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.
- REVIEW:
- 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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