How ELI The ICEman Creates Phase Shifts
If you took some classes (or did some reading) on basic electronics, you may
remember the mnemonic "ELI The ICEman," a fictional character whose name is
intended to help you remember the phase relationship between voltage and
current through an inductor and a capacitor.
The mnemonic has two complementary parts. The first part, ELI, means that in
an inductor (which is usually symbolized with the letter L in electronics),
voltage (E) comes before current (I). That is to say, if you suddenly apply a
voltage to an inductor, the voltage builds up around the inductor before any
current starts to flow through it. As the inductor gradually yields to the
voltage applied to it, it begins to allow current to flow, but in the first
instant when a voltage is applied to an inductor, very little current flows,
and most of the voltage is dropped directly across the inductor.
The second part of the mnemonic, ICE, indicates the exact opposite: In a
capacitor, current comes before voltage. When you first apply a voltage to a
capacitor, the capacitor acts as a short. Brief, transient bursts of voltage
pass right through the capacitor. Only when voltage is applied over a longer
period of time does voltage "build up" in the capacitor as it charges up.
This means that if you start ramping up the voltage across a capacitor, the
current through it will precede the buildup of voltage across it.
These principles can be applied to create a simple circuit which phase-shifts
a wave. Suppose you have a sine wave generator, and you would like to create
a separate point in the circuit in which that same wave is phase-shifted to
the left or right. By inserting a capacitor or inductor into the circuit, you
can do this.
Somewhat intuitively, then, you might imagine a circuit like this:
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This circuit places a capacitor in line with a sine-wave generator. However,
if you attach an oscilloscope where one is indicated, you will not see a
phase-shifted version of the sine wave coming from the generator, because the
point where the oscilloscope is happens to be a direct short to the output of
the generator. In fact, since AC signals (like sine waves) pretty much pass
directly through capacitors, this circuit effectively ends up shorting out
the function generator, and could damage it.
To deal with both of these problems, let's introduce a resistor to create
some element of isolation for that capacitor. Let's create a circuit like
this:
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The resistor just serves to separate the sine wave generator from the
capacitor. Since this is just an intuitive discussion, we'll avoid assigning
exact numbers to any of these components' values, but let's assume that the
resistor is of a high enough value that it provides reasonable isolation from
the sine wave source, but of a low enough value that not all of the sine
wave's voltage gets dropped across the resistor--if the resistor's value is
too high, the oscilloscope would pretty much just show a flat line.
Before you take a look at the oscilloscope, though, let's intuitively
imagine what happens to the capacitor as the sine wave starts. Let's assume
that the capacitor is completely discharged when the sine wave starts. This
means that the capacitor is essentially a short (except for its equivalent
series resistance (ESR), which is probably much lower than the value of the
actual resistor in the circuit, and therefore probably negligible). This
means that, by definition, voltage across the capacitor must be zero, since
voltage cannot build up over a dead short. What about the current through
the capacitor? Since the capacitor is a short, the current through it will
be whatever the resistor allows to pass through (by Ohm's Law, current
through the capacitor is basically the voltage divided by the resistance).
So when the circuit starts running, the capacitor has no voltage, but
considerable current going through it.
But this soon changes. As the capacitor charges up, it quickly builds up a
voltage. As this happens, the current drops off. The capacitor will keep
charging up as long as a higher voltage is applied than the voltage currently
across the capacitor. In this circuit, then, the capacitor will keep charging
up until the sine wave from the function generator starts to swing in the
opposite direction. When the sine wave generator comes back toward the
center, it meets the capacitor's voltage on the way; when these paths cross,
the capacitor stops charging up, and begins to discharge in the opposite
direction, following the sine wave input. However, these reactions by the
capacitor are delayed. The result of all this is that on the oscilloscope,
you will see essentially the same sine wave coming out of the generator,
except with a somewhat lower amplitude (because some of it's been dropped
across the resistor), and, more importantly for this discussion,
phase-shifted somewhat to the right. The waveform at the capacitor "lags" the
waveform at the generator. As in the ICE part of our mnemonic, the
capacitor's voltage comes later.
Now let's imagine the equivalent circuit with an inductor instead of a
capacitor:
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You can probably already guess what the waveform on the oscilloscope would
look like, and you'd be right: It will be the same as the sine wave coming
from the function generator, except it will, again, be of a somewhat lower
amplitude because the resistor absorbs some of the voltage, but it'll also be
phase-shifted to the left. As in the ELI part of our mnemonic, in an
inductor, the voltage arrives "early." We say that the inductor's waveform
"leads" the waveform of the function generator.
(
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