There are innumerable sites on the web (a Google search will cough up plenty) which will tell you how to work out things in decibels. Iím not going to do that.
What I want to do is emphasise two points.
Firstly, decibel notation tells us how much bigger than, or how much smaller than, one quantity is when compared with another.
Not how big or how small, just how much bigger or how much smaller.
Itís not an absolute measurement, itís a relative one.
Unless it has a subscript such as W, V or m for example, i.e. dBW (decibels greater than 1 watt), -dBV (decibels less than 1 volt) and dBm (decibels greater than 1 milliwatt.)
Secondly, unless the measurements are made at the same point in a circuit or system, e.g. increase or decrease in signal level at an output, rather than comparing the level of two signals at different points, e.g. at an input and output, the measurements MUST be made in, or across, the same value of impedance in order not to invalidate the use of decibel notation.
The input to an amplifier is 10mV. The output from it is 1V. What is its gain ?
If you are tempted to work it out in dB, go ahead.
Now consider this.
The input impedance of the amplifier is 10 kilohms. Its output is terminated (loaded if you like) in 600 ohms.
Calculate the power at the input and that at the output. Using the figures you obtain work out the gain, in dB, again.
Both answers can't be correct.
Let's change the input impedance to 600 ohms.
Calculate the power at the input again. Then, using the figure you previously obtained for power at the output, calculate the gain in dB again.