Capacitance Is Not Ground Loss: Where the Watts Actually Go

A sparse radial fan above real soil is a distributed antenna structure, not a parallel-plate capacitor. Height, radial count, radial length, soil properties, feedline balance and nearby conductors jointly determine accepted power, radiated power and loss.

1. 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.

2. 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.

3. 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.

4. 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 does not say that coupling is irrelevant. Coupling changes the current and field solution and can place more or less field inside a lossy region. It says that “coupled” and “dissipated” are different words for different physical quantities.

5. 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.

Using ε₀ alone makes the analogy weaker. ε₀ 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.

6. 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.

An antenna keeps neither radial voltage nor current distribution fixed when height changes. Its resonance, impedance, soil field and common-mode paths all change. Capacitance, conductance, resistance and power are different quantities, so a geometrical dependence cannot be copied from one to another without a complete model.

7. A Bounded Elevated-Radial Example

Figure 16 in Rudy Severns’s 2012 elevated-ground-system study regraphs modelling data by John Belrose, VE2CV. It is a useful bounded example of how radial height and radial count interact.

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 G_a as radiated power crossing a large upper hemisphere divided by antenna input power, expressed in dB. It is a useful model power-efficiency metric. It is not a measured series ground-loss resistance.

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.

Treat this as evidence for a configuration-specific height effect. It does not establish capacitance as a dissipative element or a universal reciprocal-height resistance law.

8. 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.

9. Use a Complete Average-Power Budget

The RF source, geometry and material properties establish one complete current and field solution. Reactive storage changes that solution, while only the real loss mechanisms appear in the 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.

10. Elevated Radials Are an Option, Not a Requirement

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.

11. How to Evaluate a Height-Loss Model

1. Define the radiator, radial, soil, feedline and choke geometry.
2. Measure or justify soil conductivity and permittivity at the test frequency.
3. Use several radial heights across a wide enough range to distinguish possible laws.
4. Re-tune each configuration and hold accepted feedpoint power constant.
5. Measure individual radial currents and coax common-mode current.
6. Determine the relevant loss or relative field with a validated model and/or controlled measurement.
7. Refer any equivalent resistance to the same defined current.
8. Repeat for other radial counts, soils and frequencies.
9. Plot uncertainty and test the log-log slope rather than drawing a 1/d line by eye.

A universal law needs results across the intended range of height, radial count, soil and frequency. One selected average-gain curve or a plate analogy cannot replace that measurement or field calculation.

12. 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.

In Summary

A few tuned radials extremely close to lossy ground can perform poorly, and modest elevation can produce a substantial improvement. The size of that improvement depends on the complete antenna, soil and feedline configuration.

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.

Analyze the complete current and field distribution, integrate dissipated power in the defined materials and components, and refer any equivalent resistance to a named current and reference plane.

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