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# The Decibel

Author: J.B. Hoag

The increase or decrease in power in an amplifier or, in fact, in any device, can be expressed as the ratio of the power out to the power in. There is, however, a different and more useful manner of showing the gain or loss in the device. This method employs a unit called the decibel (abbreviated dB), which is one-tenth of a "Bel" (in honor of Alexander Graham Bell who invented the telephone).1

If a certain sound is slowly increased in intensity the change will not be noticed until the power used in making the sound has been increased by 1 decibel. This loudness change is the same over wide limits regardless of the original loudness of the sound. Thus the decibel gives a measure of the response of the human ear to sounds which have a barely perceptible difference in intensity.

A gain in power is indicated by a plus sign, and a loss of power is indicated by a negative sign. Figure 2 F shows the relationship between the power ratio and the decibel units. It also shows the dB. gain or loss when voltage or current ratios are known for circuits whose input and output resistances (impedances, to be more general) are equal. Negative and positive decibels can be added numerically. A dB of zero stands for the reference power level, i.e., a power ratio of 1. Reference levels of 1, 6 and 12.5 milliwatts are used in broadcasting and telephone practice. In acoustics, a level of sound intensity of about 24·10-16 watts/cm2 under standard atmospheric pressure at 20° C. is used. On this basis the dB of painful sounds is about 130-140; of ordinary conversation, 65-75; of whispering, 25-30 and of the heart beat, 10-15.

 1 If P1 represents the power output in watts, and P2 represents the power input in watts, the number of decibels is given by: dB = log10(P1/P2)

Last Update: 2010-11-21