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A power ratio of P1/P2 expressed in bels is
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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
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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 V1 and V2 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 also known. Also, unit voltage may be selected as a reference, which allows voltage to be expressed in decibels relative to it. For example, 0.5 V expressed in decibels relative to 1 V is
Another common voltage reference is the microvolt, and 0.5 V expressed in decibels relative to 1 V is
Current ratios may also be expressed in decibels as:
And a reference current may be chosen for I2.
Decilogs
The decibel concept is extended to allow the ratio of any two like quantities to be expressed in decibel units, these being termed decilogs. For example, two temperatures T1 and T2 may be expressed as
The multiplying factor for decilogs is always 10. Decilogs may also be referred to a unit value. In practice the name decilog is seldom
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used and common practice is to use decibels referred to the selected unit. For example, a temperature of 290 K (degrees kelvin) would be given as
Another example which occurs widely in practice is that of frequency referred to 1 Hz. A bandwidth of 36 MHz is equivalent to
Apart from voltage and current, all decibel-like quantities are taken as 10 log ( ). In this book, brackets are used to denote decibel quantities, using the basic power definition. A ratio X in decibels is thus
The 3-bar symbol indicates an identity. The abbreviation dB is used, with letters added where convenient to signify the reference. For example, a bandwidth b = 3 kHz expressed in decibels is
In many cases the reference unit is understood and is not shown explicitly. For example, the temperature of 290 K in decilogs may appear as:
A quantity which occurs frequently in link-budget calculations is Boltzmann s constant, which has the dimensions of J/K:
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