Suppose we have a residential lighting dimmer switch circuit, where the output power across the load is controlled by the phase (alpha) of SCRs. Depending on the phase, the SCRs will essentially chop the input voltage, so that only part of it will appear across the load.

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From what I'v been told, this chopping of the voltage will affect the power factor of the system. However, I don't quite understand why.

I'v watched countless Youtube videos on power factor and every one of them explains how the power factor is simply dependent on the phase difference between the voltage and current. Essentially poor power factor is a result of an inductive or capacitive load, which either shifts the phase of the voltage or current. Because of this phase shift, when the voltage and current sinusoids are multiplied together to obtain the average power, some of the area under the curve of the integral will become negative. From my understanding, this essentially means that the load is feeding back some of the power to the source for part of the cycle.

In this circuit, however, there is no phase difference between the voltage and current. The current and voltage follow each other exactly when the switches are on.

In general, for a circuit where the output is switched on and off, how can we analyze the power factor? How do we calculate the real power, the reactive power, and the apparent power? Even the name "reactive power" points towards the power due to reactive components, such as inductors and capacitors. If there are no reactive components, how is there reactive power?

  • \$\begingroup\$ You can easily slide a discrete Fourier transform window across your waveforms (digitize them first) to find the fundamental frequency components (phasors) of voltage & current. That would be interesting. I have some old examples here. \$\endgroup\$ Apr 13, 2021 at 22:49
  • \$\begingroup\$ Only if the switch is on for the whole cycle, the sinusoidal voltage causes sinusoidal current that relate by the resistance so power factor is 1. Now when the switch is not on for the whole cycle, the sinusoidal voltage does not cause a sinusoidal current to be taken any more. \$\endgroup\$
    – Justme
    Apr 13, 2021 at 23:28

1 Answer 1


In general, for a circuit where the output is switched on and off, how can we analyze the power factor?

In general, the power factor in such a circuit is not the power factor defined as the cosine of the angle between the current and voltage but as the real power divided by the apparent power. In this case, the apparent power is the total RMS voltage including harmonics multiplied by the total RMS current including harmonics. Real power is calculated by multiplying the corresponding instantaneous values of voltage and current and integrating over a cycle. The power factor in this case is the "total power factor" rather than the "displacement power factor." Some people consider the "total power factor" to be the "true power factor," but that can lead to calculation errors and nasty surprises.


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