# Single-wire transmission line

For circuits using earth as a second conductor, see Single wire earth return.

A single-wire transmission line (or single wire method) is a method of transmitting electrical power or signals using only a single electrical conductor. This is in contrast to the usual use of a pair of wires providing a complete circuit, or a cable likewise containing (at least) two conductors for that purpose.

The single-wire transmission line is not the same as the single wire earth return system, which is not covered in this article. The latter system relies on a return current through the ground, using the earth as a second conductor between ground terminal electrodes. Thus, the earth effectively forms a second conductor. In a single-wire transmission line there is no second conductor of any form.

## History

As early as the 1780s Luigi Galvani first observed the effect of static electricity in causing the legs of a frog to twitch, and observed the same effect produced just due to certain metallic contacts with the frog involving a complete circuit. The latter effect was correctly understood by Alessandro Volta as an electric current inadvertently produced by what would become known as a voltaic cell (battery). He understood that such a current required a complete circuit to conduct the electricity, even though the actual nature of electric currents was not at all understood (only a century later would the electron be discovered). All subsequent development of electrical motors, lights, etc. relied on the principle of a complete circuit, generally involving a pair of wires, but sometimes using the ground as the second conductor (as with commercial telegraphy).

At the end of the 19th century, Tesla demonstrated that by using an electrical network tuned to resonance and using, what at the time would be called "high frequency AC" (radio frequencies), it was possible to transmit electric power using only a single conductor, with no need for a return wire. This was spoken of as the "transmission of electrical energy through one wire without return".[1][2]

In 1891, 1892, and 1893 demonstration lectures with electrical oscillators before the AIEE at Columbia College, N.Y.C., the IEE, London, the Franklin Institute, Philadelphia, and National Electric Light Association, St. Louis, it was shown that electric motors and single-terminal incandescent lamps can be operated through a single conductor without a return wire. Although apparently lacking a complete circuit, such a topology effectively obtains a return circuit by virtue of the load's self-capacitance and parasitic capacitance.[3][4]

"Thus coils of the proper dimensions might be connected each with only one of its ends to the mains from a machine of low E. M. F., and though the circuit of the machine would not be closed in the ordinary acceptance of the term, yet the machine might be burned out if a proper resonance effect would be obtained."[5]

The final reference to "burning out" a machine was to emphasize the ability of such a system to transmit a large power given a proper impedance match, as can be obtained through electrical resonance.

## Theory

This observation has been rediscovered several times, and described, for instance, in a 1993 patent.[6] Single-wire transmission in this sense is not possible using direct current and totally impractical for low frequency alternating currents such as the standard 50–60 Hz power line frequencies. At much higher frequencies, however, it is possible for the return circuit (which would normally be connected through a second wire) to utilize the self- and parasitic capacitance of a large conductive object, perhaps the housing of the load itself. Although the self-capacitance of even large objects is rather small in ordinary terms, as Tesla himself appreciated it is possible to resonate that capacitance using a sufficiently large inductor (depending on the frequency used), in which case the large reactance of that capacitance is cancelled out. This allows a large current to flow (and a large power to be supplied to the load) without requiring an extremely high voltage source. Although this method of power transmission has long been understood, it is not clear whether there has been any commercial application of this principle for power transmission.

## Single conductor waveguides

As early as 1899, Arnold Sommerfeld published a paper[7] predicting the use of a single cylindrical conductor (wire) to propagate radio frequency energy as a surface wave. Sommerfeld's "wire wave" was of theoretical interest as a propagating mode, but this was decades before technology existed for the generation of sufficiently high radio frequencies for any such experimentation, let alone practical applications. What's more, the solution described an infinite transmission line without consideration of coupling energy into (or out of) it.

Of particular practical interest, though, was the prediction of a substantially lower signal attenuation compared to using the same wire as the center conductor of a coaxial cable. Contrary to the previous explanation of the full transmitted power being due to a classical current through a wire, in this case the currents in the conductor itself are much smaller, with the energy transmitted in the form of an electromagnetic wave (radio wave). But in this case, the presence of the wire acts to guide that wave toward the load, rather than radiating away.

The reduction of ohmic losses compared to using coax (or other two-wire transmission lines) is especially an advantage at higher frequencies where these losses become very large. Practically speaking, use of this transmission mode below microwave frequencies is very problematic due to the very extended field patterns around the wire. The fields associated with the surface wave along the conductor are significant out to many wavelengths, therefore metallic or even dielectric materials inadvertently present in these regions will distort the propagation of the mode and typically will increase propagation loss. For these reasons, and at frequencies available prior to about 1950, the practical disadvantages of such transmission completely outweighed the reduced loss due to the wire's finite conductivity.

### Goubau line

Main article: Goubau line

In 1950 Georg Goubau revisited Sommerfeld's discovery of a surface wave mode along a wire, but with the intent of increasing its practicality.[8] One major goal was to reduce the extent of the fields surrounding the conductor so that such a wire would not require an unreasonably large clearance. Another problem was that Sommerfeld's wave propagated exactly at the speed of light (or the slightly lower speed of light in air, for a wire surrounded by air). That meant that there would be radiation losses. The straight wire acts as a long wire antenna, robbing the radiated power from the guided mode. If the propagation velocity can be reduced below the speed of light then the surrounding fields become evanescent, and are thus unable to propagate energy away from the area surrounding the wire.

