Category: loudspeakers

B&O Tech: Loudspeaker Enclosures

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

I’ve started working with a number of my colleagues on a series of videos for internal training at Bang & Olufsen. They were kind enough to make some of these videos publicly available.

This video explains why loudspeaker drivers are typically put in enclosures (boxes), the three types of enclosures that we use (sealed, ported, and passive radiators), and the differences in impact that these enclosure types have on the loudspeaker’s behaviour.

B&O Tech: Beamforming

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

I’ve started working with a number of my colleagues on a series of videos for internal training at Bang & Olufsen. They were kind enough to make some of these videos publicly available.

This one explains why loudspeaker drivers produce a narrower “beam” of sound at higher frequencies and how multiple loudspeaker drivers can be used to control both the direction and the width of an acoustic beam.

B&O Tech: Phantom imaging in two-channel stereo

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

I’ve started working with a number of my colleagues on a series of videos for internal training at Bang & Olufsen. They were kind enough to make some of these videos publicly available.

This video explains (and demonstrates) how recording engineers are able to control the perceived location of different sound sources in a two-channel stereo recording using different techniques.

B&O Tech: Sound Source Localisation

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

I’ve started working with a number of my colleagues on a series of videos for internal training at Bang & Olufsen. They were kind enough to make some of these videos publicly available.

This video explains how we are able to localise the direction of and the distance to a sound source in the real world.

B&O Tech: Human Hearing

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

I’ve started working with a number of my colleagues on a series of videos for internal training at Bang & Olufsen. They were kind enough to make some of these videos publicly available.

This one explains some basic concepts of human hearing in the frequency domain, including how our hearing changes with level, the reason we use “loudness” processing in loudspeakers, and psychoacoustic masking.

B&O Tech: Frequency vs. Time

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

I’ve started working with a number of my colleagues on a series of videos for internal training at Bang & Olufsen. They were kind enough to make some of these videos publicly available.

This one is an explanation of the relationship between the frequency and the time domains, and why we often do “impulse response” measurements.

Loudspeaker Crossovers: Part 16

This posting is just wrapping up the series. No more plots… I promise.

Of course, this entire series has focused the “greatest hits” of the crossover club which is a limited number of crossover types. There are many other options that I haven’t talked about, but my point was not to explain how to choose and design a crossover for a loudspeaker for the DIY’er. It was to

  • give a primer on some of the things to consider when implementing a crossover
  • instil instinctive suspicion and doubt when you read an advertisement (or a comment on the Internet) that says something like “this loudspeaker is good (or bad) because it has THIS kind of crossover.”

There are plenty of things that I didn’t (and won’t) talk about, such as:

On thing that I intentionally avoided was crossover designs that use filters with extremely high orders, sometimes called “brick wall” crossovers. On paper, they avoid the possible issues with a signal in a given frequency band coming from two sources (e.g. a woofer and a tweeter), so if you ONLY consider them from this perspective, they’re a good idea. However, in my opinion, this is outweighed by the facts that you will probably get a discontinuity in the power response (unless the two drivers have identical three-dimensional radiation patterns at the crossover frequency) AND you will probably have a complete mess in the time domain. Bonkers-order filters aren’t free. (If you clicked on the link to Linkwitz’s page, above and just taken a quick glance, then you’ve probably read the statement at the top of the page that says “The sum of acoustic lowpass and highpass outputs must have allpass behavior without high Q peaks in the group delay.” One way to look at the group delay of a filter is to look at the slope of the phase response. If you make a crossover with really high-order filters, then one of the artefacts will be a high slope in the phase response around the crossover frequency.)

One other thing that I have not mentioned is the incorrect naming that is often associated with crossovers and filters in general. Many people say “FIR Filter” (Finite Impulse Response) when they actually mean “Linear phase filter”. It’s important to remember that you can’t have a linear phase filter without an FIR filter implementation, but certainly not all FIR filters are linear phase. (Weirdly, a linear phase filter does, in fact, have an infinite impulse response, both forwards and backwards in time… But that’s a description of the filter’s response and not how it would be implemented in a DSP-based signal flow.) This incorrect usage drives me nuts. (Then again, many things like this do. For example, I get annoyed when HR people draw a triangle on a whiteboard and call it a pyramid. You never know what’s going to set me off on a pedantic rant about nomenclature.)

