Audio Engineering: Relating Real-World, Analog and Digital Levels
Levels through the Sound Reproduction Signal Chain
... Here, we are assuming a digital recording system. The sound in the atmosphere is captured by a microphone, which produces an electrical signal analogous to the changing pressure (or possibly velocity) in the air. The electrical signal is then digitised, ending up as a long series of numbers in a digital storage system such as a hard disk or tape.
On playback, the series of digitised numbers are retrieved, and an analog signal proportional to the numbers is generated. This analog signal is then amplified to the point where in can drive a speaker, which recreates the vibrations in the air that we perceive as sound. These vibrations are ideally a good approximation of the original vibrations present in the recording studio.
The following scales (once I clean them up a bit!) will show the relationships between sound pressure levels in the real world, and the corresponding signal levels in the analog and digital domains used in sound recording and reproduction. Notice that all use variations on the decibel (dB).
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Sound Pressure Levels (SPL) in the Real World
Fortunately, there are limits on human hearing. We can only perceive a finite range of frequencies within a finite range of sound pressure levels. Ideally, a sound reproduction system should have limits at least equal to the limits of human hearing, which should make it possible (in theory) to record and reproduce sound “perfectly” (i.e. well enough to fool the ear).
For example, most people cannot hear sounds quieter than 0 dB SPL (the hearing threshold). So, there is no need for a sound system to be quieter than this. In fact, many listening environments have a background noise level of 20–40 dB higher than this.
At the other end of the loudness scale, physical pain is experienced at around 130 dB SPL, so there is little need for a system that can reproduce sounds louder than this! In fact, continuous sound pressure levels greater than about 85 dB SPL can be harmful, and are likely to be uncomfortable to listen to for extended periods. Studies have shown that 83 dB SPL is consistently preferred as a nominal continuous average level for listening to music and film soundtracks.
Typical music has a crest factor of about 20 dB, meaning that the loudest peaks are 20 dB above the nominal level. This means the loudest peaks will occur at 103 dB SPL if we choose 83 dB SPL as the nominal level.
Levels in the Digital Domain
Monitoring System Requirements
Having recorded the audio, it may be played back. The output part of the signal chain consists of digital-to-analog (D/A) converters, power amplification, and speakers (transducers). For critical listening such as mixing and mastering, and for compelling listening for entertainment, a nominal level of 83 dB SPL is well documented as being “just right”. We need to consider the maximum levels that will be produced in the playback system if we calibrate it for a nominal level of 83 dB SPL.
As shown above, -20 dBFS in the digital domain corresponds to +4 dBu in the analog domain, which corresponds to 83 dB SPL in the monitoring system. Therefore, 0 dBFS corresponds to 103 dB SPL in the listening room. Knowing this will help in assessing whether a particular combination of speakers, power amplifier, and listening environment will be adequate.
Speaker Sensitivity
Speaker sensitivity is an important consideration in determining the effectiveness of a monitoring system (in terms of levels, anyway). The sensitivity of a speaker is the measure of how loud a sound it produces for a given input signal. In a sense, it is similar to the efficiency of the speaker. Speaker sensitivity is usually specified as dB sound pressure level (SPL) produced at a distance of 1 m by a 1 kHz input signal at a power of 1 W. Ideally, monitor speakers should be capable of producing sound pressure levels of up to 103 dB SPL at the listening position.
To illustrate, I'll consider the Behringer B2031P reference monitor (just because I happen to own a pair). The relevant specifications are the sensitivity and the maximum power handling:
Behringer B2031P: Sensitivity: 89 dB SPL @ 1 W @ 1 m Power handling: 150 W max
To calculate what sound pressure level will be produced for a given power input, add approximately 3 dB for each doubling of power:
10 * log10(2 / 1) ~= 3.010 dB
Therefore, at 2 W, this particular speaker would produce 92 dB SPL. At 4 W, the output would be 95 dB SPL. And so on:
| Power (W) | dB SPL |
|---|---|
| 1 | 89 |
| 2 | 92 |
| 4 | 95 |
| 8 | 98 |
| 16 | 101 |
| 32 | 104 |
| 64 | 107 |
| 128 | 110 |
We can also calculate exactly how loud the speaker will be at its maximum rated power:
10 * log (150 W / 1 W ) = 21.8 dB above the output at 1 W
89 dB SPL + 21.8 dB = 110.8 dB SPL @ 150 W @ 1 m
1 m is probably a reasonable listening distance for near-field monitors such as these. Since there are two speakers, the sound will combine to produce a somewhat higher level at the listening position, probably +3 dB. Therefore the maximum sound pressure level would be 113.8 dB.
Amplifier Power Requirements
Now for the power amplifier requirements. We know from the speaker specifications that we need at least 150 W per channel to drive the speakers to their maximum output. However, as we've seen, solid state active devices start introducing distortion well before they actually clip. We should really build another 6 dB analog cushion into our system at the power amp. 6 dB above 150 W is two doublings, so you could argue that a 600 W amp would be required to power these speakers cleanly! To calculate this:
10 ^ (6.02 dB / 10) = 4
4 x 150 W = 600 W
Now you can see why audio engineers recommend using amplifiers that are more powerful than the speakers they are driving! Having this kind of headroom will ensure that the loud transient peaks are reproduced cleanly even at “sturdy” listening levels.
Questions, comments, compliments, or complaints? Send Internet e-mail to “cme at ihug dot co dot nz”.
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This document last modified and © 2006-09-21 12:44:18 NZST