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

Part 1: The very basics

Let’s build a loudspeaker with a relatively decent frequency range. Actually, I should be more specific – I mean not only that it can play a wide range of frequencies, but it can do so adequately loudly to be useful. Chances are that you’ll want it to play down to something around 100 Hz (which is actually not that low… It’s only about an octave and a half below concert C – also known as Middle C to pianists) and up to about 15 000 Hz (which is probably still audible, depending on how old you are, how many hours you have spend clubbing,  how loudly your iThingy is usually playing, and whether or not you use ear plugs when you ought to…).

In order to do this, you’ll probably have to use at least two loudspeaker drivers – a woofer for the low frequencies (say, below about 2000 – 3000 Hz) and a tweeter for the high frequencies. The woofer is either big in diameter (say, about 12 to 40 cm) , or it can move very far in and out, or both. The tweeter is much smaller in diameter (on the order of 20 mm or so in diameter), and doesn’t need to move in and out as much. For the purposes of this posting, let’s say that that’s enough (which is not entirely infeasible – there are many loudspeakers in the world that are based on one woofer and one tweeter. Some of them are actually good!) The reason you need a bigger loudspeaker driver for the low frequencies is because, the lower you go in frequency, the more air molecules you need to move. Unfortunately, for every time the frequency is halved (i.e. you go down one octave), you need to quadruple the volume of air that you have to move in order to get the same sound pressure level. So, when it comes to bass, physics is your enemy.

Okay, so we have a woofer and a tweeter, and each of them has to get a different portion of the audio signal. This means that we have to divide the signal using something called a “filter” which, in its most basic form, lets some frequencies through unimpeded and makes other frequencies quieter. A “high pass filter” will let high frequencies through and make lower frequencies quieter. A “low pass filter” will do the opposite. So, we put a low pass filter in the path of the signal going to the woofer, and a high pass filter in the path of the signal going to the tweeter. The combination of those two filters are what is called the crossover, since it is the circuit that allows the audio signal to cross over from the woofer to the tweeter and back again, as is necessary.

 Part 2: Amplification

Unfortunately, loudspeaker drivers are very inefficient. Typically, you should expect about 1% of the electrical power you send into a loudspeaker driver to be available as acoustical power. The other 99% is lost as heat. This means that if you want your loudspeakers to play loudly, then you’re going to have to feed them with a lot of power (because you are throwing away 99% of what you put in). Consequently, you need something called a “power amplifier” connected to the loudspeaker drivers. This is a device that has a small audio signal coming into it (typically a change in voltage with almost no current) – it makes the signal much louder, typically by increasing the voltage by some multiplication factor (say, around 20 times) and making current available as is needed. (And since voltage multiplied by current is power, we get a power amplifier.)

Part 3: Signal flow

Now we start getting into the interesting stuff. At this point in the process of designing our loudspeaker, we have to make a choice. Either

• we put one power amplifier at the start of the chain, and filter its output before sending the signals on to the woofer and tweeter (a passive loudspeaker design), or
• we filter the signals first and then use a separate power amplifier for each driver (an active loudspeaker design) .

To be honest, if the diagram above was all there was to it, there wouldn’t really be much point in making an active loudspeaker. If all we did was to make relatively simple low pass and high pass filters, we basically could do the same filtering to the audio signal either way. The passive filtering circuit is big, and the active filtering circuit is small (basically because the passive components have to be able to dissipate more power) but the power amps in the active design take up space, so there’s not much gained there. So what’s the point?  Some people will make the claim that the amplifier has “better control” of the loudspeaker driver if there is no circuitry (like a low-pass or a high-pass filter) between them. However, to be honest, even if that were true enough to make an audible difference in things (I won’t say whether it is or it isn’t – since this is a debate best left out of this posting), it certainly wouldn’t be the first item on your list-of-things-to-worry-about. So, what IS the point?

Well, in order to get the point, we need to know a little more about how a driver behaves when you put it in an enclosure.

Part 4: Some basic acoustics

Take a really big sealed box and cut a hole in one side that has the same diameter as a woofer. Put the woofer in the hole so that the woofer is now in a “sealed enclosure”. If you do a frequency response measurement of the output of the woofer (on-axis, meaning “directly in front of the woofer” you’ll probably see that, as you go lower and lower in frequency, you’ll reach a point where the output of the woofer drops as you go lower. In fact, it has a natural high-pass characteristic. The reasons for this are beyond the scope of this discussion – you’ll either have to trust me on this one, or go read more stuff. If you thump the woofer with your thumb when it’s in this box, it will sound a little like a kick drum – it’ll go “thump”.

