Feedpoint Resistance: Why “R − 36 Ω” Is Not Ground Loss

In slide 17 of the July 2026 edition of his Antennas Primer 1, Greg Mihran, KJ6ER, presents a table that turns the number of quarter-wave surface radials into ground-loss resistance, radiation efficiency and a striking conclusion: at least 86 equivalent surface radials to reach 90% efficiency.

The method looks wonderfully simple. Begin with 37 Ω radiation resistance, subtract it from measured feedpoint resistance, call the remainder ground loss, and put those values into the efficiency equation. One impedance measurement has apparently become a ground-loss meter.

It has not. My objection is not to the efficiency equation, nor to using models. It is to treating an assumed radiation resistance and a fitted guide curve as though they independently measured the loss in a real antenna. Follow the numbers back to John Oppenheimer, KN5L, and Rudy Severns, N6LF, and the limitation becomes concrete.

What the Analyser Actually Measures

At one frequency and one calibration plane, an analyser measures complex input impedance:

At resonance, X_in is zero. That tells us that the net input reactance cancels at that frequency. It does not reveal why the remaining real part exists.

Using RMS current I₀ at a defined antenna port, we can assign power-equivalent resistances:

This is sound physics, not a controversial model. It also exposes the measurement problem: the instrument gives R_in. It does not independently give P_rad and P_loss, so it cannot separate the two equivalent resistances from that one number.

Ground loss, conductor loss, loading-coil loss, dielectric loss and connector loss may all be referred to the same port current and combined into an input-equivalent loss resistance. That mathematical referral does not make the individual contributions directly observable with a one-port impedance measurement.

Radiation Resistance Is an Accounting Quantity

Radiation resistance is not a little resistor hidden in the radiator. It is the resistance that would dissipate the same power as the antenna radiates when the chosen reference current flows.

The reference point therefore matters. Refer the same radiated power to a smaller current and the numerical radiation resistance rises; refer it to a larger current and it falls. No extra watt has been radiated. This is why every radiation and loss resistance used in an efficiency ratio must be referred to the same current and the same electromagnetic system.

Rudy Severns, N6LF, develops this point in Radiation and Ground Loss Resistances in LF, MF and HF Verticals, Part 1. Feedpoint current and input power can be measured, but radiation resistance cannot be isolated directly from input impedance. It must come from radiated power referred to the chosen current—normally through field integration, a validated electromagnetic model or an appropriate efficiency measurement.

Where 36.2 Ω Really Comes From

The familiar number is real and useful. A thin, resonant quarter-wave monopole over an infinite perfectly conducting plane has a base radiation resistance of about 36.2 Ω. Rounding it to 36 or 37 Ω is entirely reasonable for that reference case.

A practical vertical over finite radials and lossy soil is a different electromagnetic structure. Changing its radial count or length can change all of the following at once:

• current distribution on the vertical and radials;
• the position and magnitude of the current maximum;
• the vertical length needed for resonance;
• the field coupled into the soil;
• radiated power for a given feedpoint current; and
• the pattern and the external conductors carrying current.

Consequently, both R_rad and R_ground can change when the radial system changes. Ground loss is not always an independent series resistor added beneath an otherwise unchanged 36.2 Ω radiator.

The Measurement Boundary Can Move the Answer

“Feedpoint resistance” is meaningful only when the calibration plane and the system boundary are clear.

If the coax exterior carries common-mode current, the feedline has joined the radiating and loss-producing structure. Some of its power may radiate; some may be dissipated. Either way, subtracting 36 Ω cannot tell us which path received the power.

Rudy Severns Tested the Assumption Behind the Table

The fixed 37 Ω term in Greg’s slide is precisely the assumption Severns examined in Experimental Determination of Ground System Performance for HF Verticals, Part 4. For a real quarter-wave vertical, he warns that taking R_ground = R_in − 36.2 Ω is not generally valid. Radiation resistance changes with the ground system and approaches the ideal value only as that system becomes relatively extensive.

