Does the thermal noise voltage formula: \$ V_n=\sqrt{4kTBR} \$ apply even if the impedance is not matched, or is the noise power formula of \$N=kTB\$ the one that applies even if the impedance is not matched? (k=boltzmann const, T=temp, B=bandwidth.)

I'm confused if the thermal noise voltage formula was derived from matched impedance using the noise power formula or the other other way around: noise power formula was derived from matched impedance using noise voltage formula.

## Best Answer

Thermal noise voltage applies always. The series resistance of the voltage source is R.

The power depends on the impedance you connect.