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# Ripple Factor of Full Wave Rectifier

## What is Ripple Factor?

Last updated date: 15th Mar 2023
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Even after the process of rectification, there would always be a fluctuating component that can be observed in the output of the rectifier, which causes serious issues in the output obtained. With these small fluctuations, we find the output affects the sensitive devices and their working. The ripple factor is one among the vital characteristics necessary when designing a power converter. The ripple factor measures what quantity deviation the converter output parameter has, like the output current, from its nominal designed value. Let’s read ahead to know how we can define ripple factor and learn more details about it.

## Ripple Factor Formula

Ripple is the fluctuating AC component present in the output after rectification. The output of a rectifier can be either DC voltage or current. Therefore, AC fluctuating components present in DC output voltage are called voltage ripple and the ripple in DC current output is called current ripple. Ripple often comes because of the presence of circuit elements like diodes or thyristors.

The ripple factor is the ratio of the RMS value of the AC component that is present in the rectifier output to the average value of the rectifier output. The formula for the ripple factor is as follows.

$Ripple factor = \frac{RMS value of\hspace{1mm} AC \hspace{1mm} component\hspace{1mm} in \hspace{1mm} the\hspace{1mm} rectifier\hspace{1mm} output}{Average \hspace{1mm} value\hspace{1mm} of\hspace{1mm} rectifier\hspace{1mm} output}$

Depending on the ripple current or voltage, we measure the formula will vary for the ripple factor.

• For ripple voltage, the formula is as follows:

$\Gamma=\sqrt {\left( \dfrac {V_{rms}}{V_{dc}}\right)^2 -1}$

• For ripple current,

$\Gamma=\sqrt {\left( \dfrac {I_{rms}}{I_{dc}}\right)^2 -1}$

Generally, the ripple factor is denoted in percentage, the lesser the ripple factor higher the efficiency of the output.

The ripple factor value in a half wave rectifier is 1.21 while for a full wave rectifier it is 0.482. Measurement of ripple basically denotes the purity of the rectified output. The more the ripple factor, the lesser will be the purity of rectified DC output, which means more will be the presence of fluctuating AC components. Therefore we take certain measures to reduce the ripple factor.

The ripple factor is generally denoted in percentage as mentioned before. The percentage of ripple factor is obtained by just multiplying the ratio by 100. Let’s say 2.2 % of ripple content in output current, that means 2.2 A RMS alternating component of current is present against the actual 100 A DC current output. Similarly, 2.2 % ripple content in output voltage means that 2.2 V RMS alternating component of voltage is present against the actual 100 V DC voltage output.

## Significance of Ripple Factor

• The single-phase rectifier’s output isn't entirely DC. It additionally has some AC components. Ripple value describes the AC elements.

• The magnitude of the AC component within the output is indicated by the ripple issue.

• A higher value of the ripple factor indicates that the rectifier’s output features a larger AC component.

## Ripple Factor of Bridge Rectifier

A full wave rectifier that converts sinusoidal AC input to DC is called a bridge rectifier. This circuit includes four diodes, these are connected in such a way that 2 of them conduct throughout the positive half cycle of the supply input and therefore the other 2 diodes conduct throughout the negative half cycle of the rectifier.

For a bridge rectifier, the ripple factor is 0.482. In reality, the value of the ripple factor is simply determined by the wave form of the output current or load voltage.

## Ripple Factor of a Full Wave Rectifier

Consider a full wave rectifier, where the output of the single phase full rectifier is as shown below.

Input and Output of Full Wave Rectifier

If we observe the output of the full wave rectifier, it is not rectified. We were expecting pure DC but the actual output is disturbed. Let’s find the ripple factor of a full-wave rectifier.

For a full wave rectifier

$I_{rms}=\frac{I_{m}}{\sqrt{2}}$

Where Im is the maximum current.

$I_{dc}=\frac{2I_{m}}{\pi}$

$Ripple factor = \sqrt{(\frac{\frac{I_{m}}{\sqrt{2}}}{\frac{2I_{m}}{\pi}})^{2}}-1 = 0.48$

That is, the full wave factor dc component is more than AC.

## Ripple Frequency

It is the frequency of the residual AC voltage after it has been rectified to DC in a power supply. Ripple frequency depends upon the rectifier we use. For a half wave rectifier, its input frequency or supplied frequency is 50Hz, and the ripple frequency for the halfwave rectifier is the same as that of the supplied frequency, which is 50Hz. In general ripple, the frequency is double the input frequency. For a full-wave rectifier, its input frequency is 60Hz and therefore its ripple frequency is 120Hz.

## Effects of Ripples

Some equipment can work with the ripples, while some of the sensitive test instruments and audio devices do not work properly with working supplies having high ripple. The effects of ripple are as follows:

• It causes heating and damage to the capacitors

• Negatively affects sensitive instrumentation

• Interferes with TV displays

• Causes noise to audio circuits

• Causes errors in digital circuits, data corruption, and incorrect outputs in logic circuits

## How to Overcome Ripple?

We can overcome the ripple which comes in the rectified output by introducing filters. One way is by introducing capacitors, which are smoothing capacitors that convert the ripple voltage into a smoother dc voltage. Aluminum electrolytic capacitors are widely used for this purpose and with capacitances of 100uF or more. The dc pulses charge the capacitor to the peak voltage. The Factors to be considered when selecting the capacitor are the voltage and the value of capacitance. A lower value of capacitance will not be effective and capacitors may be connected in parallel to increase the value. Most of the good power supplies have ripples better than 10mV RMS.

## Summary

When the AC waveform is rectified with a rectifier unit, the rectified output isn't perfectly DC rather the DC output has pulsating components referred to as AC components. The ripple factor is a vital parameter for assessing the effectiveness of the rectifier. The lower ripple factor value shows that the ripples in the DC output are less and also the efficiency of the rectifier is better. Moreover, the higher value shows that more fluctuating AC elements are present within the rectified output.

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## FAQs on Ripple Factor of Full Wave Rectifier

1. What is the reason for ripple in DC output ?

The ripples are undesirable within the DC output, but complete elimination of them is not possible. Yes, we can reduce these to a great extent by filtering the rectified DC output voltage. If we tend to observe the rectified DC output of the complete wave rectifier, we discover that rectified DC output isn't perfectly DC instead of the rectified DC voltage or current having AC components. The output of the complete wave rectifier has pulsating voltage. the average or DC voltage reduces because of the presence of pulsating voltage within the rectified output voltage or current. The full wave rectifier has fewer ripples than a half wave rectifier.

2. Can the ripple factor be high or low?

The ratio of the RMS value of an AC component within the rectified output to the average value of rectified output. The ripple factor is denoted as γ. It's a dimensionless quantity and invariably includes a value less than unity. Smaller value of ripple factor is desirable. Ideal value of the ripple factor is zero. The ripple factor for a full wave rectifier is 0.482 which may also be written as 48.2 %. The ripple factor value in a half wave rectifier is 1.21.

3. What are the characteristics of AC waveform?

The period, (T) is the length of time in seconds that the wave form takes to repeat itself from begin to end. This could even be referred to as the Periodic Time of the waveform for sine waves, or the pulse width for square waves. The Frequency, (ƒ) is the number of times the waveform repeats itself within a one second period of time. Frequency is the reciprocal of the period, (ƒ = 1/T) with the unit of frequency being the Hertz, (Hz). The Amplitude (A) is the magnitude or intensity of the signal waveform measured in volts or amps.