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After rectification the output is DC with an AC "ripple" riding on top. Two dimensionless numbers describe its quality. The form factor (FF) is the ratio of the RMS value to the average value, FF = Vrms/Vdc. The ripple factor (RF) measures how much AC ripple remains relative to the DC: RF = Vac(rms)/Vdc = √(FF²−1). A perfect DC source has FF = 1 and RF = 0.
| Quantity | Formula |
|---|---|
| Form factor | FF = Vrms / Vdc |
| Ripple factor | RF = √(FF² − 1) |
| AC ripple (RMS) | Vac = √(Vrms² − Vdc²) |
| Rectification efficiency | η = (Vdc/Vrms)² = 1/FF² |
| Rectifier | Form factor | Ripple factor |
|---|---|---|
| 1φ Half-wave | 1.571 | 1.21 (121%) |
| 1φ Full-wave | 1.111 | 0.482 (48.2%) |
| 3φ Half-wave | 1.017 | 0.183 (18.3%) |
| 3φ Full-wave bridge | 1.0009 | 0.042 (4.2%) |
These three figures all describe the shape of a waveform rather than its size, and each answers a different question.
| Quantity | Definition | Half-wave | Full-wave |
|---|---|---|---|
| Form factor | Vrms / Vavg | 1.5708 | 1.1107 |
| Ripple factor | √(FF2 − 1) | 1.2114 | 0.4834 |
| Crest factor | Vpeak / Vrms | 1.4142 for a sine | |
The half-wave figures are exactly π/2 and the full-wave exactly π/(2√2), which is why these constants appear so often in rectifier analysis.
Ripple factor is the ratio of the AC component remaining in a rectified output to its DC component, so a perfect DC supply would have a ripple factor of zero. The jump from 1.21 to 0.48 between half-wave and full-wave rectification is the clearest single argument for full-wave: without changing a component value, the AC content of the output falls by roughly 60%. That makes the smoothing capacitor far smaller for the same output quality, which usually more than pays for the extra diodes.
Crest factor is 1.414 for a sine wave, but a rectifier feeding a capacitor draws current in brief, tall spikes with a crest factor of 3 or more. This is where cheap meters mislead: an averaging multimeter is calibrated assuming a sine, so it reads substantially low on a peaky waveform. Only a true-RMS instrument gives the right answer, and it has its own crest-factor limit stated in its specification.
The same spiky current is what makes unity-power-factor rectifiers worthwhile. The real power may be modest, but the high crest factor means large RMS current, which heats conductors and transformers out of proportion to the work being done.
Ripple factor (RF) is the ratio of the RMS value of the AC ripple component to the DC (average) value of a rectified output: RF = Vac(rms)/Vdc = √(FF²−1). A smaller ripple factor means smoother, cleaner DC.
Form factor (FF) is the ratio of the RMS value to the average value of a waveform: FF = Vrms/Vdc. For a pure DC it equals 1; the more ripple present, the larger it becomes.
They are linked by RF = √(FF²−1). Equivalently FF = √(1+RF²). Knowing either one gives the other.
About 1.21 (121%). The half-wave output is very rough because half of each cycle is missing, so it needs substantial filtering to be usable.
About 0.482 (48.2%). Full-wave rectification uses both half-cycles, roughly halving the ripple compared with half-wave and doubling the ripple frequency.
For sensitive electronics you typically want the ripple factor well below 1% after filtering. Power supplies often specify ripple as tens of millivolts on a several-volt rail, which corresponds to a fraction of a percent.
Add filtering: a smoothing capacitor, an LC filter, or a voltage regulator. Using a full-wave instead of half-wave rectifier and increasing the ripple frequency (3-phase, higher pulse number) also reduces it.
It is the fraction of the total output power that is useful DC power: η = (Vdc/Vrms)² = 1/FF². The theoretical maximum is 40.6% for half-wave and 81.1% for full-wave rectifiers.
Yes. A half-wave rectifier has a ripple factor of 1.21, meaning the RMS of the ripple actually exceeds the DC value. This shows how poor unfiltered half-wave rectification is.
Use a DC-coupled meter (or the DC/average mode) for Vdc, and a true-RMS meter (AC+DC mode) for Vrms. An oscilloscope can also read the average and RMS of the waveform directly.
A 6-pulse bridge produces six output humps per cycle, so the output never drops far from the peak. Its ripple factor is only about 4.2%, which is why large drives and chargers use three-phase rectification.
No. Ripple voltage is the actual AC amplitude (in volts, often peak-to-peak). Ripple factor is a dimensionless ratio of that ripple (RMS) to the DC value, so it lets you compare supplies of different voltages.
The ratio of RMS value to average value of a waveform. It is 1.5708 (π/2) for a half-wave rectified sine and 1.1107 (π/2√2) for a full-wave rectified sine.
The ratio of the AC component to the DC component in a rectified output, calculated as √(FF² − 1). Lower is better: half-wave gives 1.2114 while full-wave gives 0.4834, so full-wave needs far less smoothing for the same output quality.
The ratio of peak to RMS value. A sine wave has a crest factor of 1.414, but a capacitor-input rectifier draws current in narrow spikes with a crest factor of 3 or more.
Averaging meters are calibrated assuming a sine wave. On a peaky, high-crest-factor waveform they read substantially low. A true-RMS meter is required, within its own stated crest-factor limit.
Because its ripple factor is less than half that of half-wave rectification, and its output frequency is twice the supply frequency, both of which make smoothing far easier. The extra diodes are usually cheaper than the larger capacitor half-wave would need.
Yes, dramatically. The figures above are for unsmoothed rectifier output. Adding capacitance reduces ripple roughly in inverse proportion to the capacitance and the load resistance, at the cost of a much higher current crest factor.
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