Aren’t logarithms wonderful? Witness the many confusing flavours of the deciBel (dB, or “dog-biscuit,” as my old friend Mr Mike Fawcett (former technologist extraordinary, now lost to engineering and busy exploring the strange world of broadcast management) has often referred to them).
This story (like all my stories lately) starts with the telephone company: using telegraph wires for transmission, and needing a measurement to describe the losses they were encountering. They started using a unit called “miles of loss,” which described the amount that a signal would be attenuated by passing through a #19 wire loop a mile long. Later this expression was modified to “transmission unit,” and still later someone, thinking it would be nice to commemorate Alexander Graham Bell, created the Bel: the logarithm of the ratio of output and input powers. The Bel was pretty big though, like measuring your personal weight in tonnes, so they divided the Bel by 10 to make the deciBel. Ten deciBels to the Bel. A loss or gain in deciBels is ten times the logarithm of the ratio of output to input power. So far so good. (By the way, someone out there needs to know that there’s 1.056 dB to one mile of loss, but I digress).
So we had a nice, somewhat unusual unit to measure power ratios, the deciBel. Unusual, because it’s logarithmic. Specialized, because it’s intended for measuring power ratios of audio on telegraph lines. Relative, because it was only defined for ratios, and so it was ideal for stating the gain or loss of signal power through amplifiers, filters, attenuators and transmission lines.
It was right about then that all hell broke loose. First of all, people started using the dB to measure all kinds of stuff other than audio power (I swear, if some engineers had their way, the Richter Scale for measuring earthquakes would be calculated in dB). Secondly, by tacking on another letter, they came up with a number of logarithmic measures of absolute level of all kinds of stuff.
It started innocently enough, with the dBm, a level of power related to one milliWatt. 0 dBm = 1 milliWatt. Simple and effective. But trouble was on the way. It’s tough to measure power directly, so most often our instruments are actually voltmeters with a scale calibrated to read off the power at a particular impedance. Telephone guys stick to 600 ohms most of the time, but RF folks prefer 50 or sometimes 75 ohms. And the voltage across 0 dBm at 600 ohms (0.775 V) is different at 50 ohms (0.224 V) or 75 ohms (0.274 V) Uh-oh! And the dB is such a neat little package, why not let’s use it to measure ratios of all kinds of stuff, not just power! Double uh-oh! What have we wrought! It’s logarithmic bedlam! I’ve omitted some of the more obsolete expressions, but there’s still plenty in current usage left to go around:
-- 0 dB SPL = 20 uP (sound pressure) used in mic specifications.
-- 0 dBm = 1 mW (power, audio or RF)
-- 0 dBu = 1 uV/m (RF field strength); or
-- 0 dBu = 0.775 V (voltage, audio) using the same symbol for extra confusion
-- 0 dBk = 1 kW (power)
-- 0 dBmV = 1 mV (voltage, RF) the cable TV industry likes this one
-- 0 dBuV = 1 uV (voltage, RF)
-- 0 dBW = 1W (power, RF) Industry
-- 0 dBV = 1 V (voltage, audio)
-- 0 dB PWL = 1 pW (power, acoustics)
-- 0 dBrnc = -60 dBm (power related to reference noise level, c-weighting) telco audio
The trend is clear, so brace yourself for the following, as the deciBel continues to make its way into everyday usage. Fuel costs will rise 1.5 dB this summer. Computer capacity will continue to increase 6 dB per dollar every 18 months. And the Canadian dollar will continue to be worth about –1.25 dB USD (0 dB USD = 1 U.S. dollar).
And you thought switching to metric was a pain! Maybe it’s not too late to switch back to “miles of loss!”