Signal Processing Fundamentals: Crossovers


Dennis Bohn, Rane Corporation

Screaming To Be Heard

In space, no one can hear you scream ... because there is no air or other medium for sound to travel. Sound needs a medium; an intervening substance through which it can travel from point to point; it must be carried on something. That something can be solid, liquid or gas. They can hear you scream underwater ... briefly. Water is a medium. Air is a medium. Nightclub walls are a medium. Sound travels in air by rapidly changing the air pressure relative to its normal value (atmospheric pressure). Sound is a disturbance in the surrounding medium. A vibration that spreads out from the source, creating a series of expanding shells of high pressure and low pressure ... high pressure ... low pressure ... high pressure ... low pressure. Moving ever outward these cycles of alternating pressure zones travel until finally dissipating, or reflecting off surfaces (nightclub walls), or passing through boundaries, or getting absorbed -- usually a combination of all three. Left unobstructed, sound travels outward, but not forever. The air (or other medium) robs some of the sound's power as it passes. The price of passage: the medium absorbs its energy. This power loss is experienced as a reduction in how loud it is (the term loudness is used to describe how loud it is from moment to moment) as the signal travels away from its source. The loudness of the signal is reduced by one-fourth for each doubling of distance from the source. This means that it is 6 dB less loud as you double your distance from it. [This is known as the inverse square law since the decrease is inversely proportional to the square of the distance traveled; for example, 2 times the distance equals a 1/4 decrease in loudness, and so on.]

How do we create sound, and how do we capture sound? We do this using opposite sides of the same electromagnetic coin. Electricity and magnetism are kinfolk: If you pass a coil of wire through a magnetic field, electricity is generated within the coil. Turn the coin over and flip it again: If you pass electricity through a coil of wire, a magnetic field is generated. Move the magnet, get a voltage; apply a voltage, create a magnet ... this is the essence of all electromechanical objects.

Microphones and loudspeakers are electromechanical objects. At their hearts there is a coil of wire (the voice coil) and a magnet (the magnet). Speaking causes sound vibrations to travel outward from your mouth. Speaking into a moving-coil (aka dynamic) microphone causes the voice coil to move within a magnetic field. This causes a voltage to be developed and a current to flow proportional to the sound -- sound has been captured. At the other end of the chain, a voltage is applied to the loudspeaker voice coil causing a current to flow which produces a magnetic field that makes the cone move proportional to the audio signal applied -- sound has been created. The microphone translates sound into an electrical signal, and the loudspeaker translates an electrical signal into sound. One capturing, the other creating. Everything in-between is just details. And in case you're wondering: yes; turned around, a microphone can be a loudspeaker (that makes teeny tiny sounds), and a loudspeaker can be a microphone (if you SHOUT REALLY LOUD).

Crossovers: Simple Division

Loudspeaker crossovers are a necessary evil. A different universe, a different set of physics and maybe we could have what we want: one loudspeaker that does it all. One speaker that reproduces all audio frequencies equally well, with no distortion, at loudness levels adequate for whatever venue we play. Well, we live here, and our system of physics does not allow such extravagance. The hard truth is, no one loudspeaker can do it all. We need at least two -- more if we can afford them. Woofers and tweeters. A big woofer for the lows and a little tweeter for the highs. This is known as a 2-way system. (Check the accompanying diagrams for the following discussions.) But with two speakers, the correct frequencies must be routed (or crossed over) to each loudspeaker.

Passive

At the simplest level a crossover is a passive network. A passive network is one not needing a power supply to operate -- if it has a line cord, or runs off batteries, then it is not a passive circuit. The simplest passive crossover network consists of only two components: a capacitor connecting to the high frequency driver and an inductor (aka a coil) connecting to the low frequency driver. A capacitor is an electronic component that passes high frequencies (the passband) and blocks low frequencies (the stopband); an inductor does just the opposite: it passes low frequencies and blocks high frequencies. But as the frequency changes, neither component reacts suddenly. They do it gradually; they slowly start to pass (or stop passing) their respective frequencies. The rate at which this occurs is called the crossover slope. It is measured in dB per octave, or shortened to dB/octave. The slope increases or decreases so many dB/octave. At the simplest level, each component gives you a 6 dB/octave slope (a physical fact of our universe). Again, at the simplest level, adding more components increases the slope in 6 dB increments, creating slopes of 12 dB/oct, 18 dB/oct, 24 dB/oct, and so on. The number of components, or 6 dB slope increments, is called the crossover order. Therefore, a 4th-order crossover has (at least) four components, and produces steep slopes of 24 dB/octave. The steeper the better for most drivers, since speakers only perform well for a certain band of frequencies; beyond that they misbehave, sometimes badly. Steep slopes prevent these frequencies from getting to the driver.