His 40 m measurements reveal the failure in a particularly useful way: received signal still improved when the radial count rose from 32 to 64, while resonant input resistance changed hardly at all. Falling ground loss and changing radiation resistance partly offset at the feedpoint. The signal changed; the resistance sum concealed why.

An even sharper counterexample appears in Severns’s Part 3 comparison of surface and elevated radials. Four 33 ft radials elevated 48 inches produced a measured impedance of 34.8 − j9.7 Ω and a received signal within about 0.1 dB of the 64-surface-radial reference.

The fixed subtraction would give 34.8 − 37 = −2.2 Ω of “ground loss.” The antenna did not acquire negative loss. The result means that the assumed 37 Ω radiation resistance did not belong to that configuration. Cancelling the −j9.7 Ω with a low-loss tuning reactance would not repair the invalid resistance assumption.

Figure 18 in Severns’s 2015 Radiation and Ground Loss Resistances, Part 2 gives another concrete check. For a 7.2 MHz quarter-wave vertical with 64 quarter-wave radials over average soil, subtracting 36 Ω from input resistance—R_in − 36 Ω—suggests almost zero ground loss, while his power integration gives about 8 Ω. In the corresponding 1.8 MHz case, the subtraction suggests about 2 Ω rather than the approximately 6 Ω obtained from integration. Those figures belong to the stated model and its integration boundary; they are not replacement universal loss values.

What the KN5L Study Actually Supplies

Greg attributes slide 17 to John Oppenheimer’s 2013 KN5L Ground Radial Study. KN5L describes a synthesis of published studies, checked against a small experiment. His own 20 m measurements cover 16, 20 and 25 radials; an added resistance makes an EZNEC model agree with measured impedance.

The later 40 m table supplies equivalent loads for a simplified MININEC-type ground model. It is not a direct soil-loss measurement for every count from one to 120. The contributing data also use different radial lengths; KN5L flags the inherited ARRL figures below 24 radials as suspect.

That modelling guide has a use. My disagreement is with turning its values into a general table of quarter-wave-radial efficiencies by assigning 37 Ω to every configuration. The source does not establish that common radiation-resistance value, and radial count alone does not specify the antenna, soil, geometry or loss budget.

Where the “86 Radials” Result Comes From

The equation printed on Greg’s slide is:

Here N is radial count and the fitted coefficients produce resistance in ohms. To get 90% from the second equation, the loss term must be no more than 37 × (1/0.90 − 1), or approximately 4.11 Ω. Substituting that target into the fit gives N ≈ 85.69: round up and there are the 86 radials.

The algebra works. That does not make the result an experimentally established requirement. The count follows from the selected curve, the fixed 37 Ω assumption and the chosen efficiency target. It is not an independent finding that an arbitrary real vertical needs 86 quarter-wave wires.

The fit itself tells us to stop treating it as a physical law. At four radials it gives approximately 58.65 Ω, while the slide’s table lists 63 Ω. Extended beyond the displayed range, it reaches zero near N = 126.54 and then predicts negative loss. Soil does not start generating RF when we add the next radial; the numerical fit has simply run out of physical meaning.

A local curve can still help interpolation within a supported test domain. What it cannot do is remove the need to justify its radiation-resistance term or carry one geometry’s result into every ground system. That is the step I would not teach from this table.

Two Elevated Radials Need Their Own Evidence

On the same slide, Greg contrasts the surface-radial table with computer models of two elevated radials at 36 inches, assigns approximately 4 Ω loss and calculates 37/(37 + 4) ≈ 90%. Again, the arithmetic is fine. The slide does not disclose enough of that model to establish those resistance terms for a reader’s installation.

The useful question is whether the model separately determines radiation and loss power for its complete geometry, with both referred to the same current. A fitted loss resistance combined with an assumed ideal radiation resistance cannot answer that question by itself.

Elevating a small, balanced radial system can make a very effective antenna; Severns’s four-radial experiment above is positive evidence, not an objection to the idea. But four balanced radials at 48 inches and a measured path-strength comparison are not the same evidence as two radials at 36 inches with a stated 90% efficiency. Substituting one for the other would erase the conditions that made the experiment useful.

