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The Audio ExpertEverything You Need to Know About Audio
By Ethan Winer
Focal PressCopyright © 2012 Elsevier Inc.
All right reserved.
Chapter OneAudio Basics
"When you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely in your thoughts advanced to the state of science." —Lord Kelvin (Sir William Thomson), nineteenth-century physicist
Volume and Decibels
When talking about sound that exists in the air and is heard by our ears (or picked up by a microphone), volume level is referred to as sound pressure level, or SPL. Our ears respond to changing air pressure, which in turn deflects our eardrums, sending the perception of sound to our brains. The standard unit of measurement for SPL is the decibel, abbreviated dB. The "B" refers to Alexander Graham Bell (1847–1922), and the unit of measure is actually the Bel. But one Bel is too large for most audio applications, so one-tenth of a Bel, or one decibel, became the common unit we use today.
By definition, decibels express a ratio between two volume levels, but in practice SPL can also represent an absolute volume level. In that case there's an implied reference to a level of 0 dB SPL—the softest sound the average human ear can hear, also known as the threshold of hearing. So when the volume of a rock concert is said to be 100 dB SPL when measured 20 feet in front of the stage, that means the sound is 100 dB louder than the softest sound most people can hear. Since SPL is relative to an absolute volume level, SPL meters must be calibrated at the factory to a standard acoustic volume.
For completeness, 0 dB SPL is equal to a pressure level of 20 micropascals (millionths of 1 Pascal, abbreviated µPa). Like pounds per square inch (PSI), the Pascal is a general unit of pressure—not only air pressure—and it is named in honor of the French mathematician Blaise Pascal (1623–1662).
Note that decibels use a logarithmic scale, which is a form of numeric "compression." Adding dB values actually represents a multiplication of sound pressure levels, or voltages when it relates to electrical signals. Each time you add some number of decibels, the underlying change in air pressure, or volts for audio circuits, increases by a multiplying factor:
+6 dB = 2 times the air pressure or volts +20 dB = 10 times the air pressure or volts +40 dB = 100 times the air pressure or volts +60 dB = 1,000 times the air pressure or volts +80 dB = 10,000 times the air pressure or volts
Likewise, subtracting decibels results in division:
-6 dB = 1/2 the air pressure or volts -20 dB = 1/10 the air pressure or volts -40 dB = 1/100 the air pressure or volts -60 dB = 1/1;000 the air pressure or volts -80 dB = 1/10;000 the air pressure or volts
So when the level of an acoustic source or voltage increases by a factor of 10, that increase is said to be 20 dB louder. But increasing the original level by 100 times adds only another 20 dB, and raising the volume by a factor of 1,000 adds only 20 dB more. Using decibels instead of ratios makes it easier to describe and notate the full range of volume levels we can hear. The span between the softest sound audible and the onset of extreme physical pain is about 140 dB. If that difference were expressed using normal (not logarithmic) numbers, the span would be written as 10,000,000,000,000 to 1, which is very unwieldy! Logarithmic values are also used because that's just how our ears hear. An increase of 3 dB represents a doubling of power, but it sounds only a little louder. To sound twice as loud, the volume needs to increase by about 8 to 10 dB, depending on various factors, including the frequencies present in the source.
Note that distortion and noise specs for audio gear can be expressed using either decibels or percents. For example, if an amplifier adds 1 percent distortion, that amount of distortion could be stated as being 40 dB below the original signal. Likewise, noise can be stated as a percent or dB difference relative to some output level. Chapter 2 explains how audio equipment is measured in more detail.
You may have read that the smallest volume change people can hear is 1 dB. Or you may have heard it as 3 dB. In truth, the smallest level change that can be noticed depends on several factors, including the frequencies present in the source. We can hear smaller volume differences at midrange frequencies than at very low or very high frequencies. The room you listen in also has a large effect. When a room is treated with absorbers to avoid strong reflections from nearby surfaces, it's easier to hear small volume changes because echoes don't drown out the loudspeaker's direct sound. In a room outfitted with proper acoustic treatment, most people can easily hear level differences smaller than 0.5 dB at midrange frequencies.
It's also worth mentioning the inverse square law. As sound radiates from a source, it becomes softer with distance. This decrease is due partly to absorption by the air, which affects high frequencies more than low frequencies, as shown in Table 1.1. But the more important reason is simply because sound radiates outward in an arc, as shown in Figure 1.1. Each time the distance from a sound source is doubled, the same amount of energy is spread over an area twice as wide. Therefore, the level reduces by a corresponding amount, which in this case is 6 dB.
Standard Signal Levels
As with acoustic volume levels, the level of an audio signal in a wire or electrical circuit is also expressed in decibels, either relative to another signal or relative to one of several common standard reference levels. An amplifier that doubles its input voltage is said to have a gain of 6 dB. This is the same amount of increase whether the input is 0.001 volts or 5 volts; whatever voltage happens to be at the input becomes twice as large at the output. But, as with SPL, the dB is also used to express absolute levels for electronic signals using an implied reference. The most common standard reference levels used for audio are dBm, dBV, dBu, and dBFS.
