All I Know About Decibel (dB) - Part 1

Most people know that dB (decibel) is a unit, you use it when you want to tell the level of a sound. People could say, the sound of a jet engine can hit up to 140 dB; or the sound level of a normal human talking is about 60~70 dB, etc.

If I explained dB like above to my boss, I would definitely be doomed.

To avoid the embarrassing conversation, I quickly did some learning. I learnt that:

1. dB is actually a ratio
2. Because it's a ratio, there must be two things to make a fraction
3. The ratio tells us the difference between the two things
4. We use a logarithmic way to describe that ratio

If we still take the case of sound loudness, for instance, say the two things are two sounds:

• The first sound is played with the power of $p_1$
• The second sound is played with the power of $p_2$

So we can get the dB like this:

$$l = 10 \times log \frac{p_1}{p_2} (dB)$$

where the $log$ is to base $10$

Now we can say that comparing to the second sound, the first sound is $l$ dB. Note it always should be

comparing to another value, this one is some dB

If we only say some sound is some dB, it doesn't really make sense. So that's right, when people say the sound level of a jet engine is 140 dB, they actually mean

comparing to another value, the sound level of a jet engine is 140 dB

Even though they usually don't know that. And that another value, which we call it the reference, is normally a very small sound pressure level, like 20 micropascals ( $20 \mu Pa$ ).

Some dB units

Now it's easier to explain some 'dB units' we see. They actually just have different references.

For example: dBm. It uses 1 milliwatt (1 mW) as the reference:

$$10 \times log \frac{P}{1 mW} (dBm)$$

So we can say P is 10 dBm, or P is -30 dBm... It's gonna be an absolute value, no need to mention "when compared to some value (the reference), P is blah blah blah..." anymore.

The following units are also common:

• dBμ - reference is 1 microwatt (1 μW)
• dBmV - reference is 1 millivolt (1 mV)
• dBi - reference is an isotropic antenna which has a gain of 0 dB in a specific direction
• dBFS - reference is the full scale - More details on Wikipedia

Now this answer could make my boss happy for the day, or even for the week, if I was lucky enough. That's why I have to have Part 2 here.

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from: OZLab