Part 2 · Output Noise
The waveform is a random draw; the bell curve is the physics.
100 kΩ @ 300 K · en ≈ 40.7 nV/√Hz · Johnson (flat PSD)
0.1 Hz – 10 Hz: uses a 1 s capture (100 ms/div) so you can see slow noise structure. The window still cannot resolve true 0.1 Hz (need ~10 s); σ (band spec) remains the full-band integral.
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.
Try it: hit Trigger several times — the scope trace redraws but the bell barely moves. Then switch the integration band: trace and σ both change. Vrms is always “over a band,” not one scope grab.
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.
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.
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.