Power and decibels

Question

In one of the examples in a engineering textbook, I noticed that the decibel value for the Power of a transmitter (also known as modulator) was 20DB and this was said to be equivalent to 100W.

However, I thought the formula for such conversions was 20DB = 10 log (Power ratio)

For this case what would be the fraction corresponding to the power ratio (the system consists of a modulator and a demodulator, where we are given decibel value for the power of the modulator....)?

Furthermore, it seems to me that since we don't know the power value of any other point, the only way to get to the answer of 100W for the power of the transmitter is by assuming that 20DB is actually 20DBW (decibel watts). This makes the assumption that the power ratio is Power of transmitter / 1W. However, the units used in the example are DB not DBW so I am not sure if my musings are correct.

Please help/clarify

Answer 1

The only thing you got wrong is the capitalization of "dB" and "dBW". The "d" is lower case because it represnts "deci-", the SI prefix for 1/10. Meaning that a decibel is 1/10 of a bel, a unit which is almost never used in practice.

Everything else you wrote is correct. 20 dBW = 100 W. "20 dB" tells you nothing about the power until you know the reference level.