Delta Loops Above the Roof: Why Height Changes the Pattern

“I will put the delta loop above the house. It will work like the one close to the ground, only higher.” That assumption leaves out part of the antenna system. Moving the same triangle upward changes its electromagnetic relationship with the Earth, the building and its feedline. The wire can retain its shape while the elevation pattern, polarization mixture, input impedance and losses change.

When I specify a loop installation, height belongs to the electrical design. Ground interaction helps establish the installed radiation pattern. It does not follow that every delta loop should be low, or that a rooftop installation must perform poorly. It follows that a pattern established for one geometry and height cannot simply be carried to another installation.

First identify which delta loop you mean

A triangle is a mechanical description. We still need its plane, perimeter in wavelengths, shape, feed position and excitation. A full-wave loop standing in a vertical plane differs from a horizontal loop suspended over a garden. Both differ from a small magnetic loop with nearly uniform current. Moving between those cases invalidates many familiar rules of thumb.

A vertical plane also does not establish vertical polarization. Around the fundamental full-wave mode, a symmetrical loop fed at its bottom apex or at the centre of its horizontal side can produce predominantly horizontally polarized broadside radiation. Feeding an appropriate position on a sloping side can favour a vertically polarized mode. Asymmetry, installation and operation on other bands can introduce substantial cross-polarized components.

L. B. Cebik's distinction between vertically oriented, vertically polarized loops and his horizontally polarized examples is useful here: moving the feedpoint changes the electrical antenna even when the outline looks similar. His particular model results should be read with their geometry and ground assumptions; they are not a universal delta-loop specification.

Ground changes the current and the field

There are two connected effects. First, the antenna's electric and magnetic fields induce charge and current in the ground and nearby structures. Their fields act back on the antenna. This changes the input impedance and can change the amplitude and phase of the current around the loop.

Second, radiation reaching a distant direction includes contributions travelling directly from the antenna and contributions interacting with the ground. Their relative phase and amplitude depend on elevation angle, polarization, height and ground properties. They can reinforce or cancel in different directions.

A thin-wire calculation makes the first effect explicit. In a method-of-moments representation, the current coefficients I satisfy:

Z(h, ground, roof, feedline) · I = V

The impedance matrix includes self and mutual interactions, with the ground boundary included in the electromagnetic kernel. Changing height changes that matrix. Keeping the same applied source does not require the old current distribution to survive.

The far field then sums the radiation from all those current elements, with their spatial phase and polarization. For a wire in free space, suppressing a common scale factor, this can be written as:

F(ŝ) ∝ ∫ I(ℓ) [t̂(ℓ) − ŝ(ŝ · t̂(ℓ))] exp[jk ŝ · r(ℓ)] dℓ

Here ŝ is the observation direction, t̂ the local wire direction, r its position and k = 2π/λ. For ground or a roof, the corresponding reflected and scattered field contributions must also be included. The useful point is that current phase, wire direction and position all enter the result. A triangle outline or a single impedance value contains too little information to determine the pattern.

The image calculation explains why height matters

Consider a deliberately simple limiting case: an elementary electric-current source at height h above an infinite, flat, perfectly conducting plane. Hold its current fixed. Let α be elevation above the horizon, with 0° horizontal and 90° overhead.

The equivalent image of a horizontal electric-current element has opposite current direction; the image of a vertical element has the same current direction. Their direct and image path phases differ by 2kh sin α. The resulting height factors are:

Horizontal current: F_h = 2j sin(kh sin α)
Vertical current: F_v = 2 cos(kh sin α)

Each factor still multiplies the appropriate elementary radiation pattern. For example, a vertical electric-current element has its own overhead null. A sloping wire must be resolved into horizontal and vertical current components; a complete loop requires integration over different heights and complex currents. These two equations alone are not a delta-loop pattern model.

They do expose the height dependence cleanly. For the horizontal-current factor, interference maxima satisfy sin α = (2m + 1)λ/(4h), when the right-hand side is no greater than one. Nulls satisfy sin α = nλ/(2h). The horizon is also a null in this ideal horizontal-current example.

