Noise Spectral Density

Part 4 · Output Noise

Key point: en(f) is nV/√Hz. The rms you quote is √∫ en² df over the band you actually use.

Two curves, one purple band. σ_A and σ_B are that integral.

1
LF duel, 0.1–10 Hz.
Quiet floor · heavy 1/f is 67.9 nV. Higher floor · clean LF is 39.7 nV. The quiet floor loses.
2
Same curves, midband.
10 Hz–100 kHz. Quiet floor is 321.9 nV. Clean LF is 2.53 µV. The ranking flips.
3
The bump is not the integral.
1 kHz–100 kHz. Flat white is 6.29 µV. Midband peaking is 2.07 µV. You can see the bump. White is still worse.
4
Where the HF rise lives.
10 kHz–1 MHz. Ultra-clean LF is 4.97 µV. HF rise is 5.38 µV. The climb is inside this band.
5
Same curves, below the climb.
10 Hz–10 kHz. Ultra-clean LF is 499.7 nV. HF rise is 200.9 nV. The climb is outside this band, so HF rise wins.

Named parts and more overlays are in the Noise Band Explorer, linked under the lab.

NSD lab — archetypes, not part numbers

Parametric \(e_n(f)\): floor · 1/f · peaking · HF rise · max 2 overlays

Curve A Curve B

10 Hz – 100 kHz

σ_A (band) — —

σ_B (band) — —

Integration band — Purple shade on plot

Scope A (band-limited)

Hist A

Scope B (band-limited)

Hist B

Drag either edge of the purple band (or use presets). σ updates from \(\sqrt{\int e_n^2\,df}\). Scope traces are synthesized in that band only — heavy 1/f looks slower than flat white at the same RMS. Scopes A and B share one µV/div so amplitudes compare fairly; each has its own histogram.

Named parts and more overlays → Noise Band Explorer.

Why the shape beats a spot-noise number

NSD: noise per √Hz

Noise spectral density \(e_n(f)\) is plotted in nV/√Hz (log–log). Integrated Vrms over a band:

\[ V_{\mathrm{rms}} = \sqrt{\int_{f_L}^{f_H} e_n(f)^2 \, df} \]

Square → integrate (add power) → square root (back to volts). Same power-add idea as RSS in Part 3.

Why archetypes, not part numbers

Spot noise (nV/√Hz at 1 kHz or 10 kHz) does not decide a low-frequency integral. A device with a lower floor but a high 1/f corner can lose 0.1–10 Hz to a “noisier” device with almost no flicker. Peaking and HF rise flip rankings again when you widen the band. This lab freezes that geometry without datasheet brand noise.