# What is a Ripple Factor and Its Derivations

When the fluctuation occurs within the output of the rectifier then it is known as ripple. So this factor is essential to measure the rate of fluctuation within the resolved output. The ripple within output voltage can be reduced by using filters like capacitive or another kind of filter. In most of the circuits like rectifiers utilizes a capacitor within parallel of thyristor otherwise diodes to work as a filter within the circuit. This capacitor helps to decrease the ripple within the rectifier output. This article discusses an overview of the ripple factor (R.F) which includes its definition, calculation, its significance, and R.F using half-wave, full-wave, and bridge rectifier.

## What is Ripple Factor?

The rectifier output mainly includes the AC component as well as the DC component. The ripple can be defined as the AC component within the resolved output. The A.C component within the output is unwanted as well as estimates the pulsations within the output of the rectifier. Here the ripple voltage is nothing but the AC component within o/p of the rectifier. Similarly, the ripple current is an AC component within o/p current.

The definition of the ripple factor is the ratio of the AC component’s RMS value and the DC component’s RMS value within the output of the rectifier. The symbol is denoted with “γ” and the formula of R.F is mentioned below.

(R.F) = AC component’s RMS value / DC component’s RMS value

Thus the **R.F = I (AC) / I (DC)**

This is extremely significant while deciding the efficiency of rectifier output. The efficiency of the rectifier can be explained by the lesser R.F.

The extra ripple factor is nothing but fluctuating of additional ac components that are there within the resolved output.

Basically, the calculation of the ripple indicates the clarity of the resolved output. Therefore each effort can be made for diminishing the R.F. Here we will not discuss the ways to reduce the R.F. Here we are discussing why ripples occur within the output of the rectifier.

### Why Ripple Occurs?

Whenever the rectification occurs through the rectifier circuit then there is no chance of getting accurate DC output.

Some variable AC components are frequently happening within the rectifier’s output. The circuit of a rectifier can be built with diodes otherwise thyristor. The ripple mainly depends on the elements which are used within the circuit.

The best example of the full-wave rectifier with a single phase is shown below. Here the circuit uses four diodes so the output gets like the following waveform.

Here we estimated the accurate DC o/p waveform but we cannot get like that due to some ripple within the output and it is also called pulsating AC waveform. By employing a filter within the circuit, we can get almost DC waveform which can diminish ripple within the output.

### Derivation

According to the definition of R.F, the whole load current RMS value can be given by

**I _{RMS} = √I^{2}_{dc} + I^{2}_{ac} **

**(or)**

**I _{ac} = √I^{2}_{rms} + I^{2}_{dc} **

When the above equation is divided by using Idc then we can get the following equation.

**I _{ac / }**I

_{dc}

**= 1/**I

_{dc}

**√I**

^{2}_{rms}+ I^{2}_{dc}However, here Iac / Idc is the **ripple factor formula**

R.F = 1**/** I_{dc}** √I ^{2}_{rms} + I^{2}_{dc }= √ (I_{rms} / I_{dc})^{2 }-1**

### Ripple Factor of Half Wave Rectifier

For half-wave rectifier,

**I _{rms} = I_{m}/2**

**I _{dc} = I_{m}/ π**

We know the formula of **R.F = √ (I _{rms} / I_{dc})^{2 }-1**

Substitute the above **I _{rms}**

**&**

**I**in the above equation so we can get the following.

_{dc}**R.F = √ (Im/2 / I _{m}/ π)^{2 }-1 = 1.21**

Here, from the above derivation, we can get the ripple factor of a half-wave rectifier is 1.21. Therefore it is very clear that AC. component surpasses the DC component within the half-wave rectifier output. It results in extra pulsation within the output. Consequently, this type of rectifier is ineffectively intended for changing AC to DC.

### Ripple Factor of Full Wave Rectifier

For full-wave rectifier,

**I _{rms }= I_{m}/√ 2**

**I _{dc} = 2I_{m} / π**

We know the formula of **R.F = √ (I _{rms} / I_{dc})^{2 }-1**

Substitute the above **I _{rms}** &

**I**in the above equation so we can get the following.

_{dc }**R.F = √ (Im/√ 2/ 2Im / π)2 -1 = 0.48**

Here, from the above derivation, we can get the ripple factor of a full-wave rectifier is 0.48. Therefore it is very clear that in the o/p of this rectifier, the DC component is above the AC component. As a result, the pulsations within the o/p will be less than within half-wave rectifier. Because of this reason, this rectification can be always employed while converting AC into DC.

### Ripple Factor of Bridge Rectifier

The factor value of the bridge rectifier is 0.482. Actually, the R.F value mainly depends on the waveform of load otherwise o/p current. It doesn’t rely on the circuit design. Therefore its worth will be similar for rectifiers like a bridge as well as center-tapped when their o/p waveform is equal.

### Ripple Effects

Some equipment can work by ripples but some of the sensitive types of equipment like audio as well as the test cannot work properly due to the effects of high-ripple within the supplies. Some of the ripple effects of equipment mainly occur due to the following reasons.

- For sensitive instrumentation, it affects negatively
- Ripple effects can cause errors within digital circuits, inaccurate outputs in data corruption & logic circuits.
- Ripple effects can cause heating so capacitors can be damaged.
- These effects initiate noise to audio circuits

Thus, this is all about the ripple factor. From the above information finally, we can conclude that generally a rectifier is used to convert the signal from AC to the electrical signal. There are various types of rectifiers available in the market which can be used for rectification such as full-wave rectifier, half-wave rectifier and bridge rectifier. All these have dissimilar efficiency intended for applied i/p AC signal. The rectifier’s **ripple factor and efficiency** can be measured based on the output. Here is a question for you, what is the r**ipple factor of full wave rectifier with capacitor filter**?