Even this simple factor changes from a broad rise toward high angles to several lobes separated by nulls. Raising an antenna can strengthen useful low-angle radiation and simultaneously add higher lobes. For the vertical-current factor, the locations of maxima and nulls differ. That is why transferring a height rule between polarization modes is unreliable.

The factor's amplitude of two at constructive interference must not be advertised as a universal 6 dB increase in antenna gain. These equations hold the elementary current fixed. An equal-accepted-power comparison must also account for the changed radiation resistance, current and total radiated power.

Real ground has a complex reflection coefficient

Soil is neither a perfect conductor nor a single universal material. With an exp(jωt) time convention, a simple conductive dielectric model uses:

ε̃_r = ε_r − jσ/(ωε₀)

Here σ is conductivity in S/m, ε_r relative permittivity, and ω = 2πf. Both frequency and soil condition matter. ITU-R P.527-6 provides the material-property framework, including the dependence of earth materials on conditions such as moisture.

For a plane wave above a smooth, homogeneous, nonmagnetic half-space, the horizontal-electric-field reflection coefficient is:

r_TE(α) = [sin α − √(ε̃_r − cos² α)] / [sin α + √(ε̃_r − cos² α)]

The square-root branch is chosen for a passive medium. The electric field is perpendicular to the incidence plane. Vertical polarization has a different Fresnel coefficient and projection geometry. Replacing both polarizations with one real “ground reflection percentage” loses that distinction.

This plane-wave reflection picture is useful for understanding far-field interference. Accurate near-ground impedance, current and loss calculations require an appropriate ground-field solution, such as a Sommerfeld ground formulation within its numerical limits. Simply attaching a reflection coefficient to a free-space pattern does not recompute the antenna currents.

There is also no universal height at which an antenna suddenly disconnects electromagnetically from the Earth. Reactive interaction can become weaker while a ground-reflected contribution remains important to the far field. These processes occur over different spatial regions.

A delta loop does not have one electrical height

Report at least the bottom and top heights, the feedpoint height and the shape. The lowest vertex may be 2 m high while important current-carrying sections are several metres higher. On another band, the current maxima can move. An arithmetic average of the corner heights will not reproduce every elevation cut.

W8JI's delta-loop analysis makes a useful comparison between maximum support height and the heights of substantial current regions. A dipole at the top of a support and a delta extending down from that support do not put their radiating currents at the same heights. That observation is more portable than any one gain figure from the example.

This is a scale calculation, not a recommended set of installation heights. Moving a loop upward by 10 m changes every wire element's phase relationship with the ground by a frequency-dependent amount. At the same time, the loop perimeter becomes electrically larger as frequency rises, allowing a different current distribution around the loop.

Cebik's multiband loop study illustrates why matching a loop on several bands does not establish one common radiation pattern. Its models have specified shapes, feed positions and ground. They do not supply a universal verdict on every multiband loop, but they do invalidate the assumption that a low SWR preserves the fundamental-mode pattern.

A roof is not the ground moved upward

“Two metres above the roof” and “two metres above earth” describe different electromagnetic environments. An ordinary tiled roof is a finite, layered structure over an air space and a building. A concrete roof may contain a conductive reinforcement mesh. Metal roofing is a finite conducting surface with seams and edges. Gutters, solar-panel frames, mounting rails, wiring and the antenna mast can carry induced RF currents.

There are consequently several relevant distances: clearance to the roof surface, clearance to its conductive components, height above the surrounding earth, and distance to roof edges and neighbouring structures. A finite roof can scatter and diffract radiation; it may change azimuth symmetry as well as the elevation pattern. Wet materials can alter both coupling and dissipation.

A large metal roof can act as an important local reflecting structure over some frequencies and directions. Treating it as an infinite perfect plane is still an approximation that needs a size and geometry check. A tiled or reinforced roof cannot be assigned that boundary condition simply because the antenna is close to it.

I would therefore model a rooftop installation as a new configuration. Replacing “ground height = 2 m” with “roof clearance = 2 m” in a drawing does not establish electromagnetic equivalence.

Pattern redistribution and ground loss are different quantities

Constructive and destructive interference redistribute radiation with angle. Dissipation converts power into heat. Both can occur in the same installation, but one cannot be inferred from the other.