You can combine capacitors and inductors to create a third path that eliminates the highest highs and the lowest lows, and forms a mid-frequency crossover section. This is naturally called a 3-way system. (See diagram) The "mid" section forms a bandpass filter, since it only passes a specific frequency band. Note from the diagram that the high frequency passband and low frequency passband terms are often shortened to just high-pass and low-pass. A 3-way system allows optimizing each driver for a narrower band of frequencies, producing a better overall sound.

So why not just use passive boxes?

Problems

The single biggest problem is that one passive cabinet (or a pair) won't play loud enough and clean enough for large spaces. If the sound system is for your bedroom or garage, passive systems would work just fine -- maybe even better. But it isn't. Once you try to fill a relatively large space with equally loud sound you start to understand the problems. And it doesn't take stadiums, just normal size clubs. It is really difficult to produce the required loudness with passive boxes. Life would be a lot easier if you could just jack everyone into their own cans amp -- like a bunch of HC 4 or HC 6 Headphone Amps scattered throughout the audience. Let them do the work; then everyone could hear equally well, and choose their own listening level. But life is hard, and headphone amps must be restricted to practice and recording.

Monitor speakers on the other hand most likely have passive crossovers. Again, it's a matter of distance and loudness. Monitors are usually close and not overly loud -- too loud and they will feed back into your microphone or be heard along with the main mix: not good. Monitor speakers are similar to hi-fi speakers, where passive designs dominate ... because of the relatively small listening areas. It is quite easy to fill small listening rooms with pristine sounds even at ear-splitting levels. But move those same speakers into your local club and they will sound thin, dull and lifeless. Not only will they not play loud enough, but they may need the sonic benefits of sound bouncing off close walls to reinforce and fill the direct sound. In large venues, these walls are way too far away to benefit anyone.

2-way crossover

Figure 1. Passive 2-Way Crossover

3-way crossover

Figure 2. Passive 3-Way Crossover

So why not use a bunch of passive boxes? You can, and some people do. However, for reasons to follow, it only works for a couple of cabinets. Even so, you won't be able to get the high loudness levels if the room is large. Passive systems can only be optimized so much.

Once you start needing multiple cabinets, active crossovers become necessary. To get good coverage of like-frequencies, you want to stack like-drivers. This prevents using passive boxes since each one contains (at least) a high-frequency driver and a low-frequency driver. It's easiest to put together a sound system when each cabinet covers only one frequency range. For instance, for a nice sounding 3-way system, you would have low-frequency boxes (the big ones), then medium-sized mid-frequency boxes and finally the smaller high-frequency boxes. These would be stacked or hung, or both -- in some sort of array. A loudspeaker array is the optimum stacking shape for each set of cabinets to give the best combined coverage and overall sound. You've no doubt seen many different array shapes. There are tall towers, high walls, and all sorts of polyhedrons and arcs. The only efficient way to do this is with active crossovers.

Some smaller systems combine active and passive boxes. Even within a single cabinet it is common to find an active crossover used to separate the low- and mid-frequency drivers, while a built-in passive network is used for the high-frequency driver. This is particularly common for super tweeters operating over the last audio octave. At the other end, an active crossover often is used to add a subwoofer to a passive 2-way system. All combinations are used, but each time a passive crossover shows up, it comes with problems.

One of these is power loss. Passive networks waste valuable power. The extra power needed to make the drivers louder, instead boils off the components and comes out of the box as heat -- not sound. Therefore, passive units make you buy a bigger amp.

A couple of additional passive network problems has to do with their impedance. Impedance restricts power transfer; it's like resistance, only frequency sensitive. In order for the passive network to work exactly right, the source impedance (the amplifier's output plus the wiring impedance) must be as close to zero as possible and not frequency-dependent, and the load impedance (the loudspeaker's characteristics) must be fixed and not frequency-dependent (sorry, not in this universe; only on Star Trek). Since these things are not possible, the passive network must be (at best), a simplified and compromised solution to a very complex problem. Consequently, the crossover's behavior changes with frequency -- not something you want for a good sounding system.

