## Important things about the Decibel or dB

EMC engineers commonly use dB as a unit of noise measurement. Every engineer who uses the dB term must know and remember a few basic facts about dB. It is easy to misunderstand the term without these facts, which are assumed, but not mentioned. There are many such facts which together can make it difficult to understand the term. Here we describe these facts or assumptions and explain each.

First of all dB is one tenth of the unit used, called the Bel. Second, it is a unit of power, even when used to represent other units such as voltage or current, the ratio is always that for power. Third is that it is a comparison on a logarithmic scale, so we must take the log of the ratio of powers compared and then multiply by a factor of 10 because dB is one tenth of a Bel. Finally, we will explain the new units of voltage, current, field strength, etc. where the ratio comparison is with regards to some corresponding fixed physical unit such as volts, amps, volts/m etc.

### Definition:

Generally, dB refers to the log of a ratio of power of two quantities. As such, it is most commonly used for gain of an amplifier such as output power (Po) with reference to input power (Pi). So by definition,

Gain = A = 10 log (Po / Pi) dB …..…. Eqn. 1

It can also be used to represent an increase or decrease in noise levels. If you were actually using these for voltage comparison, the assumption is that the load impedance Z remains constant for input and output power, which are replaced by V2/Z, so

A = 10 log (V22/V12)

where V1 and V2 are any voltages being compared. Therefore,

A = 20 log (V2/V1)

since

log (X2) = 2 log (X)

In the EMC/EMI test and measurement field, dB is also used for current, E-field (electric field) or H-field (magnetic field) however, keep in mind the facts stated above. Since in each item mentioned above, the power is proportional to the square of the voltage, current, E-field or H-field, we must take the square of the item under consideration. The log of the square of a number is equal to twice the log of that number, in other words, 20 times the log for those physical quantities above, namely voltage, current etc. If you are calculating dB for power ratios, you would multiply by 10 as in Eqn. 1.

Such comparisons are just ratios of the quantities in consideration; therefore, they have no units such as voltage, current, etc., only dB. Then what is meant by terms like dB microvolt? In short, the ratio is with respect to microvolt as the reference (second quantity).

### Microvolts in dB:

When the units measured are with respect to a fixed quantity such as a microvolt, the ratio is referred to as dB microvolt. We may say that the reference unit for the ratio is microvolt. As an example let’s say we’re measuring 100 microvolts, given the log of 100 equals 2 it corresponds to

20 log (100 /1) = 20 x 2 = 40 dB microvolts

The reference voltage can be millivolt, volt or kilovolt etc. If we are referring to the E-field it could be microvolt/meter, or millivolts/meter or volts/meter etc. However most EMI testing specifications, CISPR for example, used for non-military testing applications such as information technology, multimedia equipment, medical devices and household appliances have applicable limits specified in dB microvolts/meter for E-field values and dB microvolts for voltage emissions. You may wonder: why in units of dB microvolts? It is because the values are so small, and it is easier to compare to microvolts. Later, below, we explain why in terms of dB?

The same concept applies to current or H-field measurements also. Let us consider 10 Amps current. This is equal to

20 log (10/1) = 20 x 1 = 20 dB A

and would equal

20 log (10,000,000/1) = 20 x7 = 140 dB micro Amps

So these units are used when measuring magnetic field emissions as in MIL-STD-461 or DO-160 requirements.