Resistor Noise

Quick Answer

Every resistance generates a noise voltage from the thermal motion of its charge carriers, called Johnson noise. It grows with resistance, absolute temperature and measurement bandwidth, and with nothing else, so construction cannot lower it. What construction decides is the excess noise a part adds when direct current flows.

The floor comes straight out of thermodynamics, and the expression for it holds no term for what the element is made of:

A metal film part and a carbon composition part of the same value in the same room produce the same figure. It goes as the square root of resistance, so dropping a source impedance by a factor of a hundred buys a factor of ten, and as the square root of bandwidth, so a measurement that does not need to be fast should not be. Noise in circuits treats the floor properly.

Excess noise sits on top of that floor and is the part a datasheet can differ on. It appears only while direct current passes through the element, it climbs as the frequency falls instead of staying flat, and it is worst in granular elements where the current has to cross countless small contacts. Carbon composition is the noisiest, thick film is better, thin film and wirewound better again — construction is the whole story here.

The design consequence is that low-noise front ends keep source resistances down, because no amplifier afterwards can subtract noise that was already present at its input. A smaller resistor value is often the cheapest noise improvement available, up to the point where the extra current it draws costs more than the noise it saved.