Many of us have heard about decibel unit in our daily lives, as it can be used to describe the loudness of our speakers, the strength of our antennas, or the signal strength from a transceiver. But what exactly are decibels (dB) and dBm? In this discussion, let’s explore these concepts and expand our understanding.

Explanation

Deci-bel is ten time of a Bel (10 x Bel)
Bel is named after an inventor Alexander Graham Bell, in Bell Lab.
It is an unit of a ratio on base 10 logarithm scale
Bel is defined as \(X = \log\frac{P2}{P1}\)

• P1: Reference Power
• P2: Measured Power

Now we have \(Decibel = 10 Bel = 10\log\frac{P2}{P1}\)

So what is the difference between dB and dBm?

dBm stands for decibel in miliwat. That means, our Reference Power will be 1 mW

\[Y = 10 \log\frac{P2}{P1} = 10 \log\frac{P2}{1 mW}\]

We can find Y by raise them to the power of 10

\[10^{\frac{Y}{10}} = 10^{\log\frac{P2}{1 mW}} => P2 = 10^{\frac{Y}{10}} 1 mW\]

So in communication, we usually use dBm because we know the reference power which is 1 mW.

Notice:
Sometime, you will see SNR = 20log10(RMS(signal)/RMS(noise))
So why do we have 20 here instead of 10?

• As I understand, RMS is an amplitude value, and in this case we want to see the ratio in power.
• Because power proportional to amplitude square so if we square both (RMS(signal)/RMS(noise)) we will get 20

In Summary:

dB, decibel is any ratio in term of base-10-logarithm, dimensionless unit.
dBm, decibel-milliwatt is any ratio with 1 mW as a reference power, dimensioned unit.