Thermal, shot, and flicker noise

Throughout this module, a one-sided power spectral density is defined for nonnegative frequency f in hertz and integrates over that domain to give variance. Voltage PSD has units V²/Hz; its square root is an amplitude spectral density in V/√Hz. For a classical resistor in thermal equilibrium, the open-circuit voltage PSD is four kBTR. This approximation requires the frequencies to be low enough that the classical thermal limit applies and the resistance is approximately real and constant.

For statistically independent Poisson charge arrivals with elementary charge magnitude e and mean current magnitude I, the one-sided current PSD is two eI. A transimpedance converts current noise into voltage noise through its magnitude squared. The Poisson assumption is essential: correlations, gain statistics, or charge partitioning can modify the result. The external net bias current of a compensated amplifier is therefore not universally sufficient to predict its internal current noise.

An amplifier can add both an input voltage-noise source and current-noise sources. The latter create voltages across the impedances they encounter. A low voltage-noise part can consequently perform poorly with a high-impedance sensor. Noise from gain-setting resistors and subsequent stages must also be propagated. Referring every contribution to a common input or output makes the comparison meaningful and prevents a small current number from being compared directly with a voltage number.

Uncorrelated zero-mean contributions add in variance, giving a root-sum-square amplitude. Correlated fluctuations require covariance or cross-spectral terms instead. Ordinary signal gain amplifies an already present input signal and its input noise together, so it does not improve their ratio by itself. It can still make downstream noise less important when referred back to the sensor, provided the chain remains linear and does not overload.

White noise often permits an average to improve as the inverse square root of the number of independent measurements. Flicker noise carries long correlations and does not generally satisfy that independence model. Extending a measurement toward lower frequencies can admit additional slow fluctuations. A measured drift may also be nonstationary, in which case a stationary PSD model over an arbitrarily long record is itself questionable.

A noise statement should therefore include its measurement duration or low-frequency limit, high-frequency filtering, temperature, source impedance, and whether the number is RMS or peak to peak. There is no duration-independent universal conversion from Gaussian RMS noise to a strict maximum excursion. Modulation can move a desired signal away from a low-frequency noise region, but it does not remove noise already present around the modulation frequency. These distinctions guide practical changes to the experiment rather than just changes to a numerical noise label.