# Ripple voltage (half-wave rectifier))

## Description

The most common meaning of ripple in electrical science is the small unwanted residual periodic variation of the direct current (DC) output of a power supply which has been derived from an alternating current (AC) source. This ripple is due to incomplete suppression of the alternating waveform within the power supply.

As well as this time-varying phenomenon, there is a frequency domain ripple that arises in some classes of filter and other signal processing networks. In this case the periodic variation is a variation in the insertion loss of the network against increasing frequency. The variation may not be strictly linearly periodic. In this meaning also, ripple is usually to be considered an unwanted effect, its existence being a compromise between the amount of ripple and other design parameters.

Ripple factor (see ripple factor) may be defined as the ratio of the root mean square (rms) value of the ripple voltage to the absolute value of the DC component of the output voltage, usually expressed as a percentage. However, ripple voltage is also commonly expressed as the peak-to-peak value. This is largely because peak-to-peak is both easier to measure on an oscilloscope and is simpler to calculate theoretically. Filter circuits intended for the reduction of ripple are usually called smoothing circuits. The simplest scenario in AC to DC conversion is a rectifier without any smoothing circuitry at all. The ripple voltage is very large in this situation; the peak-to-peak ripple voltage is equal to the peak AC voltage. A more common arrangement is to allow the rectifier to work into a large smoothing capacitor which acts as a reservoir. After a peak in output voltage the capacitor© supplies the current to the load® and continues to do so until the capacitor voltage has fallen to the value of the now rising next half-cycle of rectified voltage. At that point the rectifiers turn on again and deliver current to the reservoir until peak voltage is again reached. If the time constant, CR, is large in comparison to the period of the AC waveform, then a reasonably accurate approximation can be made by assuming that the capacitor voltage falls linearly. A further useful assumption can be made if the ripple is small compared to the DC voltage. In this case the phase angle through which the rectifiers conduct will be small and it can be assumed that the capacitor is discharging all the way from one peak to the next with little loss of accuracy.

With the above assumptions the peak-to-peak ripple voltage can be calculated as shown.

Related formulas## Variables

V_{pp} | peak-to-peak ripple voltage (V) |

I | current in the circuit (A) |

f | frequency of the AC power (Hz) |

C | capacitance (F) |