Feedpoint Resistance Is Not a Ground-Loss Meter

In slide 17 of his latest antenna primer, Greg Mihran, KJ6ER, presents a table that converts the number of quarter-wave surface radials into a supposed ground-loss resistance and then into radiation efficiency.

The method looks wonderfully simple. Begin with the familiar 37 Ω radiation resistance of a quarter-wave vertical, subtract it from the measured feedpoint resistance, call the remainder ground loss, and calculate efficiency from:

η = Rrad / (Rrad + Rloss)

One impedance measurement has apparently become a ground-loss meter.

It has not.

What the analyser actually measures

At the antenna feedpoint, an analyser measures complex input impedance:

Zin = Rin + jXin

At resonance, the input reactance Xin is zero. The measured impedance is then purely resistive, but the analyser still reports only the total input resistance. In a useful equivalent circuit we might write:

Rin = Rrad + Rground + Rconductor + Rcoil + Rdielectric + ...

That equation is valid only when all equivalent resistances are referred to the same current at the same point in the antenna system.

The analyser gives us Rin. It does not separately give us the terms on the right. One measured number cannot determine several unknown quantities.

A 50 Ω feedpoint could represent an excellent radiator. It could also represent a mediocre radiator with substantial loss that conveniently raises its resistance towards 50 Ω. A dummy load demonstrates the extreme case: superb impedance match, almost no useful radiation.

Resonance tells us that input reactance is zero. It does not identify the measured resistance, prove a 50 Ω match, or reveal radiation efficiency.

Radiation resistance is an accounting device

Radiation resistance is not a physical resistor hidden inside the antenna. It is an equivalent resistance that lets us represent radiated power in circuit form.

Using RMS current at a chosen reference point:

Rrad = Prad / Iref2

Likewise, an equivalent loss resistance can be defined as:

Rloss = Ploss / Iref2

The reference current matters. If we refer the same radiated power to a smaller current near an antenna end, the numerical radiation resistance becomes much larger. If we refer it to a current maximum, the numerical resistance becomes smaller. Nothing about the radiated power has changed.

This is why a high feedpoint radiation resistance is not automatically “more good resistance”, and why moving a feedpoint cannot manufacture efficiency. Every equivalent loss resistance must be transformed to the same reference point before a ratio is meaningful.

Rudy Severns, N6LF, explains this reference-point requirement in detail in Radiation and Ground Loss Resistances in LF, MF and HF Verticals, Part 1. He puts the measurement problem plainly: “there is no way to measure Rr directly.” Input impedance and current can be measured, but radiation resistance must be determined from the radiated power associated with the defined reference current.

Where 36.2 or 37 Ω comes from

The familiar value is not imaginary. A very thin, resonant quarter-wave monopole over an infinite perfectly conducting plane has a base radiation resistance of approximately 36.2 Ω. Rounding that to 37 Ω is perfectly reasonable when discussing that ideal antenna.

But real earth is not an infinite perfect conductor, and a finite radial system is not merely an independent resistor placed beneath an otherwise unchanged ideal monopole.

Changing the radial system can alter:

• the current distribution on the vertical and radials
• the location and magnitude of the current maximum
• the resonant length of the vertical
• the fields penetrating the soil
• the actual radiated power for a given feedpoint current
• the radiation pattern and its interaction with ground

Therefore Rrad can change at the same time as Rground. The two are not independent knobs.

Rudy Severns addressed this exact subtraction

This is not a new objection. Severns dealt with the exact assumption in his controlled 40-metre radial experiments.

In Experimental Determination of Ground System Performance for HF Verticals, Part 4, he writes that assuming Rground = Rin - 36.2 Ω for a real quarter-wave vertical “is not the case and should not be assumed.”

His reason is explicit: radiation resistance varies as the radial system changes and does not approach the ideal value until the ground system is relatively extensive. He notes that the approximation may be good for a broadcast installation with 120 radials approximately 0.4 wavelengths long. That does not make it valid for the limited radial systems normally used by radio amateurs.

There is no paradox once we stop treating the resistance components as fixed. Adding radials reduced soil loss, while retuning the antenna and changing the radial system also changed current distribution and radiation resistance. Those changes partly cancelled at the feedpoint even though the radiated signal improved.

That is the central lesson: identical feedpoint resistance does not imply identical ground loss, and changed feedpoint resistance does not tell us how much ground loss changed.

An even sharper counterexample appears in Severns’ Part 3 comparison of surface and elevated radials. Four radials elevated 48 inches produced a measured input impedance of 34.8 - j9.7 Ω and a signal within approximately 0.1 dB of the 64-surface-radial reference.

Applying the fixed subtraction to the real part gives:

Rground = 34.8 - 37 = -2.2 Ω

The antenna did not develop negative soil loss. The reactive term can be cancelled with a lossless tuning reactance; that does not turn the negative subtraction into a ground-loss measurement. The result simply proves that the assumed 37 Ω radiation resistance does not belong to that real configuration.

Severns later calculated the separate terms by integrating radiated and ground-dissipated power. In one 7.2 MHz case with 64 quarter-wave radials, the fixed-36 Ω subtraction suggested essentially zero ground loss while power integration gave approximately 8 Ω. At 1.8 MHz, subtraction suggested approximately 2 Ω while integration gave approximately 6 Ω. See Radiation and Ground Loss Resistances, Part 2.

