Three-Element Triangular Array Spacing and NEC-2 Calculator
Three-Element Triangular Array Spacing and NEC-2 Calculator
Convert a frequency range and chosen spacing fraction into an equilateral three-element layout, then export a transparent NEC-2 starting model. The calculator does not call any spacing “optimal” and does not predict RDF, null depth or installed SNR.
A spacing calculator should expose its assumption instead of hiding it behind the word “recommended.” Here you choose the centre-to-centre spacing as a fraction of wavelength at the geometric-mean frequency. The result is geometry—not a performance rating.
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.
Why There Is No Universal Best Spacing
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 in this calculator is therefore explicit and editable. A value such as 45 degrees is a weight, not a beam angle. The direction of a maximum or null follows the vector sum of spatial phase and applied channel phase. It must be calculated for the complete array and then verified after installation.
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 and requests a three-dimensional pattern at the geometric-mean frequency.
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.
Use the Result as a Measurement Plan
- 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
- 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.
Joeri's Bottom Line
Geometry is the easy part. This calculator gives exact coordinates from an openly chosen wavelength fraction and produces a model you can inspect. It deliberately refuses to tell you that one number is “RDF optimised,” because a spacing number without element, weight, coupling, noise and installation data cannot make that claim.
Use the result to build a hypothesis. Then model the complete array, calibrate every channel and measure the installed pattern and SNR. That is where array engineering begins.
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.