Thyristor Phase Control (Firing Angle) Simulator

Explore phase control: delay the firing angle of a thyristor (SCR) to adjust the power delivered to a resistive load. Change the supply voltage, firing angle, load resistance and rectifier type and watch the average and RMS output voltage, power and power factor update in real time — the principle behind light dimmers and heater controllers.

Parameters

Supply voltage (RMS) Vrms

Frequency f

Firing angle (phase control angle) α

Delay from the start of a half cycle to firing

Load resistance R

Rectifier circuit type

The number of half cycles used changes the output

Results

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Average output voltage V_avg (V)

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RMS output voltage V_rms (V)

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Output power P (W)

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Average load current I_avg (A)

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Power factor PF

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Power control ratio (%)

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Source waveform & conduction region — animation

The scrolling sine wave is the AC supply voltage. In each half cycle the conduction region from the firing angle α to π is shaded; the blocked region before α is left unshaded. The red line marks the firing instant.

Output voltage vs firing angle α

Output power & power factor vs firing angle α

Theory & Key Formulas

$$V_{avg}=\frac{V_{peak}}{\pi}\,(1+\cos\alpha)$$

Average output voltage of a full-wave controlled rectifier with a resistive load. V_peak is the peak of the supply voltage (V_peak = √2·V_rms,in).

$$V_{rms}=V_{rms,in}\sqrt{1-\frac{\alpha}{\pi}+\frac{\sin 2\alpha}{2\pi}},\qquad P=\frac{V_{rms}^2}{R}$$

RMS output voltage V_rms and output power P. R is the load resistance.

α is the firing (delay) angle, and the thyristor conducts from α to π each half cycle. For half-wave control the average voltage is half of the formula above and the RMS voltage is √(1/2) times it.

What is Thyristor Phase Control?

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You can dim the lights in a room with a "brightness knob", right? How does that actually reduce the electricity reaching the bulb — does it put a resistor in series?

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The old-fashioned way really was a resistor, but then the leftover power just turns into heat in the resistor — very wasteful. Inside a modern dimmer there is a semiconductor switch called a "thyristor" (or a "triac"). Unlike an ordinary switch, it only starts conducting at the instant you send a signal — a trigger pulse — to its gate. That lets you connect the bulb partway through the AC wave. That is phase control.

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Partway through the wave...? In the animation above, the first part of the wave is unshaded and only the later part is coloured. Is only the shaded part delivered to the bulb?

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Exactly. The delay from the start of each half cycle until the gate pulse is fired is called the "firing angle α". Once fired, the thyristor conducts until the end of the half cycle (electrical angle π), then the current naturally falls to zero and it turns off. So the larger α is, the more of the early part of the wave gets chopped off. Move the firing-angle slider from 0° to 180° and you will see the shaded conduction region shrink while the output voltage and power slide down.

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I see — so α=0° is fully on and α=180° is zero. The default is 60°, which looks pretty bright. What fraction of the power is that?

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Good question. With full-wave control at α=60°, 200V and 20Ω, the output power is about 1609W. Against the maximum 2000W at α=0°, that is roughly 80% — the power control ratio card shows exactly that fraction. The interesting part is that the relation between α and power is not a straight line. While α is small (about 0–60°) the power barely drops, then it falls sharply above 90°. Look at the curve on the "Output power vs firing angle" chart below and you will see that non-linearity clearly.

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There is a power-factor card too. Isn't the power factor 1 for a resistive load? Voltage and current should be in phase for a resistor...

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Sharp eye. The resistor itself does not shift the phase, true. But once you apply phase control, the current drawn from the supply becomes a "chopped" shape — only part of each half cycle. That is no longer a clean sine wave, so the power factor drops because of both the phase shift of the fundamental (displacement factor) and the harmonic distortion. This tool reports the power factor as output RMS voltage divided by source RMS voltage, and it falls below 1 as α grows. So "dimming to save energy" comes at the cost of a worse power factor and generated harmonics.

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There is also a half-wave / full-wave switch. What changes with half-wave?

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Half-wave control uses a single thyristor and only one half cycle of the AC. So for the same α the average voltage is half of full-wave, and the maximum output power is also halved. The circuit is cheap and simple, but the other half cycle is thrown away entirely, giving large ripple and a DC component that can magnetise a transformer one-sided. So in practice almost everything — including home dimmers — uses full-wave (a triac or two thyristors), and high-power systems use three-phase. Think of half-wave as a teaching example or something for very small loads.

