AC waveforms
When an alternator produces AC voltage, the
voltage switches polarity over time, but does so in a very
particular manner. When graphed over time, the "wave" traced
by this voltage of alternating polarity from an alternator
takes on a distinct shape, known as a sine wave:
In the voltage plot from an
electromechanical alternator, the change from one polarity
to the other is a smooth one, the voltage level changing
most rapidly at the zero ("crossover") point and most slowly
at its peak. If we were to graph the trigonometric function
of "sine" over a horizontal range of 0 to 360 degrees, we
would find the exact same pattern:
Angle Sine(angle)
in degrees
0 ............... 0.0000 -- zero
15 ............... 0.2588
30 ............... 0.5000
45 ............... 0.7071
60 ............... 0.8660
75 ............... 0.9659
90 ............... 1.0000 -- positive peak
105 .............. 0.9659
120 .............. 0.8660
135 .............. 0.7071
150 .............. 0.5000
165 .............. 0.2588
180 .............. 0.0000 -- zero
195 .............. -0.2588
210 .............. -0.5000
225 .............. -0.7071
240 .............. -0.8660
255 .............. -0.9659
270 .............. -1.0000 -- negative peak
285 .............. -0.9659
300 .............. -0.8660
315 .............. -0.7071
330 .............. -0.5000
345 .............. -0.2588
360 .............. 0.0000 -- zero
The reason why an electromechanical
alternator outputs sine-wave AC is due to the physics of its
operation. The voltage produced by the stationary coils by
the motion of the rotating magnet is proportional to the
rate at which the magnetic flux is changing perpendicular to
the coils (Faraday's Law of Electromagnetic Induction). That
rate is greatest when the magnet poles are closest to the
coils, and least when the magnet poles are furthest away
from the coils. Mathematically, the rate of magnetic flux
change due to a rotating magnet follows that of a sine
function, so the voltage produced by the coils follows that
same function.
If we were to follow the changing voltage
produced by a coil in an alternator from any point on the
sine wave graph to that point when the wave shape begins to
repeat itself, we would have marked exactly one cycle
of that wave. This is most easily shown by spanning the
distance between identical peaks, but may be measured
between any corresponding points on the graph. The degree
marks on the horizontal axis of the graph represent the
domain of the trigonometric sine function, and also the
angular position of our simple two-pole alternator shaft as
it rotates:
Since the horizontal axis of this graph can
mark the passage of time as well as shaft position in
degrees, the dimension marked for one cycle is often
measured in a unit of time, most often seconds or fractions
of a second. When expressed as a measurement, this is often
called the period of a wave. The period of a wave in
degrees is always 360, but the amount of time one
period occupies depends on the rate voltage oscillates back
and forth.
A more popular measure for describing the
alternating rate of an AC voltage or current wave than
period is the rate of that back-and-forth oscillation.
This is called frequency. The modern unit for
frequency is the Hertz (abbreviated Hz), which represents
the number of wave cycles completed during one second of
time. In the United States of America, the standard
power-line frequency is 60 Hz, meaning that the AC voltage
oscillates at a rate of 60 complete back-and-forth cycles
every second. In Europe, where the power system frequency is
50 Hz, the AC voltage only completes 50 cycles every second.
A radio station transmitter broadcasting at a frequency of
100 MHz generates an AC voltage oscillating at a rate of 100
million cycles every second.
Prior to the canonization of the Hertz unit,
frequency was simply expressed as "cycles per second." Older
meters and electronic equipment often bore frequency units
of "CPS" (Cycles Per Second) instead of Hz. Many people
believe the change from self-explanatory units like CPS to
Hertz constitutes a step backward in clarity. A similar
change occurred when the unit of "Celsius" replaced that of
"Centigrade" for metric temperature measurement. The name
Centigrade was based on a 100-count ("Centi-") scale
("-grade") representing the melting and boiling points of H2O,
respectively. The name Celsius, on the other hand, gives no
hint as to the unit's origin or meaning.
