Three-Element Triangular Array Spacing and NEC-2 Calculator
Three-Element Triangular Array Spacing and NEC-2 Calculator
Turn a frequency range and chosen electrical spacing into three positions you can lay out on a site. Then export a NEC-2 starting model with visible wire dimensions and source phases. This is a practical way to compare candidate geometries before choosing the complete receive system—not a promise of RDF, null depth or installed SNR.
RF.Guru working definition: Common-mode current is the non-cancelling phasor-sum current in a specified set of conductors, evaluated at a defined cross-section and using a declared current-direction convention. In the intended differential transmission-line mode, the outgoing and return currents are equal and opposite, so their phasor sum is zero. When they do not cancel, the remaining current must close through another reference or return path—such as the outside of a coax shield, a mast, equipment chassis, station wiring, nearby structures, earth, the operator, or distributed coupling through the environment.
This broader working definition is especially useful in practical antenna systems. On transmit, non-cancelling current on the outside of the coax can make the feedline and connected structures part of the radiating antenna system unless that path is intentional, clearly defined and properly controlled—for example by providing the required return path and placing a suitable common-mode choke at the correct boundary.
I use a wavelength-scaled layout to connect two questions: what fits in the available space, and how far apart the elements are electrically on each band. Choose the spacing fraction, see the side length and coordinates, then change the range or spacing and compare. The geometric mean gives the exercise a consistent reference; it does not select the best array for you.
Calculate the Triangular Geometry
Enter a positive frequency range and the spacing fraction k in s = kλg. The three element centres lie on an equilateral triangle with side s. The NEC export adds user-selected ideal source phases only as a modelling start.
Calculated Geometry
- Wavelength range:
- Geometric-mean frequency:
- Wavelength at geometric mean:
- Triangle side spacing:
- Radius from array centre to each element:
- Spacing across the frequency range:
Element centre coordinates:
What the Calculator Computes
For lower and upper frequencies f1 and f2, the geometric-mean frequency is:
fg = √(f1f2)
The corresponding free-space wavelength is λg = c/fg, using the exact speed of light c = 299,792,458 m/s. You choose a dimensionless spacing fraction k; the triangle side is s = kλg. For an equilateral triangle, the distance from array centre to each element is R = s/√3.
The geometric mean is a convenient logarithmic centre when a frequency ratio matters. It is not an optimisation proof. The electrical spacing still changes across the band: s/λ is smaller at the low-frequency end and larger at the high-frequency end.
Choose Spacing for the Space and the Task
The side length is the tape-measure distance between each pair of element centres; the smaller radius is the distance from the triangle's centre to each element. Keep that distinction when marking out the site. The coordinates use an arbitrary x–y orientation: rotate the whole layout to your chosen site bearing, rather than interpreting element 1 as an automatic beam direction.
Array response depends on element positions, element patterns, mutual impedance and the complex weights applied to each channel. Change frequency and the phase accumulated across the same physical spacing changes. Change the element load or the ground and the embedded element patterns and coupling change too.
A receive array also depends on channel gain and phase, cable transfer, combiner topology, receiver input, common-mode current, external-noise coherence and front-end headroom. One spacing can offer a useful compromise across a declared band, but it cannot guarantee RDF, null depth, beam direction or SNR independently of those other quantities.
The phase field is explicit and editable so you can explore the effect of changing source excitation without silently changing the geometry. A value such as 45 degrees is a phase setting, not a beam angle. In a coupled array, equal source-voltage magnitudes do not guarantee equal element currents, and their phases need not be the source phases. A receive combiner adds another network: its channel weights cannot simply be equated to these transmit-model voltages. The complete current or receive-channel response decides the pattern.
What the NEC-2 Deck Does—and Does Not—Model
The generated deck places three identical vertical wires at the calculated coordinates in free space. It excites the centre segment of each odd-segment wire with ideal voltage sources at 0, +ψ and −ψ degrees. The single-frequency pattern request samples the upper hemisphere: θ = 0–90° and φ = 0–360° in one-degree steps, at the geometric-mean frequency. It is not a full-sphere integration or a band sweep.
