# Resistor Nyquist-Johnson noise formula question

1. May 2, 2010

### telegraphic

Hi all -- I had a question about the Nyquist-Johnson noise formula:

$$E_{\nu}^{2}d\nu=\frac{4R_{\nu}hd\nu}{e^{h\nu/kT}-1}$$

which of course can be approximated for most purposes as $E_{\nu}^{2}d\nu=4R_{\nu}kTd\nu$.

I'm just wondering why the formula has $exp(h\nu/kT)-1$ in the denominator? I would have expected $exp(h\nu/kT)+1$ as electrons are fermions, so obey Fermi-Dirac statistics as opposed to Bose-Einstein. Sure I'm missing something obvious!

Cheers