Rectifier Ripple Factor⚠ unverified
Electrical / Power · Compute the ripple factor of a rectified output
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| V_rms | Vrms | V | 1.0 | RMS value of the output voltage |
| V_dc | Vdc | V | 1.0 | Average (DC) value of the output voltage |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | ripple | — | Ripple factor as a dimensionless ratio. Returns 0.0 if ``V_dc`` is not positive |
The science & history
Understanding the Parameters
- $V_{rms}$ — the true RMS of the whole (pulsating) waveform.
- $V_{dc}$ — its average/DC component (see Rectifier Average Voltage).
- $r$ — 0 would be perfect DC; full‑wave rectified sine is $\approx 0.48$ before filtering, dropping far below with a smoothing capacitor.
Derivation (Approaching a Proof)
Any periodic waveform splits into a DC part plus a zero‑mean AC (ripple) part, and their powers add:
$$V_{rms}^2 = V_{dc}^2 + V_{ac,rms}^2 \;\Rightarrow\; V_{ac,rms} = \sqrt{V_{rms}^2 - V_{dc}^2}.$$
The ripple factor is defined as the ratio of the ripple RMS to the DC value:
$$r = \frac{V_{ac,rms}}{V_{dc}} = \frac{\sqrt{V_{rms}^2 - V_{dc}^2}}{V_{dc}} = \sqrt{\left(\frac{V_{rms}}{V_{dc}}\right)^2 - 1}.$$
The identity $V_{rms}^2 = V_{dc}^2 + V_{ac,rms}^2$ is the same orthogonal (Parseval) decomposition that underlies Total Harmonic Distortion — DC and each AC component contribute independently to the total mean‑square.
History
Ripple factor became a standard supply‑quality metric with the first vacuum‑tube power supplies, driving the development of LC and capacitor‑input smoothing filters — and later active regulation — to feed clean DC to sensitive electronics.
Related Concepts: Rectifier Average Voltage, Total Harmonic Distortion, Apparent Power
Notes: Registry calculator rectifier-ripple-factor (unverified). Depends on the rectifier topology
and any filtering; the raw full‑wave value ($\approx0.48$) drops sharply once smoothed.