Converting PSD to dB scale
A dB scale is simply a logarithmic scale.  Bels are base 10, and decibels are base $ 10^{1/10} $.  Because $log(a/b) = log(a) - log(b)$, a decibel scale converts ratios to intervals.  3 dB corresponds roughly to a factor of 2.  So, what you are really asking when you say looking for a dB value that is 3 dB down is equivalent to asking for where the raw value is half of the original raw value.  

Added:  The units of the raw values don't matter since you are taking a ratio.  Simply take $ dB = 10 \cdot \log( raw ) $ to convert to a dB scale.

One thing you have to be careful of when taking the log of PSD values is that the PSD may have a zero value which makes the log undefined, but can be thought of as negative infinity.

Hope this helps,

Ced