Decibel (dB)

Decibel is the logarithm unit used to describe a ratio. The ratio may be power, voltage sound or several other things. The decibel is also commonly used as a measure of gain or attenuation. It is dimensionless number.

Mathematically,

                Power ratio in dB             =             10 log₁₀ (P₂/P₁)   

Where P₁ and P₂ are the two power level to be compared.  If power level P₂ is higher then P₁ , the decibel is positive and vice versa. Since

                                P             =             V²/R

The voltage definition of decibel is given by

                Voltage ratio in dB           =             20 log₁₀ (V₂/V₁)   

The Decibel was originally named for Alexandra Graham Bell. The unit was used as a measure of attenuation in telephone cable, i.e. the ratio of the power of the signal emerging from one end of a cable to the power of the signal fed in at the other end. It so happened that one decibel almost equaled the attenuation of one mile of telephone cable.

The decibel is used for a wide variety of measurements in science and engineering, most prominently in acoustics, electronics, and control theory. In electronics, the gains of amplifiers, attenuation of signals, and signal to noise ratio are often expressed in decibels.

Decibel as absolute unit

Decibel can be used to express values of power. All that necessary is to establish some absolute unit of power as a reference. The often used reference units are 1mW and 1W. If 1mW is used as a reference, dBm is expressed as decibel relative to 1mW

                                P(in dBm)            =             10 log P(in mW)

If 1W used as a reference, dBw is expressed as decibel relative to 1W. i.e.

                                P(in dBw)              =             10 log P(in W)

Difference between dBm and dBc

dBm :- It indicates the power measurement relative to 1 milliwatt. dBm is the relative difference to a fixed reference power of 1 mW.

dBc:- It indicates the power relative to the power of the main carrier frequency; typically used to describe spurs, noise, channel crosstalk, and intermodal signals which may interfere with the carrier. dBc is the relative difference to an arbitrary reference power level, the power level of the carrier frequency.