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Understanding that Troublesome Decibel

by Daniel Kumin

The decibel, “dB” for short, is all over audio like flies on a forgotten Twinkie. Sure, you can ignore it, or sort-of understand it, but if your really want to know who’s who and what’s what in audio, it really ain’t that hard.

Work, in the physics sense, is not a linear phenomenon. A crude example: if a 100-horsepower car with a top speed of 120 mph is turbocharged to 200 HP, with no other changes, it won’t suddenly reach 240 mph top speed; it might hit 135.

And so it is with the sound-pressure (“loudness”) we hear, and the various kinds of “power” we use to characterize amplifiers and other audio components. Scientists have long used logarithmic scales to measure such phenomena, and that’s exactly what we do in audio, with a unit called the decibel, abbreviated “dB.”

I won’t bore you with the dB’s history (early telephone tech) or math (10log(P1/P2)) – see what I mean?). Instead I’ll simply try to lay out a few fundamentals.

Concept #1: Any figure in dB always defines a comparison of two power quantities. For example: an amplifier frequency response spec of “20 Hz-20 kHz, ±3 dB” means that where the amp produce a given power level (for this example we’ll say 1 watt) at a given frequency (we’ll say 1 kHz -- very roughly B5 on a piano), it won’t yield more than 2 watts (+3 dB), or less than 0.5 watts (-3 dB) at any other frequency over that humanly audible range. Put another way, albeit crudely: the musical notes higher or lower than B5 won’t be represented unduly louder or softer. (Yeah, dB expressions of voltage work a bit differently, but in audio almost always infer power anyway.)

Concept #2: Since the dB is a scale of comparison, there always has to be a reference, even if it is more often than not implied rather than stated. In the example above, the reference “1 watt” is implicit, though 2 watts, or 4-and-two-thirds watts could serve just as well. (The 1 kHz reference frequency is also unstated, but it’s the de facto standard starting point.) It doesn’t matter, since we’re interested in the difference in power delivered, not the absolute values. One semi-exception:, sometimes amplifier power is expressed in “dB watts” (dBw), which states power relative to 1 watt: 3 dBw is 2 watts; 20 dBw is 100 watts.

Concept #3: Through the magic of logarithms, the decibel scale lets us refer to huge numbers representing powers literally billions of times stronger or weaker, with simple 2- or 3-place numbers: 100 dB is a 10-to-the-tenth ratio, or 10 billion. So while a signal-to-noise ratio of 60 dB may not look very sexy in today’s digital-audio world, it still represents noise that is just one part per million.

Contrarians will argue that the decibel is a relic of the slide-rule era – quite literally, since slide rules are essentially mechanical logarithm-calculators: a relic with no place in our computerized, digital-calculating age. They may have a point, but I say we’re stuck with the familiar “dB,” so get used to it, by coming to understand it a little bit better.