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

 

Introduction

Occasionally, I read other people’s blogs and forum postings to see what’s happening outside my little world. This week, I came across this page in which one of the contributors made some comments about B&O’s loudspeaker specifications – or, more precisely, the lack of them – or the lack of precision in them – particularly with respect to the Frequency Range specifications.

So, this posting will be an attempt to explain how we determine the frequency range of our loudspeakers.

 

Bandwidth (also known as “Frequency Range”)

Ask any first-year electrical engineering student to explain how to find the “bandwidth” of an audio product and they’ll probably all tell you the same thing – which will be something like the following:

1. Measure the magnitude response (what many people call the “frequency response”) of the product.
2. Find the peak in the magnitude response
3. Going upwards in frequency, find the point where the magnitude drops by 3.01 dB relative to the peak.
4. Going downwards in frequency, find the point where the magnitude drops by 3.01 dB relative to the peak.
5. Subtract the lower frequency from the upper frequency and you get the bandwidth.

(If you’re curious, the 3.01 dB threshold is chosen because -3.01 dB is equivalent to one-half of the power of the peak. This is why the -3.01 dB points are also known as a the “half-power points”)

 

Figure 1 shows a pretty typical looking curve for an audio device (admittedly, not a very good one…). The magnitude response is flat enough, and it extends down to 34 Hz and up to 15.6 kHz.

This same technique can be used to find the bandwidth of an audio processing device, as is shown in Figure 2.

 

Loudspeaker Frequency Range

Let’s try applying that same method used for audio “black boxes” on a loudspeaker. We’ll measure the on-axis magnitude response of the loudspeaker in a free field (one without reflections), and find the frequencies where the magnitude drops 3.01 dB below the peak value. An example of this is shown below.

 

Hmmmm… that didn’t turn out as nicely as I had hoped. It seems that (using this definition) the loudspeaker whose response is shown in Figure 3 has a Frequency Range of 7.3 kHz to 13.9 kHz. This is unfortunate, since it is not a tweeter – it’s a rather large, commerically-available, floor-standing loudspeaker with a rather good reputation.

Okay, maybe we’re being too stringent. Let’s say that, instead of defining the Frequency Range as the area between the – 3 / + 0 dB points, we’ll make it ± 3 dB instead. Figure 4 shows the same loudspeaker with that version of Frequency Range.

 

 

Great- it got better! Now the Frequency Range of this loudspeaker (under the new ±3 dB definition) is from 2.2 kHz to 15.9 kHz. On paper, that still makes it a tweeter – so we’re still in trouble here. Note that I have scaled the magnitude response here to “help” the loudspeaker as much as I can by putting the peak in the magnitude response on the + 3 dB line. If I had not done this (for example, if I had said “±3 dB relative to the magnitude at 1 kHz” the numbers would certainly not get better…)

Let’s try the same definition on a different loudspeaker – shown in Figure 5.

 

 

This loudspeaker (also a commerically-available floor-standing model with a good reputation) has a Frequency Range (using the ± 3 dB points) of 5.4 kHz to 18.0 kHz. This ±3 dB definition isn’t working out very well. Let’s try one more loudspeaker to see what happens.

 

 

Yay! It worked! For loudspeaker #3, shown in Figure 5, the Frequency Range is from 83 Hz to 20.9 kHz. Ummmm… except that, of the 3 loudspeakers I measured for this experiment, this is, by far the smallest. It’s a little 2-way loudspeaker that I can easily lift with one hand whilst sipping a cup of coffee from the other (and I don’t work out – ever!)

So, what we have learned so far is that it’s better to buy a small loudspeaker than a big one, since it has a much wider frequency range. No, wait. that can’t be right…

Hmmmm… what if we were to smooth the magnitude responses? Maybe that would help…

 

 

That’s a little better, but Loudspeaker #1 (the black curve), still bottoms out in the midrange, causing its frequency range to resemble that of a tweeter. And Loudspeaker #2 loses out on the high end due to the peaks. (Note that, in this plot, I’ve scaled them all to have the same magnitude at 1 kHz – just trying something out to see if that helps. It didn’t.) How about more smoothing?