One last thing to make matters worse. There is something called back-emf (back-electromotive force: literally, back-voltage) which further contributes to poor sounding speaker systems. This is the phenomena where, after the signal stops, the speaker cone continues moving, causing the voice coil to move through the magnetic field (now acting like a microphone), creating a new voltage that tries to drive the cable back to the amplifier's output! If the speaker is allowed to do this, the cone flops around like a dying fish. It does not sound good! The only way to stop back-emf is to make the loudspeaker "see" a dead short, i.e., zero ohms looking backward, or as close to it as possible -- something that's not gonna happen with a passive network slung between it and the power amp.

All this, and not to mention that inductors saturate at high signal levels causing distortion -- another reason you can't get enough loudness. Or the additional weight and bulk caused by the large inductors required for good low frequency response. Or that it is almost impossible to get high-quality steep slopes passively, so the response suffers. Or that inductors are way too good at picking up local radio, TV, emergency, and cellular broadcasts, and joyfully mixing them into your audio.

Such is life with passive speaker systems.

2-way crossover

Figure 3. Active 2-Way Crossover

3-way crossover

Figure 4. Active 3-Way Crossover

Active

Active crossover networks require a power supply to operate and usually come packaged in single-space, rack-mount units. (Although of late, powered loudspeakers with built-in active crossovers and power amplifiers are becoming increasingly popular.) Looking at the accompanying diagram shows how active crossovers differ from their passive cousins. For a 2-way system instead of one power amp, you now have two, but they can be smaller for the same loudness level. How much smaller depends on the sensitivity rating of the drivers (more on this later). Likewise a 3-way system requires three power amps. You also see and hear the terms bi-amped, and tri-amped applied to 2- and 3-way systems.

Active crossovers cure many ills of the passive systems. Since the crossover filters themselves are safely tucked away inside their own box, away from the driving and loading impedance problems plaguing passive units, they can be made to operate in an almost mathematically perfect manner. Extremely steep, smooth and well-behaved crossover slopes are easily achieved by active circuitry.

There are no amplifier power loss problems, since active circuits operate from their own low voltage power supplies. And with the inefficiencies of the passive network removed, the power amps more easily achieve the loudness levels required.

Loudspeaker jitters and tremors caused by inadequately damped back-emf all but disappear once the passive network is removed. What remains is the amplifier's inherent output impedance and that of the connecting wire. Here's where the term damping factor comes up. [Note that the word is damp-ing, not damp-ning as is so often heard; impress your friends.] Damping is a measure of a system's ability to control the motion of the loudspeaker cone after the signal disappears. No more dying fish.

Siegfried & Russ

Active crossovers go by many names. First, they are either 2-way or 3-way (or even 4-way and 5-way). Then there is the slope rate and order: 24 dB/oct (4th-order), or 18 dB/oct (3rd-order), and so on. And finally there is a name for the kind of design. The two most common being Linkwitz-Riley and Butterworth, named after Siegfried Linkwitz and Russ Riley who first proposed this application, and Stephen Butterworth who first described the response in 1930. Up until the mid `80s, the 3rd-order (18 dB/oct) Butterworth design dominated, but still had some problems. Since then, the development (pioneered by Rane and Sundholm) of the 4th-order (24 dB/oct) Linkwitz-Riley design solved these problems, and today is the norm.

What this adds up to is active crossovers are the rule. Luckily, the hardest thing about an active crossover is getting the money to buy one. After that, most of the work is already done for you. At the most basic level all you really need from an active crossover are two things: to let you set the correct crossover point, and to let you balance driver levels. That's all. The first is done by consulting the loudspeaker manufacturer's data sheet, and dialing it in on the front panel. (That's assuming a complete factory-made 2-way loudspeaker cabinent, for example. If the box is homemade, then both drivers must be carefully selected so they have the same crossover frequency, otherwise a severe response problem can result.) Balancing levels is necessary because high frequency drivers are more efficient than low frequency drivers. This means that if you put the same amount of power into each driver, one will sound louder than the other. The one that is the most efficient plays louder. Several methods to balance drivers are always outlined in any good owner's manual.

PDF "Signal Processing Fundamentals" This note in PDF.

Courtesy Rane . Used by permission.

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