Aside it might be a good idea to register You are correct on two main issues a reference to power in the definition of decibel is misleading restrictive b the decibel is simply a mapping from a logarithmic to a linear scale However your calculations are incorrect since the logarithm is defined only for dimensionless quantities so log y Watts is meaningless Here is the problem with explaining the decibel satisfactorily any definition of the decibel based on its historical roots instead of mathematical good practice will remain troublesome A cleanup yields the following a Define B bel as a function such that x B for any positive number x Define d deci for any x by x d x 10 Define dB decibel by x dB x d B hence x dB Example 20 dB 100 Similarly x B and correspondingly dB example 20 dB 10 for purposes shown next b Define dBW by x dBW x dB W example 20 dBW 100 W and dBV by x dBV x dB V example 20 dBV 10 V Similarly x dBW x dB W and so on Done Insofar as a definition which is always a convention can be called correct the criterion is conceptual clarity plus convenience and safety in calculation You can verify that the definitions a and b also work out nicely and correctly for your examples