DEFINITIONS ABOUT 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: Figure 1.8

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: Figure 1.9

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

An instrument called an oscilloscope, Figure 1.10, 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 (electrocardio-
graph) 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 phys-
ical 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 °ute or whistle consist of the same type of vibrations in
the air, only vibrating at a much faster rate (higher frequency). Figure 1.11 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 ¯rst 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 ¯rst 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: Figure 1.12

As you can see, one octave is equal to seven white keys' worth of distance on a piano keyboard.
The familiar musical mnemonic (doe-ray-mee-fah-so-lah-tee) { 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 in ¯gure 1.13

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 classi¯cation 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 di®erent 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)
• 1.3 Measurements of AC magnitude
• So far we know that AC voltage alternates in polarity and AC current alternates in direction. We
• also know that AC can alternate in a variety of di®erent ways, and by tracing the alternation over