Capacitance Does Not Burn Watts

Why the parallel-plate explanation and reciprocal-height loss law are wrong.

Slide 18 of Greg Mihran’s July 2026 antenna primer makes a partly correct observation: raising a sparse set of tuned radials above lossy soil can improve antenna performance, sometimes substantially.

The explanation that follows is not correct.

The slide says that capacitive coupling decreases reciprocally with height according to C = ε0A/d, and that the loss therefore falls in inverse proportion to the radial height. Slide 23 asks us to imagine the radials and ground as the two plates of a capacitor and says that capacitive coupling “steals potential radiation current”. Slide 25 upgrades the analogy into a general rule: loss resistance drops as the reciprocal of distance.

Three different propositions have been merged:

• radial height can affect soil loss
• the radial system can be represented by a parallel-plate capacitor
• ground-loss resistance must therefore follow 1/d

The first can be true. The second is a poor model of the actual field geometry. The third does not follow even from the equation being quoted.

What the primer actually claims

An ideal capacitor consumes no average power

For an ideal capacitor driven by a sinusoidal voltage, the current is:

I = jωCV

The current is 90 degrees out of phase with the voltage. Using RMS phasors, the complex power is:

S = VI* = -jωC|V|2

The result is purely imaginary. Its real part is zero:

P = Re{S} = 0 W

During part of each RF cycle the source supplies energy to the capacitor’s electric field. During the next part, that energy returns to the circuit. The instantaneous power moves in both directions, but the average energy converted to heat is zero.

This does not mean that every physical capacitor remains cold. A real component has conductor resistance, equivalent series resistance and dielectric loss. Those non-ideal resistive or conductive terms dissipate power. Capacitance itself does not.

Real soil has both reactive and dissipative current

Soil is not an ideal conductor and not an ideal dielectric. In a simple sinusoidal field description, its current density contains both terms:

J = (σ + jωε)E

The jωεE term is displacement current associated with stored electric-field energy. The σE term is conduction current in phase with the electric field. That is the term that converts RF energy into heat.

Using RMS electric-field magnitude, the soil power loss is represented by:

Psoil = ∫soil σ|E|2 dV

Dielectric relaxation losses can be included through a complex permittivity or an effective conductivity. Either way, a dissipative term is required. Permittivity or capacitance alone is not a wattmeter.

If we force a small part of the system into a lumped parallel equivalent, its admittance would look like:

Y = G + jωC

Capacitive coupling can certainly deliver RF energy to a lossy path, just as a series coupling capacitor can deliver power to a resistor. But the resistor or conductance burns the watts. The capacitor controls coupling and voltage distribution; it is not the heat-producing element.

The perfect-ground counterexample

Consider an ideal quarter-wave monopole above an infinite perfect conducting plane. The antenna interacts strongly with that plane, produces an image current and stores reactive field energy near the structure.

The ideal ground plane dissipates no power.

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

This single counterexample is enough to disprove the phrase “capacitive coupling steals radiation current” as a general physical law. Coupling changes a system. Dissipation requires loss.

Why the parallel-plate formula does not describe radial wires

The familiar equation:

C = εA/d

is a useful approximation when two large conducting plates face one another, the separation is small compared with their lateral dimensions, the region between them is filled by a reasonably uniform dielectric and fringing fields can be neglected.

A quarter-wave radial fan over soil violates nearly every assumption.

Using ε0 makes the analogy even less suitable. ε0 is the permittivity of free space. The relevant field occupies both air and soil, and the soil has a complex, frequency-dependent material response.

Most importantly, capacitance is measured in farads and loss resistance in ohms. One cannot relabel the reciprocal distance in a capacitance equation as the reciprocal distance of a series loss resistance. A physical model connecting fields, power and a defined reference current is missing.

Even a real parallel-plate model gives a different answer

Suppose, for illustration, that we really did have two parallel plates filled with a homogeneous material having permittivity ε and conductivity σ. The capacitance and conductive shunt path would be:

C = εA/d

G = σA/d

The corresponding parallel resistance is:

Rparallel = 1/G = d/(σA)

So even in the geometry for which the plate formula is valid, resistance increases with spacing. It does not drop as 1/d.

At fixed voltage, the dissipated power would be P = V2σA/d, which does fall with spacing. At fixed current, the voltage changes and the scaling is different. An antenna preserves neither the same radial voltage nor the same current distribution as height changes, because its resonance and impedance change too.

This exposes the hidden category error. Capacitance, conductance, resistance and dissipated power are four different quantities. A geometrical dependence found for one cannot be copied to another without defining the excitation and solving the complete circuit or field problem.

What the cited Severns graph actually represents

The graph reproduced on slide 18 is internally labelled “VE2CV modelling data”. Its detailed context appears as Figure 16 in Rudy Severns’ 2012 article on elevated ground systems, where Severns credits John Belrose, VE2CV, and states that the data points were re-graphed from Belrose’s work.

The graph is conditional on:

• frequency: 3.75 MHz
• soil conductivity: 0.005 S/m
• relative permittivity: 13
• radial length: one quarter wavelength
• separate curves for four, eight and sixteen radials

The horizontal axis is radial height in wavelengths on a logarithmic scale. The vertical axis is average gain, Ga, in decibels. It is not a graph of capacitance and not a graph of loss resistance.

In Severns’ definition, Ga is obtained from the ratio of power crossing a large upper hemisphere to input power. It is a useful power-efficiency metric for the model, and it captures the improvement as less energy is dissipated in or directed through the ground. But it does not identify a unique series Rloss.

Severns explicitly says that even a small elevation can make a large difference, especially when the radial count is small. His controlled 7.2 MHz measurements also showed a rapid initial improvement as four radials were raised.

