## Ripple Factor of single-phase center-tap full-wave rectifier

The pulsating output of a rectifier can be considered to contain a dc component and ac component called the ripples. The ripple current is undesirable and its value should be the smallest possible in order to make the rectifier effective.

The ripple voltage or current is measured in turn of the ripple factor which is defined as the ratio of the effective value of the ac components of voltage (or current) present in the output from the rectified to the direct or average value of the output voltage (or current)

The effective value of the load current is given as

#### I^{2} = I_{dc}^{2} + I_{1}^{2} + I_{2}^{2} + I_{4}^{2} + ……=I_{dc}^{2} + I_{ac}^{2}

Where I_{1}, I_{2}, I_{4} etc. are the rms values of fundamental, second, fourth etc. harmonics and I_{ac}^{2} is the sum of the square of the rms Value of the ac components.

So ripple factor, **γ = I _{ac} /I_{dc} = √{(I^{2} + I_{dc}^{2})/I_{dc}} = √[{I_{rms}/I_{dc}}^{2} – 1] = √(K_{f}^{2} – 1)**

Where K_{f} is the form factor of the input voltage. For half-wave rectifier, from factor is given as

#### K_{f} = I_{rms} / I_{av} = (I_{max}/√2)/(2I_{max} / π) = π/2√2 = 1.11

Now, Ripple factor is given as

#### γ = √(K_{f}^{2} – 1) = √(1.11^{2} – 1) = 0.482

**Related topic**

**Single-phase full-wave rectifier****Average and RMS value of center-tap full wave rectifier****Efficiency of single-phase center-tap full wave rectifier****Frequency Component of single-phase center-tap full wave rectifier****Regulation of single-phase full-wave center-tap rectifier****Peak Inverse Voltage of single-phase center-tap full-wave rectifier****Peak Current of single-phase center-tap full-wave rectifier****Transformer Utilization Factor (TUF) of single-phase center-tap full-wave rectifier****Advantage of center-tap Full-wave rectifier**

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