Analog Intuition

Part 4 · Output Noise

Noise Spectral Density

The datasheet plot — and how ∫ NSD² df gives you the Vrms from part 2.

NSD: noise per √Hz

Noise spectral density \(e_n(f)\) is plotted in nV/√Hz (log–log on datasheets). It answers: “how much noise power lives near this frequency?”

To get integrated Vrms over a band \(f_L\) to \(f_H\):

  1. Square the density — power-like units (nV²/Hz).
  2. Integrate under the curve across the band (add power in each Hz slice).
  3. Take the square root — back to volts RMS, because the system still cares about voltage.
\[ V_{\mathrm{rms}} = \sqrt{\int_{f_L}^{f_H} e_n(f)^2 \, df} \]

Connect to the bell curve

Part 2’s σ and part 3’s RSS are the same story in the frequency domain: summing uncorrelated contributions in power, then √ for voltage. The shaded band on an NSD plot is literally that integral — which is why pk-pk on a log plot can mislead you about which part is noisier.

Capstone

The live Noise Band Explorer lets you drag \(f_L\) and \(f_H\), overlay parts, and compare integrated RMS — use it after this part.

Part 4 interactive (simple NSD curve + shaded ∫ band) ships alongside the capstone link.