Ripple Factor: Definition, Formula, Effect on Other Rectifiers (2024)

Ripple in electronics means the residual variation caused by DC voltage within an alternating current (AC) power supply. It’s possible that the rectified DC output is either direct current (DC) current or DC voltage. The term ‘current ripple’ refers to the fluctuating AC component in DC current, whereas ‘voltage ripple’ refers to the fluctuating AC component in DC voltage.

The ripple factor is critical in determining the efficacy of rectifier output. The lesser the ripple factor, the more effective the rectifier is. More fluctuating AC components are present in the rectified output if the ripple factor is higher.

In this article we will learn what a ripple factor is and its formula, uses and significance. We will also calculate the ripple factor of a half-wave rectifier, a full-wave rectifier and a bridge rectifier with FAQs.

Ripple Factor

Ripple factor is defined as the ratio of RMS value of the AC component to the output of the DC component in the rectifier. In other terms,

Ripple Factor = RMS (root mean square) value of AC/ RMS value of DC

The ripple factor plays a major role in describing the efficiency of any rectifier. In simpler terms, ripple factor determines the quality of rectified output. Thus, less ripple factor in any circuit is preferred.

Learn more about Electrical Resistance here.

Ripple Factor Formula

The ripple factor is expressed as the ratio of the RMS value of the AC component to the RMS value of the DC component.

\(\begin{align} & {{I}_{rms}}=\sqrt{I_{dc}^{2}+I_{ac}^{2}} \\ & \\ \end{align} \)

We know there are two criteria that need to be determined based on the definition of ripple factor:

The RMS value of the ripple in the rectifier’s output current or voltage.
The difference between the actual output and the predicted DC output for one time period, T. Ripple is given as the difference between the actual output and the expected DC output for one time period, T. The mathematical formula is as follows:
Ripple = \(i_L – I_{dc} = v_L – V_{dc}\)

Where,

-the output current is \(i_L\).
-the output voltage is denoted by\( v_L\).
\(I_{dc}\) is the load current’s average value.
\(V_{dc}\) is the load voltage’s average value.
-the voltage ripple RMS value is calculated as follows:
\(\begin{align}
& RMS=\sqrt{\frac{1}{T}}\int_{0}^{T}{({{i}_{L}}}-{{I}_{dc}}{{)}^{2}}d(\omega t) \\
& =\sqrt{\frac{1}{T}}\int_{0}^{T}{[({{i}_{L}}}{{)}^{2}}-{{({{I}_{dc}})}^{2}}-2({{i}_{L}})({{I}_{dc}})]d(\omega t) \\
& =\sqrt{{{({{I}_{rms}})}^{2}}+\frac{1}{T}}\int_{0}^{T}{[({{i}_{L}}}{{)}^{2}}-{{({{I}_{dc}})}^{2}}-2({{i}_{L}})({{I}_{dc}})]d(\omega t) \\
& =\sqrt{{{({{I}_{rms}})}^{2}}+\frac{1}{T}}\int_{0}^{T}{[}{{({{I}_{dc}})}^{2}}d(\omega t)-(\frac{2{{I}_{dc}}}{T})\int_{0}^{T}{(}{{i}_{L}})d(\omega t) \\
& {{I}_{dc}}=\sqrt{\frac{1}{T}}\int_{0}^{T}{({{i}_{L}}})d(\omega t) \\
& RMS=\sqrt{{{({{I}_{rms}})}^{2}}+{{({{I}_{dc}})}^{2}}-2{{({{I}_{dc}})}^{2}}} \\
& =\sqrt{{{({{I}_{rms}})}^{2}}-{{({{I}_{dc}})}^{2}}} \\
& \Gamma =\frac{\sqrt{{{({{I}_{rms}})}^{2}}-{{({{I}_{dc}})}^{2}}}}{{{I}_{dc}}} \\
& \Gamma =\frac{\sqrt{{{({{V}_{rms}})}^{2}}-{{({{V}_{dc}})}^{2}}}}{{{V}_{dc}}} \\
\end{align} \)

So now we have the ripple factor formula. The definition of ripple factor can be used to quickly derive the ripple factor. The ripple factor is defined as the ratio of the RMS of the AC component to the RMS of the DC component in rectified output.

Also, read about Electrical Power here.

Ripple Factor of Half-Wave Rectifier

A half-wave rectifier is a diode circuit that converts alternating voltage (AC supply) to direct voltage (DC supply). The half-wave rectifier circuit converts AC to DC with the help of a single diode.

