One Wire, No Magic: What a Goubau Line Really Proves
One Wire, No Magic: What a Goubau Line Really Proves
A red wire across a garden, two metal cones and an old television make a much better starting point than another argument about whether electricity needs a second wire.
RF.Guru working definition: Common-mode current is the non-cancelling phasor-sum current in a specified set of conductors, evaluated at a defined cross-section and using a declared current-direction convention. In the intended differential transmission-line mode, the outgoing and return currents are equal and opposite, so their phasor sum is zero. When they do not cancel, the remaining current must close through another reference or return path—such as the outside of a coax shield, a mast, equipment chassis, station wiring, nearby structures, earth, the operator, or distributed coupling through the environment.
This broader working definition is especially useful in practical antenna systems. On transmit, non-cancelling current on the outside of the coax can make the feedline and connected structures part of the radiating antenna system unless that path is intentional, clearly defined and properly controlled—for example by providing the required return path and placing a suitable common-mode choke at the correct boundary.
The video behind this article: Electricity Doesn’t Actually Need a Return Wire, by Electromagnetic Videos, demonstrates an insulated single-wire RF link. The central result is sound: a suitably excited surface wave needs no second metal conductor alongside the wire. The interesting question is how the fields and currents make that possible—not how to dismiss the experiment.
The Picture Appears—and the Question Changes
In the garden setup, a battery-powered laptop and SDR supply an analogue television signal near 890 MHz. Coax connects to a metal cone at each end of the insulated wire. At about three minutes, the television’s snow gives way to a picture. Bringing a hand around the line disrupts reception.
I like this demonstration because it forces us to ask a better question. Not “where is the missing black wire?” but “which electromagnetic mode is carrying the power?”
The television is receiving RF signal power; the wire is not supplying its operating power. And the hand test establishes sensitivity to a nearby object, not a calibrated loss figure or proof that every received watt used the guided path. Neither qualification makes single-wire transmission imaginary. It is established engineering.
The Cones Change the Mode
Ordinary coax carries its intended TEM mode between its centre conductor and shield. TEM means that the electric and magnetic fields are transverse to the direction of travel. The cone is a transition: it couples that coaxial field arrangement into the wire’s surface-wave mode. The receiving cone performs the reverse conversion.
The Goubau mode also has a longitudinal electric-field component—along the wire—so it is not simply ordinary coax with the shield deleted. In the ideal straight-line description, this is a fundamental TM surface wave. Stulle and Bergoz’s beam-instrumentation paper describes both that mode and its conversion from coax using tapered cones.
Coaxial mode → launcher → guided surface wave → receiving transition → coaxial mode.
The wire count changes because the field configuration changes. That is the achievement.
Near the wire, some field components can resemble those in coax. Resemblance is useful for intuition; it does not make the two complete modes identical. Their boundary conditions, field extent and voltage definitions matter.
The Insulation Is Doing an RF Job
The red covering is more than something that stops fingers touching copper. A dielectric coating can slow the guided wave’s phase velocity relative to free space and concentrate its field nearer the conductor. That makes a practical difference to confinement and to the launcher needed to excite it. Georg Goubau’s surface-wave transmission-line patent explicitly develops this approach.
“Bound to the wire” does not mean “inside the copper.” A substantial part of the working field occupies the surrounding space. Bring a lossy object, wet vegetation or metal into that region and you can change propagation, reflection and attenuation. The coating, diameter, frequency and surroundings determine how widely that field extends; a universal clearance in wavelengths is not a complete design rule.
The video's field-line animation is a useful picture, but field lines are not elastic threads that physically snap off and choose an easier destination. The transition obeys Maxwell’s equations continuously. The dielectric-and-boundary explanation is stronger than the cartoon.
No Return Wire Is Not No Current Continuity
Here is the distinction worth keeping. A second longitudinal metal conductor is not a universal requirement for electromagnetic power transmission. Conservation of charge is.
The creator does not simply ignore the return question. Around 08:51, the explanation turns to the cone and the alternating fields that accompany current at the coax port. That is the right direction: expand the circuit picture to include the fields.
Conduction current can put charge onto a region or remove it. The exact local relation is:
∇ · J = −∂ρ/∂t
J is free-current density (conduction current here); ρ is free-charge density. A local imbalance changes stored charge—it does not make charge disappear.
Maxwell’s magnetic-field equation includes a second term, ∂D/∂t, called displacement-current density. It describes changing electric displacement, not electrons flying through empty space. Combining the equations gives ∇ · (J + ∂D/∂t) = 0. MIT’s differential treatment shows the relationship; its integral charge-conservation discussion gives the corresponding region-by-region picture.
