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The unit of measure for frequency is the hertz (Hz), where
1 hertz (Hz) � 1 cycle per second (c/s)
SINUSOIDAL ac VOLTAGE CHARACTERISTICS AND DEFINITIONS ⏐⏐⏐ 525
(13.1)
The unit hertz is derived from the surname of Heinrich Rudolph Hertz
(Fig. 13.6), who did original research in the area of alternating currents
and voltages and their effect on the basic R, L, and C elements. The frequency
standard for North America is 60 Hz, whereas for Europe it is
predominantly 50 Hz.
As with all standards, any variation from the norm will cause difficulties.
In 1993, Berlin, Germany, received all its power from eastern
plants, whose output frequency was varying between 50.03 and
51 Hz. The result was that clocks were gaining as much as 4 minutes
a day. Alarms went off too soon, VCRs clicked off before the
end of the program, etc., requiring that clocks be continually reset. In
1994, however, when power was linked with the rest of Europe, the
precise standard of 50 Hz was reestablished and everyone was on
time again.
Using a log scale (described in detail in Chapter 23), a frequency
spectrum from 1 Hz to 1000 GHz can be scaled off on the same axis, as
shown in Fig. 13.7. A number of terms in the various spectrums are
probably familiar to the reader from everyday experiences. Note that the
audio range (human ear) extends from only 15 Hz to 20 kHz, but the
transmission of radio signals can occur between 3 kHz and 300 GHz.
The uniform process of defining the intervals of the radio-frequency
spectrum from VLF to EHF is quite evident from the length of the bars
in the figure (although keep in mind that it is a log scale, so the frequencies
encompassed within each segment are quite different). Other
frequencies of particular interest (TV, CB, microwave, etc.) are also
included for reference purposes. Although it is numerically easy to talk
about frequencies in the megahertz and gigahertz range, keep in mind
that a frequency of 100 MHz, for instance, represents a sinusoidal
waveform that passes through 100,000,000 cycles in only 1 s—an
incredible number when we compare it to the 60 Hz of our conventional
power sources. The new Pentium II chip manufactured by Intel can run
at speeds up to 450 MHz. Imagine a product able to handle 450,000,000
instructions per second—an incredible achievement. The new Pentium
IV chip manufactured by Intel can run at a speed of 1.5 GHz. Try to
imagine a product able to handle 1,500,000,000,000 instructions in just
1 s—an incredible achievement.
Since the frequency is inversely related to the period—that is, as one
increases, the other decreases by an equal amount—the two can be
related by the following equation:
1
f � �� T
f � Hz
T � seconds (s)
(13.2)
or T � � (13.3)
1
f �
German (Hamburg,
Berlin, Karlsruhe)
(1857–94)
Physicist
Professor of Physics,
Karlsruhe
Polytechnic and
University of Bonn
Courtesy of the
Smithsonian Institution
Photo No. 66,606
Spurred on by the earlier predictions of the English
physicist James Clerk Maxwell, Heinrich Hertz produced
electromagnetic waves in his laboratory at the
Karlsruhe Polytechnic while in his early 30s. The
rudimentary transmitter and receiver were in essence
the first to broadcast and receive radio waves.
He was able to measure the wavelength of the
electromagnetic waves and confirmed that the velocity
of propagation is in the same order of magnitude
as light. In addition, he demonstrated that the
reflective and refractive properties of electromagnetic
waves are the same as those for heat and light
waves. It was indeed unfortunate that such an ingenious,
industrious individual should pass away at the
very early age of 37 due to a bone disease.
FIG. 13.6
Heinrich Rudolph Hertz.