Goubau investigated the beneficial effect of a wire whose surface is structured (rather than an exact cylinder) such as would be obtained using a threaded wire. More significantly, Goubau proposed the application of a dielectric layer surrounding the wire. Even a rather thin layer (relative to the wavelength) of a dielectric will reduce the propagation velocity sufficiently below the speed of light, eliminating radiation loss from a surface wave along the surface of a long straight wire. This modification also had the effect of greatly reducing the footprint of the electromagnetic fields surrounding the wire, addressing the other practical concern.[9]

Finally, Goubau invented a method for launching (and receiving) electrical energy from such a transmission line. The patented[10] Goubau line (or "G-line") consists of a single conductor coated with dielectric material. At each end is a wide disk with a hole in the center through which the transmission line passes. The disk may be the base of a cone, with its narrow end connected typically to the shield of coaxial feed line, and the transmission line itself connecting to the center conductor of the coax.

Even with the reduced extent of the surrounding fields in Goubau's design, such a device only becomes practical at UHF frequencies and above. With technological development at terahertz frequencies, where metallic losses are yet greater, the use of transmission using surface waves and Goubau lines appears promising.[11]

### E-Line

From 2003 through 2008 patents were filed for a system using Sommerfeld's original bare (uncoated) wire, but employing a launcher similar to that developed by Goubau.[12][13] It was promoted under the name "E-Line" through 2009.[14] Thus the resulting wave velocity is not reduced by a dielectric coating, however the resulting radiation losses may be tolerable for the transmission distances intended. The intended application in this case is not power transmission but power line communication, that is, creating supplementary radio frequency channels using existing power lines for communications purposes. This has been proposed for transmission of frequencies from below 50 MHz to above 20 GHz using pre-existing single or multistrand overhead power conductors.[citation needed]

While Goubau-Line, which uses a conductor having an outer dielectric or special surface conditioning provided to reduce the velocity of the wave on the conductor, has long been known, a more general transverse-magnetic (TM) mode does not have this limitation. The E-Line is similar to the Goubau-Line in its use of launchers to couple to and from a radially symmetric wave propagating in the space around a single conductor but different in that it can operate on insulation-free conductors, including those that are polished and completely unfeatured. The propagation velocity of the wave is not reduced and is accordingly quite close to that of a wave traveling in the same medium in the absence of any conductor at all.

The behavior of such a system is dependent on the operating frequency, and details of the power conductor and its environment. "A nearby conductor other than the line itself may provide a termination point and thereby reduce energy coupled into the TM wave"[15] due to the larger extent of the surrounding E-field at lower frequencies (longer wavelengths). (This has relevance to Tesla's 1891-1893 table-top demonstrations.) At very high frequencies, the increased losses of the metal conductor, despite the advantage obtained using the surface wave mode, are increased. The effects of line taps, bends, insulators and other impairments normally found on power distribution systems have been described as "predictable and manageable".[citation needed] Depending on these factors, the resulting insertion loss, along with the transmitted power and receiver sensitivity, will determine the maximum distance attained by such a system. An increased end-to-end communications path can be obtained through the use of repeaters.[citation needed]

To take advantage of existing lines, the conical launcher elements are built with a slot through the cone, so that they can be fitted over an existing power line (rather than having to be threaded through the cone). Systems using higher microwave frequencies can employ a launch device of only 15–20 cm in diameter.[citation needed]

## References

1. ^ "Why did Tesla make his coil in the first place? . . . do they have any practical purposes?," 21st Century Books.
2. ^ Nikola Tesla, "Talking with the Planets (1901)". Collier's Weekly, February 19, 1901, pp. 4–5.
"Some ten years ago, I recognized the fact that to convey electric currents to a distance it was not at all necessary to employ a return wire, but that any amount of energy might be transmitted by using a single wire. I illustrated this principle by numerous experiments, which, at that time, excited considerable attention among scientific men."
3. ^ Experiments with Alternate Currents of Very High Frequency and Their Application to Methods of Artificial Illumination, American Institute of Electrical Engineers, Columbia College, N.Y., May 20, 1891.
4. ^ Experiments with Alternate Currents of High Potential and High Frequency, Institution of Electrical Engineers Address, London, February 1892.
5. ^ On Light and Other High Frequency Phenomena, Franklin Institute, Philadelphia, February 1893, and National Electric Light Association, St. Louis, March 1893.
6. ^ U.S. Patent 6,104,107, "Method and apparatus for single line electrical transmission".  Avramenko, et al.
7. ^ A. Sommerfeld, Ann. Phys. u. Chemie (Neue Folge) 67-1, 233 (1899)
8. ^ Georg Goubau, "Surface waves and their Application to Transmission Lines," Journal of Applied Physics, Volume 21, Nov. (1950)
9. ^ U.S. Patent 2,685,068, "Surface wave transmission line". George J. E. Goubau
10. ^ U.S. Patent 2,921,277, "Launching and receiving of surface waves". George J. E. Goubau
11. ^ Tahsin Akalin, "Single-wire transmission lines at terahertz frequencies", IEEE Transactions on Microwave Theory and Techniques (IEEE-MTT), Volume 54, Issue 6, June 2006 Page(s): 2762 - 2767
12. ^ U.S. Patent 7,009,471, "Method and apparatus for launching a surfacewave onto a single conductor transmission line using a slotted flared cone". Glenn E. Elmore
13. ^ U.S. Patent 7,567,154, " Surface wave transmission system over a single conductor having E-fields terminating along the conductor " Glenn E. Elmore
14. ^ "E-Line". Corridor Systems Inc. 2010. Retrieved November 6, 2013.
15. ^ Glenn Elmore (July 27, 2009). "Introduction to the Propagating TM Wave on a Single Conductor". Corridor Systems. Retrieved November 6, 2013.