How to convert amplitude (V) to dB (V^2/Hz or V/sqrt(Hz) or V?)

Question

I took the FFT of a signal and am currently plotting amplitude (V) vs. frequency (Hz). I'd like to change the Y-Axis units to dB. How would I go about doing this? What would be the units?

It is from my understanding that:

dB = 10log10(power/reference_power)

= 20log10(voltage/reference_voltage)

= 20log10(amplitude/reference_amplitude) (units of amplitude is volts)

= 20log10(amplitude) (reference amplitude can be thought of as 1 Volt)

Is this the correct way to convert from amplitude to dB? Also, wouldn't this make the units be "dB (V)"?

Thanks!

Answer 1

Is this the correct way to convert from amplitude to dB? Also, wouldn't this make the units be "dB (V)"?

Yes, that's correct. Note that a reference voltage of 0.7746 is also used in the audio world and is denoted "dBu".

Some examples:

$$ \begin{align} \text{"in dBV"} &= 20\log\left(\frac{V_{in}}{1\text{V}}\right) \\ \text{"in dBu"} &= 20\log\left(\frac{V_{in}}{0.775\text{V}}\right) \\ \text{"in dBV"} - \text{"in dBu"} &= -20 \log \left( \frac{1}{0.775} \right) \\ \text{"in dBV"} &= \text{"in dBu"} - 2.214 \\ \end{align} $$