Ripple Factor
A pulsating output of a rectifier contains a d.c. component and an a.c. component. The output of a rectifier consists of a d.c. component and an a.c. component (also known as ripple). The a.c. component is undesirable and accounts for the pulsations in the rectifier output. The effectiveness of a rectifier depends upon the magnitude of a.c. component in the output; the smaller this component, the more effective is the rectifier. The ratio of r.m.s. value of a.c. component to the d.c. component in the rectifier output is known as ripple factor i.e.
\[\text{Ripple factor} = \frac{\text{r.m.s. value of a.c component}}{\text{value of d.c. component}} = \frac{I_{ac}}{I_{dc}}\]
Therefore, ripple factor is very important in deciding the effectiveness of a rectifier. The smaller the ripple factor, the lesser the effective a.c. component and hence more effective is the rectifier.
The output current of a rectifier contains d.c. as well as a.c. component. The undesired a.c. component has a frequency of 100 Hz (i.e. double the supply frequency 50 Hz) is the ripple. It is a fluctuation superimposed on the d.c. component.
By definition, the effective (i.e. r.m.s.) value of total load current is given by : \[I_{rms} =\sqrt{I_{dc}^{2} + I_{ac}^{2}}\] or \[I_{ac} =\sqrt{I_{rms}^{2} - I_{dc}^{2}}\] Dividing throughout by \(I_{dc}\), we get,
\[\frac{I_{ac}}{I_{dc}} = \frac{\sqrt{I_{rms}^{2} - I_{dc}^{2}}}{I_{dc}}\]
But \(I_{ac}/I_{dc}\) is the ripple factor.
\[\therefore\qquad\qquad \text{Ripple factor} = \sqrt{\left(\frac{I_{rms}}{I_{dc}}\right)^{2} - 1}\]
For half-wave rectification
In half-wave rectification, \[I_{rms} = \frac{I_{m}}{2}\] \[I_{dc} = \frac{I_{m}}{\pi}\]
\[\therefore\qquad\qquad \text{Ripple factor} = \sqrt{\left(\frac{\frac{I_{m}}{2}}{\frac{I_{m}}{\pi}}\right)^2-1} = \sqrt{\left(\frac{\pi}{2}\right)^2-1} \]
\[\qquad\qquad \text{Ripple factor} = \sqrt{\left(\frac{\pi^2}{4}-1\right)}= 1.21 \]
It is clear that a.c. component exceeds the d.c. component in the output of a half-wave rectifier. This results in greater pulsations in the output. Therefore, half-wave rectifier is ineffective for conversion of a.c. into d.c.
For full-wave rectification.
In full-wave rectification, \[I_{rms} = \frac{I_{m}}{\sqrt{2}}\] \[I_{dc} = \frac{2I_{m}}{\pi}\]
\[\therefore\qquad\qquad \text{Ripple factor} = \sqrt{\left(\frac{\frac{I_{m}}{\sqrt{2}}}{\frac{2I_{m}}{\pi}}\right)^2-1} =\sqrt{\left(\frac{\pi}{2\sqrt{2}}\right)^2-1} \]
\[\therefore \qquad\qquad \text{Ripple factor} = \sqrt{\left(\frac{\pi^2}{8}\right)-1} =0.48 \]
i.e., \[\text{Ripple factor} = \frac{\text{effective a.c. component}}{\text{d.c. component}} = 0.48\]
This shows that in the output of a full-wave rectifier, the d.c. component is more than the a.c. component. Consequently, the pulsations in the output will be less than in half-wave rectifier. For this reason, full-wave rectification is invariably used for conversion of a.c. into d.c.
