What is Electrical and Thermal Noise with Regards to Resistors?

Resistors are dissipative elements and as such even ideal resistors will naturally produce a fluctuating noise voltage across its terminals. When using resistors in precision applications it is frequently required to minimize electronic noise. This noise known as Johnson–Nyquist noise is a fundamental noise source which depends only upon the resistance and temperature of the resistor. Johnson–Nyquist noise is predicted by the fluctuation dissipation theorem. For instance, the gain in a simple non-inverting op-amp is set with a voltage divider. For the consideration of noise the smallest practical resistance ought to be used. Since the Johnson–Nyquist noise voltage scales with resistance, and any resistor noise in the voltage divider will be impressed upon the amplifier's output.

Additionally, small differential voltages can appear on the resistors owing to the thermoelectric effect if their ends are not kept at the same temperature.

Resistors frequently demonstrate other, non fundamental, sources of noise typically known as excess noise. This excess noise results in a noise index for a given type of resistor. Excess Noise is cause by current flow in the resistor; it is specified as µV/V/decade. Broken down this means µV of noise per volt applied across the resistor per decade of frequency. The µV/V/decade value is regularly given in the form of dBs. So, a resistor with a noise index of 0 dB will exhibit 1 µV root mean square (RMS) of excess noise for each volt across the resistor in each frequency decade.

Excess noise is an example of 1/f noise. 1/f noise is a process or signal with a frequency spectrum where the power spectral density (PSD) is inversely proportional to the frequency.

Carbon composition and thick film resistors generate more noise than other types of resistors at low frequencies; thin film and wire wound resistors, despite being more expensive, are frequently utilized for their superior noise characteristics.

Surface mount thin film resistors usually have better thermal stability and lower noise than surface mount thick film resistors. Though, designers would likely need to read the resistor's data sheets to weigh the various tradeoffs.