« EPIC Workshop on Photonic Integrated Circuits, St. Florian am Inn, Austria | Metro 100G - is it really plug-and-pray? » |

## DeciBel – an Introduction

In electrical and communication engineering, quantities such as power levels, voltages, currents, and so on are commonly described in decibel.

DeciBel itself is unit-less as it expresses the logarithm of the ratio between two values of same dimension.

When the ratio is taken with an explicitly specified reference level, a quantity in decibels can express an absolute magnitude. Example: dBW and dBm, represents absolute power level, where the power is expressed relative to 1W and 1mW, respectively.

Generally gains and losses (attenuation, insertion loss) in communications systems are expressed in decibel units rather than in linear units. The reason behind is via logarithm large and small number can be easily expressed and conveniently compared due to its simple properties. Performing large number multiplication and division in linear scale corresponds to simple addition and subtraction in logarithmic scale. For example, doubling the power level corresponds to 3-dB addition. Power of +30dBm corresponds to 1W.

Therefore a transceiver launch power of +27 dBm can be easily calculated as 3dB (in linear reduction of half) decrease wrt 1W, i.e. 0.5 W. To calculate a power in dBW from dBm, one should subtract 30dB from dBm value or dBm = dBW + 30dB.

One must take care not to add two powers in logarithm which correspond to W2 in linear scale, i.e., invalid unit. Division (or ratio-> gain or loss) in linear scale is equivalent to subtraction of two powers (dBm or dBW) in logarithmic scale and measured in dB. One can add or subtract ratios (dB) to power (dBW or dBm) which still results in power (dBW or dBm).

Some quantities that you might have encountered recently: **dB** - power budget, fiber attenuation, amplifier gain, insertion loss, performance penalty, link margin **dBm** - transceiver receiver sensitivity, transceiver transmit power, laser power.