The output of a practical rectifier is not pure DC. The output current or voltage contains both DC as well as AC components. The presence of the AC component in the DC component causes ripples. **Ripple factor** measures the percentage of AC component present in the rectifier output.

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## What is Ripple factor?

It is defined as the ratio of the RMS value of the AC component of rectifier output to the average value of the rectifier output. It is denoted by the symbol gamma ‘**γ**‘.

$\text{Ripple factor} = \frac{\text{RMS value of AC component of output}}{\text{Average value of output}}$

**Ideally**, the value of the ripple factor is **zero**. It is because of the absence of an AC component in the rectifier output. Hence the output of the rectifier is perfectly dc quantity.

## Ripple factor formula derivation

**Using Current Ripple**

Let I_{rms}, I_{dc} and I_{ac} denote the RMS value, average value and RMS value of AC component of the output current, respectively.

As we know that,

$I_{rms}=\sqrt{I_{dc}^{2}+I_{ac}^{2}}$

We can rearrange it as

$I_{ac}=\sqrt{I_{rms}^{2}-I_{dc}^{2}}$

dividing both side by I_{dc}, we get

$\frac{I_{ac}}{I_{dc}}=\frac{\sqrt{I_{rms}^{2}-I_{dc}^{2}}}{I_{dc}}$

$\text{But}\; \frac{I_{ac}}{I_{dc}}\; \text{is the ripple factor. Therefore,}$

$\text{Ripple factor}=\frac{\sqrt{I_{rms}^{2}-I_{dc}^{2}}}{I_{dc}}=\sqrt{\left ( \frac{I_{rms}}{I_{dc}} \right )^{2}-1}$

The above equation is the ripple factor formula in terms of current.

**Using Voltage Ripple**

Let V_{rms}, V_{dc} and V_{ac} denote the RMS value, average value and RMS value of AC component of the output voltage, respectively.

As we know that,

$V_{rms}=\sqrt{V_{dc}^{2}+V_{ac}^{2}}$

We can rearrange it as

$V_{ac}=\sqrt{V_{rms}^{2}-V_{dc}^{2}}$

dividing both side by V_{dc}, we get

$\frac{V_{ac}}{V_{dc}}=\frac{\sqrt{V_{rms}^{2}-V_{dc}^{2}}}{V_{dc}}$

$\text{But}\; \frac{V_{ac}}{V_{dc}}\; \text{is the ripple factor. Therefore,}$

$\text{Ripple factor}=\frac{\sqrt{V_{rms}^{2}-V_{dc}^{2}}}{V_{dc}}=\sqrt{\left ( \frac{V_{rms}}{V_{dc}} \right )^{2}-1}$

The above equation is the ripple factor formula in terms of voltage.

## Ripple factor of half wave rectifier

The RMS value of output voltage of half-wave rectifier is given by

$V_{rms}=\frac{V_{m}}{2}$

where, V_{m} is the peak value of output voltage.

The average value of output voltage of half-wave rectifier is given by

$V_{dc}=\frac{V_{m}}{\pi }$

where, V_{m} is the peak value of output voltage.

As we know that ripple factor is given by

$\text{Ripple factor}=\sqrt{\left ( \frac{V_{rms}}{V_{dc}} \right )^{2}-1}$

Therefore, we get

$\text{Ripple factor}=\sqrt{\left ( \frac{\frac{V_{m}}{2}}{\frac{V_{m}}{\pi }} \right )^{2}-1}$

∴ Ripple factor = 1.21

The ripple factor of half wave rectifier is 1.21

## Ripple factor of full wave rectifier

The RMS value of output voltage of full-wave rectifier is given by

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

where, V_{m} is the peak value of output voltage.

The average value of output voltage of half-wave rectifier is given by

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

where, V_{m} is the peak value of output voltage.

As we know that ripple factor is given by

$\text{Ripple factor}=\sqrt{\left ( \frac{V_{rms}}{V_{dc}} \right )^{2}-1}$

Therefore, we get

$\text{Ripple factor}=\sqrt{\left ( \frac{\frac{V_{m}}{\sqrt{2}}}{\frac{2V_{m}}{\pi }} \right )^{2}-1}$

∴ Ripple factor = 0.48

The ripple factor of full wave rectifier is 0.48

## Ripple factor of bridge rectifier

The RMS value of output voltage of bridge rectifier is given by

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

where, V_{m} is the peak value of output voltage.

The average value of output voltage of bridge rectifier is given by

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

where, V_{m} is the peak value of output voltage.

As we know that ripple factor is given by

$\text{Ripple factor}=\sqrt{\left ( \frac{V_{rms}}{V_{dc}} \right )^{2}-1}$

Therefore, we get

$\text{Ripple factor}=\sqrt{\left ( \frac{\frac{V_{m}}{\sqrt{2}}}{\frac{2V_{m}}{\pi }} \right )^{2}-1}$

∴ Ripple factor = 0.48

The ripple factor of bridge rectifier is 0.48