# DeciBel dB: Formulas Equations & Calculations

### The deciBel, dB is a logarithmic scale used for comparing two physical quantities especially in electronics. There are several easy to remember formulas that enable the values to be calculated

the decibel, db utilises a logarithmic scale based to compare two quantities. it is a convenient way of comparing two physical quantities like electrical power, intensity, or even current, or voltage.

the decibel uses the base ten logarithms, i.e. those commonly used within mathematics. by using a logarithmic scale, the decibel is able to compare quantities that may have vast ratios between them.

the abbreviation for a decibel is db - the capital "b" is used to denote the bel as the fundamental unit.

## DeciBel applications

typically the decibel, db is used for defining amplifier gains, component losses (e.g. attenuators, feeders, mixers, etc), as well as a host of other measurements such as noise figure, signal to noise ratio, and many others.

## How the deciBel arrived

since the beginning of telecommunications there has been the need to measure the levels of relative signal strengths so that loss and gain can be seen.

original telecommunications systems used the loss that occurred in a mile of standard cable at a frequency of 800hz.

however this was not a particularly satisfactory method of determining loss levels, or relative signal strengths and as radio and other electronics based applications started to need to use some form of standard unit for comparison, the bel was introduced in the 1920s. this gained its name from the scot, alexander graham bell who was originally credited with the invention of the telephone.

## DeciBel formula for power comparisons

${N}_{\mathrm{dB}}=10{\mathrm{log}}_{10}\left(\frac{{P}_{2}}{{P}_{1}}\right)$

Where:
Ndb is the ratio of the two power expressed in deciBels, dB
P2 is the output power level
P1 is the input power level

Use our deciBel power calculator

## DeciBel formulas for voltage & current

${N}_{\mathrm{dB}}=10{\mathrm{log}}_{10}\left(\frac{{V}_{2}^{2}}{{V}_{1}^{2}}\right)$

And this can be expressed more simply as

${N}_{\mathrm{dB}}=20{\mathrm{log}}_{10}\left(\frac{{V}_{2}}{{V}_{1}}\right)$

Where:
Ndb is the ratio of the two power expressed in deciBels, dB
V2 is the output voltage level

${N}_{\mathrm{dB}}=10{\mathrm{log}}_{10}\left(\frac{{I}_{2}^{2}}{{I}_{1}^{2}}\right)$

And this can be expressed more simply as

${N}_{\mathrm{dB}}=20{\mathrm{log}}_{10}\left(\frac{{I}_{2}}{{I}_{1}}\right)$

Where:
Ndb is the ratio of the two power expressed in deciBels, dB
I2 is the output current level
I1 is the input current level

## Voltage & current deciBel formulas for different impedances

as a decibel, db is a comparison of two power or intensity levels, when current and voltage are used, the impedances for the measurements must be the same, otherwise this needs to be incorporated into the equations.

${N}_{d}=20{\mathrm{log}}_{10}\left(\frac{{V}_{2}}{{V}_{1}}\right)+10{\mathrm{log}}_{10}\left(\frac{{Z}_{1}}{{Z}_{2}}\right)$

Where:
Ndb is the ratio of the two power expressed in deciBels, dB
V2 is the output voltage level
V1 is the input voltage level
Z2 is the output impedance
Z1 is the input impedance

## DeciBel abbreviations

the decibel is used in many areas from audio to radio frequency scenarios. in all of these it provides a very useful means of comparing two signals.

DeciBel abbreviation Meaning / usage
dBA "A" weighted sound pressure or sound intensity measurement.
dBc Level of a signal with reference to the carrier being measured - normally used for giving the levels of spurious emissions and noise
dBd Gain of an antenna with reference to a half wave dipole in free space
dBFS Level with reference to full scale reading
dBi Gain of an antenna with reference to an isotropic source, i.e. one that radiations equally in all directions.
dBm Power level with reference to 1 mW
dBV Level with reference to 1 volt
dBµV Level with reference to 1 microvolt
dBW Power level with reference to 1 watt

More Basic Concepts:
Voltage     Current     Resistance     Capacitance     Power     Transformers     RF noise     Decibel, dB     Q, quality factor