Author: geoff

Loudspeaker Crossovers: Part 1

What is a crossover?

A crossover is a set of filters that take an audio signal and separate it into different frequency portions or “bands”.

For example, possibly the simplest type of crossover will accept an audio signal at its input, and divide it into the high frequency and the low frequency components, and output those two signals separately. In this simple case, the filtering would be done with

  • a high-pass filter
    (which allows the high frequency bands to pass through and increasingly attenuates the signal level as you go lower in frequency), and
  • a low-pass filter
    (which allows the low frequency bands to pass through and increasingly attenuates the signal level as you go higher in frequency).

This would be called a “Two-way crossover” since it has two outputs.

Crossovers with more outputs (e.g. Three- or Four-way crossovers) are also common. These would probably use one or more band-pass filters to separate the mid-band frequencies.

Why do we need crossovers?

In order to understand why we might need a crossover in a loudspeaker, we need to talk about loudspeaker drivers, what they do well, and what they do poorly.

It’s nice to think of a loudspeaker driver like a woofer or a tweeter as a rigid piston that moves in and out of an enclosure, pushing and pulling air particles to make pressure waves that radiate outwards into the listening room. In many aspects, this simplified model works well, but it leaves out a lot of important information that can’t be ignored. If we could ignore the details, then we could just send the entire frequency range into a single loudspeaker driver and not worry about it. However, reality has a habit of making things difficult.

For example, the moving parts of a loudspeaker driver have a mass that is dependent on how big it is and what it’s made of. The loudspeaker’s motor (probably a coil of wire living inside a magnetic field) does the work of pushing and pulling that mass back and forth. However, if the frequency that you’re trying to produce is very high, then you’re trying to move that mass very quickly, and inertia will work against you. In fact, if you try to move a heavy driver (like a woofer) a lot at a very high frequency, you will probably wind up just burning out the motor (which means that you’ve melted the wire in the coil) because it’s working so hard.

Another problem is that of loudspeaker excursion, how far it moves in and out in order to make sound. Although it’s not commonly known, the acoustic output level of a loudspeaker driver is proportional to its acceleration (which is a measure of its change in velocity over time, which are dependent on its excursion and the frequency it’s producing). The short version of this relationship is that, if you want to maintain the same output level, and you double the frequency, the driver’s excursion should reduce to 1/4. In other words, if you’re playing a signal at 1000 Hz, and the driver is moving in and out by ±1 mm, if you change to 2000 Hz, the driver should move in and out by ±0.25 mm. Conversely, if you halve the frequency to 500 Hz, you have to move the driver in and out with an excursion of ±4 mm. If you go to 1/10 of the frequency, the excursion has to be 100x the original value. For normal loudspeakers, this kind of range of movement is impractical, if not impossible.

Note that both of these plots show the same thing. The only difference is the scaling of the Y-axis.

One last example is that of directivity. The width of the beam of sound that is radiated by a loudspeaker driver is heavily dependent on the relationship between its size (assuming that it’s a circular driver, then its diameter) and the wavelength (in air) of the signal that it’s producing. If the wavelength of the signal is big compared to the diameter of the driver, then the sound will be radiated roughly equally in all directions. However, if the wavelength of the signal is similar to the diameter of the driver, then it will emit more of a “beam” of sound that is increasingly narrow as the frequency increases.

So, if you want to keep from melting your loudspeaker driver’s voice coil you’ll have to increasingly attenuate its input level at higher frequencies. If you want to avoid trying to push and pull your tweeter too far in and out, you’ll have to increasingly attenuate its input level at lower frequencies. And if you’re worried about the directivity of your loudspeaker, you’ll have to use more than one loudspeaker driver and divide up the signal into different frequency bands for the various outputs.

Loudspeaker Crossovers: Part 0 (Introduction)

I recently received a question in my inbox:

In passive crossovers, many are phase incoherent,
meaning that the phase shift of one frequency will be different than another frequency.
Do you agree?  Am curious how this is dealt with in the active crossover’s of B&O products?

