Part 3 · Output Noise
Uncorrelated sources add in power — not by adding Vrms on a napkin.
Independent Gaussian noise · 10 ms · v₁ v₂ sum naive pk-pk
Pk-pk trap — peaks don’t add either; specs use Vrms
Scope auto-scale follows the RSS total so large sources stay on-screen.
Read left → right: (1) Blue v₁ and magenta v₂ are independent. (2) Gold is the real sum — red dashed lines are naive pk-pk (this capture’s pk-pk of A plus pk-pk of B), usually way outside the sum. Green dotted = actual sum pk-pk this capture. (3) Histogram of the sum → σ tracks RSS, not naive A+B Vrms. Try 10 + 10 for a clear gap between red and the gold waveform.
Instantaneous voltages do add: \(v = v_1 + v_2\). For zero-mean uncorrelated noise, average the squares:
\[ \overline{v^2} = \overline{v_1^2} + \overline{v_2^2} + \overline{2 v_1 v_2} \]The cross term averages to zero when sources are uncorrelated. Then take the square root to get back to volts:
\[ V_\mathrm{rms} = \sqrt{\overline{v^2}} = \sqrt{V_{1,\mathrm{rms}}^2 + V_{2,\mathrm{rms}}^2} \]| Term | Accumulated mean square |
|---|---|
| \(\overline{v_1^2}\) | — |
| \(\overline{v_2^2}\) | — |
| \(\overline{2 v_1 v_2}\) | — |
| \(\overline{(v_1+v_2)^2}\) | — |
| \(\sqrt{\overline{(v_1+v_2)^2}}\) | — |
| RSS \(\sqrt{A^2+B^2}\) | — |
Spec: \(V_{1,\mathrm{rms}} =\) —, \(V_{2,\mathrm{rms}} =\) —. Correlated sources would keep a non-zero cross term — not covered here.
An LDO after a switcher, or two noise contributors in the same band, combine as root-sum-square — not a straight sum of scope pk-pk numbers or Vrms guesses.