Capacitance Does Not Burn Watts

Slide 18 of Greg Mihran, KJ6ER's July 2026 antenna primer shows a striking improvement as sparse radials are lifted above soil. That observation deserves to stay. The explanation attached to it does not.

The slide connects the improvement to the parallel-plate formula C = ε₀A/d. Slide 23 asks us to treat the radial fan and earth as the two plates and says their coupling steals potential radiation current. By slide 25, the analogy has become a rule that loss resistance falls as the reciprocal of height.

That is the point I am challenging. Height can reduce loss; a radial fan is not a plate; and farads do not become ohms because both appear beside the letter d. If we want to explain why an elevated system works better, we need the physical mechanism—not just an equation that slopes in a convenient direction.

The Three Steps in the Primer's Argument

This is not an argument against elevating radials. It is an argument for explaining their advantage correctly. Otherwise a useful result becomes a rule that gets carried into antennas and sites where its assumptions no longer exist.

Separate Storage, Dissipation, Coupling and Equivalent Resistance

Four related quantities must remain distinct. A change in geometry can alter all four, but none can be inferred from another without the excitation, geometry, material properties and reference plane.

An Ideal Capacitor Consumes Zero Average Watts

For an ideal capacitor driven sinusoidally, using the e^jωt convention and RMS phasors:

The current is 90° ahead of voltage. During one part of the RF cycle, energy enters the electric field; during another, it returns to the circuit. Instantaneous power reverses direction, but an ideal capacitor converts no net energy into heat.

A physical capacitor can still become warm. Leads and electrodes have resistance, the dielectric has loss and the component may be represented with ESR, conductance or loss tangent. Those dissipative properties burn watts. The capacitance value alone does not.

Real Soil Carries Reactive and Dissipative Current

For a simple linear isotropic material under sinusoidal excitation, one useful form for total current density is:

The jωεE term represents displacement current associated with electric-field energy. The σE term is the conduction current in phase with E for real positive σ. Using RMS field magnitude, its time-average loss is:

For a dispersive dielectric, ε is complex and its loss component contributes an additional in-phase term. NIST’s treatment of RF fields in dielectric materials combines dielectric loss and DC conductivity through complex permittivity and Poynting’s theorem. ITU-R P.527-6 likewise treats earth-surface electrical properties through conductivity and complex relative permittivity, with soil response dependent on composition, moisture, temperature, structure and frequency. Either notation reaches the same engineering conclusion: a dissipative term is required before field energy becomes heat.

If a small part of the system is approximated by a lumped parallel admittance:

Capacitive coupling can deliver energy to a lossy path, just as a series coupling capacitor can deliver power to a resistor. The capacitor influences coupling and voltage distribution; the conductance or resistance is what dissipates the watts.

Perfect Conducting Ground Separates Coupling from Loss

An ideal quarter-wave monopole couples strongly to an infinite perfect conducting plane. The ground plane supplies the image relationship and reshapes the fields, yet the ideal conductor dissipates no power.

Strong electromagnetic coupling therefore does not imply loss. Dissipation appears only when finite conductivity, dielectric loss or another resistive mechanism permits real power to be converted into heat.

This is why the current-stealing picture on slide 23 is incomplete. Coupling changes the current and field solution and can place more or less field inside a lossy region. But “coupled” and “dissipated” are different physical quantities: the perfect-ground example has strong interaction without ground heating.

Why C = εA/d Does Not Describe a Radial Fan

The familiar expression is useful when two large conducting plates face each other, their spacing is small relative to lateral dimensions, the material between them is approximately homogeneous and fringing is negligible.

The ε₀ in the primer's plate formula does not supply the missing soil model. It is the vacuum permittivity; the relevant fields occupy air and soil, and the soil response is complex and frequency dependent.

There is also a dimensional and reference-plane problem. Capacitance is measured in farads; equivalent loss resistance is measured in ohms and is defined only after both dissipated power and a reference current are specified. A factor of 1/d in a capacitance expression cannot simply be relabelled as a 1/d series resistance.

What a Lossy Parallel-Plate Model Predicts

Suppose two genuine plates are filled with a homogeneous medium of permittivity ε and conductivity σ:

The shunt resistance increases with spacing; it does not decrease as 1/d. At fixed voltage, the dissipated power |V|²σA/d falls as spacing grows. At a different excitation constraint, voltage and current change and so does the scaling.

This does not give us an alternative radial-loss formula: the plates are still an illustration, not the antenna. It exposes the missing step in slide 25. An antenna keeps neither radial voltage nor current distribution fixed when height changes. Its resonance, impedance, soil field and common-mode paths change too. A dependence of capacitance on distance cannot simply be copied into a series loss resistance.

The Graph on Slide 18 Is Evidence—but for What?

The plot reproduced on slide 18 is labelled as VE2CV modelling data. Its detailed provenance appears in Figure 16 of Rudy Severns's 2012 elevated-ground-system study, where he credits John Belrose, VE2CV, and explains that he regraphed the data. I followed that source because the meaning of the graph matters more than the caption added around it.

The figure states:

• frequency: 3.75 MHz;
• soil: 0.005 S/m conductivity and relative permittivity 13;
• radial length: one quarter wavelength;
• height shown in wavelengths on a logarithmic axis; and
• separate curves for four, eight and sixteen radials, plus resonant four-radial data.

