Noise on the Scope — Output Noise

Synthetic scope — band-limited noise

100 kΩ @ 300 K · 10 Hz–100 kHz · e_n ≈ 40.7 nV/√Hz

Time window

Mean (this capture) — Wanders more on short windows

Pk-pk (this capture) — Short windows miss LF peaks

V_rms (this capture) — Settles toward spec on long windows

V_rms (spec) — 100 kΩ thermal · 10 Hz–100 kHz

Triggers 0 —

Fixed 20 µV/div vertical scale (8 divisions). Time base: 10 divisions across the window. Short captures cannot resolve low-frequency content — stats reflect the band visible in that window.

Try it: compare 100 µs vs 100 ms. Measured V_rms and pk-pk shift with window length; the spec (~12.9 µV) is the long-band integral, not one graticule snapshot.

The scope trace is random

Output noise on a regulator or reference looks like fuzz around a DC level. It is not a sine wave you can measure once and be done. Each trigger gives a different waveform even when the underlying physics did not change.

The average of the AC noise tends to 0 V.
Peak-to-peak on the graticule is a snapshot — not a spec number.
You cannot add noise like a DC offset; it is zero-mean and uncorrelated sample to sample.

Why 100 kΩ?

Johnson noise at 300 K: \(e_n = \sqrt{4kTR} \approx 40.7\,\text{nV}/\sqrt{\text{Hz}}\) for \(R = 100\,\text{k}\Omega\). Integrate over 10 Hz–100 kHz and you get \(V_\text{rms} \approx 12.9\,\mu\text{V}\) — the fixed readout above. Real parts (LDOs, op amps) use the same vocabulary with different curves; part 4 introduces noise spectral density plots.

10 second captures matter when the band includes very low frequency (0.1–10 Hz). For 10 Hz–100 kHz, a few milliseconds of trace already contains the fuzz you care about.