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Signal Processing Fundamentals
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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 tr avel 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 movingcoil (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 dignal, and the loudspeaker translates an electrical signal into sound. One capturing, the other creating. Everything inbetween 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).

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/oct. The slope increases or decreases so many dB/oct. At the simplest level, each component gives you a 6 dB/oct 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/oct. 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 on page 2)

 

 

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