Q.Differentiate between half-wave and full-wave rectification. With the help of a circuit diagram, explain the working of a full-wave rectifier.

Concept: P-N Junction Rectification

Rectification converts AC to DC using the one-way conduction of a p-n junction diode. The key difference between half-wave and full-wave rectification lies in how much of the input AC cycle is utilised.

Half-wave rectifier uses only one diode and conducts only during one half-cycle (positive or negative). This means half the input waveform is wasted, resulting in low efficiency and high ripple.

Full-wave rectifier uses two diodes (with a centre-tapped transformer) or four diodes (bridge rectifier) to conduct during both half-cycles. This gives a smoother DC output with higher average voltage and lower ripple.

Working of a Full-Wave Rectifier (Centre-Tap Type)

Circuit: A centre-tapped transformer supplies two equal voltages that are $180^\circ$ out of phase. Two diodes $D_1$ and $D_2$ are connected to the two ends of the secondary, with their cathodes joined together at the load; the other end of the load returns to the centre tap.

Step 1 — Positive half-cycle: The upper end of the secondary is positive, lower end negative. $D_1$ is forward-biased and conducts; $D_2$ is reverse-biased and does not. Current flows from the centre tap, through the load, through $D_1$, and back to the upper end. …

The Core Idea: Why Rectification?

A rectifier is the simplest power supply stage — it turns alternating current (AC) into pulsating direct current (DC). The key difference between half-wave and full-wave lies in how much of the AC cycle they use.

Half-wave rectification uses only one half (say, the positive half) of each AC cycle. The negative half is simply blocked. This wastes half the input power and produces a large gap between pulses, making the output very "ripply" — hard to smooth into clean DC.

Full-wave rectification uses both halves of the AC cycle. It cleverly inverts the negative half so that it also contributes to the output. The result is a stream of pulses at twice the input frequency, with no dead time between them. This gives:

• Higher average output voltage
• Lower ripple (easier to filter)
• Better transformer utilisation

Step-by-Step: Full-Wave Rectifier with Centre-Tapped Transformer

1. The Circuit Setup

The full-wave rectifier requires:

• A centre-tapped transformer — the secondary winding has a tap exactly at its midpoint
• Two diodes ($D_1$ and $D_2$)
• A load resistor ($R_L$)

Draw the circuit like this. The AC mains connects to the transformer primary. The secondary winding has three terminals: end A at the top, end B at the bottom, and the centre tap (CT) at the midpoint. Diode $D_1$'s anode connects to A; diode $D_2$'s anode connects to B. The cathodes of both diodes are joined together at a common point, and the load resistor $R_L$ is connected from this common cathode point back to the centre tap. The centre tap serves as the return (reference) terminal.

The voltage from A to CT is $V_{AC} = V_m \sin(\omega t)$, and from B to CT is $V_{BC} = -V_m \sin(\omega t)$ — they are $180^\circ$ out of phase.

2. How It Works: The Two Half-Cycles

During the positive half-cycle (when A is positive with respect to CT):

• Diode $D_1$ is forward-biased (anode > cathode) and conducts
• Diode $D_2$ is reverse-biased (its anode at B is negative relative to CT) and does not conduct
• Current flows: A $\to$ $D_1$ $\to$ $R_L$ $\to$ CT
• Voltage across $R_L$ is positive: $V_{out} = V_m \sin(\omega t)$ (ignoring the 0.7 V diode drop)

During the negative half-cycle (when A is negative, B is positive with respect to CT):

• Now $D_2$ is forward-biased and conducts
• $D_1$ is reverse-biased and blocks
• Current flows: B $\to$ $D_2$ $\to$ $R_L$ $\to$ CT
• Notice: current through $R_L$ flows in the same direction as before (from the joined cathodes toward the centre tap)
• Voltage across $R_L$ is again positive: $V_{out} = V_m \sin(\omega t)$ (but this time from the B-side)

3. The Output Waveform

The output is a series of positive half-sine pulses, one from each half-cycle of the input. There is no gap — the next pulse starts immediately after the previous one ends.

The average (DC) output voltage is:

Compare this to a half-wave rectifier, where $V_{dc} = \frac{V_m}{\pi}$ — exactly half.

The ripple frequency is $2f$, where $f$ is the input AC frequency (e.g., 100 Hz for a 50 Hz input). This higher frequency makes filtering much easier.

4. Key Differences: Half-Wave vs Full-Wave

| Parameter | Half-Wave | Full-Wave (Centre-Tap) | …