COMPLEX NUMBERS TUTORIAL
Table of Contents
Section 1: Complex Numbers and Electrical Engineering
- The Motivation Behind the
Tutorial
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Complex numbers are used a great deal in electrical engineering. The
main reason for this is they make the whole topic of analyzing and
understanding alternating signals much easier. The problem is
understanding what they 'mean' and how to use them in the first place. To help
you get a clear picture of how they're used and what they mean we can look at a
mechanical example...
The above animation shows a rotating wheel. On the wheel there is a blue blob
which goes round and round. When viewed 'flat on' we can see that the blob is
moving around in a circle at a steady rate. However, if we look at the wheel
from the side we get a very different picture. From the side the blob seems to
be oscillating up and down. If we plot a graph of the blob's position (viewed
from the side) against time we find that it traces out a sinewave shape which
oscillates through one cycle each time the wheel completes a rotation. Here,
the sine-wave behavior we see when looking from the side 'hides' the underlying
behavior which is a continuous rotation.
We can now reverse the above argument when considering
a.c. (sinewave) oscillations in electrical circuits. Here we can regard the
oscillating voltages and currents as 'side views' of something which is
actually 'rotating' at a steady rate. We can only see the 'real' part of this,
of course, so we have to 'imagine' the changes in the other direction. This
leads us to the idea that what the oscillation voltage or current that we see
is just the 'real' portion' of a 'complex' quantity that also has an
'imaginary' part. At any instant what we see is determined by a phase angle
which varies smoothly with time
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In the following sections we present
modules, which can be used as a self-tutorial in reviewing complex numbers,
phasors and their roles in analyzing electrical circuits. |