Frequently Asked Questions

The firing angle α is the delay between the start of each half cycle of the AC supply (the zero crossing) and the instant the gate trigger pulse is applied to the thyristor. Once fired, the thyristor conducts until the end of the half cycle (electrical angle π), where the current naturally falls to zero. The larger α is, the more of the early part of each half cycle is chopped off, so less power reaches the load. At α=0° you get full power, at α=180° the output is zero.

A full-wave controlled rectifier uses both the positive and negative half cycles of the AC supply, with an average output voltage Vavg=(Vpeak/π)(1+cosα). A half-wave controlled rectifier uses only one half cycle, so its average voltage is half that, Vavg=(Vpeak/2π)(1+cosα), and the maximum output power is also halved. Half-wave circuits are simpler but have large ripple and a DC component, so practical designs almost always use full-wave (or three-phase) control.

Even with a purely resistive load, increasing the firing angle α makes the current drawn from the supply a 'chopped' sinusoid — only part of each half cycle remains. Once the current is no longer a clean sine wave, the power factor drops because of both the phase shift of the fundamental (displacement factor) and the harmonic distortion. This tool reports the power factor as PF=Vrms_out/Vrms, the ratio of the output RMS voltage to the source RMS voltage, so you can see PF fall as α rises.

Everyday examples include incandescent light dimmers, temperature controllers for electric heaters, speed controls for hand drills and fans, and the dimmer desks used for stage lighting. All of them vary the firing angle of a thyristor or triac to continuously adjust the power delivered to a resistive load. At higher power levels, phase control is used for electric-furnace temperature control, DC motor drives and soft starters.

Real-World Applications

Lighting dimmers: Adjusting the brightness of incandescent and halogen lamps is the most familiar use of phase control. Wall-mounted light dimmers, and the dimmer desks of theatres and studios, vary the firing angle of a triac or thyristor to continuously change the power reaching the bulb. A bulb is a resistive load, so the full-wave model in this tool applies directly — the more you delay the firing angle, the dimmer it gets.

Electric heaters and temperature control: Temperature controllers for electric stoves, electric heaters, soldering irons and industrial electric furnaces also use phase control. The heating element is a purely resistive load; the firing angle is adjusted automatically in response to a thermostat or temperature-sensor signal to hold a set temperature. Because rapidly moving the firing angle causes flicker and harmonics, heaters often use zero-cross (burst) control instead, depending on the application.

Motor speed control: For universal motors in hand drills, mixers and fans, and for DC motor drives, phase control varies the average voltage applied to the armature to set the speed. For larger induction motors, phase control acts as a "soft starter" — gradually advancing the firing angle only during start-up to limit the inrush current.

Power supplies and rectifiers: High-power DC supplies, electroplating rectifiers, battery chargers and the converter stations of HVDC (high-voltage DC transmission) all use thyristor-based controlled-rectifier circuits to produce a variable DC from AC. The single-phase controlled rectifier covered here is the basic model that extends to three-phase and multi-pulse versions — and the starting point for understanding the relationship between firing angle and output voltage.

Common Misconceptions and Pitfalls

A common misconception is that "phase control just lowers the voltage, so there is no loss". It is indeed more efficient than the old resistive dimmer, but it is not lossless. A thyristor has an on-state voltage (roughly 1–2V), and passing a large current causes heating there. Furthermore, the current rises steeply at the firing instant, generating electromagnetic noise (EMI) and harmonic currents that demand input-side filtering and power-factor-correction design. This tool is an idealised-switch, resistive-load theory calculation; a real device must account separately for the on-state voltage drop, snubber circuits and noise suppression.

Next, the assumption that "the output voltage falls in proportion to the firing angle". As Vavg=(Vpeak/π)(1+cosα) makes clear, the output voltage is a non-linear function containing cosα. In the small-angle region (about 0–60°) the voltage barely drops; the change is steepest near 90°, and beyond 150° it is almost zero. This is why turning a dimmer knob "halfway" does not halve the brightness. Be sure to check this near-S-shaped curve on the "Output voltage vs firing angle" chart.

Finally, "applying the resistive-load formulas to an inductive load". The formulas in this tool are only for a resistive load (heaters, incandescent bulbs and the like). With an inductive load such as a motor or transformer, the current lags the voltage and does not reach zero even after π — the thyristor keeps conducting — so the conduction-region and average-voltage formulas change completely. A freewheeling diode may be required. When dealing with an inductive load, do not reuse the resistive-load results: a separate analysis that accounts for the load's power-factor angle is needed.

Thyristor Phase Control (Firing Angle) Simulator

What is Thyristor Phase Control?

Frequently Asked Questions

Real-World Applications

Common Misconceptions and Pitfalls

How to Use

Worked Example

Practical Notes