full-wave rectifier

full-wave rectifier

1. What a Full-Wave Rectifier Is

Full-wave rectifier = two-diode center-tapped or four-diode bridge that converts both half-cycles of AC to pulsating DC (both positive), giving higher average DC, lower ripple, higher efficiency than half-wave.

Types:

• Center-tapped: 2 diodes + center-tapped transformer (secondary $V_m$ per half). During positive half, D1 conducts, D2 blocks; during negative half, D2 conducts, D1 blocks — both halves appear across $R_L$ as positive.
• Bridge: 4 diodes in bridge (no center tap) — 2 diodes conduct each half (pair diagonal): during positive, D1 & D3 conduct; negative, D2 & D4 conduct.

2. Output Characteristics (ideal, no filter)

• Average DC:

(twice half-wave) — for bridge, same but $V_m$ is full secondary.

• RMS:

• PIV: Center-tapped:

(non-conducting diode sees $V_m$ from its half plus $V_m$ from other half); Bridge:

per diode (only $V_m$ across, advantage).

• Frequency ripple: $2f$ (100 Hz for 50Hz mains) — easier to filter (smaller $C$ needed).
• Efficiency: 81.2% theoretical (vs 40.6% half-wave).

3. With Capacitor Filter

Capacitor $C$ across $R_L$ charges to $V_m$ each half-cycle and discharges slightly between peaks ⇒ ripple

for full-wave (since frequency doubled, ripple half of half-wave for same $C$).

4. Worked Examples

(a) Secondary 12V RMS center-tapped per half V_m≈17V: ideal center-tapped Vdc=10.8V, Vrms≈12V ⇒ PIV per diode 34V (2·17)

(b) Bridge with same 12V RMS (no center tap V_m=17V): Vdc=10.8V but PIV per diode 17V (better)

(c) Need DC 12V at 100mA with <1V ripple at 100Hz full-wave: C≈ I/(2f·V_rip)=0.1/(100·1)=1000µF ✓

(d) Why bridge preferred? No center-tap transformer (cheaper), lower PIV, but 2 diode drops (1.4V vs 0.7V).

(e) Center-tapped needs center-tapped transformer (extra cost, copper).

5. Exam Points

• Draw center-tapped (2 diodes) and bridge (4 diodes) circuits with waveforms ($v_s$ sine, $v_{out}$ both halves positive) — 7-10 marks, very frequent (the most common rectifier question, often ask both).
• State $V_{dc}=2V_m/π$, $V_{rms}=V_m/√2$, PIV $2V_m$ vs $V_m$ — 5-7 marks, very frequent.
• Distinguish center-tapped vs bridge (diodes, PIV, transformer) — 5 marks, frequent.
• Mention ripple $2f$ and filter $V_{ripple}=I/2fC$ — 3-5 marks, frequent.