distinguish graphically between half-wave and full-wave rectification

Rectification and Smoothing

Objective

To distinguish graphically between half‑wave and full‑wave rectification.

1. Introduction

Rectification is the process of converting an alternating‑current (AC) voltage into a unidirectional (pulsating) voltage. The most common rectifier circuits are:

• Half‑wave rectifier – uses a single diode.
• Full‑wave rectifier – uses either two diodes in a centre‑tapped transformer or four diodes in a bridge configuration.

The resulting pulsating voltage can be smoothed with a capacitor to obtain a near‑DC supply.

2. Half‑Wave Rectification

In a half‑wave rectifier the diode conducts only during the positive half‑cycle of the input sinusoid.

The input voltage can be expressed as

\$V{\text{in}} = Vm \sin(\omega t)\$

and the output voltage \$V_{\text{out}}\$ is

\$\$V_{\text{out}} =

\begin{cases}

V_m \sin(\omega t) & \text{for } \sin(\omega t) \ge 0 \\

0 & \text{for } \sin(\omega t) < 0

\end{cases}\$\$

3. Full‑Wave Rectification

Full‑wave rectifiers invert the negative half‑cycle so that the output voltage is always positive.

For a bridge rectifier the output voltage is

\$V{\text{out}} = |Vm \sin(\omega t)|\$

Thus both positive and negative halves of the input appear as positive pulses at the output.

4. Graphical Comparison

The key visual differences are:

• Half‑wave: output exists only for one half of each input period; the waveform is discontinuous for half the cycle.
• Full‑wave: output exists for the entire input period; the waveform consists of pulses at twice the input frequency.

5. Summary Table of Features

6. Practical Implications for Smoothing

Because a full‑wave rectifier provides a higher ripple frequency, a smoothing capacitor discharges less between peaks, giving a lower ripple voltage for the same capacitance. This makes full‑wave rectification the preferred choice for most DC power supplies.

7. Quick Checklist for Students

1. Identify the diode configuration (single diode vs bridge/centre‑tap).
2. Sketch the input sinusoid and then apply the rectification rule to obtain the output waveform.
3. Note the ripple frequency: \$f\$ for half‑wave, \$2f\$ for full‑wave.
4. Remember that the smoothing capacitor sees a higher frequency in full‑wave circuits, reducing ripple.

8. Conclusion

Graphically, half‑wave rectification shows a single pulse per input cycle, whereas full‑wave rectification shows two pulses per cycle, effectively doubling the ripple frequency and improving the efficiency of subsequent smoothing. Understanding these differences is essential for designing reliable DC power supplies in A‑Level physics experiments and practical electronics.