At first, I debated just sending a quick email back with a short answer saying something pithy. But while I was thinking about what to write, I realised that:

  • This is actually a really good question / topic
  • I haven’t posted anything about crossovers in a long time
  • I’ve learned a lot about crossovers since the last time I did post something
  • I still have a LOT more to learn about crossovers.

As a result, this will be the first in what I expect to be a long series of postings about loudspeaker crossovers, starting with basic questions like

  • Why do we use them?
  • What do we think they do?
  • What do they really do? and
  • How are the ones we implement these days different from the ones you read about in old textbooks?

As usual, I’ll probably get distracted and wind up going down more than one rabbit hole along the way… But that’s one of the reasons why I’m doing this – to find out where I wind up, and hopefully to meet some new rabbits along the way.

Rødgrød med fløde

If you’re visiting Denmark or learning Danish, a favourite activity (especially after a few beers) is when people try to get you to say “rødgrød med fløde”. (It’s a classic dessert. If you want to see it or the recipe, look it up.).

Personally, I don’t find this one too challenging to say (which is NOT to say that I pronounce it correctly… I just don’t get the laughs that other people get when I say it). “Røget ørred” (smoked trout) was my nemesis until this week when I learned a new word at lunch last week: “smergellærred” (a roll of sandpaper).

What has been interesting about learning this word is how few Danes know what it is (even when I show it written out).

So, if you’re a Dane, and you’re at a party, and you want to get a good laugh at the expense of the foreigner (say, me, for example…) forget about the rødgrød med fløde and bring out the smergellærred. However, I’ll warn you that I suspect that I might be able to pronounce that word better after a couple of beers.

B&O Tech: A little history

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

Okay… this posting has nothing to do with technology, or B&O loudspeakers…

One part of my job these days is to dig into the history of B&O, looking into some of the technologies that are “under the hood” of our older products, as well as the people and processes behind them.

Once in a while, I stumble across something that doesn’t fit into any category other than something that I find interesting. This is one example.

Once-upon-a-time, Bang & Olufsen had a bakelite press. I’ll probably talk about this sometime in the future, but the short version is that bakelite was an early kind of plastic that gave people a whole new way of making products with new shapes (do a search for Beolit 39 for example).

B&O used its bakelite press to make items other than radios and parts for their audio products. One example of this is the ashtrays you see in the photos below. One thing to notice is the B&O logo up on the underside of the cigar/cigarette rest.

Excelsior Cylinder Player

Once-upon-a-time, before there was streaming, and SACDs, and CDs, and vinyl records, and 78 RPM shellac disks, there were cylinders.

I’m part-way through a three-part lecture at the local museum on the history of recorded sound. A portion of Part 1 was to talk about cylinders, and I was lucky enough to meet a local collector who owned a number of cylinder players, one of which he loaned to me for a demonstration.

After some back-and-forth, he agreed to sell me the player to add to my collection. And, after a little (but very little) internal debate, I decided to do a partial restoration as a little weekend project.

The player is about 120 years old, so there’s plenty of dirt and oxide on it. My goal was not to make it as-good-as-new, rather to just clean it up a little.

The easiest part was polishing the screw heads. I made a small brass handle to make this easier…
Before and after polishing one of the steel rods that are used to support the sled.
The various parts of the speed governor, dismantled, and ready for polishing.
Back together again after polishing
The cast-iron base before stripping the paint.
The end support for the two arms and the threaded rod that moves the sled in sync with the groove on the cylinder, before stripping. Note the professional decorative artwork…
The support arm for the speed governor before stripping.
The sled before polishing.
Most of the steel and brass bits and pieces after polishing.
The belt on the top left of the photo is made of thin leather.
The original wooden knob for the brake cracked sometime in the past 120 years. So, I made a new one from Cumberland ebonite. I didn’t feel too bad about using this instead of wood, since ebonite was a common material for such things back in those days. The reason I have it on hand is for making fountain pens and replacement parts in restorations.

