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I have the following formula to calculate the average power dissipated in a non-linear load:

enter image description here

I would like to know what happens if the phase between the voltage and the current (for a specific harmonic) is greater than 90 degrees.

Mathematically, it's clear that the average power will be negative, but logically loads aren't supposed to supply real power. Should I always take the absolute value of each multiplicand?

ocrdu
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JustCurious
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  • The phase should be between 0 and 90° or between 0 and -90°. So, cos( x) is always positive? – Antonio51 Jun 08 '22 at 11:23
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    I've encountered an hypothetical question in which the phase difference is greater than 90, hence the real power comes out negative, How should that be interpreted ? – JustCurious Jun 08 '22 at 14:37
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    According to the standard sign conventions, if the power comes out negative, the load indeed sources power. There's nothing stopping you from sticking, say, a voltage source in series with a load resistor and treating the combined element as the new "load." You should definitely not take the absolute value. Just consider the case where V and I are perfectly 180deg out of phase -- that's not a positive resistance. – LetterSized Jun 08 '22 at 15:16
  • Instantaneous power of a non-linear load is V(t) * I(t). The average power is the mathematical average of V(t) * I(t). If the load power is periodic, you can average the power over one period. V is load voltage, I is load current, and t is time. – user57037 Jun 08 '22 at 18:13
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    In the time domain, reactive linear loads sometimes store energy during one part of the cycle and return it to the source during a later part of the cycle. In the frequency domain, there is no reason why a non-linear load could not absorb power at one frequency, and supply power at another frequency. – user57037 Jun 08 '22 at 18:30
  • Exactly the job of the frequency "varactor" multiplier ... with no "negative" device. For information https://www.rfwireless-world.com/ApplicationNotes/Application-note-on-varactor-diode-as-frequency-multiplier-and-tuner.html#:~:text=Varactor%20diode%20frequency%20multipliers%20generate,by%20breakdown%20of%20the%20device. – Antonio51 Jun 08 '22 at 18:45

1 Answers1

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A non-linear load could theoretically "appear" to supply power at one of its harmonics but, that power has to come from somewhere and it'll be at the expense of power absorbed at the fundamental or other harmonics. Consider the tunnel diode. It could be one component inside an unspecified non-linear load and, it has a negative resistance slope like this: -

enter image description here

In the grey/gray area as V1 rises to V2 current falls from I1 down to I2 and this would appear to generate negative power. Of course, for a simple tunnel diode, there is a net power consumed by the device that prevents total power consumed being negative but, in principal, at some specific harmonic, it could be used in a "non-linear-load" to generate some negative power.

Andy aka
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