Noise on the Scope

Part 1 · Output Noise

Key point: one scope shot is a lottery. The spec for this 100 kΩ example is 12.9 µV, integrated from 10 Hz to 100 kHz.

Fixed 20 µV/div. 100 kΩ at 300 K, about 40.7 nV/√Hz.

1
One capture, 5 ms.
Window is 5 ms, 500 µs/div. Spec Vrms is 12.9 µV. Mean sits near 0. Pk-pk is whatever this draw got.
2
Trigger again.
Same 5 ms window. The fuzz redraws. Spec is still 12.9 µV. The resistor did not change. The trace did.
3
100 µs misses the bottom of the band.
This window only sees 10 kHz–100 kHz, about 12.2 µV in that slice. 10 µs/div. The spec readout stays 12.9 µV.
4
100 ms covers the spec band.
Window band is 10 Hz–100 kHz. 10 ms/div. Measured Vrms can sit on the 12.9 µV spec. Pk-pk still jumps from shot to shot.
5
The spec does not follow the window.
Back to 100 µs. Spec readout is still 12.9 µV. This window’s band is 10 kHz–100 kHz again. Do not write the graticule pk-pk into a datasheet.

Part 2 is the bell curve. σ is the stable number behind this fuzz.

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.

Why the spec is 12.9 µV

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.