Phase Subtraction

Voltage is the difference between andy two points in a cicuit and it needs a reference, which is usually 0 V.

 

When you measure between two conductors, you are effectively subtracting one waveform from another.

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In a 120/240 V system:

      L1 = +120 V (relative to neutral)
      L2 = −120 V (relative to neutral)

They are 180° out of phase with respect to each other. If you measure between them:

     VL1–L2 = VL1 − VL2

So at any instant:

     If L1 is +120 V
     and L2 is −120 V

Then:

     120 − (−120) = 240 V

That’s phase subtraction.

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Why they don’t cancel out?

In audio, if you add two equal and opposite waves, they cancel.

But in power systems:

     You are not adding L1 + L2, you are measuring the difference between them.

 

That’s why:

     Same phase → 0 V (no difference)
     Opposite phase → maximum voltage

A good way to think about it:

If two conductors are identical, there’s no voltage between them. If they’re opposite, the difference is doubled.

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Phase subtraction occurs in live event power:

1. 120/240 V loads

     Line-to-neutral = 120 V
     Line-to-line = 240 V (because of subtraction)

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2. Multi-wire branch circuits

     Balanced loads → neutral current cancels
     That’s also phase subtraction, but with current

 

3. 3-phase systems

     Line-to-line voltage is the vector difference between phases.
     That’s where the √3 factor comes from

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Phase subtraction is really vector subtraction of sinusoidal waveforms, not simple arithmetic. You’re subtracting the magnitude and phase angle.

That’s why in 3-phase power:

     VL-L = √3 × VL-N

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