Applied to an ideal bound Goubau mode, the surrounding longitudinal displacement-current distribution supplies the balance that a second wire would supply in a two-conductor circuit. This is a whole-cross-section balance, including the coating and surrounding space—not necessarily a cancellation within a small ring beside the wire. It follows by applying Ampère–Maxwell to the mode’s decaying exterior field. The balance is distributed through the field, not concentrated in an invisible copper wire. A buried earth connection is not a prerequisite for that mode to exist.
Real launchers, instrument enclosures and nearby ground can still couple to the system. Those are installation effects to account for—not grounds for declaring every single-wire guide a disguised earth-return cable.
The Fields Carry Power; the Copper Still Matters
The video returns to energy flow around 18:15. The Poynting vector is the appropriate description:
S = E × H
Using instantaneous E and H, S is instantaneous electromagnetic power flow per unit area, in W/m². Integrate its component through a cross-section to obtain power in watts.
This is not a choice between “real electricity” and “mere radio waves.” The guided wave transports electromagnetic energy, and currents in the conductor help establish its boundary conditions. With finite conductivity, energy also enters the conductor and becomes heat. Conductor loss and field-carried power are compatible descriptions, not rival explanations. Poynting’s theorem accounts for transport, storage and transfer to matter in one energy balance.
At an ordinary TEM port, voltage and current give the same power accounting as the field integral. For sinusoidal signals using RMS phasors, average real power is Re{V I*}, not generally the product of the two magnitudes. Nor should an undefined “voltage on the wire” be substituted blindly into a non-TEM surface-wave calculation. MIT’s TEM-wave treatment makes the field-to-circuit connection explicit.
The power is counted once. Voltage/current and fields are compatible ways of describing the same transfer where the circuit representation is valid.
Non-TEM guides can also use power-consistent modal voltage and current, provided those quantities are properly defined and normalised. Marks and Williams’ waveguide circuit theory develops that more general framework. The objection is to undefined variables, not to circuit theory.
The Same Field Idea Appears on a Cellular Tower
There is a less surprising place to meet guided RF without a centre wire: microwave backhaul carrying traffic from cellular sites. Think of the directional dishes connecting network sites, rather than the link between your phone and its nearest base station. Cambium’s backhaul equipment, for example, serves connections from small cells to aggregation sites.
A radio can feed its dish through a hollow metallic waveguide. Cambium’s installation-planning documentation explicitly includes flexible waveguide for non-integrated licensed-band antennas. Other installations mount the radio directly to the antenna, avoiding a separate feeder run. The guide is part of the equipment or its antenna connection; between the dishes, the wave travels through free space. Not every cellular installation uses an external waveguide: fibre, other cables and direct-mounted equipment have their own roles.
That makes the garden experiment less exotic without making it the same system. A hollow guide carries power in its interior electromagnetic field, with currents on the metal walls establishing the boundary conditions. A Goubau line guides a surface wave around a coated conductor. Both engineer the fields; neither is an electron hose with the return pipe forgotten.
| What changes? | Coated-wire Goubau line | Conventional hollow metal waveguide |
|---|---|---|
| Structure | One conductor with a dielectric coating; open surroundings | A conducting enclosure without a centre conductor |
| Working fields | Around the wire, in the coating and surrounding space | Inside the guide, bounded by its walls |
| Typical mode | Fundamental TM surface wave: electric field includes a longitudinal component | For an ordinary rectangular guide, dominant TE₁₀: magnetic field includes a longitudinal component |
| Nearby objects | Objects within the exposed field can disturb the mode | The enclosure screens the guided interior field; openings and joints still matter |
Frequency Decides Which Guide Works
In an ideal air-filled rectangular guide with broad internal dimension a, the dominant TE₁₀ mode has the cutoff:
fc = c / (2a)
With a = 20 mm, fc is approximately 7.5 GHz. This is a rectangular-guide example, not a formula for every guide shape.
Below cutoff, that mode is evanescent—it decays along the uniform guide instead of propagating freely. Higher frequencies eventually permit additional modes, so the preferred single-mode band is bounded too. MIT’s rectangular-waveguide treatment derives these limits. Scaling the cross-section down moves them upward: millimetre-wave hardware is small for an electromagnetic reason.
Actual operating bands also account for loss, matching and dispersion. For a concrete, different-shaped example, ANDREW’s HELIAX EW63 elliptical guide specifies 5.925–7.125 GHz, while listing its eTE₁₁ cutoff as 4.001 GHz. The recommended band is plainly not “everything above cutoff.”
