Ham Radio Antenna Modelling Basics: NEC2 & Method of Moments

Antenna modelling software lets you design, test, and optimise antennas on your computer before cutting a single piece of wire. This guide explains how the underlying mathematics works, what the software actually computes, how to interpret its outputs, and what its limits are — so you can trust the results that matter and ignore the artefacts that do not.

Before antenna modelling software existed, antenna design was a combination of measured experience, published formulae, and expensive trial and error. A Yagi designer would build an antenna, measure its performance, adjust element lengths and spacings, rebuild, and repeat — a process requiring weeks of work and significant material cost for each design iteration. Antenna modelling collapses this cycle to minutes per iteration. A designer can explore hundreds of element configurations, compare their gain and pattern, evaluate the feed point impedance across a band, and arrive at an optimised design before ordering a single metre of aluminium tubing.

For the home amateur builder, modelling serves three equally important purposes. First, it predicts the performance of a planned antenna before construction — answering questions like "will this inverted-V on 40 m actually work at my site height, or will ground proximity kill the radiation angle?" Second, it helps diagnose unexpected antenna behaviour after construction — if your measured SWR does not match predictions, something real-world differs from the model and finding the discrepancy is diagnostic. Third, it builds deep intuition about how antenna geometry affects performance, making you a better antenna builder even when you are working from published designs without modelling them yourself.

The Numerical Electromagnetics Code (NEC2) was developed at Lawrence Livermore National Laboratory in the 1970s and remains the foundation of virtually all free amateur antenna modelling software. It implements the Method of Moments (MoM), a numerical technique for solving integral equations that describe the electromagnetic behaviour of wire structures.

The core idea is straightforward in concept. You divide the antenna into many short wire segments. On each segment, the current distribution is assumed to follow a simple mathematical function — typically a sinusoidal basis function. Maxwell's equations then tell us that the electric field at any point in space is the sum of contributions from all current elements everywhere in the structure. By requiring that the boundary conditions at the wire surface are satisfied at each segment — specifically that the tangential electric field at the conductor surface must equal zero for a perfect conductor — we get a system of simultaneous linear equations. One equation per segment, one unknown (the current amplitude on that segment) per segment.

NEC2 assembles the impedance matrix [Z] — an N × N matrix where N is the number of segments — and then solves the linear system using LU decomposition. This gives the current on every segment. From the current distribution, every other antenna parameter follows: feed point impedance from the voltage-to-current ratio at the source segment, far-field radiation pattern from the superposition of all current elements' contributions, gain from the ratio of maximum radiated power density to the total radiated power divided by 4π steradians.

The computational cost scales as N³ for matrix factorisation — doubling the segment count multiplies computation time by eight. This is why high-segment-count models are noticeably slower and why choosing the right segment count is an important modelling skill.

Gain vs. directivity

These two terms are frequently confused. Directivity is a purely geometric property — it measures how much more power a real antenna radiates in its maximum direction compared to a theoretical isotropic radiator that spreads power equally in all directions. It depends only on the shape of the radiation pattern, not on efficiency. Gain is directivity multiplied by efficiency — it accounts for power actually lost in the antenna conductors, loading coils, and ground return path. A lossless antenna has gain = directivity. A lossy short loaded antenna may have directivity of +1 dBi but gain of −3 dBi if efficiency is only 50%.

NEC2 reports gain in dBi, which already includes the efficiency of any resistive loads in the model. When you read "gain = 7.8 dBi" from a dipole model, that number assumes the conductor has the loss resistance you specified. If you omitted loss resistance (modelling ideal conductors), the gain is slightly optimistic — typically 0.1–0.3 dB high for a well-constructed dipole using good wire.

dBi vs. dBd

Antenna gain is expressed relative to either an isotropic radiator (dBi) or a free-space half-wave dipole (dBd). The relationship is fixed: 0 dBd = 2.15 dBi, because a half-wave dipole in free space has 2.15 dBi of gain over an isotropic source. NEC2 and all modern antenna modelling software report gain in dBi. Commercial antenna specifications sometimes use dBd — which makes the numbers look smaller — to compare with amateur radio publications that may use dBi. Always check which reference is being used before comparing antenna gain figures.

Take-off angle (elevation angle)

The take-off angle (TOA) or elevation angle of the main radiation lobe is one of the most practically important numbers from an antenna model. For DX operation on HF, you want low-angle radiation — signals that leave the antenna at shallow angles bounce off the ionosphere and travel long distances. A typical DX contact on 20 m involves signals leaving the antenna at 5–20° elevation. An antenna with a 45° TOA radiates most of its power skyward — useful for NVIS regional contacts but poor for DX.

TOA is primarily determined by antenna height above ground, expressed in wavelengths. A dipole at λ/4 height has a high TOA (around 60–70°). At λ/2 height the TOA drops to around 30°. At λ height it drops further to around 15°. For verticals, the TOA is determined more by the ground quality and radial system — a good ground system brings the TOA down to 20–30° which is a principal advantage of verticals over low dipoles for DX.

