Diode Applications: Half-wave rectifier

Diode Applications: Half-wave rectifier

1. What a Half-Wave Rectifier Is

Half-wave rectifier = one diode + load (+ transformer) that converts AC to pulsating DC by passing only one half-cycle (positive) and blocking the other (negative).

Circuit: AC source (secondary) → diode (anode to source, cathode to load) → load resistor $R_L$ → source return. Often with transformer to step down/isolation.

2. Operation

• Positive half-cycle ($v_s>0.7V$): diode forward biased (p +, n -) ⇒ conducts, $v_{out}≈v_s -0.7V$ across $R_L$ (if ideal, $v_{out}=v_s$).
• Negative half-cycle ($v_s<0$): diode reverse biased ⇒ blocks, $v_{out}=0$, $v_{diode}=v_s$ (PIV).

Output pulsating DC with fundamental + harmonics, average DC over full cycle:

(for ideal, without filter; with $V_m$ peak secondary), RMS across $R_L$:

Peak Inverse Voltage (PIV) diode must withstand:

(for half-wave, when diode blocks, full peak appears across it).

3. With Capacitor Filter (next topic preview)

Add capacitor $C$ in parallel with $R_L$ ⇒ charges to $V_m$ during conduction and holds during blocking, smoothing to near DC with ripple

(half-wave $f$ = mains $50$ Hz).

4. Worked Example

(a) Transformer secondary 12V RMS ⇒ Vm=17V: ideal half-wave Vdc=5.4V, Vrms=8.5V across load (pulsating) ✓
    With 0.7V drop: Vdc≈(17-0.7)/π≈5.19V

(b) Need PIV >17V, choose diode 1N4007 (1000V) safe.

(c) Efficiency: half-wave theoretical max DC power / AC in ≈40.6% (low).

(d) Need smoother? Use full-wave.

5. Exam Points

• Draw circuit (source→diode→R_L) and input vs output waveforms ($v_s$ sine, $v_{out}$ only positive halves) — 5-7 marks, very frequent (almost certain to ask half-wave).
• State $V_{dc}=V_m/π$, $V_{rms}=V_m/2$, $PIV=V_m$ — 5 marks, very frequent.
• Explain diode conducts positive half, blocks negative — 3-5 marks, frequent.
• Mention need for filter with $C$ — 3 marks.