# The Importance of Decibels in Electronics

Engineers use decibels everywhere for calculating power levels, voltage levels, reflection coefficients, noise figures, field strengths, and more. Most instruments use it, whether they are signal generators, spectrum analyzers, test receivers, power meters, network analyzers, or audio analyzers. Despite this, decibels remain a mystery to most people, sometimes including experienced engineers.

Engineers deal with numbers in all their professional activities, with some numbers being very large or very small. However, most of the time, rather than the numbers themselves, it is the ratio of two quantities that is more important. For instance, the base station of a mobile radio system many be transmitting 80 W of power, of which only 2×10-8 W or 2.5×10-8 percent reaches a mobile phone.

For dealing with very large or very small numerical figures, it becomes easier to use the logarithm of the numbers instead. For instance, the above base station transmits at +49 dBm, while the signal strength reaching the mobile phone is at -57 dBm. This makes the level difference between the two 106 dBm.

The main advantage in expressing ratios in decibels is they become far easier to manipulate. Adding and subtracting decibel values needs a much lower mental effort than to multiply or divide linear values.

Although a ratio cannot have dimensions, engineers use units of Bel to honor the inventor of the telephone, Alexander Graham Bell. The use of decibel makes the numbers more manageable, with decibel being one tenth of the Bel. Just as we multiply meters with 1000 to convert them to millimeters, we need to multiply Bel values by 10 to convert them to decibels. Therefore, dB represents ten times the ratio of two power values expressed as a logarithm to the base 10.

Since the decibel is a ratio, engineers must express arbitrary power levels with reference to a fixed quantity, as this allows proper comparison of the power levels. Telecommunication and radio frequency engineers most commonly use the reference quantity as the power of 1 mW into a 50-Ohm load. That is how in our example above, expressing 80 W of power in dBm becomes 10 x log (80/0.001) = 49 dBm. Although earlier, some engineers used the natural logarithm with a base of e, nowadays, engineers use the base 10 logarithm almost exclusively for calculating dBm.

Although the concept of decibels involves the ratio between two power levels, this can be easily converted to a ratio between two voltage levels, since the knowledge of power and resistance helps in finding the voltage across the resistance.

Apart from dBm, engineers use other reference quantities such as 1 W, 1 V, 1 µV, 1 A or 1 µA as well. In these cases, they express the dB quantities as dBW, dBV, dBµV, dBA, and dBµA. Similarly, for field strength measurements, these become dBW/m2, dBV/m, dBA/m and dBµA/m.

Engineers obtain absolute values when expressing power level ratios using the reference values above. Therefore, they call these absolute values as levels. For instance, a level of 10 dBm represents a value 10 dB above 1 mW, while a level of -20 dBµV represents a value 20 dB below 1 µV.