TABLE OF CONTENTS A power ratio of P 1/ P 2 expressed in bels is
The bel was introduced as a logarithmic unit which allowed addition and subtraction to replace multiplication and division. As such, it proved to be inconveniently large, and the decibel, abbreviated dB, is the unit now in widespread use. The same power ratio expressed in decibels is
Because the base 10 is understood, it is seldom, if ever, shown explicitly.
The abbreviation dB, as shown below, is often modified to indicate a reference level. Although referred to as a unit, the decibel is a dimensionless quantity, the ratio of two powers. Power by itself cannot be expressed in decibels. However, by selecting unit power as the denominator in the ratio, power can be expressed in decibels relative to this. A power expressed in decibels relative to 1 W is shown as dBW. For example, 50 W expressed in decibels relative to 1 W would be equivalent to
Another commonly used reference is the milliwatt, and decibels relative to this are shown as dBm. Thus 50 W relative to 1 mW would be
By definition, the ratio of two voltages V 1 and V 2 expressed in decibels is
The multiplying factor of 20 comes about because power is proportional to voltage squared. Note carefully, however, that the definition of voltage decibels stands on its own and can be related to the corresponding power ratio only when the ratio of load resistances is...
