[AC Signals] - Leading/Lagging ambiguity

Discussion in 'Homework Help' started by nDever, Mar 20, 2015.

  1. nDever

    Thread Starter Active Member

    Jan 13, 2011
    154
    4
    Hey guys,

    I have a general question about classifying a signal as leading or lagging another signal.

    Consider the two currents,

    i_{1}=4cos(32t+145) A
    i_{2}=5cos(32t-65) A

    We're interested in whether i_{1} leads or lags i_{2}.

    i_{1} could lead i_{2} because it's 210 degrees in front of i_{2}, but couldn't it also lag i_{2} because it's 150 degrees behind?
     
  2. WBahn

    Moderator

    Mar 31, 2012
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    The nearly-universal convention is that the lead/lag amount between two signals is never more than half a cycle. Thus the only ambiguous case is whether a signal that is 180° out of phase is 'leading' or 'lagging', but in that case it makes no difference.
     
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  3. nDever

    Thread Starter Active Member

    Jan 13, 2011
    154
    4
    That makes sense. The above example was actually from my textbook, and it stated the correct answer as i_{1} in the lead by 210 degrees, so, I'm guessing it doesn't go by the convention unfortunately.
     
  4. WBahn

    Moderator

    Mar 31, 2012
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    Where they are probably coming from is that I1 is leading a hypothetical cosine wave that has zero phase shift and I2 is lagging that same hypothetical wave. So then it makes intuitive sense that I1 is leading I2. But that is a false premise because there is no hypothetical cosine wave that is acting as a transitive reference for the other two.

    We can add or subtract 360° of phase without changing the waveform, so we could write the first as having a phase of -215°. Similarly, we could write the second as having a phase of 295°. None of that affects the lead/lag relationship between them.
     
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