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

The expression R_in = R_rad + R_loss is legitimate when every term shares one system boundary and reference current. A one-port impedance measurement supplies only the total, however. It does not independently separate radiated power from soil, conductor, network or common-mode loss.

1. 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.

2. 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.

3. 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.

4. 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.

5. Controlled Measurements Show Why the Terms Can Move Together

Severns addressed this assumption directly 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.

Part 2 of Severns’s later analysis makes the same point through power integration. In one 7.2 MHz, 64-radial quarter-wave model, subtracting input resistance from 36 Ω suggested almost zero ground loss, while integration gave about 8 Ω. At 1.8 MHz the subtraction suggested about 2 Ω, while integration gave about 6 Ω. See Radiation and Ground Loss Resistances, Part 2.

6. Empirical Radial Fits Stay Inside Their Test Domain

The KN5L Ground Radial Study combines several published studies with three 20 m measurements and equivalent resistive loads added to a simplified model. Its later 40 m values are presented as guide-line model loads, not as direct universal measurements of ground-loss resistance for every radial count.

A fitted curve can interpolate inside a defined dataset, but it does not become an electromagnetic law. A radial-count formula must state the frequency, soil constants, radial length and geometry, radiator, model boundary and assumed radiation resistance. If an extrapolation reaches zero and then predicts negative loss, it has left its physical domain.

Severns’s 7.2 MHz experiment provides a constructive counterexample to fixed radial tables: four carefully balanced radials elevated 48 inches produced field strength within about 0.1 dB of the 64-surface-radial reference for that installation. That result is valuable, but it does not assign a universal loss resistance or efficiency to every elevated-radial system. The full configuration and measurement are documented in Ground Systems, Part 3.

7. 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.

8. 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.

9. 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.

10. 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 not universal direct measurements of ground-loss resistance.
• 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.

In Summary

Equivalent circuits are indispensable, but every term belongs to a declared reference current and system boundary. Freezing the radiation term at the ideal perfect-ground value while the radial system, soil, resonant length, current distribution and external return paths change does not isolate ground loss.

Ground loss is real, and reducing it can improve radiation efficiency. But a feedpoint resistance is a total, not a label. Separating radiated watts from heat requires more information than R_in − 36 Ω.

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