The last part of the restoration was to hammer and rub out the dents in the bell, and to spend an hour or two sanding the surface with 800-grit paper, and then polishing on a wheel.

After everything went back together, the only thing left to do was to make a wooden base so that the cast iron won’t scratch anything. Rather than try to re-create the original base and cover, I just made a simple one from teak.

The player is NOT sitting on an anti-gravity device. It’s floating above the concrete because it’s sitting on a piece of wood to keep the sand off it before bringing it inside. Note that equally-amateurish decorative paint job on the end piece. I debated making a computer-generated stencil and spray-painting a “perfect” decoration, but I chose to do this instead, in keeping with the original.

“How does it sound?” you ask. I did this recording before the restoration, but you can decide for yourself. Note that, back then, the player still wasn’t mine, and I was hesitant to wind it up enough to play a full two minutes… Hence the rescue mission half-way through.

Now I have to go find some more cylinders. That one is the only one I have, and I’m getting a little tired of “In the Wildwood Where the Bluebells Grew”…

Reading Specs – Part 3

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

This week, a question came in from a B&O customer about their Beovox Cona subwoofer, starting with this photograph:

The question (as it was forwarded to me, at least…) was “what does ‘Long term max power 125w’ and ‘Max noise power 60w’ mean?”

This caused me to head to our internal library here in Struer and look at an ancient kind of document called a ‘book’ that contained the information for the answer.

The first clue is at the top of the photo where it says “IEC 268-5”, which is a reference to a document from the International Electrotechnical Commission in Switzerland called

CEI/IEC 268-5 International Standard
Sound System Equipment
Part 5: Loudspeakers

As you can see there, we happen to have two copies in our library: the second edition from 1989 and 3.1 from 2007, so I took a look at the 1989 edition.

Long Term Max Power

This term is defined in part 18.2 of that document, where it says that it’s the “electrical power corresponding to the long term maximum input voltage.” In order to convert voltage to power, you need to know the loudspeaker’s rated impedance, which is 6 Ω, as is shown in the photograph above.

Power = Voltage2 / R

So, in order to find the Long Term Maximum Power rating of the loudspeaker, we have to do a Long Term Maximum Input Voltage test, and then a little math to convert the result to power.

The Long Term Maximum Input Voltage is defined in section 17.3 as:

“… the maximum voltage which the loudspeaker drive-unit or system can handle, without causing permanent damage, for a period of 1 min when the signal is a noise signal simulating normal programme material (according to IEC 268-1).”

“The test shall be repeated 10 times with intervals of 2 min between the application of the signal.”

So, if I do the math backwards, I can calculate that the Cona was subjected to that special noise signal with an input voltage of 27.39 V with a pattern of

  • 1 minute of continuous noise
  • 2 minutes of silence
  • repeated 10 times

After this was done, the Cona was tested again to make sure that it worked. It did.

How I did the math to figure this out:

  • P = V2/R
  • therefore sqrt(P * R) = V
  • sqrt(125 * 6) = 27.39 V

To do the test, the loudspeaker is placed in a room of not less than 8 m3 with controlled temperature and humidity requirements. An amplifier droves the noise signal into the loudspeaker for 100 h

Max Noise Power

The Maximum Noise Power is tested in a similar way, however, instead of delivering the signal in 1 minute bursts with 2 minute rest periods, the speaker has to play the noise continuously for 100 hours. After the 100 hours are over, then the speaker is put in a room to recover for 24 hours. After this:

“The loudspeaker may be considered to have fulfilled the requirements of this test if, at the end of the storage period, there is no significant change in the electrical, mechanical or acoustical characteristics of the loudspeaker itself compared to those stated in the data sheet for the loudspeaker type, other than a change in the resonance frequency. The acceptability of this change is subject to negotiation; it shall therefore be stated when presenting the results.”

