Inductors at radio frequency
The radio frequencies range from 9 kHz to well above 100 GHz. At the low end of this
range, inductors are similar to those at audio frequencies. As the frequency increases,
cores having lower permeability are used. Toroids are quite common up through about
30 MHz. Above that frequency, air-core coils are more often used.
In radio-frequency (rf) circuits, coils are routinely connected in series or in parallel
with capacitors to obtain tuned circuits. Other arrangements yield various characteristics
of attenuation versus frequency, serving to let signals at some frequencies pass,
while rejecting signals at other frequencies. You’ll learn more about this in the chapter
on resonance.
Transmission-line inductors
At radio frequencies of more than about 100 MHz, another type of inductor becomes
practical. This is the type formed by a length of transmission line.
A transmission line is generally used to get energy from one place to another. In radio
communications, transmission lines get energy from a transmitter to an antenna,
and from an antenna to a receiver
Types of transmission line
Transmission lines usually take either of two forms, the parallel-wire type or the coaxial
type.
A parallel-wire transmission line consists of two wires running alongside each other
with a constant spacing (Fig. 10-10). The spacing is maintained by polyethylene rods
molded at regular intervals to the wires, or by a solid web of polyethylene. You have
seen this type of line used with television receiving antennas. The substance separating
the wires is called the dielectric of the transmission line.
A coaxial transmission line has a wire conductor surrounded by a tubular braid or
pipe (Fig. 10-11). The wire is kept at the center of this tubular shield by means of polythylene
beads, or more often, by solid or foamed polyethylene dielectric, all along the
length of the line.
Line inductance
Short lengths of any type of transmission line behave as inductors, as long as the line is less than 90 electrical degrees in length. At 100 MHz, 90 electrical degrees, or 1⁄4
wavelength, in free space is just 75 cm, or a little more than 2 ft. In general, if f is the frequency
in megahertz, then 1⁄4 wavelength (s) in free space, in centimeters, is given by
s = 7500/f
The length of a quarter-wavelength section of transmission line is shortened from
the free-space quarter wavelength by the effects of the dielectric. In practice, 1⁄4 wavelength
along the line can be anywhere from about 0.66 of the free-space length (for
coaxial lines with solid polyethylene dielectric) to about 0.95 of the free-space length
(for parallel-wire line with spacers molded at intervals of several inches).
The factor by which the wavelength is shortened is called the velocity factor of the
line. This is because the shortening of the wavelength is a result of a slowing-down of
the speed with which the radio signals move in the line, as compared with their speed
in space (the speed of light). If the velocity factor of a line is given by v, then the above
formula for the length of a quarter-wave line, in centimeters, becomes
s = 7500v/f
Very short lengths of line—a few electrical degrees—produce small values of inductance.
As the length approaches 1⁄4 wavelength, the inductance increases.
Transmission line inductors behave differently than coils in one important way: the
inductance of a transmission-line section changes as the frequency changes. At first, the inductance will become larger as the frequency increases. At a certain limiting frequency,
the inductance becomes infinite. Above that frequency, the line becomes capacitive
instead. You’ll learn about capacitance shortly.
A detailed discussion of frequency, transmission line type and length, and inductance
is beyond the level of this book. Texts on radio engineering are recommended for
further information on this subject.
Unwanted inductances
Any length of wire has some inductance. As with a transmission line, the inductance of
a wire increases as the frequency increases. Wire inductance is therefore more significant
at radio frequencies than at audio frequencies.
In some cases, especially in radio communications equipment, the inductance
of, and among, wires can become a major bugaboo. Circuits can oscillate when they
should not. A receiver might respond to signals that it’s not designed to intercept. A
transmitter can send out signals on unauthorized and unintended frequencies. The
frequency response of any circuit can be altered, degrading the performance of the
equipment.
Sometimes the effects of stray inductance are so small that they are not important;
this might be the case in a stereo hi-fi set located at a distance from other electronic
equipment. In some cases, stray inductance can cause life-threatening
malfunctions. This might happen with certain medical devices.
The most common way to minimize stray inductance is to use coaxial cables between
and among sensitive circuits or components. The shield of the cable is connected
to the common ground of the apparatus.