The other thing that I didn’t talk about was another way to look at a Butterworth two-way crossover, in which you see it as lacking a component in the s-domain (using Laplace analysis), which is the reason its sum has an allpass characteristic. If you add the missing component (for example, using a third loudspeaker driver), then the allpass behaviour disappears. This is the concept behind Bang & OIufsen’s “Uni-phase” series of loudspeakers in the 1970s and 1980s. If you want to learn more about this, I’ve already written about it here, and Erik Bækgaard’s original paper from 1977 describing the idea more fully can be found here.

Finally, hopefully, you won’t come away from all of this with a conclusion that one crossover is the winner. A crossover is just one component in a long series- and parallel-chain of components that make up a loudspeaker. Changing any of the other components may require making a different decision about another. And, in order to make that decision, you can’t just consider the on-axis response (unless you live alone in an anechoic chamber (or outdoors…). You also need to think about things like

  • the off-axis responses
  • the power response
  • the phase response
  • the time response
    and maybe also
  • the implications on latency
  • your required signal processing power (e.g. in MIPS)
  • maybe some other stuff if you have checked all those boxes.

On the other hand, after all this, you should also know that you can’t just implement a crossover ignoring everything else in the chain, and think that it’ll just work. It won’t.

Loudspeaker Crossovers: Part 15

This will be another short one.

Part 14 showed the power responses of a theoretical loudspeaker made with two point-sources using a linear-phase crossover using the method that I explained in Part 7.

In Part 11, I showed the power responses when the loudspeaker is made with real drivers in a real enclosure.

This posting shows the same as Part 11, except that I’ve implemented the crossover (at 1 kHz) using linear phase filters (again, with a really long window to avoid any discussion) instead of minimum phase filters.

Figure 15.1

Figure 15.1 shows the real-world power responses of an actual two-way loudspeaker using two crossover strategies. (The top plot was already shown in Part 11.)

Based on the conclusions from Part 14, it should not come as a surprise that a linear phase crossover will result in the same power response as a 4th-order Linkwitz Riley crossover. The only reason I’m showing this here is to prove that the earlier conclusion based on a theoretical simulation holds true in real life.

One important conclusion to make at this point is to realise that a loudspeaker that is implemented with a 4th-order Linkwitz Riley crossover and the same loudspeaker implemented with a linear phase crossover will have identical magnitude responses (in any direction – not just on-axis) and identical power responses. However, they will have different phase responses (in any chosen direction) and different temporal responses (aka impulse responses).

Loudspeaker Crossovers: Part 14

This will be a short one.

In Part 7, I showed the power responses of three loudspeakers made with point-source (and therefore perfectly omnidirectional at all frequencies, which also means that they have the same response in all direction) drivers.

In that posting, I calculated the power response for a loudspeaker made of two loudspeaker drivers, floating in space, with the assumption that both drivers are point-sources, and that they do not live in an enclosure that has any acoustical effects. I also calculated the responses for 3 different distances between the drivers, which were chosen as a function of the crossover frequency’s wavelength.

One of the crossover types whose power responses that I showed was the 4th-order Linkwitz Riley. The plots that I showed back then for that crossover type is reproduced here in Figure 14.1.

Figure 14.1: Power responses for a 2-way theoretical loudspeaker for three different distances between the drivers.

As I said, the details of how I calculated these power responses is detailed in Part 7.

I calculated the power responses for a similar loudspeaker, using a linear phase crossover (with a really long window to avoid any discussion about this…) and with the same crossover frequency of 100 Hz and the same distances between the “drivers”. These power responses are shown below in Figure 14.2.

Figure 14.2: Power responses for a 2-way theoretical loudspeaker for three different distances between the drivers.

If you look at Figures 14.1 and 14.2 you could be forgiven for thinking that they look VERY similar. In fact, they’re essentially identical. This is because the 0º difference in phase caused by the linear phase crossover is the same as a 360º difference in phase caused by the 4th order Linkwitz Riley.

In other words, the message of this posting is that the power responses of a loudspeaker that has been implemented with a 4th order Linkwitz Riley crossover and the same loudspeaker with a linear phase crossover will have the same power responses, assuming that all other aspects of the loudspeaker are the same.