Noise Spectral Density — Output Noise

Along the way

1
NSD is density. \(e_n(f)\) in nV/√Hz — noise power near each frequency.
2
Square → integrate → √. Purple band is \(\int e_n^2\,df\); σ is that Vrms.
3
Shape beats spot noise. Quiet floor + heavy 1/f can lose LF to a noisier clean floor.
4
Same band → scope. Time trace is band-limited to the purple region (Part 2’s idea).
5
Capstone: Noise Band Explorer for named parts and more overlays.

Try recipe LF duel, then Midband duel — ranking can flip.

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.

Try it: LF duel — quiet floor + heavy 1/f vs higher floor + clean LF. Then Midband duel with the same pair: who wins can flip.

Named parts and more overlays → Noise Band Explorer.

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.