The reason the Maximum Noise Power is lower than the Long Term Maximum Power is the 2 minute rest time in the test. It’s important to remember that a loudspeaker driver is very inefficient when it comes to converting electrical power to acoustical power, and so most of the electrical power that goes into it is just lost as heat caused by inefficiency. The 2 minute rest time allows the loudspeaker to cool down a little before the signal starts heating it up again, and therefore it can handle more power (a little more than 3 dB more – which is the same as 2 x the power) than when it’s playing continuously.

Traditions

One of my favourite pithy quotes is ‘Tradition is just peer pressure from dead people’. When you start looking at some of the things we ‘just do’, you start asking yourself ‘why, exactly?’

For example, when you attend a wedding, you’ll see the bride standing on the groom’s left. This is so that he can use his sword to fight off her family as he carries away from the town over his left shoulder.

Another example is the story that’s often told about how the distance between railway tracks is related to the width of a horse’s ass.

There’s a similar thing that happens in multichannel audio systems. When people ask me what I would recommend for loudspeakers when building a multichannel (or ‘surround’) system, I always start with the ITU’s Recommendation BS.775 which says that you should use matching loudspeakers all-round. Of course, almost no one does this, so the next best thing is to say something like the following:

  • use big loudspeakers for your Left Front and Right Front
  • use smaller (but matched) loudspeakers for your surround channels (including back and height channels)
  • make some intelligent choice about your Centre Front loudspeaker
    (which is not terribly helpful, but there are many issues to consider when thinking about your centre front loudspeaker)

This raises a question:

‘Why is it okay to use smaller, less capable loudspeakers for the surround channels?’

The simple answer to this is that for most materials, there isn’t as much signal in the surround channels, and there’s certainly less low-frequency, high-level content.

However, let’s keep asking questions:

‘Why isn’t there more content (in terms of both bandwidth and level) in the surround and height channels?’

The answer to this is that surround sound (like stereo, which is in effect the same thing) originated with movies. The first big blockbuster that was released in Dolby Stereo (later re-branded as Dolby Surround) was Star Wars in 1977 or so. Dolby Stereo was a 4-2-4 ‘encoding’ system that relied heavily on M-S encoding and decoding. If I over-simplify this a little, then the basic idea was:

  • The Centre channel was sent to both the Left and Right channels on the film
  • Left channel was sent to Left
  • Right channel was sent to Right
  • The Surround channel (there was only one) was mixed into the Left and Right channels in opposite polarity (aka ‘out of phase’)

So, the re-recording engineer (the film world’s version of a recording engineer) mixed in a 4-channel world: Left, Right, Centre, and Surround, but the film only contained two channels: Left Total and Right Total (with the Centre and Surround content mixed in them).

When the film was shown in a theatre with a Dolby Stereo decoder, the two channels on the film were ‘decoded’ to the original four channels and send out to the loudspeakers in the cinema.

This was a great concept based on an old idea, since M-S processing was part of Blumlein’s original patent for stereo back in 1931. When you’re looking at a two-channel stereo signal, you can think of it as independent Left and Right channels. However, usually, if you look at the content, the two channels contain related information. For example, the lead vocal of almost every pop tune is identical in the Left and Right channels so that its phantom image appears in the centre.

So, another way of thinking of the same two-channel stereo signal is by considering the two channels as

  • ‘M’ (for Mid or Mono, depending on which book you read):
    the signal that is identical in the Left and Right
  • ‘S’ (for Side or Stereo):
    the signal that is identical except in opposite polarity in the Left and Right

For example, FM Stereo is not sent as Left and Right channels, it’s sent as M and S channels. There’s less bandwidth and less level in the S component, so when you lose the FM signal to your antenna, the first thing to go is the S, and you’re left with a Mono radio station.

Wait… there’s that ‘less bandwidth and less level in the S component’ again – just like what I said above about the surround channels in a surround system.

Let’s back up a little to vinyl records. A groove of a vinyl record is a 90º cut, with the needle resting gently on both walls of that trough. If the left wall moves up and down (on a 45º angle to the surface of the vinyl) then the needle bounces up and down with it, but only for that left channel. In other words, it slides along the right wall of the tough.