That height trend is real and deserves to be preserved.

Severns does not derive it from the parallel-plate formula, does not call capacitance the dissipative element and does not state that Rloss ∝ 1/d. His work treats the vertical, radials and real ground as a coupled field problem.

There is also a numerical error in the primer annotation. At 3.75 MHz, 0.005% of one wavelength is approximately 4.0 mm, or 0.157 inch—not 0.02 inch. The separate 0.100% annotation is approximately 3.15 inches and is consistent.

What raising the radials actually changes

Raising a radial fan can reduce soil loss, but several things change simultaneously:

• the electric-field amplitude and distribution inside the soil
• the radial electrical length and resonant frequency
• current magnitude and phase on each radial
• mutual coupling between the vertical, radials and earth
• feedpoint impedance and the current used as the resistance reference
• pattern shape and the division between skyward and ground-wave power
• the tendency for coax or nearby conductors to join the return system

With the fields farther from a conductive medium, the integral ∫σ|E|2dV can fall. Close to the surface, even a thin air gap can also shift the radial resonance and current distribution sharply. Those mechanisms can produce the steep initial improvement seen in the model.

As the radial height increases further, the fields and currents approach a different limiting distribution and the improvement tends to flatten. That is why the plotted curves show diminishing returns rather than an endlessly improving reciprocal law.

The radial count matters because more conductors share current and smooth the electric field near the earth. Radial length matters because the wires are resonant. Soil matters because σ and ε determine both dissipation and phase. Frequency matters because displacement and conduction current scale differently.

A one-variable plate analogy cannot contain all of that physics.

“Stealing radiation current” is the wrong accounting model

The phrase suggests that the feedpoint supplies a fixed bucket of current and capacitance diverts some predetermined portion that would otherwise radiate.

An antenna does not work that way.

The excitation, geometry and material properties establish one complete current and field distribution. Some accepted real power crosses outward as radiation. Some is dissipated in soil, wire, matching components and other resistive elements. Reactive electric and magnetic fields store energy and return it during each cycle.

A useful power balance is:

Paccepted = Pradiated + Psoil + Pwire + Pmatching + ...

There is no independent “capacitance burn” term. Capacitance affects the solution, but only the real loss mechanisms appear in the average-watt budget.

Likewise, an equivalent loss resistance is defined only after the dissipated power and reference current are known:

Rloss = Ploss / Iref2

If radial height changes both Ploss and Iref, the equivalent resistance need not follow the geometrical scaling of any guessed capacitance.

A quarter-wave vertical does not require elevated radials

The title of slide 23—“Quarterwave Antenna Needs to be Elevated off the Ground”—turns one useful design option into a requirement.

A quarter-wave vertical can use:

• a large surface radial field
• buried radials
• a smaller, carefully controlled elevated radial system
• a conductive roof or engineered ground plane
• other return structures designed for the installation

Elevating a few tuned radials can trade wire count for height, tuning sensitivity, high radial voltage and increased susceptibility to imbalance. A dense surface system trades more wire and installation labour for mechanical simplicity and reduced sensitivity.

Neither approach is universally superior. The answer depends on frequency, soil, space, safety, bandwidth, surrounding conductors and the required repeatability.

How a reciprocal-height claim should be tested

If someone wishes to establish Rloss ∝ 1/d, the test is straightforward in principle, though demanding in practice:

1. Define the complete radiator, radial, soil, feedline and choke geometry.
2. Measure or justify soil conductivity and permittivity at the operating frequency.
3. Set several radial heights over a sufficiently wide range.
4. Re-tune each configuration and keep accepted feedpoint power constant.
5. Measure individual radial currents and common-mode current on the feedline.
6. Determine dissipated soil power by validated field modelling or a controlled power/field experiment.
7. Refer every equivalent resistance to the same defined current.
8. Repeat for several radial counts, soils and frequencies.
9. Plot the result on log-log axes with uncertainty and test whether the slope is actually -1.

One selected gain curve cannot establish that law. A parallel-plate mnemonic cannot replace the measurement.

Takeaways you can trust

• Raising sparse elevated radials can substantially reduce soil interaction and improve average gain.
• An ideal capacitance stores and returns energy; it consumes zero average watts.
• Real soil dissipates power through conductivity and dielectric loss, represented by the in-phase part of its response.
• Capacitive coupling can influence how strongly the field excites a lossy path, but capacitance is not itself the loss.
• C = εA/d is a restricted parallel-plate approximation, not a field solution for resonant wires over soil.
• Even a lossy parallel-plate model does not yield the claimed series Rloss ∝ 1/d.
• The cited VE2CV graph plots modelled average gain for specified conditions, not measured loss resistance.
• Height, radial count, length, soil, frequency, current balance and feedline isolation interact.
• A quarter-wave vertical does not inherently require elevated radials.
• A practical height recommendation can be useful without being a universal law of loss.

In Summary

Greg’s primer starts with a valid observation: a few tuned radials very close to lossy ground can perform poorly, and raising them can produce a large improvement.

The error is using the parallel-plate capacitance formula as the explanation and then copying its reciprocal distance into a supposed law for loss resistance.

Capacitance is reactive. Conductivity and dielectric loss dissipate watts. A radial fan is not a plate. The cited graph is a model of average gain under stated conditions, not a measurement of resistance. And the curves themselves depend on radial count and approach a plateau.

The correct explanation is richer but not mysterious: elevation changes the complete electric field, current distribution, resonance and coupling of the antenna to lossy soil. Calculate those fields, integrate the lost power and refer it to a defined current. Then we may speak about equivalent loss resistance.

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