I'm reading the datasheet of a DAC (see page 6), and the "Output Noise Spectral Density" has units V / Hz^(1/2).
The Wikipedia article on noise spectral density however states that the noise spectral density has unit Watt / Hz.
Those two units are not equivalent. Why is there a discrepancy in the units?
Answer
The \$\mathrm{W/Hz}\$ may be a bit confusing as it looks like it refers to a single frequency. But that's just the dimension, it actually refers to a bandwidth, which is also expressed in Hz: maximum frequency - minimum frequency. So it's the power over a given bandwidth.
If you divide power by the load's resistance you get voltage squared. So for a given load you can express noise power as
\$ \mathrm{\dfrac{V^2}{BW}}\$
where \$\mathrm{BW}\$ is bandwidth. If you want to know the voltage you take the square root:
\$ \mathrm{\sqrt{\dfrac{V^2}{BW}} = \dfrac{V}{\sqrt{BW}}}\$
which indeed has the dimension of \$\mathrm{V/\sqrt{Hz}}\$.
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