 

 

Got it! Now all of the loudspeakers’ responses have been smeared out enough… uh… adequately smoothed… to make our definition of Frequency Range have a little meaning. The “big” loudspeakers have wider Frequency Ranges than the “little” loudspeaker. So, we’ll just octave-smooth all of our measurements. Well…  at least until we find another loudspeaker that needs even more smoothing…

 

Sidebar: In case you’re wondering: the three loudspeakers I’m talking about above are all commercially available products. One of the three is a Bang & Olufsen loudspeaker. Don’t bother asking which is which (or which B&O loudspeaker it is) – I’m not telling – mostly because it doesn’t matter.

The moral thus far…

Of course, the point that I’m trying to make here is that Frequency Range, like any specification for any audio device, needs to make sense. If we arbitrarily set some test method (i.e. “measure the on-axis magnitude response – and then smooth it”) and apply arbitrary criteria (i.e. ± 3 dB) then we may not get a useful description of the device’s behaviour.

So, at this point, you’re probably asking “Well… how does B&O measure Frequency Range?” Well, I’m glad you asked!

After we’re done with the sound design of the loudspeaker, we have to make sure it has the correct sensitivity. This is a measure of how loud it is for a given voltage at its input.  So, we put the loudspeaker in the Cube and measure its final on-axis magnitude response.

I’ll illustrate this using a magnitude response that I invented, shown in Fig 8. Note that this response is not a real loudspeaker – it’s one that I invented just for the purposes of this discussion.

 

 

 

We then look at the average level of the magnitude response between 200 Hz and 2 kHz and adjust the gain in the signal processing of the loudspeaker to make the sensitivity what we want it to be. For almost all B&O loudspeakers, that sensitivity corresponds to an output level of 88 dB SPL for an input with a level of 125 mV RMS. (The only exceptions are BeoLab 1, BeoLab 5, and BeoLab 9 which produce 91 dB SPL for a 125 mV RMS input.)

So, after the gain has been adjusted, the magnitude response looks like Figure 9, below.

 

 

We then look for the frequencies that have a magnitude that are 10 dB lower than the average level between 200 Hz and 2 kHz. This is illustrated in Figure 10.

 

 

The values that correspond to the -10 dB points (relative to the average level between 200 Hz and 2 kHz) are the frequencies stated in the Frequency Range specification.

This is how B&O specifies Frequency Range for all of its loudspeakers. That way, you (and we) can directly compare their specifications to each other. Of course, some other manufacturer may (or probably will) use a different method – so you cannot use B&O’s Frequency Range specifications to compare to another company’s products. We don’t use a ±3 dB threshold, not only because this would require arbitrary smoothing in order to prevent weird things from happening (as I showed above) but also because the on-axis magnitude response of B&O loudspeakers is a result of the loudspeakers’ sound design (which includes a consideration of its power response) which means that, if you just look at the on-axis response, it might not be as flat as a magazine would lead you to believe it should be.

 

 

The Fine Print

1. The method I described above is a slightly simplified explanation of what we actually do – but the difference between what I said and the truth is irrelevant. The details are in the method we use to do the averaging – so it’s not really a big deal unless you’re actually writing the software that has to do the work.

2. We do this measurement of the Frequency Range using a signal with a level of 125 mV at the input of the loudspeaker. So, if your music is playing with a similar level (or lower) then you will have a loudspeaker that is performing as specified. However, if you play the music louder, the frequency range will change. In most cases, the low frequency limit will increase due to the ABL and thermal protection algorithms. The details of (1) how much it will increase, (2) what level of music will cause it to increase, and (3) what frequency content in the music will cause it to increase, are different from loudspeaker model to loudspeaker model.  This was the root of some confusion for some people when they compare the frequency range of the BeoLab 12-3 to the BeoLab 12-2. These two loudspeakers have almost identical low frequency cutoffs, despite the fact that one of them has 2 woofers and the other has only 1. At “normal” listening levels, they have both been tuned to have similar magnitude responses – however, as you turn up the volume, the BeoLab 12-2 will lose bass earlier than the BeoLab 12-3.

3. Subwoofers are different – since it doesn’t make sense to try and find the average magnitude response of a subwoofer between 200 Hz and 2 kHz.