EFHW High Feedpoint Resistance Is Not Free Efficiency

An end-fed half-wave can be an excellent antenna. It can be mechanically convenient, lightweight and efficient when the radiator, matching network, return path and installation are all engineered well. None of those virtues is created by the number 2,450 Ω.

In the July 2026 edition of his antenna primer, Greg Mihran, KJ6ER, moves from roughly 37 Ω for a quarter-wave vertical to 2,450 Ω near a half wavelength. Slide 85 calls the larger value “good resistance”, adds an assumed 12 Ω counterpoise loss and arrives at 99.5% efficiency. It then contrasts that result with a quarter-wave vertical needing more than 100 surface radials to exceed 90%.

The calculation is tidy. The physical inference is not. My objection is not to end feeding. It is to using a high input-resistance number as proof of an efficiency advantage, without establishing that the radiation and loss terms belong to the same current system. The slide references below identify that archived edition, not any later revision.

What the Primer's Own Examples Tell Us

Slide 81 already contains the clue: a half-wave can have a modest centre-feed resistance and a much larger end-feed impedance. The feedpoint moved. The laws of conservation of energy did not.

The 99.5% Calculation Needs One Physical Model

Slide 85's calculation can use equivalent radiation and loss resistances only when both are referred to the same current in the same complete lossy model:

The arithmetic is 99.5%, but that result is physically meaningful only if 2,450 Ω is the radiation component and 12 Ω represents every declared loss at the same reference current. A total input resistance contains whatever radiation, conductor, ground and coupled-path effects the model includes; it cannot automatically be treated as radiation resistance.

A half-wave radiator can present tens of ohms near a current maximum and thousands of ohms near a current minimum. Moving the source changes the voltage-to-current ratio and may alter the complete current distribution, but a larger port resistance does not create energy.

Why the End Impedance Is High

A resonant half-wave supports a standing current and voltage distribution. Current is high near the centre and approaches a minimum near an open end; voltage behaves oppositely. The port impedance is:

Moving a source from the centre towards the end therefore raises the measured voltage-to-current ratio. That is a feedpoint transformation produced by the current distribution. It does not add RF energy to the field.

A mathematical open end has zero terminal current and cannot accept power from an ordinary two-terminal source. A practical “end-fed” antenna is consequently fed near the end, through finite transformer and stray capacitances, with a second RF terminal and a non-zero source current. Its impedance depends on wire diameter, electrical length, height, slope, bends, soil, nearby conductors, counterpoise, feedline routing, choke position and frequency.

The AA5TB EFHW analysis illustrates the high-voltage, low-current end condition and gives a practical range of roughly 1,800–5,000 Ω. It also shows that the return conductor and coupling arrangement affect the result. That range is a useful matching estimate, not an efficiency measurement.

Radiation Resistance Requires a Reference Current

Radiation resistance is an equivalent resistance defined from radiated power and a named reference current. Using RMS current:

If the reference current is moved to a point where current is ten times smaller, the equivalent radiation and loss resistances both become 100 times larger for the same powers. Their ratio—and therefore the efficiency—does not change.

This is the important qualifier behind “higher radiation resistance reduces the effect of loss.” That can be true when a physical change increases the ratio of radiated power to dissipated power at a common reference. It is not true when the number becomes larger only because the reference current became smaller.

Rudy Severns, N6LF, makes the reference explicit in Radiation and Ground Loss Resistances, Part 1. In Part 2, he also shows why familiar monopole resistance values depend on the soil and radial model before approaching the ideal limit.

The 12 Ω Question: Referred to Which Current?

The 12 Ω counterpoise assumption on slide 85 may be valid in a disclosed equivalent circuit. Sharing the unit “ohm” with the 2,450 Ω term is not enough; these conditions must hold:

• The 2,450 Ω term must be the radiation component of the same lossy installed model, not the total resistance of a separate perfect-ground model.
• The 12 Ω must equal dissipated counterpoise-and-ground power divided by the square of that same source current.
• Wire, connection, transformer, choke, feedline and external common-mode losses must be included or explicitly excluded.
• The geometry, ground model, materials, source position and accepted-power budget must be published well enough to reproduce the result.

Distributed ground loss is obtained from the lossy fields and conductivity. Wire heating follows current along the conductor. Transformer loss follows winding current, core flux, capacitance, frequency and load. These physical losses cannot be combined safely by copying resistance numbers from different reference planes.