When a signal is the same in the left and right channels on a vinyl record (the M-component, like the lead vocal) then, when one side of the groove pushes the needle UP, the other side drops DOWN. This means that the M-component signal results in the needle moving horizontally (or laterally), in parallel with the surface of the disc. Signals in the S-component (when the Left and Right channels are ‘out of phase’) result in the two walls moving upwards and downwards together, pushing the needle vertically.

The reason for this is that the old mono shellac discs used laterally-cut grooves, and the reason for this was (apparently) that Emile Berliner was getting around a Thomas Edison patent. Also, by making the needle sensitive to lateral movements, it was less sensitive to vibrations caused by footsteps, which primarily cause the gramophone to vibrate vertically. When they made the first two-channel discs, it was smart to make the format backwards-compatible with Berliner’s existing gramophones.

So, if you have a lot of level and a lot of low-frequency content in the signal on a vinyl record, it causes the needle to jump up and down, and it will likely get thrown out of the groove and cause the record to skip. This is why the bass on vinyl records has to be monophonic, even though the record itself is two-channel stereo. Mono bass causes the needle to wiggle left-right, but not up-down.

So, the historically-accurate answer to explain why it’s okay to use smaller loudspeakers for most of the outputs in a modern 7.1.4 system is that we are maintaining compatibility with a format from 1892.

The original Loudness War

The June, 1968 issue of Wireless World magazine includes an article by R.T. Lovelock called “Loudness Control for a Stereo System”. This article partly addresses the issue of resistance behaviour one or more channels of a variable resistor. However, it also includes the following statement:

It is well known that the sensitivity of the ear does not vary in a linear manner over the whole of the frequency range. The difference in levels between the threshold of audibility and that of pain is much less at very low and very high frequencies than it is in the middle of the audio spectrum. If the frequency response is adjusted to sound correct when the reproduction level is high, it will sound thin and attenuated when the level is turned down to a soft effect. Since some people desire a high level, while others cannot endure it, if the response is maintained constant while the level is altered, the reproduction will be correct at only one of the many preferred levels. If quality is to be maintained at all levels it will be necessary to readjust the tone controls for each setting of the gain control

The article includes a circuit diagram that can be used to introduce a low- and high-frequency boost at lower settings of the volume control, with the following example responses:

These days, almost all audio devices include some version of this kind of variable magnitude response, dependent on volume. However, in 1968, this was a rather new idea that generated some debate.

In the following month’s issue The Letters to the Editor include a rather angry letter from John Crabbe (Editor of Hi-Fi News) where he says

Mr. Lovelock’s article in your June issue raises an old bogey which I naively thought had been buried by most British engineers many years ago. I refer, not to the author’s excellent and useful thesis on achieving an accurate gain control law, but to the notion that our hearing system’s non-linear loudness / frequency behaviour justifies an interference with response when reproducing music at various levels.

Of course, we all know about Fletcher-Munson and Robinson-Dadson, etc, and it is true that l.f. acuity declines with falling sound pressure level; though the h.f. end is different, and latest research does not support a general rise in output of the sort given by Mr. Lovelock’s circuit. However, the point is that applying the inverse of these curves to sound reproduction is completely fallacious, because the hearing mechanism works the way it does in real life, with music loud or quiet, and no one objects. If `live’ music is heard quietly from a distant seat in the concert hall the bass is subjectively less full than if heard loudly from the front row of the stalls. All a `loudness control’ does is to offer the possibility of a distant loudness coupled with a close tonal balance; no doubt an interesting experiment in psycho-acoustics, but nothing to do with realistic reproduction.