That is an illustrative reciprocal passive-array model. It is not an active receive-array model. It omits sensor input impedance, amplifier transfer, cable loss and delay, terminations, combining error, ground, structures, mounting and common mode. Add those features deliberately before treating a computed pattern as an installed prediction.
Segmentation and wire radius must also suit the wavelength and geometry. A deck that parses is not automatically converged. Repeat the model with finer segmentation, check current continuity and compare the result. NEC limitations become especially important for very short segments, thick wires, close spacing, junctions and wires at or through ground.
Coordinates, radius and frequency are exported to six decimal places. The generator rejects dimensions that collapse at that precision, a frequency that rounds to zero, and wires that touch or overlap. Those checks prevent obvious invalid output; they do not certify thin-wire accuracy or model convergence. Editing an input clears the earlier result and deck so you cannot mistake them for the new settings.
Take the Candidate Layout into the Complete Design
- Record the physical reference points. Spacing means centre-to-centre distance between defined element coordinates, not enclosure edge or cable entry.
- Characterise each channel. Measure complex input impedance and gain/phase transfer across the band with the actual element, front end, cable and load.
- Map common-mode current. A cable that carries exterior current becomes another element and can move both maxima and nulls.
- Verify headroom. Strong local signals can compress one channel differently and destroy the intended vector sum without an obvious warning.
- Measure pattern and SNR separately. Use a controlled source or several stable bearings for pattern work, and simultaneous or rapid A/B/B/A observations for wanted-signal and noise comparisons.
- Repeat after environmental changes. Soil moisture, temporary wiring, nearby metal and cable routing can alter coupling and the installed result.
Primary Technical Sources
- NEC-2 user documentation — Wire geometry (GW), excitation (EX) and radiation-pattern request (RP): coordinates, source voltage and angular sampling.
- MIT — Antenna Arrays: current excitation, spatial phase and field superposition.
- ITU-R BS.705-2 — HF transmitting and receiving antenna characteristics and diagrams: array factors, gain and pattern calculations, ground influence, practical measurements and surrounding-structure effects.
- IEEE 149-2021 — Recommended Practice for Antenna Measurements: radiation-pattern and antenna-property measurement for passive linear reciprocal devices.
- Lawrence Livermore National Laboratory — The Numerical Electromagnetics Code: A Brief History: NEC's method-of-moments development and model lineage.
- ITU-R P.372-17 — Radio noise: external-noise planning data and the boundary between array pattern and site noise.
Practical Conclusion
Use this tool to make the first design decision tangible: a chosen electrical spacing becomes a side length, three site coordinates and an editable model. Compare candidate layouts while keeping their assumptions visible. Then develop the element, matching and receive network around the layout that serves your space and wanted directions, and verify the result. The benefit is a reproducible starting point—not an unexplained magic spacing.
Mini-FAQ
- What does the spacing fraction mean? It is the equilateral triangle's centre-to-centre side length divided by wavelength at the geometric-mean frequency. It is a user-selected design input, not an optimum certified by the calculator.
- Why use the geometric-mean frequency? It is a convenient logarithmic centre for a frequency range. It gives one transparent reference wavelength, but it does not equalise array performance across the band.
- Does a 45-degree phase step create a 45-degree beam? No. Applied channel phase is not beam bearing. Direction follows the combination of physical spacing, frequency, element response, coupling and all complex channel weights.
- Does the NEC-2 export model an active receive array? No. It uses three passive wires and ideal voltage sources in free space. Real sensor ports, loads, cables, combining, ground, structures and common-mode paths must be added.
- Does the calculator predict RDF or null depth? No. It computes geometry and an illustrative deck. RDF and nulls require a complete validated model or calibrated installed-pattern measurements.
- Why must the segment count be odd? An odd count gives each straight wire one unambiguous centre segment for the illustrative source. Model convergence still needs to be checked with suitable finer segmentation.