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In a controlled rectifier, thyristors (SCRs) replace the diodes. By delaying the gate trigger by a firing angle α (measured from the point where a diode would naturally start conducting), the average DC output is reduced — giving smooth, lossless control of DC voltage for motor drives, heaters and chargers. At α = 0 the SCR behaves like a diode and delivers full output; increasing α lowers the output.
| Configuration | Average output Vdc |
|---|---|
| 1φ Half-wave, R load | (Vm/2π)(1 + cosα) |
| 1φ Full-bridge, R load | (Vm/π)(1 + cosα) |
| 1φ Full-bridge, RL (continuous) | (2Vm/π) cosα |
| 3φ Full-bridge (continuous) | (3VmL/π) cosα |
Here Vm = √2×Vphase is the peak phase voltage and VmL = √2×√3×Vphase is the peak line-to-line voltage. For a fully-controlled bridge with a highly inductive (RL) load the current is continuous, and the output follows the cosine law — it even goes negative for α > 90°, which is the inverter mode that returns energy to the AC line.
A thyristor conducts only after it is both forward-biased and gated, and it stops only when its current falls to zero. Phase control exploits this by delaying the gate pulse: the later it arrives within each half cycle, the smaller the conducting portion and the lower the average output.
For a single-phase full-wave controlled rectifier with a resistive load, the average output voltage is
Vdc = Vm(1 + cos α) / π
From a 230 V supply (Vm ≈ 325 V):
| Firing angle α | Vdc | Percent of maximum |
|---|---|---|
| 0° | 206.9 V | 100% |
| 30° | 193.0 V | 93.3% |
| 60° | 155.2 V | 75.0% |
| 90° | 103.5 V | 50.0% |
| 120° | 51.7 V | 25.0% |
Notice how uneven the control is. The first 30° of delay costs under 7% of output, while the step from 60° to 90° costs 25%. Control resolution is best around 90° and poor near the extremes — a direct consequence of the cosine term, and something that has to be accounted for in any closed-loop design.
With inductance in the load, current cannot stop instantly at the zero crossing. The thyristor keeps conducting into the next half cycle, pulling the output waveform negative for part of it and reducing the average below what the resistive formula predicts. A freewheeling diode across the load gives that current a path and restores the resistive-load behaviour.
Chopping the waveform injects substantial harmonic current back into the supply, and the delayed current draw lags the voltage, so the displacement power factor worsens as the firing angle increases. Phase control is simple and robust, but it is comparatively unkind to the supply, which is why PWM rectifiers have replaced it in applications where supply quality matters.
The firing (or delay) angle α is how far the gate trigger is delayed, measured from the instant the thyristor would start conducting if it were a diode. Increasing α delays conduction and lowers the average DC output.
By delaying when each SCR turns on, less of each AC half-cycle reaches the load, so the average output falls. For a continuous-current bridge, Vdc follows (2Vm/π)cosα, giving smooth control from full output down to zero (and negative).
At α = 0° the SCR fires immediately, behaving like a diode, so the controlled rectifier delivers the same full output as the equivalent uncontrolled (diode) rectifier.
For a fully-controlled bridge with continuous current, the average voltage becomes negative beyond 90°. The converter then operates in inverter mode, transferring power from the DC side back to the AC supply — used in regenerative drives and HVDC.
With a purely resistive load the current stops when the voltage crosses zero, so the output uses (1+cosα) terms. With a highly inductive (RL) load the current is continuous and the output follows the cosα law, which can go negative.
Vm is the peak of the phase voltage, Vm=√2×Vphase(rms). For the three-phase bridge, VmL is the peak line-to-line voltage, √2×√3×Vphase.
A controlled rectifier gives adjustable, lossless DC output — ideal for varying motor speed, charging current, or heater power — and, in the fully-controlled form, allows regenerative power flow back to the mains.
A fully-controlled bridge uses SCRs in all legs and can invert (negative output). A half-controlled (semi-converter) bridge mixes SCRs and diodes; it is cheaper but cannot go negative, so it operates only as a rectifier.
Yes. As α increases the input current lags further behind the voltage, so the displacement power factor falls (approximately cosα). High firing angles give poor power factor, which is a drawback of phase control.
It is the same as the equivalent diode rectifier: twice the line frequency for a single-phase bridge and six times the line frequency for a three-phase bridge. Phase control changes the amplitude, not the pulse number.
This tool covers the most common cases: single-phase half-wave and full-bridge, and the three-phase full bridge. For a three-phase half-wave controlled rectifier the output is (3√3·Vm/2π)cosα for continuous current.
Rearrange the formula for α. For a continuous bridge, α = arccos(Vdc / Vdc0), where Vdc0 is the α=0 output (2Vm/π for single-phase, 3VmL/π for three-phase).
The delay, measured in electrical degrees from the point where the device becomes forward-biased, before the gate pulse is applied. A larger firing angle means a shorter conduction period and lower average output.
Vdc = Vm(1 + cos α)/π for a resistive load, where Vm is the peak supply voltage. At α = 0 this reduces to 2Vm/π.
Because the relationship contains a cosine. The output changes most rapidly around 90° and barely at all near 0° or 180°, so control resolution is worst at very high and very low outputs.
Stored energy keeps current flowing past the voltage zero crossing, so the thyristor conducts into the next half cycle and the output goes negative for part of it, lowering the average below the resistive-load prediction.
It provides a path for inductive load current at the zero crossing, preventing the output from going negative and restoring behaviour closer to the resistive case. It also protects the thyristors from the inductive voltage transient.
Delaying conduction shifts the current waveform later relative to the voltage, which degrades displacement power factor, and chopping the waveform introduces harmonics that further reduce true power factor. PWM rectifiers avoid both problems at the cost of complexity.
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