The ideal ordinary coated-wire Goubau line is different: its fundamental TM surface mode has no corresponding nonzero hollow-guide cutoff. Overfelt and colleagues show this in their standard dielectric reference case, Figure 2. That is a statement about a mode—not a promise of useful transmission from DC upwards.
For a fixed ordinary coated wire, confinement weakens as frequency falls and the field spreads farther into the surroundings. Launching and collecting that mode efficiently then becomes harder in a compact installation. Wire diameter, coating thickness and permittivity, conductor and dielectric losses, transitions and nearby objects all help set the practical band. At higher frequencies, tighter confinement can be useful, but additional modes and losses can matter too. “Higher” is not automatically “better.”
Similar field-guiding principle, different boundaries and frequency behaviour. The hollow guide encloses its working field; the Goubau guide binds it around a wire. Choose the geometry and mode for the frequency—not the frequency because the copper happens to be available.
Why This Does Not Abolish the Choke on Your HF Antenna
There is an obvious temptation: “If that wire works without a second wire, my end-fed antenna needs no return arrangement either.” That conclusion does not follow.
A Goubau link deliberately launches a guided mode and deliberately collects it at the other end. An antenna deliberately couples energy into radiated fields. An ordinary coax-fed HF installation can also excite an unwanted mode on the shield exterior and connected structures. Those are different jobs, even when each photograph contains one prominent wire.
For the intended coax mode, centre-conductor and inner-shield currents cancel at a defined cross-section. If the complete coax carries a non-cancelling current, its exterior and environment belong in the system model. At an end-fed antenna, provide the intended return arrangement and control where the feedline stops being part of the radiator. A suitable choke establishes a mode-control boundary; it does not manufacture a missing return path.
The standard common-mode definition above is useful precisely because it declares the conductor set. A nonzero current on the single conductor of a Goubau guide is intentional. It is not automatically an installation fault to suppress. Identify the wanted mode before deciding which current is unwanted.
A Good RF Demonstration Is Not a Mains-Wiring Proposal
The video’s enormous 60 Hz launcher thought experiment makes a memorable point about electrical scale. The free-space wavelength is about 5,000 km at 60 Hz and 6,000 km at 50 Hz. Those numbers follow from λ = c/f; they are not a universal formula fixing every possible launcher’s diameter.
This UHF surface-wave arrangement does not become a useful household power circuit by slowing it down to mains frequency. It also does not authorise removing a neutral or protective earth. Keep a demonstration within suitably controlled low-power RF practice and lawful spectrum use; do not copy an outdoor transmitting frequency merely because it appears in a video.
The Lesson Is Better Than the Headline
The Goubau line earns its place in the RF toolbox because it replaces a second longitudinal conductor with a deliberately engineered surface-wave mode. That is a real capability, not a semantic trick.
For a link that must sit beside structures, tolerate handling and keep its working fields away from the surroundings, coax’s shield is a major practical advantage. For an experiment or instrument that needs access to the fields around one wire, the open guide can be exactly the useful feature. Stulle and Bergoz demonstrate that latter role in beam-instrumentation testing.
One wire can carry guided RF power. No second wire does not mean no electromagnetic balance. And counting the visible wires still does not tell you the current paths of an antenna.
Explore the Source
Watch the complete Electromagnetic Videos demonstration. The creator also provides a collection of historical papers, patents and a Radio-Electronics article. The links alongside the explanations above lead to the field theory and primary engineering references.
Mini-FAQ
- Can one wire really guide RF power? Yes. A Goubau line uses a suitably excited surface-wave mode on a single conductor, commonly with a dielectric coating.
- Does a Goubau line need an earth-return wire? No. The ideal guided mode exists without a second metal conductor or an earth-return connection. Its conduction and displacement currents must still satisfy Maxwell’s equations.
- Is a Goubau line just coax without the shield? No. The launcher converts between the coaxial TEM mode and a surface-wave TM mode with different fields and boundary conditions.
- Are waveguides used in cellular networks? Yes, in microwave-backhaul equipment and radio-to-dish connections. The inter-site hop itself is through free space; this is not the handset-to-base-station link.
- Do Goubau lines and hollow waveguides have the same frequency limits? No. Hollow guides have geometry-dependent modal cutoffs. The ideal ordinary Goubau fundamental mode has no equivalent nonzero cutoff, but confinement, loss, launchers and surroundings still limit practical bandwidth.
- Did the wire power the television? It delivered the television signal’s RF power to the receiver, not the television’s operating power.
- Does this prove an end-fed antenna needs no choke? No. A designed surface-wave guide and the unwanted exterior-current mode of an antenna feedline are different systems. Control the actual antenna return path and feedline boundary.