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Easier way to convert dB from one reference/unit to another

 I had a request from a customer wanting convert velocity data taken with units of dB (reference to 1 nm/s) to dB (reference to 1 micro inch/s).

The "hard" way to do this conversion would be:

  1. Convert dB (reference to 1 nm/s) to linear units of nm/s)
  2. Convert units of nm/s to micro inch/s (aka microns/s). There are 0.03937 micro inch/s per nm/s
  3. Convert linear units of micro inch/s to dB (reference to 1 micro inch/s )

The "easy" way is to take 20*log(0.03937 micro inch/s / nm/s) to get the dB to dB conversion of -28.1.

Add -28.1 to any dB (reference to 1 nm/s) to get dB (reference to 1 micro inch/s).

Other common dB relationships are:
  • Add 2.22 dB (20* Log (0.7746/1) to go from dBV to dBVu
  • Subtract 2.22 dB to go from dBu to dBV
  • Add 3 db (20*Log (sqrt(2)) to go from RMS to Peak dB
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