presta
Legendary Member
Power factor is True power/Apparent Power.
If you have a linear network, and a sinusiodal source, the current will also be a sinusoid, and the true power will be the product of rms voltage and current (apparent power), and the cosine of the phase angle, φ, (which is the power factor):
P = VIcosφ
However, if your load is non-linear it gets a bit more complicated than that.
A prime candidate for a non-linear load is the rectifier on the input to a power supply such as that found in any electronic equipment, so let's look at that as an example:
In the top plot of the top window, the green waveform is the sinusoidal supply voltage, and the blue waveform is the current, and as you can see, this is anything but a sinewave. The reason for this is that when the PSU output is smoothed, so the rectifier only conducts whilst the input voltage exceeds the voltage stored on the smoothing capacitor, and the current waveform is a large amplitude spike of short duration.
The red wave below is the instantaneous product of the voltage and current, showing how the power varies throughout the cycle, and it's the mean of this waveform that's the true power. This is always the case for any circuit, mean true power over an interval T1 to T2 is the mean of the instantaneous product of voltage and current:
Note that the trace math box above gives the value for the integral too, which is the energy, power being energy divided by time.
The problem is that you can't measure and multiply voltage & current thousands of times a second with a multimeter, so you need an instrument that will do it for you: a power meter. Concepts like RMS values and power factor are shortcuts devised to avoid the need for this, but only in the very specific circumstances for which they're applicable. The difference is between the average of a product and the product of two averages.
In the case of the rectifier above, your voltmeter is measuring the voltage over the whole cycle, but the majority of that is not generating power because the current is zero. If you look at the trace math boxes to the right of the plot, you will see that the true power is ~123W, but the product of rms voltage and rms current is 226W, a +84% error.
The bottom window shows what happens with a moving coil multimeter instead of one that reads true rms. The blue trace shows rectified current (because moving coil meters contain a rectifier themselves and respond to the mean of the rectified current), and the scale is then calibrated to read 1.11 times the mean because the rms value of a sinusoid is 1.11 times the rectified mean. The math box shows a mean current of ~395mA, so multiplying this by 1.11 to get what your meter would be indicating, and then by the voltage, you now get 105W, a -14% error.
These errors aren't fixed, or generalisable, because they depend on the size of the smoothing capacitor. The larger the capacitor the closer the current spike gets to the peak voltage, the shorter the duration, and the higher the peak amplitude.
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