Why hasn't the impedance taken into consideration in Thermal Noise?

Answer 1

It hasn't? That would be new to me. Thermal noise voltage is proportional to the square root of the real part of the impedance, current noise is inverse proportional to the square root of the real part of the impedance.

If you are developing low noise amplifiers, what you do all day long is to balance noise voltages and noise currents on ideally chosen impedances. If you get the impedance wrong in a critical part of your circuit, your amplifier will be noisy as hell.

Impedance absolutely matters... they will even show you a noise plot over source impedance in most opamp data sheets to simplify your life.

Answer 2

I think you may be getting a bit confused. As jludvig said, the voltage noise is proportional to the square root of real part of the impedance and the current noise is proportional to the inverse of the square root of the real part of the impedance. But the key term is 'the real part' of the impedance. Since reactances neither use power nor generate noise power, they're usually -not- mentioned on data sheets, noise equations, etc. So the noise equations you'll see are related -only- to the resistive part of the total impedance.

Doug