The "m" in dBm stands for milliwatt, with 0 dBm equal to 1 milliwatt (thousandth of a watt) of power. Other dBm values describe absolute amounts of power either lower or higher than the 1 milliwatt reference level. Therefore, 10 dBm is the same as 10 milliwatts, 20 dBm is the same as 100 milliwatts, and -3 dBm is 0.5 milliwatt. The "V" in dBV stands for volts. So 0 dBV equals 1 volt, 20 dBV equals 10 volts, and -6 dBV is half a volt.
The dBu standard is similar to dBV, but the reference level for 0 dBu is 0.775 volts. The value 0.775 is used because telephone systems (and older audio devices) were originally designed with an input and output impedance of 600 ohms. The electrical symbol for ohms is the Greek letter omega, shown as . When 0.775 volts is applied to 600 ohms, the result is 1 milliwatt of power. Impedance is explained in more depth in later chapters.
The unit dBFS is specific to digital audio, with FS standing for full scale. This is the maximum level a digital device can accommodate or, in other words, the largest number a converter can accept or output. No reference voltage level is needed or implied. Whatever input and output level your particular sound card or outboard converter is calibrated for, 0 dBFS equals the maximum level possible before the onset of gross distortion.
Again, more complete explanations of volts, amps, watts, and impedance are provided in later chapters. But for now, the main point is that dB levels are always relative, even though there's often an implied reference to a specific voltage or power level.
Signal Levels and Metering
Level meters are an important part of recording and mixing because every recording medium has a limited range of volume levels it can accommodate. For example, when recording to analog tape, if the audio is recorded too softly, you'll hear a "hiss" in the background when you play back the recording. And if the music is recorded too loudly, an audible distortion can result. The earliest type of audio meter used for recording (and broadcast) is called the VU meter, where VU stands for volume units. This is shown in Figure 1.2.
Early VU meters were mechanical, made with springs, magnets, and coils of wire. The spring holds the meter pointer at the lowest volume position, and then when electricity is applied, the coil becomes magnetized, moving the pointer. Since magnets and coils have a finite mass, VU meters do not respond instantly to audio signals. Highly transient sounds such as claves or other percussion instruments can come and go before the meter has a chance to register their full level. So when recording percussive instruments, and instruments that have a lot of high-frequency content, you need to record at levels lower than the meter indicates to avoid distortion.
Adding "driver" electronics to a VU meter offers many potential advantages. One common feature holds the input voltage for half a second or so, giving the meter time to respond to the full level of a transient signal. Another useful option is to expand the range displayed beyond the typical 23 dB. This is often coupled with a logarithmic scale, so, for example, a meter might display a total span of 40 or even 50 dB, shown as 10 dB steps equally spaced across the meter face. This is different from the VU meter in Figure 1.2, where the nonlinear log spacing is incorporated into the dB scale printed on the meter's face.
Modern digital meters use either an LED "ladder" array as shown in Figure 1.3 or an equivalent as displayed on a computer screen by audio recording software. Besides showing a wider range of volumes and holding peaks long enough to display their true level, many digital meters can also be switched to show either peak or average volumes. This is an important concept in audio because our ears respond to a sound's average loudness, where computer sound cards and analog tape distort when the peak level reaches what's known as the clipping point. Mechanical VU meters inherently average the voltages they receive by nature of their construction. Just as it takes some amount of time (50 to 500 milliseconds) for a meter needle to deflect fully and stabilize, it also takes time for the needle to return to zero after the sound stops. The needle simply can't keep up with the rapid changes that occur in music and speech, so it tends to hover around the average volume level. Therefore, when measuring audio whose level changes constantly—which includes most music—VU meters are ideal because they indicate how loud the music actually sounds. But mechanical VU meters won't tell you whether audio exceeds the maximum allowable peak level unless extra circuitry is added.
Modern digital meters often show both peak and average levels at the same time. All of the lights in the row light up from left to right to show the average level, while single lights farther to the right blink one at a time to indicate the peak level, which is always higher. Some digital meters can even be told to hold peaks indefinitely. So you can step away and later, after the recording finishes, you'll know if the audio clipped when you weren't watching. The difference between a signal's peak and average levels is called its crest factor. By the way, the crest factor relation between peak and average levels applies equally to acoustic sounds in the air.
The concept of peak versus average levels also applies to the output ratings of power amplifiers. Depending on their design, some amplifiers can output twice as much power for brief periods than they can provide continuously. Many years ago, it was common practice for amplifier makers to list only peak power output in their advertisements, and some of the claims bordered on fraud. For example, an amplifier that could output only 30 watts continuously might claim a peak power output of hundreds of watts, even if it could provide that elevated power for only one millisecond. Thankfully, the US Federal Trade Commission passed a law (FTC Rule 46 CFR 432) in 1974 making this practice illegal.
Excerpted from The Audio Expert by Ethan Winer Copyright © 2012 by Elsevier Inc.. Excerpted by permission of Focal Press. All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
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