The Decibel is a unit which is used to compare two levels of power. It is rather like a percentage, because it is comparative and does not have any absolute value.

It was originated by the telephone industry to ease the calculation of gains and losses in telephone circuits. Normally the total effect of a combination of gains and losses has to be be calculated by multiplication, but the decibel was defined as a logarithmic unit so that simple addition and subtraction could be used for the calculation.

The Bel is the logarithm (to base 10) of the ratio of two power levels. The decibel is one tenth of a Bel (which is a far more practical unit).

When the ratio represnts a reduction, the decibels become negative:

The example below shows a long distance telephone line fed with amplified signals. At the receiving end, further amplification is needed in order to return the signal to its previous level.

The calculation to check that there is no overall loss or gain can be done two ways:

or

When the calculations become more elaborate in a complex system, the decibel method is much easier to use.

The measurement of power is sometimes difficult or inconvenient, so another parameter is measured and the power is calculated from that measurement. In electrical work, the voltage is usually measured, and it is assumed that the power is proportional to the voltage squared. In acoustic work, the sound pressure is measured and it is assumed that the sound power is proportional to the pressure squared. The table below shows some useful ratios (approximate figures are shown in brown)

In thses circumstances the mathematical expression for decibels is often modified to: dB = 20 Log10 (Voltage 1 / Voltage 2), but great care must be taken to ensure that this simplification is not used in circumstances where the voltage to power relationship does not hold true. For instance, decibels cannot be used to compare voltages measured in two circuits of different impedance.

The concept of decibels is so useful that it has been extended to cover other types of measurment. Sometimes the decibel is used to compare a power level with a fixed standard. In that case it is written as dBz, where the z suffix represents an agreed standard level. For example dBm is an electrical measurement of power compared with one milliwatt.

In audio work the standard level for comparison is usually the smallest sound which can be heard, but there are two suffixes in common use. In industrial noise situations, the measurements are expressed in dBA, which takes less account of low frequency sounds. This is appropriate because the majority of hearng damage results from medium and high frequency sound. Sound measurement in dBC covers equally the whole spectrum of sound within human hearing.

Footnote: If somebody expresses a sound level in decibels without specifying the standard for comparison, they are either being lazy or they are ignorant of what a decibel really is.

Various authorities differ in the detail of allowable noise exposure and the methods of measuring it; however, the table below is a fair summary of the maximum allowable levels:

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