The one-half cycle of the AC supply waveform passes through the half-wave rectifier circuit, while the other half cycle is blocked. The ripple factor (expressed by γ or r) is used to quantify how successfully the half-wave rectifier can convert AC voltage into DC voltage. The ripple factor is the ratio of the AC voltage’s RMS value (on the input side) to the rectifier’s DC voltage (on the output side).

To calculate the ripple factor of half-wave rectifier, use this formula:

\(\begin{align}& \Gamma =\sqrt{{{(\frac{{{V}_{rms}}}{{{V}_{dc}}})}^{2}}-1} \\ & \Gamma =\sqrt{{{(\frac{{{I}^{2}_{rms}}-{I}^{2}_{dc}}{{{I}_{dc}}})}^{2}}-1}=1.21 \\\end{align} \)

For the positive half cycle of the supply, the diode will be forward biased, whereas for the negative half cycle, it will be reverse biased. As a result, the diode will only conduct during the positive half cycle and not during the negative half cycle. As a result, the current output will only be conducting and allowing current to flow during the supply’s positive half cycle.

This is why it is referred to as a single-phase half-wave rectifier. Note that we want to keep the ripple factor as low as possible while building a rectifier. To decrease the ripples in the circuit, we utilise capacitors and inductors as filters.

You may be interested in our Kirchhoff’s Circuit Laws article.

Ripple Factor of Full-Wave Rectifier

A full-wave rectifier is a circuit that allows current to flow in one direction through the load for the duration of the input voltage cycle. Two diodes are connected across the terminals of the secondary terminals of a centre tapped transformer in such a way that one diode conducts for the positive half-cycle and the other for the negative half cycle of the supply input.

As a result, the load resistance maintains a unidirectional current flow. This is essentially an improvement over a half-wave rectifier, which only allows output current to flow during the positive half of the input supply cycle.

The full-wave rectifier has a ripple factor of 0.482. When this number is compared to the ripple factor of a half-wave rectifier (ripple factor 1.21 for half wave), it can be seen that the DC output quality of the full-wave rectifier has increased by about 40%. This means the DC output will be smoother and the AC component will be less erratic. Let’s use the formula to get the ripple factor.

\(\begin{align}
& \Gamma =\sqrt{{{(\frac{{{V}_{rms}}}{{{V}_{dc}}})}^{2}}-1} \\
& \Gamma =\sqrt{{{(\frac{{{V}_{rms}}}{{{V}_{dc}}})}^{2}}-1}=0.48 \\
\end{align}\)
The ripple factor can be determined by combining the values of RMS current \(I_{rms}\) and average current \(I_{dc}\)

The ripple factor can be determined by combining the values of RMS current \(I_{rms}\) and average current \(I_{dc}\)

Don’t forget to read about Electric Potential.

Ripple Factor of Bridge Rectifier

A full-wave rectifier that converts sinusoidal AC input to DC is known as a bridge rectifier. This circuit is made up of four diodes that are connected in such a way that two of them conduct during the positive half cycle of the supply input and the other two diodes conduct during the negative half cycle of the rectifier. A full-wave rectifier converts both the positive and negative halves of the input AC supply power into DC voltage.

For a bridge rectifier, the ripple factor is 0.482. In actuality, the value of the ripple factor is solely determined by the waveform of the output current or load voltage.

\(\begin{align}
& \Gamma =\sqrt{{{(\frac{{{V}_{rms}}}{{{V}_{dc}}})}^{2}}-1} \\
& \Gamma =\sqrt{{{(\frac{{{V}_{rms}}}{{{V}_{dc}}})}^{2}}-1}=0.48 \\
\end{align} \)

The circuit configuration has no bearing on this. As their output waveforms are identical, their value will be the same for both centre tapped and bridge rectifiers.

Keep yourself updated on the Electrostatic Coulomb Law

Significance of Ripple Factor

The single-phase rectifier’s output isn’t entirely DC. It also has some AC components. Ripple describes the AC component. The magnitude of the AC component in the output is indicated by the ripple factor.

A higher ripple factor indicates that the rectifier’s output has a larger AC component.

Study everything about Current and Electricity here.

Uses of Ripple Factor

The ripple factor is critical in determining the efficacy of rectifier output. The lesser the ripple factor, the more effective the rectifier is. More fluctuating AC components are present in the rectified output if the ripple factor is higher.

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