Converting PSD into equivalent sound pressure for an underwater hydrophone

[nauman]

Hi all

I have a underwater hydrophone with known receive sensitivity e.g. -190dB ref 1v/upa with a preamplifier having gain of 40dB at frequency e.g. 200Hz. I measure preamplifier output using spectrum analyzer and it gives PSD of around -80dBvrms/sqrtHz. I need to convert this PSD value into equivalent underwater sound pressure level with unit of dB ref 1upa.
Any help is much appreciated.

 

[tech99]

The measurement is of a single frequency, so that Power Spectral Density is not the appropriate measurement. All you need to measure is voltage. PSD is used for measuring noise like signals.

 

[tech99]

If you are actually measuring a noise-like signal, then the electronics must respond to the full sound spectrum and you need to know what the total bandwidth is.

 

[DaveE]

If you have a narrow resolution bandwidth you can use that to convert the spectral density into a voltage. You can assume the psd is flat and just multiply by the measurement BW squared sqrt(BW). Of course the BW measured may only be part of the time domain signal.

For a more complex situation, it's like doing an inverse Fourier transform. It can't really be done without the phase information the spectrum analyzer threw out, but you could do the integral to get an estimate.

https://www.ti.com/content/dam/videos/external-videos/en-us/1/3816841626001/4078827152001.mp4/subassets/opamps-noise-calculating-root-mean-squared-noise-presentation-quiz.pdf#:~:text=To convert voltage spectral density to RMS,,to convert back to voltage or current.

edit: Oops! it's $\sqrt{BW}$ not $BW^2$. Duh!, sorry