Noise is a bandwidth-dependent error budget

Random variation differs from a DC offset

Noise varies with time; offset is a systematic shift in the average. They require different measurements and remedies. For a white-noise voltage density en in V/√Hz and an ideal rectangular noise bandwidth B, RMS noise is $e_n\sqrt{B}$. Real filters have an equivalent noise bandwidth, which need not equal the −3 dB signal bandwidth. A one-pole low-pass has white-noise bandwidth π/2 times its corner frequency.

An ideal resistor at absolute temperature T has thermal voltage-noise density $\sqrt{4kTR}$, using Boltzmann constant k = 1.380649 × 10⁻²³ J/K. At T = 300 K and R = 10 kΩ, this is 12.8716 nV/√Hz. Over a specified rectangular 100 Hz bandwidth, RMS is 128.716 nV. Through an ideal gain of 11, that becomes 1.41588 μV RMS at the output.

Combine independent sources correctly

If two independent input-referred RMS noise contributions are 2 μV and 3 μV, total is $\sqrt{2^2+3^2}=3.605551$ μV, rather than 5 μV. Correlated noise requires cross terms and cannot use this shortcut. An op amp also has current-noise density; flowing through source impedance it creates voltage noise. Therefore the lowest voltage-noise part is not automatically best for a high-impedance sensor.

For an assumed 1 pA/√Hz current-noise density and 100 kΩ resistive source, the equivalent voltage density is 100 nV/√Hz. That can exceed the amplifier's voltage-noise term. At low frequency, flicker noise and drift may dominate, so a white-noise-only estimate must state its frequency range.

Measure without creating a new problem

Specify gain, bandwidth, averaging, and whether the result is input- or output-referred. Check for 50/60 Hz pickup, supply coupling, and grounding before labeling every unwanted signal “device noise.” Repeat measurement with the signal source replaced by a representative impedance, rather than an unrealistic short that erases current-noise effects. ADI MT-047 explains the source-impedance dependence and resistor-noise model.