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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.
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).
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