8.5 Ripple efficiency $\left( \eta \right)$

  Semi-conductor Devices and Electronics

    1.0 Introduction
    2.0 Types of semiconductor
    3.0 Mass action law
    4.0 Electrical conductivity in semiconductor
    5.0 $p-n$ junction
    6.0 Breakdown voltage
    7.0 $I-V$ characteristics of a $p-n$ junction
    8.0 Rectifier
    9.0 Light emitting diode (LED)
    10.0 Zener diode
    11.0 Transistor
    12.0 Boolean identities
    13.0 Logic gates
    14.0 De Morgan's theorem

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8.5 Ripple efficiency $\left( \eta \right)$The rectification efficiency tells us what percentage of total input AC power is converted into useful DC output power.

Thus, rectification efficiency is defined as,
$$\eta = \frac{{{\text{DC power delivered to load}}}}{{{\text{AC input power from transformer}}}}$$

For half wave rectifier

DC power delivered to the load is, $$\begin{equation} \begin{aligned}
{P_{DC}} = I_{DC}^2{R_L} \\
{P_{DC}} = {\left( {\frac{{{I_m}}}{\pi }} \right)^2}{R_L} \\\end{aligned} \end{equation} $$
Input AC power, $$\begin{equation} \begin{aligned}
{P_{AC}} = I_{rms}^2\left( {{r_f} + {R_L}} \right) \\
{P_{AC}} = {\left( {\frac{{{I_m}}}{2}} \right)^2}\left( {{r_f} + {R_L}} \right) \\\end{aligned} \end{equation} $$
Rectification efficiency, $$\begin{equation} \begin{aligned}
\eta = \frac{{{P_{DC}}}}{{{P_{AC}}}} \\
\eta = \frac{{{{\left( {\frac{{{I_m}}}{\pi }} \right)}^2}{R_L}}}{{{{\left( {\frac{{{I_m}}}{2}} \right)}^2}\left( {{r_f} + {R_L}} \right)}} \times 100\% \\
\eta = \left( {\frac{{40.6}}{{1 + \frac{{{r_f}}}{{{R_L}}}}}} \right)\% \\\end{aligned} \end{equation} $$
If ${r_f} \ll {R_L}$,

Maximum rectification efficiency, $\eta = 40.6\% $

For full wave rectifier

DC power delivered to the load is, $$\begin{equation} \begin{aligned}
{P_{DC}} = I_{DC}^2{R_L} \\
{P_{DC}} = {\left( {\frac{{2{I_m}}}{\pi }} \right)^2}{R_L} \\\end{aligned} \end{equation} $$
Input AC power is, $$\begin{equation} \begin{aligned}
{P_{AC}} = I_{rms}^2\left( {{r_f} + {R_L}} \right) \\
{P_{AC}} = {\left( {\frac{{{I_m}}}{{\sqrt 2 }}} \right)^2}\left( {{r_f} + {R_L}} \right) \\\end{aligned} \end{equation} $$
Rectification efficiency, $$\begin{equation} \begin{aligned}
\eta = \frac{{{P_{DC}}}}{{{P_{AC}}}} \\
\eta = \frac{{{{\left( {\frac{{2{I_m}}}{\pi }} \right)}^2}{R_L}}}{{{{\left( {\frac{{{I_m}}}{{\sqrt 2 }}} \right)}^2}\left( {{r_f} + {R_L}} \right)}} \times 100\% \\
\eta = \left( {\frac{{81.2}}{{1 + \frac{{{r_f}}}{{{R_L}}}}}} \right)\% \\\end{aligned} \end{equation} $$
If ${r_f} \ll {R_L}$,

Maximum rectification efficiency, $\eta = 81.2\% $