The cited slide does not supply the model power budget or a derivation of the 12 Ω at the source-current reference. That does not prove the counterpoise is lossy. It means the displayed quotient does not establish the claimed advantage over the quarter-wave radial system. In particular, the perfect-ground impedance plot on slide 82 is not a substitute for the radiation term of the lossy installation on slide 85.

The Ideal-Transformer Test

Suppose a 50 Ω antenna-port equivalent contains 40 Ω of radiation resistance and 10 Ω of loss resistance. Its radiation efficiency is 80%. Refer it through an ideal lossless transformer with a 49:1 impedance ratio:

The transformer created a 2,450 Ω port representation. It did not create efficiency. Radiation and loss resistances transformed together.

This thought experiment does not claim that physically moving the source along a real wire is identical to inserting a transformer. Moving the source can alter the current distribution because the return conductor and feed structure are part of the antenna. It shows only that impedance magnitude, by itself, cannot change the ratio of radiated power to loss.

A Real Transformer Adds Frequency- and Load-Dependent Loss

The large terminal impedance does not remove a matching problem; it creates a demanding one. A practical EFHW network must provide a high impedance ratio while controlling:

• core loss, flux density and temperature rise;
• copper resistance and proximity effect;
• leakage inductance and inter-winding capacitance;
• load-dependent loss, mismatch and bandwidth;
• high RF voltage, insulation and connector spacing; and
• capacitive and common-mode coupling to the coax, mast and station.

A 49:1 label states an ideal impedance ratio corresponding to a 7:1 turns ratio. It does not specify insertion loss, safe power, temperature or behaviour into the installed antenna’s complex load.

Stray capacitance can bypass part of the intended winding path and couple the high-voltage node to the enclosure, coax or environment. Leakage inductance adds a series term; dielectric and insulation leakage dissipate power and can become voltage- or moisture-dependent. Measure the complete network with the intended complex load, enclosure, connectors and frequency span rather than inferring loss from turns ratio or SWR.

Fair-Rite’s broadband-transformer guidance treats insertion loss as frequency-dependent and identifies material, core geometry and winding construction as design variables. The applicable limits still have to be established for the actual core, flux, temperature, load and duty cycle.

The primer's own component table on slide 91 lists 1.08 dB and 0.51 dB total transformer-plus-choke losses for the Dominator arrangements. Those correspond to power factors of about 78.0% and 88.9%. Slide 96 separately gives a 99.5% average structural efficiency for its model. If those terms describe compatible operating conditions and meet at the same downstream plane, their product is:

These are conditional bookkeeping results from the primer's published numbers, not new measurements of either arrangement. The cited slides do not establish compatible test conditions across frequency, complex load, drive level and temperature. The useful conclusion is nevertheless firm: a 99.5% structural model does not include a matching network that separately loses half to one decibel. Credit to the primer for listing that network loss; it must remain in the comparison when the complete antenna is discussed.

The Second RF Terminal Is Part of the Antenna

Every RF source has two terminals. If one drives the half-wave wire, return current must occupy a deliberate counterpoise, the transformer’s other terminal, the coax exterior, a mast, station wiring, capacitance to the environment or some combination.

Slide 84 usefully recommends a deliberate counterpoise and a choke. What does not follow is its suggestion that the counterpoise completes the half wavelength and thereby guarantees full efficiency. Current continuity can include conduction and displacement current through the complete electromagnetic structure. The return-path geometry changes impedance, current distribution, pattern, common-mode current and loss.

A feedpoint choke changes that structure again. It can reduce current on the coax exterior, but it may also move current into another return path and alter the match or pattern. The coax exterior is neither automatically required nor automatically harmless; it must be treated as a possible radiating conductor and measured.

Match, Mismatch and Efficiency Are Separate

The active IEEE 145-2025 antenna-terms standard supplies the current terminology framework. A NIST antenna-efficiency paper explains the practical distinction clearly: radiation efficiency uses power accepted by the antenna, whereas a total or realised result can also include mismatch.

A low SWR shows that little power is reflected at the measurement plane. It does not reveal how accepted power divides between radiation and heat. A dummy load is the limiting example: an excellent match and essentially no useful radiation.

That is the distinction between the Dominator model on slide 105 and the field analyser images on slide 109. The model-port SWR is referenced to 2,450 Ω; the physical matching network presents its input to the analyser. The field images are useful evidence that the installed system could be matched. They do not validate slide 96's structural efficiency, average gain or elevation angle. Match is one result; it cannot certify all the others.

