AC phase
Things start to get complicated when we need
to relate two or more AC voltages or currents that are out
of step with each other. By "out of step," I mean that the
two waveforms are not synchronized: that their peaks and
zero points do not match up at the same points in time. The
following graph illustrates an example of this:
The two waves shown above (A versus B) are
of the same amplitude and frequency, but they are out of
step with each other. In technical terms, this is called a
phase shift. Earlier we saw how we could plot a "sine
wave" by calculating the trigonometric sine function for
angles ranging from 0 to 360 degrees, a full circle. The
starting point of a sine wave was zero amplitude at zero
degrees, progressing to full positive amplitude at 90
degrees, zero at 180 degrees, full negative at 270 degrees,
and back to the starting point of zero at 360 degrees. We
can use this angle scale along the horizontal axis of our
waveform plot to express just how far out of step one wave
is with another:
The shift between these two waveforms is
about 45 degrees, the "A" wave being ahead of the "B" wave.
A sampling of different phase shifts is given in the
following graphs to better illustrate this concept:
Because the waveforms in the above examples
are at the same frequency, they will be out of step by the
same angular amount at every point in time. For this reason,
we can express phase shift for two or more waveforms of the
same frequency as a constant quantity for the entire wave,
and not just an expression of shift between any two
particular points along the waves. That is, it is safe to
say something like, "voltage 'A' is 45 degrees out of phase
with voltage 'B'." Whichever waveform is ahead in its
evolution is said to be leading and the one behind is
said to be lagging.
Phase shift, like voltage, is always a
measurement relative between two things. There's really no
such thing as a waveform with an absolute phase
measurement because there's no known universal reference for
phase. Typically in the analysis of AC circuits, the voltage
waveform of the power supply is used as a reference for
phase, that voltage stated as "xxx volts at 0 degrees." Any
other AC voltage or current in that circuit will have its
phase shift expressed in terms relative to that source
voltage.
This is what makes AC circuit calculations
more complicated than DC. When applying Ohm's Law and
Kirchhoff's Laws, quantities of AC voltage and current must
reflect phase shift as well as amplitude. Mathematical
operations of addition, subtraction, multiplication, and
division must operate on these quantities of phase shift as
well as amplitude. Fortunately, there is a mathematical
system of quantities called complex numbers ideally
suited for this task of representing amplitude and phase.
Because the subject of complex numbers is so
essential to the understanding of AC circuits, the next
chapter will be devoted to that subject alone.
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REVIEW:
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Phase shift is where two or more
waveforms are out of step with each other.
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The amount of phase shift between two
waves can be expressed in terms of degrees, as defined by
the degree units on the horizontal axis of the waveform
graph used in plotting the trigonometric sine function.
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A leading waveform is defined as
one waveform that is ahead of another in its evolution. A
lagging waveform is one that is behind another.
Example:
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Calculations for AC circuit analysis must
take into consideration both amplitude and phase shift of
voltage and current waveforms to be completely accurate.
This requires the use of a mathematical system called
complex numbers.
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