Period and frequency are mathematical
reciprocals of one another. That is to say, if a wave has a
period of 10 seconds, its frequency will be 0.1 Hz, or 1/10
of a cycle per second:
An instrument called an oscilloscope
is used to display a changing voltage over time on a
graphical screen. You may be familiar with the appearance of
an ECG or EKG (electrocardiograph) machine,
used by physicians to graph the oscillations of a patient's
heart over time. The ECG is a special-purpose oscilloscope
expressly designed for medical use. General-purpose
oscilloscopes have the ability to display voltage from
virtually any voltage source, plotted as a graph with time
as the independent variable. The relationship between period
and frequency is very useful to know when displaying an AC
voltage or current waveform on an oscilloscope screen. By
measuring the period of the wave on the horizontal axis of
the oscilloscope screen and reciprocating that time value
(in seconds), you can determine the frequency in Hertz.
Voltage and current are by no means the only
physical variables subject to variation over time. Much more
common to our everyday experience is sound, which is
nothing more than the alternating compression and
decompression (pressure waves) of air molecules, interpreted
by our ears as a physical sensation. Because alternating
current is a wave phenomenon, it shares many of the
properties of other wave phenomena, like sound. For this
reason, sound (especially structured music) provides an
excellent analogy for relating AC concepts.
In musical terms, frequency is equivalent to
pitch. Low-pitch notes such as those produced by a
tuba or bassoon consist of air molecule vibrations that are
relatively slow (low frequency). High-pitch notes such as
those produced by a flute or whistle consist of the same
type of vibrations in the air, only vibrating at a much
faster rate (higher frequency). Here is a table showing the
actual frequencies for a range of common musical notes:
Astute observers will notice that all notes
on the table bearing the same letter designation are related
by a frequency ratio of 2:1. For example, the first
frequency shown (designated with the letter "A") is 220 Hz.
The next highest "A" note has a frequency of 440 Hz --
exactly twice as many sound wave cycles per second. The same
2:1 ratio holds true for the first A sharp (233.08 Hz) and
the next A sharp (466.16 Hz), and for all note pairs found
in the table.
Audibly, two notes whose frequencies are
exactly double each other sound remarkably similar. This
similarity in sound is musically recognized, the shortest
span on a musical scale separating such note pairs being
called an octave. Following this rule, the next
highest "A" note (one octave above 440 Hz) will be 880 Hz,
the next lowest "A" (one octave below 220 Hz) will be 110
Hz. A view of a piano keyboard helps to put this scale into
perspective:
As you can see, one octave is equal to
eight white keys' worth of distance on a piano keyboard.
The familiar musical mnemonic (doe-ray-mee-fah-so-lah-tee-doe)
-- yes, the same pattern immortalized in the whimsical
Rodgers and Hammerstein song sung in The Sound of Music
-- covers one octave from C to C.
While electromechanical alternators and many
other physical phenomena naturally produce sine waves, this
is not the only kind of alternating wave in existence. Other
"waveforms" of AC are commonly produced within electronic
circuitry. Here are but a few sample waveforms and their
common designations:
These waveforms are by no means the only
kinds of waveforms in existence. They're simply a few that
are common enough to have been given distinct names. Even in
circuits that are supposed to manifest "pure" sine, square,
triangle, or sawtooth voltage/current waveforms, the
real-life result is often a distorted version of the
intended waveshape. Some waveforms are so complex that they
defy classification as a particular "type" (including
waveforms associated with many kinds of musical
instruments). Generally speaking, any waveshape bearing
close resemblance to a perfect sine wave is termed
sinusoidal, anything different being labeled as
non-sinusoidal. Being that the waveform of an AC voltage
or current is crucial to its impact in a circuit, we need to
be aware of the fact that AC waves come in a variety of
shapes.
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REVIEW:
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AC produced by an electromechanical
alternator follows the graphical shape of a sine wave.
-
One cycle of a wave is one complete
evolution of its shape until the point that it is ready to
repeat itself.
-
The period of a wave is the amount
of time it takes to complete one cycle.
-
Frequency is the number of complete
cycles that a wave completes in a given amount of time.
Usually measured in Hertz (Hz), 1 Hz being equal to one
complete wave cycle per second.
-
Frequency = 1/(period in seconds)
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