Feedline loss changes the reference plane again. With propagation constant γ = α + jβ and one-way line length l, the load reflection is attenuated on the round trip:

A lossy feedline can therefore make source-end SWR look better while reducing power delivered to the matching network. Complete station efficiency must include forward line loss, the extra loss created by mismatch on that line, connector and tuner loss, matching-network loss and antenna-structure loss. Use a transmission-line loss model or measurement appropriate to the actual cable, frequency, temperature and load.

Keep the System Boundary Visible

A structure can be 99.5% efficient in a model while the transformer-input system is below 80%. Both percentages can be mathematically consistent if they describe different boundaries. A percentage without its denominator and reference plane is incomplete.

Efficiency and Pattern Answer Different Questions

End feeding can change real loss in a particular geometry. Low current near the end may reduce heating in a specific connection or short return element. The feed structure and return path can also change the current distribution, near field and radiation pattern.

Radiation efficiency measures total radiated power relative to accepted power. Directivity describes how that radiated power is distributed by angle; gain combines efficiency and directivity, and realised gain additionally includes mismatch at the declared plane. A stronger signal in one direction can result from pattern redistribution without any increase in total efficiency.

A fair comparison holds frequency, conductor, orientation, environment and accepted power constant. It includes the complete matching and return structures, and it compares the full radiation pattern—not only peak gain or one elevation cut. The high-voltage end also increases electric-field and insulation stress, while a high-ratio transformer may add losses that another feed arrangement avoids.

A Measurement Workflow for Efficiency and Pattern

1. Document the complete model. Include source file, NEC engine, ground formulation, soil, conductor properties, segmentation, loads, source, counterpoise, mast, feedline and choke representation.
2. Close the model power budget. State accepted, radiated, wire-loss and ground-loss power at one reference plane.
3. Show current references. Record source current and enough current-distribution information to establish every equivalent resistance.
4. Measure the transformer under the real load. Give frequency, complex load, fixture, calibration, de-embedding, drive level, duty cycle, temperature and uncertainty.
5. Measure the external path. Record counterpoise, coax-exterior and mast current before and after the choke.
6. Use a calibrated radiation comparison. Normalize to equal accepted power and sample enough azimuth and elevation directions to avoid mistaking a pattern change for an efficiency change.
7. Report uncertainty and state. Include geometry, weather or soil state, calibration limits and repeatability. Signal reports, contacts and SWR demonstrate operation, not absolute efficiency.

IEEE 149-2021 provides the current recommended-practice framework for antenna-pattern and related measurements. At HF, a controlled equal-accepted-power field comparison can establish relative gain in sampled directions for the systems at that declared plane. Realised gain additionally includes mismatch relative to incident power. Absolute efficiency requires a recognised power-balance, full-pattern, reverberation-chamber or applicable Wheeler method with stated uncertainty.

Engineering Checklist

• An EFHW can be efficient and effective.
• Its high input impedance comes from feeding near a current minimum and voltage maximum.
• A high resistance number does not create radiated power or gain.
• Radiation and loss resistances require the same named reference current.
• A 49:1 transformer transforms impedance; it does not add efficiency.
• Transformer, choke, wire, ground, feedline and return-path losses belong in the complete budget.
• The second RF terminal may include a counterpoise, coax exterior, mast or environmental capacitance.
• Low SWR proves a match at its measurement plane—not radiation efficiency.
• High feedpoint voltage creates real insulation and RF-safety obligations.

The Advantage Must Come From the Antenna, Not the Ohm Number

Mihran's primer starts from a legitimate high-impedance end-feed condition. The leap I reject is making that number the reason the half-wave must outperform a quarter-wave with a substantial radial system. Its 12 Ω assumption needs a common-current derivation, and its own matching-component table shows losses that the structural percentage leaves outside the boundary.

The same radiated and dissipated powers can be represented by very different equivalent resistances when the reference current changes. The decisive quantity is radiated power divided by accepted power after the chosen structure, matching network and return path have been counted consistently.

For a station builder, the choice is concrete: an end feed buys a convenient mechanical arrangement and may suit a useful current distribution; a directly fed or lower-transformation-ratio arrangement can avoid the demanding high-ratio network. Choose the arrangement that serves the installation and account for that network—not the one with the most impressive resistance number. A good EFHW earns its performance through the whole design. It does not receive 99.5% efficiency as a birthright.

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