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FEED LINE BASICS 297

crosstalk are minimized by the screen, and such line is prevalent in LANs. The reader can
continue this procedure with any line in Figure 6.2.1 and 6.2.2.
6.4.2 Coaxial Lines

More interesting and essential option is to modify a single wire line above the ground to make
it a closed line. Let us fold the ground screen into solid tube 3 around the wire 1 as shown in
Figure 6.4.1b. To be sure that the central wire and tube do not touch each other we can put the
dielectric isolator 2 between them. The plastic jacket 4 protects the outer conductor against
wear, corrosion, and abrasion. To reduce a cable weight, the center conductor in some cases
can be fabricated as a pipe of a smaller diameter. Apparently, such rigid design deprives the
coaxial cable of such a significant advantage as flexibility or ability to bend and flex without
causing damage or visible propagating signal distortion. The latter can be retrieved in several
ways. The simplest and cheapest one is the replacement of the rigid outer tube with a copper
braid like shown in Figure 6.4.1a while the center conductor is fabricated as a bendable set of
intertwined copper or aluminum wires of small diameter. Another approach is a semi-rigid
coaxial cable with corrugated outer and inner conductors like shown in Figure 6.4.1c. The
corrugation let diminish dielectric volume thereby minimizing the dielectric loss. Such coax is
typically more expensive and dispersive since the TEM-mode converts into a quasi-TEM while
follows the corrugation.

A coaxial line called a cage line is pictured in Figure 6.4.1d , used for high-power, low-
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frequency applications. The inner and outer conductors are made as a set of multiple
longitudinal wires discretely imitating the solid metal surface and forming a coaxial cable of
extra-large sizes to deliver ultra-high power to AM-LW (Long Wave) antenna. The picture was
taken in the city of Konstantynów, Poland at the radio station that operated on RF power of
1200 kW (120 kV of voltage) until 1991.
Coaxial lines are widely used as the great feed lines and called coaxial cable. It was invented
and patented by British engineer and mathematician Oliver Heaviside in 1880. Since the coaxial
line consists of two separate wires, it widely used as DC power line. Evidently, it means that
the dominant wave mode is TEM, its electric and magnetic field pattern shown in Figure 6.1.1d
must be frequency independent. In general, its variations due to the skin effect can mainly be
ignored for even broadband signals. The characteristic impedance of coaxial cables are

highly standardized by 50, 75 and sometimes 100 Ohms.
It is quite thinkable the existence of an infinite spectrum of TE- and TM-modes in coaxial line.
Just to prove it we need to write and solve the wave equations (6.2) in cylindrical coordinates
with proper boundary conditions (see Chapter 3). Well, it is hardly worth the efforts since it
requires the introduction of highly complicated Bessel’s functions. Besides, such higher modes
are never actually used for the transportation of EM energy in coaxial line and their sound
knowledge unlikely to be of keen interest. Meanwhile, we try to go around the mathematics
again with the idea of the incident and reflecting waves. Assuming that all metal surfaces are
perfectly conductive, and the dielectric filling is loss-free, we can represent the propagation EM

11 Public Domain Image, source: https://en.wikipedia.org/wiki/Transmission_line