Wireless Optical Telecommunications

Appendix 2

The Decibel Unit (dB)

The decibel (dB) is one tenth of the Bel unit, defined in honor of Alexander Graham Bell. It is a logarithmic unit of measurement of the ratio of two powers, voltages, currents, pressures, etc. It is particularly used in the fields of acoustics, physics and electronics, etc.

This unit of measurement (dB) is defined by the logarithmic ratio:

– of potential (V) or current (I):

– 20log ( V_output / V_input)

20log (I_output/I_input)

– of power (P):

–10log (P_output/P_input)

If the result is positive, this is a case of amplification. If the result is negative, this is a case of attenuation.

NOTE:— The term “log” refers here to the base 10 logarithm.

There are different dB variants: dBm, dBW (dB watt), dBi, dBd, dBc, dBµV (dB microvolt), dBµVm¹ (dB microvolt/m):

– dB: −10log₁₀(P_output/P_input).

– dBm: −10log₁₀(P_output/1mW).

– dBW: −10log₁₀(P_output/1W) .

– dBi: the antenna’s gain versus the gain for an isotropic antenna. An isotropic antenna is an antenna that emits the same amount of energy in all directions. Such an antenna does not exist in reality.

– dBd: the antenna’s gain versus the gain for a half-wave dipole antenna. This antenna has a physical reality.

Note that catalogs often do not specify whether we are dealing with dBi or dBd. Yet, the difference is important. A 10 dBd antenna gain is a 12.15 dBi antenna gain. We see that the temptation is great to display dBi rather than dBd without explaining it.

– dBc: −10log₁₀(P_output/P_c). Here, an output ...