Analog Intuition

Scope + distribution — time base follows the band · auto V/div

100 kΩ @ 300 K · en ≈ 40.7 nV/√Hz · Johnson (flat PSD)

Pk-pk (this capture) — Lottery — changes every trigger
Mean (this capture) — Near 0 V for AC noise
σ (accumulated) — Stabilizes as triggers add samples
σ (band spec) — —
Triggers 0 Window · time/div

Vertical auto-scale follows band σ (shared on scope + histogram) so LF bands (~0.1 µV) aren’t a flat line on 20 µV/div. Blue bars = accumulated histogram; green curve = Gaussian at σ; purple lines = ±1σ, ±3σ, ±3.3σ. Each band line reads: ±nσ = voltage span = % of samples. Reset histogram clears the bell.

Why σ is the spec number

Pk-pk is not a spec number

Part 1 showed pk-pk jumping shot-to-shot. Datasheets quote integrated noise in Vrms — the standard deviation σ of the zero-mean Gaussian that models the fuzz.

For Gaussian noise, most samples fall in a bell curve. σ is stable once you have enough data; pk-pk depends on how lucky you were in one capture.

σ is Vrms for zero-mean noise

With mean ≈ 0, RMS and σ are the same number: \(V_\text{rms} = \sqrt{\frac{1}{N}\sum x_i^2} = \sigma\). That is what ADC dynamic range, headroom, and datasheet plots converge on.

Bandwidth is part of the answer

Flat Johnson noise: \(V_\text{rms} = e_n \sqrt{f_H - f_L}\). Widen the band → more noise power → larger σ. Part 4 will draw the nV/√Hz curve; here you only pick the integration limits.