# What is Ripple and Ripple Factor? – Formula of Ripple Factor

**What is Ripple?**

Ripple is the fluctuating AC component present in rectified DC output. The output of a rectifier may either be DC current or voltage. In view of this, AC fluctuating component present in DC output voltage is called voltage ripple and that in DC current output is called current ripple.

**Why Ripple is Present?**

Ripple is always present in the rectifier output. This is because of the behavior of circuit elements like diode or thyristor. Let us consider an example of single phase full wave rectifier to better understand the reason for presence of ripple. The output current waveform of single phase full wave rectifier is shown below.

The above figure is self-explanatory. The expected output from full wave rectifier should be a pure DC but actually the output current is different. Since the average value of output current is the pure, therefore the ripple present is equal to the difference of output current or load current minus average current.

**What is Ripple Factor?**

Ripple Factor is the ratio of rms value of ac component present in the rectified output to the average value of rectified output. It is a dimensionless quantity and denoted by γ. Its value is always less than unity.

This is basically a measurement of ripple which denotes the purity of rectified output. The more the ripple factor, the lesser will be the purity of rectifier DC output. This means more will be fluctuating AC component. Thus every effort is made to reduce the ripple factor. Here we will not discuss the ways to reduce the ripple factor.

Ripple factor is generally denoted in percentage like 3 % or 4 %. Percentage ripple factor is obtained by just multiplying γ by 100. 3 % ripple content in output current means that 3 A rms alternating component of current is present against the actual 100 A DC current output. Similarly, 3 % ripple content in output voltage means that 3 V rms alternating component of voltage is present against the actual 100 V DC voltage output.

**Ripple Factor Formula **

The formula for ripple factor is given in terms of rms value and average value of rectifier output.

**Derivation of Ripple Factor Formula**

The ripple factor formula can easily be derived from its definition. As per definition, we need to find two parameters: rms value of ripple present in rectifier output current or voltage and average value of output of rectifier for one time period T. For calculating rms value of ripple I_{rms}, first we need to find the ripple. Ripple is equal to the difference between the actual output minus expected DC output. Thus,

Ripple = i_{L} – I_{dc} = v_{L} – V_{dc}

Here, i_{L} and v_{L} are the output current and voltage through the load connected at the terminals of rectifier. Similarly, V_{dc} and I_{dc} are the average value of load voltage and current.

Let us now find the rms value of current ripple. Though rms value of voltage ripple can also be used for deriving the formula for ripple factor but here we are using current ripple.

Since the ripple factor is equal to the ratio of rms value of ripple content and average value of rectifier output, therefore its formula becomes

Hope, ripple and ripple factor is clear. If you have any doubt, please write in comment box.

I dc value will not contain square root but in your derivation part you have shown that.

(2idc) whole square is shown but here only idc

Should be squared

Thank you very much for your correcting the typo. Please check, it has been corrected.