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[Design of Analog CMOS Integrated Circuits by Behzad Razavi]

Can someone explain to me why the noise spectrum (S_X(f)) is measured in watts per hertz? There was no load resistance taken into account, so where does the Watts come from?

It would make sense to me for it to be in Vrms^2/Hz or Vrms/sqrt(Hz) but not Watts/Hz. Where does the watts come from?

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As we are talking about noise, the noise power of a resistor for instance is usually expressed as a power 4kTB, regardless of the resistance. Power is a fundamental 'degrees of freedom' thing, so the natural quantity to use. This is just carrying over that use.

Once you get to numerical calculations, you might find the resistance of the system is taken into account, and then you might find the power expressed as V2/R or I2R. And then the R might be mysteriously dropped, assumed, to leave you with V2.

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