DECIBLES

The decibel is ubiquitous in audio, though many do not understand what exactly it is. It has many uses and can refer to so many different things that it can be difficult to keep them straight. During the early days of telephone, in order to compare the performance of equipment, engineers needed a unit of measurement that matched the logarithmic nature of human audio perception. They named the new unit the Bel, in honor of Alexander Graham Bell. The difference between the levels of two signals was one Bel if the log of their power ratio was 1, which equated to a tenfold increase in power. However, needing a smaller unit that better reflected the minor changes in level that people can hear, the more common unit became the decibel, or one tenth of a Bel.

A decibel is a ratio that compares two levels. Without a stated reference, it is not an absolute level, rather a relative difference between two levels. Mathematically, this works out to be 10 log P1/P2, where P is a power level measured in watts. For voltages, it is 20 log E1/E2, where E is energy, or electrical potential measured in volts. The 20 log figure is used because the power is proportional to the square of the voltage, and doubling the log is equivalent to squaring.

History and theory aside, what does this mean to you in practical terms? Some rule of thumb relationships to keep in mind are that a 10 dB difference equates to a 10 fold increase or decrease in the power level, while 3 dB is a doubling or halving. A 20 dB increase is 10 times the voltage, while 6 dB is a doubling. Acoustically, a 1 dB difference is usually the smallest increment that most people can perceive, while 10 dB is generally considered by most to be subjectively “twice as loud.“

To make a decibel refer to an absolute level, rather than a relative difference between two levels, one of them must be a reference value that never changes. The decibel level will then be in comparison to that fixed reference value. This is where all of those extra letters at the end of dB measurements come in. Some common references include dBV, which is relative to 1 Volt, and dBm, which is relative to 1 milliwatt. Historically, 600 ohms was the standard impedance for most audio and telephone circuits, and 0 dBu references 0.775V, the voltage required to generate 1 mW into a 600 ohm load.

In digital audio systems, 0 dBFS relates to digital full scale, the greatest value that can be represented by the digital word. If you had 20 dB of headroom left before reaching full scale on your digital recorder, the signal level would be -20 dBFS. In acoustics, decibels refer to sound pressure level, or dB SPL. The reference value is 0.00002 Pascals, the smallest pressure fluctuation that humans can hear, called the threshold of hearing. Below 0 dB, less than .00002 Pa, our ears cannot detect the sound. At 120 dB SPL, the dynamic range of human hearing is exhausted and we reach the threshold of pain. A rock concert may be 100 dB SPL or more, while the average conversation is around 70 dB SPL.

Decibels can mean different things in different situations, and may be a relative difference, or an absolute value. They can be used to describe loudness, amplifier gain, or voltages in a circuit. Anybody actively involved in professional audio will come into contact with decibels, and understanding their meanings and uses will help you get the most out of sound systems. -Jay Frigoletto

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