If you make the box much, much smaller in volume, you’ll see that the natural frequency response of the system changes. This is because the air in the box acts as a spring behind the woofer, and as the box gets smaller, the spring gets stiffer. The result of this in the frequency response is that you get a peak at some frequency. If you thump the woofer in this smaller box, you’ll now hear it ringing (at the frequency where you see that peak in the response) – now it goes ‘boommmmmm’, humming at one pitch – a bit like a big bell. The smaller you make the box, the higher in frequency the pitch go, and the longer it will ring. In addition, you’ll notice that there is a lot less low-frequency output below the ringing frequency.

If you take a look at the plot below, you can see examples of this. The curves show the response of the same woofer in different sized sealed enclosures. The flattest curve is the biggest box – notice that it doesn’t have a peak poking up, and it has about 40 dB (this is a LOT) more output at the very bottom end (okay, okay, it’s 1 Hz, but the absolute values aren’t important here – it’s the difference in the curves that counts). The curve with the biggest peak is the result of putting a woofer in a box that’s just too small for it. (If you’d like to know the details behind this plot, read this.)

Part 5:  Bringing it all together

Let’s start this section by admitting a simple fact: if the only thing criterion you use to judge a loudspeaker with is the volume of the enclosure behind the loudspeaker drivers, Bang & Olufsen loudspeakers are too small (yes – even the BeoLab 5). Take any of our loudspeakers, and you have an example of a woofer that is put in an enclosure that has too little volume for it to behave well naturally. In other words, when we look at the natural response of any of our loudspeakers, they look more like the “bad” curve than the “good” curve in the plots above. This means that we have to encourage  it to behave a little better. This means, in the simplest case (still looking at the curves above) that we have to boost the bass and remove the peak in the natural response of the system.

We do this by making a filter (in addition to the low pass filter) that overcomes the natural behaviour of the woofer in its enclosure. If we want more bass out of the system, we turn up the bass. If we want to remove a 7.3 dB peak at 143.5 Hz that has a Q of 4.6, then we put in a dip of 7.3 dB at 143.5 Hz and a Q of 4.6 (If those terms don’t make any sense, don’t worry – all that’s really important to know is that we can “undo” the effects of a peak in the natural response of the system by putting in a reciprocal dip in the signal that we feed it.)

In theory, this is possible using filters that happen after the amplifier – but it is certainly MUCH MUCH easier to make those filters (even without going to digital processing) using small resistors and capacitors and op amps before you get to the amplifiers. For example, you can see in the photo above, the SMD resistor and capacitor (which can be used in a modern active crossover) are much smaller than the power resistor and the inductor (which we would still have to use in a passive crossover).

So, even if you’re not doing anything other than trying to customise the sound of a loudspeaker using some filters (also known as equalisers) – as we do in almost all of our loudspeakers – it is smarter to make an active loudspeaker than a passive one.

Part 6: The beneficial side effects

So, in order to compensate for the acoustical effects of putting a woofer in too small a package, we have to make an active loudspeaker design instead of a passive one.

But this then raises the question, now that we have an active loudspeaker, what else can we do? The answer is lots of stuff!

Since we can apply filtering independently to each loudspeaker driver we can do some serious customisation of the system. To give just a few simple examples:

• You have a resonance in the woofer at a frequency that is above the crossover. You want to correct the problem in your filtering (because you can hear and/or measure it), but the problem does not exist in the midrange. So, you want to have a filter on the woofer alone – not the woofer and midrange and a passive crossover.
• You want to do some dynamic processing on a driver without affecting the others. (for example, ABL)
• You want to compensate for small differences in loudspeaker driver sensitivity on a production line by doing an automated measurement and a gain offset on a driver-by-driver, loudspeaker-by-loudspeaker basis to ensure that loudspeakers leaving the factory are better matched to the “golden sample”

An active loudspeaker design makes all of these examples MUCH easier (or perhaps even “possible”) to achieve.

Conclusion 

All of that being said,

• if your electroacoustical behaviour of every component in your audio chain was “perfect” (whatever that means) AND
• if loudspeakers behaved linearly (i.e. they gave you the same frequency response at all listening levels, and they didn’t change their behaviours when they heat up, and so on and so on) AND
• if you did everything properly (meaning that your cabinets were the right size and shape) AND
• if your production tolerances of every component in the system was +/- 0%.

Then MAYBE a passive loudspeaker design could work just as well as an active design…