Front-to-back ratio (F/B)

For directional antennas (Yagis, quads, delta loops), the front-to-back ratio is the gain in the forward direction minus the gain in the exact opposite (180°) direction, expressed in dB. A 20 dB F/B ratio means the antenna radiates 100× more power forward than backward. High F/B is useful for reducing interference from stations behind the beam. Note that the F/B ratio is a single-direction figure — the worst-case rejection may occur at an angle other than exactly 180°, which is why some engineers use the front-to-rear ratio (worst-case rejection over the rear hemisphere) as a more conservative measure.

Ground is the most influential environmental factor in antenna modelling, and choosing the appropriate ground model is one of the most important decisions you make before running a simulation. All major NEC2-based tools offer the same three broad options:

Free space

No ground is present — the antenna radiates into infinite homogeneous space in all directions. Free-space models are useful for comparing two antenna designs on equal terms (removing ground as a variable), for VHF and UHF antennas mounted on towers where the antenna height is many wavelengths above ground, and for verifying element geometry and feed point impedance before adding ground complexity. A free-space half-wave dipole shows the classic figure-8 pattern with 2.15 dBi maximum gain — this is the reference value against which ground effects are measured.

Perfect ground (infinite perfect conductor)

The ground plane is a perfect conductor at Z = 0. This is the easiest ground to compute and gives theoretical maximum performance for any antenna above ground — no ground loss, maximum image current reinforcement. Perfect ground results are optimistic: real ground always has higher loss and lower conductivity. Use perfect ground for quick feasibility checks and for studying image current effects on verticals, where the perfect-ground model clearly shows the image antenna pattern. Never use perfect ground for predicting real-world performance of low-mounted antennas.

Real ground (Sommerfeld-Norton or MININEC)

Real ground uses measured or estimated soil parameters (conductivity σ and relative permittivity ε_r) to model the loss and reflection effects of realistic earth. Two implementations are common: the MININEC ground model (used in MMANA-GAL and early NEC programs) and the Sommerfeld-Norton ground model (used in NEC-4 and some NEC-2 implementations). MININEC ground is faster but less accurate for horizontal antennas below 0.2λ height. Sommerfeld-Norton is more accurate across all heights and is preferred for publication-quality results. For practical design work, either gives useful results for antennas above 0.15λ height.

The radiation pattern is the most visually distinctive output of antenna modelling software, and learning to read it correctly is essential for understanding what a model is telling you. Patterns are displayed in two forms: polar plots (a 2D circular diagram showing gain vs. angle in one plane) and 3D surface plots (a three-dimensional surface where the distance from the origin represents gain in any direction).

Elevation plot

The elevation pattern shows gain as a function of elevation angle above the horizon, typically as a polar plot where 0° is the horizon and 90° is straight up. For HF DX antennas, you want to see a strong lobe at low elevation angles — 5–20° for most long-distance HF propagation. NVIS antennas deliberately peak at 70–90° elevation for regional coverage. The take-off angle is the elevation angle where the main lobe has its maximum gain.

Azimuth plot

The azimuth pattern shows gain as a function of compass direction at a fixed elevation angle (usually the take-off angle). For an omnidirectional antenna (dipole, vertical), this plot is a circle or figure-8. For directional antennas (Yagi, quad beam), it shows clearly the forward gain, sidelobe levels, and front-to-back ratio. The azimuth plot at the take-off angle is the most operationally relevant pattern — it shows what the antenna actually does at the angles where signals travel.

Interpreting the pattern scale

Polar patterns are displayed on a dB scale, with the outer ring representing the maximum gain value. The rings inside represent successively lower gain levels — check the software's legend for the dB per ring. A 5 dB per ring scale means the inner ring is 5 dB below maximum, the second ring is 10 dB below, and so on. A lobe that reaches only the innermost ring is 5 dB weaker than the main lobe — still significant. A lobe that only reaches halfway to the centre ring is 20–25 dB below maximum — negligible in practice.

All NEC2-based software writes and reads a standard text file format using two-letter card codes. Understanding this format lets you read antenna files from any NEC2 program, modify them in a text editor, and import them into any NEC2 engine. The key cards you will encounter are:

The GW card (Geometry Wire) is the most important — every wire in the antenna is one GW card. The EX card places the excitation source. The GN card sets ground parameters. The FR card sets frequency. The RP card requests a radiation pattern calculation. All graphical NEC2 interfaces write exactly this format behind the scenes — understanding it demystifies what the software is doing and lets you edit models directly when the GUI is inconvenient.

A model that has never been compared to a real antenna measurement should be treated as an educated estimate rather than a fact. Model validation closes the loop between simulation and reality and builds confidence in your modelling workflow. The gold standard is to build the antenna, measure its impedance with a NanoVNA or antenna analyser, compare to the model prediction, identify discrepancies, and update the model until it matches.