For peak-value electric-field phasors in a simple conductive soil model, the conduction loss is:

P_soil = ½ ∫_soil σ |E|² dV

Additional dielectric loss must be included when it is not already represented by the material's effective conductivity. The installed radiation efficiency is the radiated power divided by net power accepted at the chosen antenna-system input. With that reference stated:

η_rad = P_rad/P_accepted
G(α, φ) = η_rad D(α, φ)

Directivity D describes the distribution of radiated power. Gain G additionally includes dissipation within that defined system. Realized gain includes mismatch at the specified input; feeder and tuner losses belong in the accounting if they lie inside that system boundary.

An elevated installation may reduce soil absorption or clear a nearby obstruction and become more efficient. It can still develop a null toward a particular path. Conversely, a strong lobe in a normalized pattern does not prove high efficiency. I want gain in useful directions and a power budget, not just the angle of the largest lobe.

The feedline can change when the loop moves

Raising a loop usually changes the coax route, the amount suspended in the air and its proximity to a mast or wall. If there is significant common-mode current on the outside of the shield, that conductor contributes radiation and coupling. Moving a choke or adding cable can then change the installed antenna as well as the impedance seen at a measuring instrument.

A 1:1 current choke introduces a finite, frequency-dependent impedance in that exterior current path. It does not remove the Earth's boundary condition. Nor does a tuner reproduce the former current distribution merely by restoring a 50 Ω input match.

This is why I record feeder routing and choke position alongside wire heights. Otherwise an alleged “height comparison” can contain two uncontrolled changes: the loop-to-ground geometry and the exterior feedline current path.

How I would compare the garden and rooftop installations

1. Define both structures. Record all wire coordinates, conductor sizes, feed position, roof construction, nearby conductors, feeder route and choke positions. Specify bottom and top heights above earth as well as roof clearance.
2. Evaluate every intended band. Solve the installed current distribution and impedance. Include the feedline exterior when it carries significant current; an ideal nonradiating transmission-line element alone cannot represent that radiation.
3. Vary uncertain material properties. Use plausible soil and roof cases, including dry and wet conditions. Show the spread rather than presenting an assumed material value as a measured property.
4. Check numerical convergence. Refine segmentation and relevant structures. Use a solver and ground treatment appropriate to the minimum clearance, wire geometry and building materials. A more detailed picture is not proof of a valid solution.
5. Compare absolute patterns on a common basis. Inspect both polarization components, elevation cuts in relevant azimuths and the full pattern. First normalize to equal accepted power at the antenna-system input; then add the actual feeder, matching and transmitter constraints.
6. Measure what can be measured. Record calibrated complex impedance at a declared reference plane, feedline common-mode current at several positions, cable loss and repeatability. Controlled field-strength tests can test selected directions; a shack SWR sweep cannot establish a three-dimensional pattern.
7. Use on-air comparisons with propagation controls. Alternate rapidly where practical, record frequency and path, and collect repeated observations. A single strong contact proves that a path worked; it does not map an elevation lobe.

For regional coverage, high-angle radiation can be useful when ionospheric conditions support it. For a particular DX path, lower angles may matter more. There is no universally best pattern without a communications objective.

My installation advice

If a delta-loop design is intended to operate close to the ground, retain that specified geometry as the starting point. If you want to put it above the house, treat the change as an antenna-system redesign and evaluate it accordingly. It may work very well; the original pattern is no longer an adequate prediction.

Height, ground, feed position and current distribution belong in the same technical description. The ground helps shape the radiation pattern, while the loop geometry and excitation determine what interacts with it. Raising the triangle changes that relationship. Matching the new installation is only one part of making it work.

Technical references

• ITU-R BS.705-2 — HF transmitting and receiving antennas characteristics and diagrams: reference treatment of HF antenna patterns and ground reflection.
• ITU-R P.527-6 — Electrical characteristics of the surface of the Earth: earth-material parameters for propagation and ground models.
• L. B. Cebik, W4RNL — Notes on All-Band Use of Vertical-Plane Deltas: examples with explicitly different feed positions and electrical sizes; model-specific conclusions.

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