So this is not “two radials cannot work.” It is “the 90% claim needs the actual model or measurement behind it.” That distinction lets us retain the practical advantage of a well-designed elevated system without manufacturing an efficiency certificate from 37 and 4.

Why Resonance and SWR Cannot Separate the Power Budget

Tuning the antenna until X_in = 0 removes net input reactance. Matching it to 50 Ω transforms the impedance seen by the transmitter. Neither operation separately measures radiated power.

• A lossless matching network can turn many impedances into 50 + j0 Ω without changing antenna efficiency.
• A lossy network can produce an attractive SWR while consuming power.
• A low-loss antenna can present a resistance far from 50 Ω.
• A lossy antenna can be naturally close to 50 Ω.

Match describes power transfer at a port. Efficiency describes where accepted power goes. Those are related engineering questions, not interchangeable measurements.

When the Resistance Ratio Is Legitimate

The familiar expression remains useful:

It is legitimate when:

1. the antenna-system boundary is stated;
2. all resistance terms are referred to the same port current;
3. radiation and loss powers have been independently determined or credibly modelled;
4. feedline, matching-network and common-mode effects are included or controlled; and
5. the model is appropriate to the actual soil, geometry and conductors.

Subtraction is not forbidden. It is merely unable to manufacture an independently unknown radiation resistance. With a validated full-wave model, a measured loss budget or a sufficiently extensive system for which the perfect-ground approximation has been shown adequate, input resistance can be a useful consistency check.

A Better Ground-System Experiment

A serious comparison should combine impedance data with evidence that can distinguish radiation from dissipation:

1. Define the antenna port, matching network and feedline boundary.
2. Document frequency, radiator, radial wire, count, length, height, soil and nearby metal.
3. Characterise the feedpoint choke and measure coax-exterior current.
4. Re-resonate each configuration without hiding network loss.
5. Apply equal accepted power at the antenna port.
6. Use rapid A/B switching or a tightly controlled repeat sequence.
7. Measure several azimuths or enough of the pattern to separate redistribution from efficiency.
8. Compare with a disclosed full-wave model and publish uncertainty as well as the best result.

A one-path field-strength comparison can establish the change on that path. It does not by itself integrate total radiated power. That distinction matters when altered radial currents or common-mode current reshape the pattern.

Practical Takeaways

• A VNA measures complex input impedance at its calibration plane.
• At resonance, zero net reactance does not identify the real-resistance components.
• R_in = R_rad + R_loss is valid only as a same-port, same-current power-equivalent decomposition.
• The 36.2–37 Ω value belongs to a particular thin quarter-wave monopole over perfect ground.
• Radiation resistance can change with the radial system, soil and current distribution.
• Feedpoint resistance alone cannot separate radiation, soil loss, conductor loss or common-mode participation.
• KN5L’s guide values are equivalent model loads, not a universal direct soil-loss measurement.
• Greg’s 86-radial count follows from a fit plus the fixed 37 Ω assumption; it is not an experimental requirement for every vertical.
• Low SWR, a convenient 50 Ω input and successful contacts do not independently establish efficiency.
• Efficiency needs a radiated-versus-accepted power measurement or a validated model, not one subtraction.

The Conclusion I Would Take Into the Field

The problem with Greg’s slide 17 is not its use of an equivalent circuit. It is freezing the radiation term at an ideal value, applying a mixed-source radial fit, and presenting the resulting efficiencies and radial count with more certainty than the evidence supports.

I would use the KN5L study as the modelling guide it describes, and Severns’s measurements to understand how real radial systems behave. I would not use the slide’s 86-radial figure as a purchasing or installation rule, nor its two-radial figure as a guaranteed 90% efficiency. The engineering advantage of a better ground system is less power lost in soil—not a particular resistance on an analyser.

Ground loss is real. Feedpoint resistance is still not a ground-loss meter. Precision after an unsupported assumption is still unsupported: the analyser gives us the total, and subtracting 37 does not tell us how much became radiation and how much became heat.

Questions, antenna-factor records or height trials to share? Contact RF.Guru.