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.
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.
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”…
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.
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.
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.
This episode of The Infinite Monkey Cage is worth a listen if you’re interested in the history of recording technologies.
There’s one comment in there by Brian Eno that I COMPLETELY agree with. He mentions that we invented a new word for moving pictures: “movies” to distinguish them from the live equivalent, “plays”. But we never really did this for music… Unless, of course, you distinguish listening to a “concert” from listening to a “recording” – but most of us just say “I’m listening to music”.
If you have a vinyl record, and you’re curious about where in the world it was pressed, this site might have some information to help you trace its roots.
I had a little time at work today waiting for some visitors to show up and, as I sometimes do, I pulled an old audio book off the shelf and browsed through it. As usually happens when I do this, something interesting caught my eye.
I was reading the AES publication called “The Phonograph and Sound Recording After One-Hundred Years” which was the centennial issue of the Journal of the AES from October / November 1977.
In that issue of the JAES, there is an article called “Record Changers, Turntables, and Tone Arms – A Brief Technical History” by James H. Kogen of Shure Brothers Incorporated, and in that article he mentions US Patent Number 1,468,455 by William H. Bristol of Waterbury, CT, titled “Multiple Sound-Reproducing Apparatus”.
Before I go any further, let’s put the date of this patent in perspective. In 1923, record players existed, but they were wound by hand and ran on clockwork-driven mechanisms. The steel needle was mechanically connected to a diaphragm at the bottom of a horn. There were no electrical parts, since lots of people still didn’t even have electrical wiring in their homes: radios were battery-powered. Yes, electrically-driven loudspeakers existed, but they weren’t something you’d find just anywhere…
In addition, 3- or 2-channel stereo wasn’t invented yet, Blumlein wouldn’t patent a method for encoding two channels on a record until 1931: 8 years in the future…
But, if we look at Bristol’s patent, we see a couple of astonishing things, in my opinion.
If you look at the top figure, you can see the record, sitting on the gramophone (I will not call it a record player or a turntable…). The needle and diaphragm are connected to the base of the horn (seen on the top right of Figure 3, looking very much like my old Telefunken Lido, shown below.
But, below that, on the bottom of Figure 3 are what looks a modern-ish looking tonearm (item number 18) with a second tonearm connected to it (item number 27). Bristol mentions the pickups on these as “electrical transmitters”: this was “bleeding edge” emerging technology at the time.
So, why two pickups? First a little side-story.
Anyone who works with audio upmixers knows that one of the “tricks” that are used is to derive some signal from the incoming playback, delay it, and then send the result to the rear or “surround” loudspeakers. This is a method that has been around for decades, and is very easy to implement these days, since delaying audio in a digital system is just a matter of putting the signal into a memory and playing it out a little later.
Now look at those two tonearms and their pickups. As the record turns, pickup number 20 in Figure 3 will play the signal first, and then, a little later, the same signal will be played by pickup number 26.
Then if you look at Figure 6, you can see that the first signal gets sent to two loudspeakers on the right of the figure (items number 22) and the second signal gets sent to the “surround” loudspeakers on the left (items number 31).
So, here we have an example of a system that was upmixing a surround playback even before 2-channel stereo was invented.
Mind blown…
NB. If you look at Figure 4, you can see that he thought of making the system compatible with the original needle in the horn. This is more obvious in Figures 1 and 2, shown below.
In Part 2, I showed the raw magnitude response results of three pairs of headphones measured on three different systems, each done 5 times. However, when you plot magnitude responses on a scale with 80 dB like I did there, it’s difficult to see what’s going on.
Differences in measurements relative to average
One way to get around this issue is to ignore the raw measurement and look at the differences between them, which is what we’ll do here. This allows us to “zoom in” on the variations in the measurements, at the cost of knowing what the general overall responses are.
Figure 1 in Part 2 showed the 5 x 3 sets of raw magnitude responses of the open headphones. I then take each set of 5 measurements (remember that these 5 measurements were done by removing the headphones and re-setting them each time on the measurement rig) and find their average response. Then I plot the difference between each of the 5 measurements and that average, and this is done for each of the three measurement systems, as shown below in Figure 1.
Figure 1: Open headphones: The difference between each of the 5 measurements done on each system and the mean (average) of those 5 measurements.
Figure 2: Semi-open headphones: The difference between each of the 5 measurements done on each system and the mean (average) of those 5 measurements.
Figure 3: Closed headphones: The difference between each of the 5 measurements done on each system and the mean (average) of those 5 measurements.
Some of the things that were intuitively visible in the plots in Part 2 are now obvious:
There is a huge change in the measured magnitude response in the high frequency bands, even when the pair of headphones and the measurement rig are the same. This is the result of small changes in the physical position of the headphones on the rig, as well as changes in the clamping force (modified by moving the headband extension). I intentionally made both of these “errors” to show the problem. Notice that the differences here are greater than ±10 dB, which is a LOT.
Overall, the differences between the measurements on the dummy head are bigger and have a lower frequency range than for the other two systems. This is mostly due to two things:
because the dummy head has pinnae (ears), very small changes in position result in big changes in response
it is easier to have small leaks around the ear cushions on a dummy head than with a flat surrounding of a metal plate or an artificial ear. This is the reason for the low-frequency differences with the closed headphones. Leaks have no effect on open headphone designs, since they are always leaking out through the diaphragm itself.
