Noise – Does a Battery Powered Resistor Have Johnson Noise?


The mean noise voltage for Johnson (Thermal) Noise is given by the formula:

\$ v_n = \sqrt{4kTR\Delta{f}} \$.

The bigger the resistance of a resistor or the higher the frequency of a voltage supply, the higher the thermal noise the resistor will have. Does the formula also indicate if the voltage is supplied by a battery (DC, or a voltage of 0Hz frequency), any noise you measured on the resistor cannot be due to thermal noise because:

\$ v_n = \sqrt{4kTR \cdot 0} = 0V \$ ?

The question should be – what is \$ \Delta f? \$

Best Answer

yes. Even a resistor with no power source will generate Johnson noise. This is thermal noise due to random movement of electrons in the resistor itself.

f in the formula is the bandwidth across which you wish to calculate the noise, it has nothing to do with the signal applied (or not) to the resistor.