8.4 Ripple factor

  Semi-conductor Devices and Electronics

The ripple factor is a measure of purity of the DC output of a rectifier. It is defined as,
$$\begin{equation} \begin{aligned}
r = \frac{{{\text{ rms value of the component of wave}}}}{{{\text{Average or DC value}}}} \\
r = \sqrt {{{\left( {\frac{{{I_{rms}}}}{{{I_{DC}}}}} \right)}^2} - 1} \\\end{aligned} \end{equation} $$

• For half wave rectifier, $$\begin{equation} \begin{aligned}
  {I_{rms}} = \frac{{{I_m}}}{2},\;{I_{DC}} = \frac{{{I_m}}}{\pi } \\
  r = \sqrt {{{\left( {\frac{{\frac{{{I_m}}}{2}}}{{\frac{{{I_m}}}{\pi }}}} \right)}^2} - 1} \\
  r = 1.21 \\\end{aligned} \end{equation} $$

• For full wave rectifier, $$\begin{equation} \begin{aligned} {I_{rms}} = \frac{{{I_m}}}{{\sqrt 2 }},\;{I_{DC}} = \frac{{2{I_m}}}{\pi } \\ r = \sqrt {{{\left( {\frac{{\frac{{{I_m}}}{{\sqrt 2 }}}}{{\frac{{2{I_m}}}{\pi }}}} \right)}^2} - 1} \\ r = 0.482 \\\end{aligned} \end{equation} $$