Circuit Design – Is kTC Noise in an RC Filter Dependent on Bandwidth?

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An RC filter has intrinsic noise called the kTC noise which is given by the equation
v_\text{noise} = \sqrt{\frac{kT}{C}}.
Does this equation calculate a noise density with units of volts per root hertz? Or does this equation calculate an RMS noise voltage that is not bandwidth dependent?

Best Answer

the ktC noise formula simply happens when you insert the noise bandwidth of an RC filter, B=1/(4RC), into the formula for voltage square over a resistor. The R cancels out.

So, no, there's correctly no bandwidth in that formula, because the bandwidth is "hidden" in the C.

The wikipedia article on Johnson-Nyquist Noise actually containst this explanation, and a lot more stuff that you might want to know about kTC noise, considering you seem to be coming at this from a non-intuitive, formularistic side. It's usually easier to understand what's happening than to have all the right formulas exactly right :)