In my experience the reaction of most serious music listeners to the unnaturally thick-textured sound (for its loudness) offered at low levels by an amplifier fitted with one of these abominations is to switch it out of circuit. No doubt we must manufacture things to cater for the American market, but for goodness sake don’t let readers of Wireless World think that the Editor endorses the total fallacy on which they are based.

with Lovelock replying:

Mr. Crabbe raises a point of perennial controversy in the matter of variation of amplifier response with volume. It was because I was aware of the difference in opinion on this matter that a switch was fitted which allowed a variation of volume without adjustment of frequency characteristic. By a touch of his finger the user may select that condition which he finds most pleasing, and I still think that the question should be settled by subjective pleasure rather than by pure theory.

and

Mr. Crabbe himself admits that when no compensation is coupled to the control, it is in effect a ‘distance’ control. If the listener wishes to transpose himself from the expensive orchestra stalls to the much cheaper gallery, he is, of course, at liberty to do so. The difference in price should indicate which is the preferred choice however.

In the August edition, Crabbe replies, and an R.E. Pickvance joins the debate with a wise observation:

In his article on loudness controls in your June issue Mr. Lovelock mentions the problem of matching the loudness compensation to the actual sound levels generated. Unfortunately the situation is more complex than he suggests. Take, for example, a sound reproduction system with a record player as the signal source: if the compensation is correct for one record, another record with a different value of modulation for the same sound level in the studio will require a different setting of the loudness control in order to recreate that sound level in the listening room. For this reason the tonal balance will vary from one disc to another. Changing the loudspeakers in the system for others with different efficiencies will have the same effect.

In addition, B.S. Methven also joins in to debate the circuit design.

The debate finally peters out in the September issue.

Apart from the fun that I have reading this debate, there are two things that stick out for me that are worth highlighting:

  • Notice that there is a general agreement that a volume control is, in essence, a distance simulator. This is an old, and very common “philosophy” that we forget these days.
  • Pickvance’s point is possibly more relevant today than ever. Despite the amount of data that we have with respect to equal loudness contours (aka “Fletcher and Munson curves”) there is still no universal standard in the music industry for mastering levels. Now that more and more tracks are being released in a Dolby Atmos-encoded format, there are some rules to follow. However, these are very different from 2-channel materials, which have no rules at all. Consequently, although we know how to compensate for changes in response in our hearing as a function of level, we don’t know what the reference level should be for any given recording.

3-channel vinyl

Another gem of historical information from the Centennial Issue of the JAES in 1977.

This one is from the article titled “The Recording Industry in Japan” by Toshiya Inoue of the Victor Company of Japan. In it, you can find the following:

Notice that this describes a 3-channel system developed by the Victor Company using FM with a carrier frequency of 24 kHz and a modulation of ±4kHz to create a third channel on the vinyl. The resulting signal had a bandwidth of 50 Hz to 5 kHz and a SNR of 47 dB.

Interestingly, this was developed from 1961-1965: starting 9 years before CD-4 quadraphonic was introduced to the market, which used the same basic principle of FM modulation to encode the extra channels.

Phantom imaging

The July 1968 issue of Wireless World Magazine contains a description of an early, but interesting analysis of the relationship between phantom image placement in a 2-channel stereo system and interchannel level differences. This is an old favourite topic of mine, originally inspired by the work of Michael Williams and his “Stereophonic Zoom”, and extending to my first AES paper in 1999.

If you, like me, are interested in this (for example, if you’re making a panning algorithm or you’re testing the veracity of headphone-based “virtual” systems), some important figures from that article are shown below.

The typical way of showing the relationship between IAD and phantom image placement.
This one is interesting because it shows the different results in different rooms, (which would also be influenced by loudspeaker directivity.)

Note that, for the plots above and below, the x-axes show the position of the image in the stereo sound stage, where 0 is the centre point between the two loudspeakers and 0.5 is a position in one of the two loudspeakers. This is 0.5 because it’s one-half of the total angular distance between the two loudspeakers. So, you can consider the loudspeaker aperture as ±0.5.

The relationship between image WIDTH and position. This is something I’ve not seen expressed so clearly before.

For more information similar to this, see these links as a start: