Proper definition of lag/lead and phase angle - Page 1
Forum section: electronics / general

author: eV1Te
author_rank: Regular Contributor
timestamp: October 24, 2017, 10:21:52 pm
content: I ran into an annoying contradiction today and can't seem to remember the real definitions so the problem got stuck in my head. Please help1.When applying an AC voltage over a capacitor, the resulting current into the capacitor leads the voltage (current is shifted to the left) and this is normally represented by a negative phase angle (-90 deg).This is also mentioned on:https://en.wikipedia.org/wiki/Leading_and_lagging_current2.For a simple RC high-pass filter, the output signal is also leading the input. The output is measured over the resistor so it is also proportional to the current in the circuit, hence it is very similar to the first case. However, for a high-pass filters most literature denoted the phase as positive number (between 0 and +90).Examples of this here:https://en.wikipedia.org/wiki/Bode_plotWhich is correct, is a leading signal denoted by a positive or negative phase and why is there a discrepancy between these two cases?

author: Andy Watson
author_rank: Super Contributor
timestamp: October 24, 2017, 10:58:37 pm
content: I don't know if this works in other languages but in English a useful mnemonic for remembering lead/lag relationship is CIVIL. I.e. for a capacitor (C) the current (I) leads the voltage (V). For the case of your high-pass RC, remember that the voltage across the resistor is in-phase and determined by the current ... which, in this case is the current through the capacitor ... and the current through the capacitor leads the voltage applied to it. The voltage across the capacitor is Vin - Vout, this is NOT the same as Vin, nor Vout, i.e. you have to be careful in your choice of reference phase.

author: IanMacdonald
author_rank: Frequent Contributor
timestamp: October 24, 2017, 11:07:16 pm
content: Capacitors take time to charge, therefore they always delay the voltage change relative to the current flow.Inductors slow the current buildup or reduction in relation to applied voltage.That is really all there is to it. To say that current 'leads' voltage by a negative amount, is basically mathematical yuckspeak. Time cannot go backwards (as far as we know) so that cannot make sense.The only difference between a capacitor across an AC supply and a low pass filter is that in the former case, the series resistance is of a much lower value. When across a supply with virtually zero series resistance, the current flow in the capacitor is proportional to the rate of change of voltage. Hence it will be highest at the zero crossing points.

author: rfeecs
author_rank: Frequent Contributor
timestamp: October 24, 2017, 11:28:17 pm
content: Quote from: eV1Te on October 24, 2017, 10:21:52 pmIt looks like the Wikipedia article is wrong or at least damn confusing. Try this article instead:http://hyperphysics.phy-astr.gsu.edu/hbase/electric/phase.htmlQuoteThe phase angle defined here is voltage divided by current, not current divided by voltage.For the high pass filter Bode plot, you are looking at the ratio of output to input, which is the current (multiplied by the resistance) divided by the input voltage. So, in this case, it is current divided by voltage, resulting in a positive phase.

author: eV1Te
author_rank: Regular Contributor
timestamp: October 28, 2017, 11:15:52 pm
content: Quote from: rfeecs on October 24, 2017, 11:28:17 pmThanks for the explanation and finding that small but important quote about the phase of voltage with respect to current.So if I understand it correctly: let's say that wave B is leading wave A, then B would have a positive phase shift compared to A, if it instead is lagging the phase would be negative. However when comparing voltage and current waves, the convention is to describe the phase of the voltage with respect to current, and not the opposite.Hence if one connects a signal generator to a capacitor the current would lead the voltage and the current therefore would have a +90 degree phase shift with respect to the signal generator's output voltage. But this is not the proper way of describing it.From convention it is more correct to say that the voltage has a phase shift of -90 degrees with respect to current. Or simply: driving capacitive loads results in a negative phase shift (implying that it is the voltage phase with respect to current one is talking about).

author: IanB
author_rank: Super Contributor
timestamp: October 29, 2017, 03:15:26 am
content: I think it is even simpler than that.If the current is behind the voltage then it lags the voltage by some angle, say 90 degrees for an inductor. Now, if the current is ahead of the voltage, then the "lag" is negative, say -90 degrees for a capacitor. Either the current "lags" by -90 degrees or it leads by +90 degrees.Mathematically it is convenient to maintain a consistent sign convention for phase angles, and the convention is that lagging angles are positive and leading angles are negative. That's all there is to it.