Rectifier waveforms — half-wave, full-wave, 3-φ 6-pulse, SCR control
V_dc equations, ripple factor, firing-angle control, and 6-pulse line-current harmonics (5th, 7th, 11th, 13th).
Step 1 — Single-phase half-wave: 1 diode, V_dc = V_m / π ≈ 0.318·V_m
Reference notes
Use Next → on the narrator above to walk through five rectifier topologies plus their ripple, harmonic, and firing-angle behaviour.
Rectifier output equations (no filter)
| Topology | V_dc / V_m | Ripple factor | f_ripple / f_line |
|---|---|---|---|
| 1-φ half-wave (1 diode) | 1/π ≈ 0.318 | 1.21 (121 %) | 1 |
| 1-φ full-wave bridge (4 diodes) | 2/π ≈ 0.637 | 0.482 (48 %) | 2 |
| 3-φ half-wave (3 diodes, 3-pulse) | 3√3 / (2π) ≈ 0.827 | 0.183 (18 %) | 3 |
| 3-φ full-wave bridge (6 diodes, 6-pulse) | 3√3 / π ≈ 1.654 (V_LN peak basis) or 3/π · V_LL,peak ≈ 1.35 · V_LL,RMS | 0.042 (4.2 %) | 6 |
| 12-pulse (two 6-pulse, 30° shift) | Same as 6-pulse | ~0.010 (1.0 %) | 12 |
More pulses → smoother DC, smaller filter capacitor, and cleaner line current.
Thyristor (SCR) firing-angle control
Replace each diode with a thyristor (SCR) and delay its turn-on by firing angle α (measured from the natural commutation point). The DC output scales as:
- α = 0°: SCRs act like diodes — full output.
- α = 60°: V_dc drops to 50 % of maximum.
- α = 90°: V_dc = 0.
- α > 90°: V_dc < 0 — the converter operates as a line-commutated inverter and sends power back to the AC source. This is regenerative-braking operation in DC drives.
SCR converters dominated industrial DC drives until the 1990s. Today they're used in HVDC line-commutated converters and very large drives (rolling mills, etc.); IGBT-based PWM converters have replaced them in most applications below a few megawatts.
Line-current harmonics
A non-controlled rectifier draws line current only when its diodes conduct — typically a square-shaped pulse per phase per half-cycle. The Fourier decomposition of this current gives harmonics at specific orders:
- 1-φ full-wave bridge: odd harmonics 3, 5, 7, 9, 11, … with amplitudes ~1/h. Significant 3rd and 5th.
- 3-φ 6-pulse bridge: harmonics only at h = 6n ± 1 → 5th, 7th, 11th, 13th, 17th, 19th, …. Triplens (3, 9, 15) cancel by symmetry. Amplitude ≈ 1/h.
- 3-φ 12-pulse: harmonics only at h = 12n ± 1 → 11th, 13th, 23rd, 25th. The 5th and 7th cancel between the two paralleled 6-pulse bridges (30° phase shift via Δ-Y/Y-Y transformer windings).
Total harmonic distortion (THD) for a bare 6-pulse VFD line current is typically 25–35 %. IEEE Std 519 sets allowable limits depending on the short-circuit ratio (I_sc / I_load) at the point of common coupling — typically 5 % total or less. Mitigation:
- Line reactor (3–5 % impedance): reduces THD to ~30 %, cheap.
- DC-bus choke: similar effect.
- Tuned passive filter (LC trap at 5th harmonic): targeted reduction.
- Active harmonic filter: injects compensating current, broadband.
- 12-pulse or 18-pulse converter: replaces the rectifier with one that draws cleaner current.
- Active front end (AFE): IGBT-based rectifier with PWM, draws near-sinusoidal current at unity PF. Most expensive but cleanest.
Worked example: VFD DC-bus voltage
A 6-pulse VFD fed by a 480 V (V_LL,RMS) supply has a DC-bus voltage:
(In practice the DC bus voltage drops slightly under load due to line/transformer impedance and DC-bus capacitor ripple; nominal is 650 V.)
Keyboard shortcuts
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- On step 5 (SCR control), click + / − on the canvas to adjust firing angle α and watch the DC output and waveform shift.