Inductors at RF

The radio frequency (RF) spectrum ranges from a few kilohertz to well above 100 GHz. At the low end of this range, inductors are similar to those at AF. As the frequency increases, cores having lower permeability are used. Toroids are common up through about 30 MHz. Above that frequency, aircore coils are more often used.

In RF applications, 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 through, while rejecting signals at other frequencies.

Transmission-Line Inductors

At frequencies 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.

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(A) Parallel-wire transmission line. The spacers are made of sturdy insulating material (B) Coaxial transmission line. The dielectric material keeps the center conductor along the axis of the tubular shield

Most transmission lines are found in either of two geometries, the parallel-wire type or the coaxial type. A parallel-wire transmission line consists of two wires running alongside each other with constant spacing (above Figure (A)). The spacing is maintained by polyethylene rods molded at regular intervals to the wires, or by a solid web of polyethylene. 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 (above figure (B)). The wire is kept at the center of this tubular shield by means of polyethylene beads, or more often, by solid or foamed polyethylene, 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 length is less than 90° (1⁄ 4 of a wavelength). At 100 MHz, 90° in free space is 75 cm, or a little more than 2 ft. In general, if f is the frequency in megahertz, then 1⁄ 4 wavelength in free space, expressed in centimeters (scm), is given by this formula:

scm = 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 (or 66 percent) of the free-space length for coaxial lines with solid polyethylene dielectric to about 0.95 (or 95 percent) of the free-space length for parallel-wire line with spacers molded at intervals of several centimeters. The factor by which the wavelength is shortened is called the velocity factor of the line.

The shortening of the wavelength in a transmission line, compared with the wavelength in free space, is a result of a slowing down of the speed with which the radio signals move in the line compared with their speed in space (the speed of light). If the velocity factor of a line is given by v, then the preceding formula for the length of a quarter-wave line, in centimeters, becomes:

scm = 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 coil, particularly an air-core coil, is independent of the frequency. But the inductance of a transmission- line section changes as the frequency changes. At first, the inductance becomes larger as the frequency increases. At a certain limiting frequency, the inductance becomes theoretically infinite. Above that frequency, the line becomes capacitive rather than inductive.