power - Types of decibels

Why we use dBA or any other type of decibel unit instead of basic decibels unit (dB)? Why we have so many types of this unit?

Answer

Decibels are a nice way to measure things which come in a very wide dynamic range as it is a logarithmic measurement.

At a certain amount of zeros it just gets hard to understand what's going on and decibels help greatly. Someone telling you a signal is 10000000000 more powerful is just harder to grasp then a number of 100dB.

But as Olin already said, a decibel is not a unit as it is, it is a ratio. But a ratio is often only useful when you know which was the reference given.

So when you talk about 100dB more power - it still makes some orders of magnitude of a difference if the reference was 1mW, 1W or 1µW.

dBA was specifically designed for sound or noise measurement. dBA has a frequency dependent weighting behind it, so not all frequencies are considered to have the same strength or effect on the ear. The usefulness of dBA is quite debated, but that is covered quite well on Wikipedia.

Then there is also the difference between field quantities and power quantities. A value of 100dBV is different to a value of 100dBW. The factor to the reference is different:

For power quantities: $$L_P = 10 \log_{10}\!\left(\frac{P}{P_0}\right)\!~\mathrm{dB}$$

For field quantities: $$L_F = 20 \log_{10} \left(\frac{F}{F_0}\right)\!~\mathrm{dB}$$

So 100dBV turns out to be a factor of 10^5 = 100 000 to 1V. Whereas 100dBW is a factor of 10^10 = 10 000 000 000 to 1W.

So giving the reference is quite critical to handle the ratios correctly.