The differences that you can see here are the reason that, when we’re measuring headphones, we never measure just once. We always do a minimum of 5 measurements and look at the average of the set. This is standard practice, both for headphone developers and experienced reviewers like this one, for example.
In addition to this averaging, it’s also smart to do some kind of smoothing (which I have not done here…) to avoid being distracted by sharp changes in the response. Sharp peaks and dips can be a problem, particularly when you look at the phase response, the group delay, or looking for ringing in the time domain. However, it’s important to remember that the peaks and dips that you see in the measurements above might not actually be there when you put the headphones on your head. For example, if the variations are caused by standing waves inside the headphones due to the fact that the measurement system itself is made of reflective plastic or metal (but remember that you aren’t…) then the measurement is correct, but it doesn’t reflect (ha ha…) reality…
One additional thing to remember with these plots is that something that looks like a peak in the curve MIGHT be a peak, but it might also be a dip in the average curve because we’re only looking at the differences in the responses.
System differences
Instead of looking at the differences between each individual measurement and the average of the measurement set, we can also look at the differences between what each measurement system is telling us for each headphone type. For example, if I take one measurement of a pair of headphones on each system, and pretend that one of them is “correct”, then I can find the difference between the measurements from the other two systems and that “reference”.
Figure 4. One measurement for each pair of headphones on each measurement system. The red curves are the dummy head and the blue curves are the artificial ear RELATIVE TO THE FLAT PLATE.
In Figure 4, I’m pretending that the flat plate is the “correct” system, and then I’m plotting the difference between the dummy head measurement (in red) and the artificial ear measurement (in blue) relative to it.
Again, it’s important to remember with these plots is that something that looks like a peak in the curve might actually be a dip in the “reference” curve. (The bump in the red lines around 2 – 3 kHz is an example of this…)
Of course, you could say “but you just said that we shouldn’t look at a single measurement”… which is correct. If we use the averages of all 5 measurements for each set and do the same plot, the result is Figure 5.
Figure 5. The average of all 5 measurements for each pair of headphones on each measurement system. The red curves are the dummy head and the blue curves are the artificial ear relative to the flat plate.
You can see there that, by using the averaged responses instead of individual measurements, the really sharp peaks and dips disappear, since they smooth each other out.
Comparing headphone types
Things get even more complicated if you try to compare the headphones to each other using the measurement systems. Figure 6, below, shows the averages of the five measurements of each pair of headphones on each measurement system, plotted together on the same graphs (normalised to the levels at 1 kHz), one for each measurement system.
Figure 6: Comparing the three pairs of headphones on each measurement system.
This is actually a really important figure, since it shows that the same headphones measured the same way on different systems tell you very different things. For example, if you use the “simplified ear” or the “flat plate” system, you’ll believe that the closed headphones (the yellow line) is about 10 – 15 dB higher than the open headphones (the blue line) in the low frequency region. However, if you use the “dummy head” system, you’ll believe that the closed headphones (the yellow line) is about 5 – 10 dB lower than the open headphones (the blue line) in the low frequency region.
Which one is correct? They all are, even though they tell you different things. After all, it’s just data… The reason this happens is that one measurement system cannot be used to directly compare two different types of headphones because their acoustic impedances are different. With experience, you can learn to interpret the data you’re shown to get some idea of what’s going on. However, “experience” in that sentence means “years of correlating how the headphones sound with how the plots look with the measurement system(s) you use”. If you aren’t familiar with the measurement system and how it filters the measurement, then you won’t be able to interpret the data you get from it.
That said, you MIGHT be able to use one system to compare two different pairs of open headphones or two different pairs of closed headphones, but you can’t directly compare measurements of different headphone types (e.g. open and closed) reliably.
This also means that, if you subscribe to two different headphone magazines both of which use measurements as part of their reviews, and one of them uses a flat plate system while the other uses a dummy head, the same pairs of headphones might get opposite reviews in the two magazines…
Which review can you trust? Both of them – and neither of them.
Conclusions
Looking at these plots, you could come to the conclusion that you can’t trust anything, because no two measurements tell you the same things about the same devices. This is the incorrect conclusion to draw. These measurement systems are tools that we use to tell us something about the headphones on which we’re working. And people who use these tools daily know how to interpret the data they see from them. If something looks weird, they either expected it to look weird, or they run the measurement on another system to get a different view.
The danger comes when you make one measurement on one device and hold that up as The Truth. A result that you get from any one of these systems is not The Truth, but it is A Truth – you just need more information. If you’re only shown one measurement (or even an average of measurements) that was done on only one measurement system, then you should raise at least one eyebrow, and ask some questions about how that choice of system affects the plots that you see.
In many ways, it’s like looking at a recipe in a cookbook. You might be able to determine whether you might like or probably hate a dish by reading its description of ingredients and how to prepare it. But you cannot know how it’ll taste until you make it and put it in your mouth. And, if you cook like I do, it’ll be just a little different next time. It’s cooking – not a chemistry experiment. If you use headphones like I do, it’ll also be a little different next time because some days, I don’t wear my glasses, or I position the head band a little differently, so the leak around the ear cushion or the clamping force is a little different.