The vertical axis is average gain G_a in decibels. Severns defines it through power crossing a large upper hemisphere relative to antenna input power; power outside that skyward accounting is not credited. It is a model power ratio, not measured series ground-loss resistance. The chart cannot identify R_loss simply by reading a decibel value from its axis.

Severns also reports that the steep early height improvement was observed experimentally. His controlled 7.2 MHz measurements compared feedpoint impedance, relative S21 and radial-current division with common-mode isolation. This preserves the useful result: raising four radials from the surface can produce a large relative field improvement in that installation.

That is a real engineering advantage for the right sparse-radial installation. It supports the useful part of Greg's argument. It does not make capacitance the dissipative element, and neither the graph nor the measurement derives a universal reciprocal-height resistance law.

What Raising the Radials Actually Changes

Several coupled quantities move at once:

• electric-field amplitude and distribution inside the soil;
• radial electrical length and resonant frequency;
• current magnitude and phase on each radial;
• mutual coupling among radiator, radials and earth;
• feedpoint impedance and the current chosen as a resistance reference;
• pattern and the division of power crossing the upper hemisphere;
• coax-exterior, mast and nearby-conductor currents; and
• touch voltage and accessibility of the elevated wires.

Moving fields farther from conductive soil can reduce ∫σ|E|²dV. Near the surface, even a small air gap can also shift radial resonance and current distribution. The combination can produce the steep initial improvement in the model and the experiment. At greater height the system approaches another field distribution and the curve flattens.

Radial count matters because more conductors divide current and change the near-ground field. Length matters because the wires are resonant. Soil matters because σ and complex ε set both phase and dissipation. Frequency changes the balance between conduction and displacement current. Feedline isolation matters because the coax exterior can become another radial.

Current Is Not a Bucket That Capacitance Steals From

The slide's current-diversion picture suggests a fixed supply of radiation current, with capacitance taking a share away. But the RF source, geometry and materials establish one complete current and field solution. Reactive storage changes that solution; only the real loss mechanisms appear in its average-power budget.

For a stated system boundary:

Reactive electric and magnetic energy is stored and returned each cycle. It influences the solution but does not appear as an independent “capacitance burn” term in the average-watt budget.

An equivalent loss resistance is meaningful only when referred to a named RMS current:

If height changes both P_loss and I_ref, the equivalent resistance need not follow the scaling of any guessed capacitance.

Elevated Radials Are an Option, Not a Requirement

Slide 23 presents elevation as a requirement for a quarter-wave antenna. That turns one useful solution into the only solution. A quarter-wave vertical can use:

• a substantial surface radial field;
• buried radials;
• a smaller tuned elevated-radial system;
• a conductive roof or engineered ground plane; or
• another documented return structure.

Elevating a few tuned radials trades wire count for support height, tuning sensitivity, imbalance sensitivity and accessible RF voltage. A dense surface system trades more wire and installation work for lower individual radial current and often less tuning sensitivity. Neither is universally superior.

What I Would Take from This for an Actual Antenna

If a few tuned radials are lying almost on lossy soil and there is room to raise and support them safely, elevation is a worthwhile design change. It can move the strong near fields away from the loss region and change an unfavourable resonant current distribution. That is a mechanism-backed reason to expect improvement—not an obligation to believe the plate analogy.

If a substantial surface radial field is practical, it is another sound way to control the return system without the same elevated-wire support and tuning demands. Choose the architecture for the space, bandwidth and access you actually have. Greg's reported preference for 2–5% wavelength elevation on slide 18 is his field recommendation; it is not derived by the displayed graph, whose height axis ends at 1% wavelength, nor by C = εA/d.

For a quantitative comparison, keep the accepted-power reference consistent and track radial currents, exterior-coax current and field strength as height changes. For the much stronger claim of a universal 1/d loss-resistance law, the burden is different: derive the loss and named reference current across the stated geometry and soil range. The primer has not supplied that missing derivation.

Engineering Takeaways

• Raising sparse tuned radials can substantially reduce interaction with lossy soil.
• An ideal capacitance stores and returns energy; it consumes zero average watts.
• Real soil dissipates power through conductivity and dielectric loss.
• Capacitive coupling can change how strongly a lossy path is excited without being the loss mechanism itself.
• C = εA/d is not a field solution for resonant wires over soil.
• A lossy parallel-plate example yields G = σA/d and R_parallel = d/(σA), not a universal series R_loss ∝ 1/d law.
• The Severns/VE2CV example plots modelled average gain under stated conditions, not measured loss resistance.
• Height, radial count, length, soil, frequency, balance and feedline isolation interact.
• A quarter-wave vertical does not inherently require elevated radials.
• Practical height recommendations remain conditional on the complete installed antenna.

Keep the Height Advantage; Drop the False Mechanism

Greg starts from an observation that I agree with: a few tuned radials extremely close to lossy ground can perform poorly, and modest elevation can produce a substantial improvement. The disagreement is the jump from that observation to a capacitor-plate model and then to a universal resistance law.

Capacitance is reactive. Conductivity, dielectric loss and resistance dissipate average power. A sparse radial fan is not an ideal parallel-plate capacitor, and the Severns/VE2CV example is a model of average gain for stated soil, frequency, length and radial count—not a resistance measurement.

We do not need that jump to explain why the better radial installation wins. It changes where current flows and where fields enter dissipative material. That is an engineering explanation a builder can use. Calling capacitance the heat source obscures the very advantage the example is supposed to teach.

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