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?

 

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.

 

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.

 

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.