Question

Calculate the noise power and noise voltage generated by a 1M resistor at 37C

over a 1 MHz bandwidth.

Answer 1

The noise power is given by the following formula (see https://en.wikipedia.org/wiki/Johnson–Nyquist_noise):

$$P =k_BT\Delta f$$

where $k_B = 1.38\times 10^{-23}J/K$ is the Boltzmann's constant, $T = 37\degree C = 310K$ is the absolute temperature, and $\Delta f = 1\times 10^{6}Hz$ is the bandwidth. Thus, obtian:

$$P = 1.38\times 10^{-23}\cdot 310K\cdot 10^{6} = 4.28\times 10^{-15}W$$

The noise voltage is:

$$E = \sqrt{4Rk_BT\Delta f}$$

where $R = 1M\Omega = 10^{6}\Omega$ is the resistance. Thus, obtain:

$$E = \sqrt{4\cdot 10^6\cdot 1.38\times 10^{-23}\cdot 310\cdot 10^6} \approx 1.31\times 10^{-4}V$$

Answer. $4.28\times 10^{-15}W$ and $1.31\times 10^{-4}V$.