What happened to the KN5L data?

Greg’s slide attributes its radial-loss values to John Oppenheimer, KN5L. The original KN5L Ground Radial Study deserves to be read directly because its scope is much narrower than the slide suggests.

KN5L states that the page examines three published radial studies together with limited empirical data used as a sanity check. KN5L’s own 20-metre measurements covered three radial counts: 16, 20 and 25. EZNEC was then used to add a resistive load until the model matched the measured impedance.

The later 40-metre table is presented as a set of equivalent ground-loss loads for a simplified MININEC-type ground model. It is not a measurement campaign covering every radial count from one to 120. KN5L even labels the inherited ARRL data below 24 radials as suspect.

Greg’s slide turns this mixed-source modelling guide into a smooth table of apparent ohmic ground-loss values, applies a fixed 37 Ω radiation resistance to every row, and publishes an efficiency percentage for each radial count.

A curve fit is not a law of nature

The primer prints the equation:

Rloss = 139N-0.285 - 34.985

where N is the number of radials. It is then used to claim that approximately 86 equivalent quarter-wave surface radials are required to reach 90% efficiency.

The formula can be a convenient interpolation through selected data. It cannot be a universal physical relationship. If extended slightly beyond its displayed range, it reaches zero near 126 radials and then predicts negative ground-loss resistance.

It does not even reproduce every displayed table entry: at four radials the printed equation gives approximately 58.7 Ω, while the slide lists 63 Ω.

That does not mean curve fitting is illegitimate. It means the equation is a local numerical fit, not a law connecting radial count to soil loss for every vertical, soil, frequency and installation.

The “86 radials” result is therefore not an experimental requirement. It is the algebraic consequence of combining that particular curve with an assumed 37 Ω radiation resistance and a chosen 90% target. Change the antenna, soil, radial geometry or actual radiation resistance and the answer changes.

The two-elevated-radial calculation repeats the same error

The slide then compares its surface-radial numbers with a model claiming approximately 4 Ω loss for two elevated radials. It calculates:

η = 37 / (37 + 4) = 90%

The arithmetic is correct. The evidence is not.

For the result to establish real antenna efficiency, the model would have to determine both radiation and loss power for the complete geometry, refer both equivalent resistances to the same current, include relevant conductors and feedline behaviour, use appropriate soil parameters, and survive experimental validation.

Severns experimentally showed that four carefully balanced elevated radials at 48 inches on 40 metres could perform within approximately 0.1 dB of 64 surface radials at his test site. That is important work. It is not experimental proof that two elevated radials universally have 4 Ω loss or 90% efficiency. See Ground Systems Part 3.

Two radials may form a useful portable antenna. They may also produce current imbalance, pattern asymmetry and feedline sensitivity. None of those questions can be settled by inserting 37 and 4 into a calculator.

When can subtraction be useful?

Subtraction is not forbidden. It becomes meaningful when the quantities being subtracted are independently justified.

For example, an engineer may use:

• a validated full-wave model of the exact antenna, radial system and real ground
• radiated-power integration to determine radiation resistance at a specified reference current
• separate estimates or measurements of conductor and loading losses
• an extensive radial system for which the ideal approximation has been shown to be sufficiently accurate

In those cases, the equivalent-circuit identity can be useful. What is not legitimate is assuming the unknown radiation resistance is always 37 Ω and declaring whatever remains to be measured ground loss.

How ground-system performance should be evaluated

Severns’ method is instructive because he did not rely on feedpoint impedance alone. He measured input impedance and relative signal strength while changing radial systems, controlled the test geometry, measured soil properties, re-resonated the antenna, and compared the results with calculation and modelling.

A serious ground-system comparison should therefore include as many of the following as practical:

• equal accepted power at the antenna feedpoint
• rapid A/B switching or tightly controlled repeated measurements
• stable field-strength or transmission measurements
• documented frequency, soil and radial geometry
• feedline common-mode control and current measurements
• consistent resonance and matching conditions
• a disclosed model that includes the real ground and relevant loss mechanisms

A VNA remains valuable. It tells us impedance, resonance, bandwidth and how changes affect the feedpoint. It simply cannot decompose one real resistance into radiated watts and lost watts without additional information.

Takeaways you can trust

• Ground loss directly reduces radiation efficiency.
• Feedpoint resistance alone does not measure ground loss.
• The 36.2-37 Ω value belongs to a specific ideal quarter-wave monopole reference case.
• Radiation resistance is reference-current dependent and can change with the radial system.
• The efficiency equation is valid only when its resistance terms represent the same real system at the same current reference.
• KN5L’s values are a mixed-source modelling aid, not a universal measured law.
• Low SWR, convenient feedpoint resistance and successful contacts do not independently establish efficiency.
• Controlled field measurements and validated power-budget modelling are required to separate radiation from loss.

In Summary

The mistake is not using an equivalent circuit. Equivalent circuits are indispensable.

The mistake is silently freezing one component of that circuit at its ideal perfect-ground value while the real antenna, radial system, current distribution and surrounding earth are all changing.

Greg’s slide converts a measured total resistance into an apparently precise ground-loss resistance, then converts that into apparently precise efficiencies and a required radial count. But precision after an unsupported assumption is still unsupported.

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