the Uni-Phase loudspeakers. Without knowing what’s going on, it looks like a typical three-way loudspeaker with a woofer, midrange and tweeter. However, this is not the case. The woofer and the tweeter form a two-way loudspeaker and the middle driver is used as the Phase Link. So, instead of having two crossover frequencies, this loudspeaker has only one – and the peak in the bandpass response of the middle driver is at the same frequency as the crossover between the other two drivers.

BeoVox 120.2 (1983-1988) one of the many "Uni-Phase" loudspeakers with a woofer, tweeter and "phase link" driver.
Figure 6: BeoVox 120.2 (1983-1988) one of the many “Uni-Phase” loudspeakers with a woofer, tweeter and “phase link” driver.

Post-script: Of course, as I mentioned above, everything that I’ve said in this posting makes a lot of assumptions, not only about loudspeaker drivers, but cabinet effects and room acoustics. However, in order to keep things as simple as possible, it’s easier to isolate the issues described above as being the only problem with crossovers and loudspeakers. Sadly, this is not true…

BeoLab 90: Articles and reviews

“So how did the BeoLab 90 make us feel? When we closed our eyes in Bang & Olufsen’s special listening room, the pair of master reference speakers (#2 and #3 ever made)—along with the room—seemed to vanish the instant a song played. We weren’t listening to sound emanating from two specific points; instead, the Weeknd was singing his heart out right in front of us. Benny Goodman’s band performed an intimate set, and you could picture where each musician was sitting. The BeoLab 90’s ability to create such a lifelike three-dimensional sound stage is unparalleled when you’re sitting in the sweet spot. It certainly brings up the question of whether a speaker can be “too” good for the music—some now-classic albums weren’t necessarily well-recorded and mastered (think of when the Rolling Stones turned the basement of a rented French mansion into a makeshift studio slash drug den). But when all the variables align perfectly, the music engulfs listeners entirely and hits the guts. The result of such incredible technology and engineering happens to be a very visceral human experience.”

Coolhunting.com

 

“Die Abbildung war phänomenal, jedes Instrument der gewählten Musik nahm ganz selbstverständlich den für sich bestimmten Platz im Raum ein, jedes Element war von Anfang bis Ende verfolg- und erlebbar. Aber nicht nur die Ortung verblüffte, auch die Detailgenauigkeit, mit der selbst kleinste Feinheiten bis zum erkälteten Backgroundsänger aufgedeckt wurde, sucht ihresgleichen.”
modernhifi.de

 

“Vi kan bevidne, at effekten er besnærende. Højttalerne spiller sammen med lytterummet på en måde, vi ikke har oplevet før. Personligt har jeg aldrig hørt et mere holografisk realistisk lydbillede, hverken i eller uden for sweet spot. BeoLab 90 er også en fuldblods, fullrange-højttaler, der ikke overlader noget til tilfældighederne.”
lydogbillede.dk

 

“I found that the size of the soundstage was consistently proportional to the size of the ensemble and the recording. I found that the bass was very well extended, taut, and satisfying. Most of all, I was impressed by the prototypes’ reproduction of detail throughout the audio band, and the uniformity of that quality across the soundstage.”
– Kalman Rubinson, Stereophile magazine (print version, October, 2015)

 

“Wohl noch nie haben Lautsprecher die musikali­ schen Akteure so scharf ins Wohnzimmer projiziert. Ganz gleich, ob grosse Orchester oder kleine Jazz­-Formationen – jedes ein­ zelne Instrument hat seinen exakten Platz im virtuellen Raum, der auch seine Tiefen­ dimension verblüffend genau zu erkennen gibt: Der Hörer kann zum Beispiel fast in Zentimetern abzählen, wie weit das Schlag­ zeug hinter dem Kontrabass placiert ist. Dass der Beolab 90 auch für schwärzeste Bass­Tiefe, überbordende Dynamik und feinen, luftigen Obertonglanz steht, müssen Test­Hörer der Vollständigkeit halber natür­ lich ebenfalls zu Protokoll geben, aber das eigentlich Spektakuläre des Lautsprechers ist tatsächlich seine überragende räumliche Abbildung.”
– NZZ am Sonntag 18. Oktober 2015

For more comments and reviews:

How Bang & Olufsen’s BeoLab 90 Became a Reality: www.coolhunting.com

Skønheden eller udhyret? Bag om B&O BeoLab 90: www.recordere.dk

BeoLab 90: B&O laver banebrydende højttaler: www.lydogbillede.dk

Beolab 90 is Bang & Olufsen’s striking 90th anniversary speaker: www.whathifi.com

Der Traum vom Raum: Frankfurter Allgemeine

Bang & Olufsen BeoLab 90: Erster Hörtest: www.modernhifi.de

 

How big is my woofer?

One of the questions that has come up with regards to the specifications of the new BeoLab 90 is about the size of the woofers. The specifications state that it has one 13″ front woofer and three 10″ woofers for the sides and rear. However, if you look in the technical specifications in the Technical Sound Guide, you’ll see that the “effective diameter” of the front woofer is 260 mm (about 10″) and the remaining woofers is 212 mm (about 8″). Why is there a discrepancy?

The difference is in how a woofer – or any loudspeaker driver – is measured. When you say 13″ woofer, the measurement is the external diameter of the circular metal frame around the front of the driver. If you look on the first page of the datasheet shows that this diameter is 320 mm for the BeoLab 90’s front woofer – so it’s a 13″ driver. (I’ve copied the technical drawing from the datasheet below – see the two dimensions given on the left side of the drawing.) However, this diameter includes non-moving parts (at least they should not move – they’re screwed to the enclosure).

If you measure the moving parts of the woofer, then we have to decide on where to measure – what is the actual diameter of the diaphragm? Normally, the way to measure this is from the high points on the surround that encircles the diaphragm and connects it to the loudspeaker frame. As you can see in that same drawing, this diameter is 258.8 mm, which, in the “official” datasheet is rounded to 260 mm.

 

 

The technical drawing of the Scan-Speak 13" Revelator front woofer.
The technical drawing of the Scan-Speak 13″ Revelator front woofer from the official datasheet.