Rectifiers

Rectifiers convert AC to DC. Learn half-wave, centre-tapped and bridge single-phase circuits, three-phase bridges, capacitor filtering and ripple, PIV ratings, and the design of a complete linear DC supply.

Almost every electronic device needs DC, but the mains is AC. A rectifier uses diodes — one-way valves for current — to let only one polarity through, turning AC into pulsating DC. A reservoir capacitor then smooths the pulses into nearly steady DC.

Rectifiers are the input stage of power supplies, battery chargers, variable-speed drives and DC links in HVDC and EV chargers.

An analogy

A rectifier is like a set of one-way valves on a pump that sloshes back and forth: whichever way the water moves, the valves steer it the same way into a tank (the capacitor) that smooths the flow.

Half-wave vs full-wave

A single diode passes only positive half-cycles (half-wave): simple but wasteful, with ripple at 50 Hz. A centre-tapped transformer with two diodes, or a four-diode bridge, uses both half-cycles (full-wave), doubling the average and the ripple frequency to 100 Hz.

Smoothing capacitor

The capacitor charges to the peak each half-cycle and supplies the load between peaks, discharging slightly. Bigger C or smaller load current → smaller ripple. The output sits near V_m minus diode drops, well above the unfiltered average.

Diode ratings

Choose diodes for average current, surge current (the capacitor's inrush at switch-on), and PIV: a bridge diode must block V_m; a centre-tapped circuit's diodes must block 2V_m. Add margin (≈ 1.5–2×) for mains transients.

Three-phase rectifiers

A six-pulse bridge on a 400/415 V three-phase supply gives ≈ 540–560 V DC with small, 300 Hz ripple — the DC link inside every VFD and many EV fast chargers.

Input current harmonics and PFC

A capacitor-input rectifier draws current only in short pulses near each peak, so the input current is rich in harmonics and its power factor is ~0.5–0.7. Above ~75 W, standards require power-factor correction: a boost converter shapes the input current into a sine in phase with the voltage (pf > 0.95).

Formulas

• Half-wave average: V_dc = V_m / π
• Full-wave / bridge average: V_dc = 2V_m / π
• Three-phase bridge: V_dc = 3√2·V_LL / π ≈ 1.35 V_LL
• Capacitor-filter ripple (full-wave): ΔV ≈ I_load / (2 f C)

Worked example: Bridge rectifier with capacitor filter

Given: 12 V RMS secondary, 50 Hz; Two diode drops = 1.4 V; I_load = 1 A, C = 4700 µF

Find: Peak output, ripple and approximate average.

• V_m = √2 × 12 = 16.97 V → V_peak,out = 16.97 − 1.4 = 15.57 V
• ΔV = 1/(2 × 50 × 4700e-6) = 2.13 V
• V_avg ≈ 15.57 − 2.13/2 ≈ 14.5 V

Answer: 15.6 V peak, 2.1 V ripple, ≈ 14.5 V average

Worked example: VFD DC link

Given: 415 V three-phase

Find: DC-link voltage.

• V_dc ≈ 1.35 × 415 = 560 V (with a capacitor, close to the peak √2 × 415 = 587 V at light load)

Answer: ≈ 560–587 V DC

Common mistakes

• Wrong: Assuming the DC output equals the RMS secondary voltage. — Right: With a capacitor filter, output ≈ √2 × V_rms minus diode drops, minus ripple.
• Wrong: Ignoring mains tolerance in low-headroom designs. — Right: Check the trough voltage at −10 % mains so the regulator never drops out.

Applications

• Linear power supplies: Transformer + bridge + capacitor + linear regulator: low noise, used in audio and lab supplies.
• Motor drives: Six-pulse diode bridges create the DC link of VFDs.
• Chargers & SMPS: The first stage of every switch-mode supply rectifies mains to ~325 V DC.

Key takeaways

• Half-wave V_m/π, full-wave 2V_m/π, three-phase ≈ 1.35 V_LL.
• Capacitor filters hold near V_m; ripple ≈ I/(2fC).
• Size diodes for PIV, average and surge current.
• Capacitor-input rectifiers have poor pf — PFC fixes it.

Going further

• Active PFC boost: A boost converter in continuous-conduction mode, controlled so its average inductor current follows a rectified-sine reference, gives pf ≈ 0.99 and a regulated ~400 V bus for the following converter.
• Inrush limiting: Charging a large capacitor from mains draws huge inrush current; NTC thermistors, resistor + relay bypass or controlled SCR pre-charge limit it.
• Diode reverse recovery: Fast and Schottky diodes (and SiC Schottky at high voltage) reduce recovery charge, cutting switching loss and EMI in high-frequency rectifiers.