Antenna Build Lab
Pick an antenna, a band and a height. A thin-wire method-of-moments solver — the same physics family as NEC-2 — runs in your browser and computes the feed impedance, SWR and the full 3D radiation pattern as you change things. A companion to the RF / Antenna calculator and the antenna theory guide.
Half-Wave Dipole
3D needs WebGL 2, which this browser does not provide. Here are the same results as 2D cuts.
Reading the 3D pattern
The surface is the solver's far-field gain in every direction. Its radius uses the same 30 dB scale as the 2D plots, so a direction 10 dB down sits two thirds of the way out, and the colour runs from deep blue (30 dB down) to warm orange at the peak. The wire in the middle is the antenna, drawn for orientation; the amber dot is the feedpoint and the amber tick on the outer ring marks azimuth 0°. Over ground the pattern stops at the horizon.
Keyboard: focus the view, then ← → ↑ ↓ orbit (hold Shift for bigger steps), + − zoom and Home resets. The readout above has every number in text.
Bench analyzer
Measured at the antenna feedpoint.
Drag the cursor across the SWR plot, or focus it and use the arrow keys (PgUp/PgDn for bigger steps), to read R, X, |Z| and SWR at any frequency. Every point is a full solver run with the antenna's dimensions held fixed. The dashed amber circle on the Smith chart is SWR 2:1; inside it is a usable match. Coax loss is not included here: loss makes a real analyzer at the shack end read a lower SWR than the antenna really presents. The Feedline tab shows by how much.
Why height matters for DX
A horizontal antenna and its reflection in the ground act as a two-element array. Raise it and the lowest lobe drops: over a perfectly reflecting ground the first lobe peaks where sin(elevation) = λ / 4h, which is 30° at ½ λ and about 14.5° at 1 λ. Low angles travel farthest by skywave (DX); at 0.1 λ almost everything goes straight up, which is good for short-range NVIS and poor for DX.
ApproximateReal ground (poor, average, very good, salt water) is a flat, uniform earth. The feed impedance and currents use the Sommerfeld half-space solution, the method of NEC-2's most accurate ground (GN 2); the far field uses Fresnel reflection coefficients, as NEC-2 does. Against NEC-2 for a 40 m dipole from 0.05 to 1 λ over average and poor ground, feed R agrees within 2%, X within 2 Ω and gain within 0.11 dB. Real soil is layered and changes with rain, so treat ground numbers as typical, not exact. Perfect ground is exact.
The line between the radio and the antenna
Every line loses some power even when it is perfectly matched: the matched loss, from resistance in the conductors (it grows as √f) and from the dielectric (it grows as f). When the antenna does not match the line, power reflected at the antenna travels back and forth and the line takes its cut each trip, so the total loss grows. The lab computes that exactly from the line’s complex propagation constant and characteristic impedance, with the solver’s feed impedance as the load.
The point to take away: SWR measured at the radio always looks better than the SWR at the antenna on a lossy line. The reflected wave is attenuated going up and again coming back, so a long run of thin coax can make a poor antenna read 1.5:1 in the shack. That is the line turning your power into heat, not a match. Open-wire and window line lose so little that a high SWR on them costs only a fraction of a dB, which is why ladder line and a tuner make an efficient multiband system.
Yagi explorer
There is no free lunch in a Yagi. Shorter, closer directors push the forward gain up; the price is a lower feed resistance and a narrower SWR bandwidth. The deepest rear null (the best front-to-back) and the highest gain happen at different lengths, so every published design is a compromise between the two, and the trade-off plot fills in as you drag: each dot is a design you tried, its size the 2:1 bandwidth. (D. Lawson W4RNL’s Yagi Antenna Design, ARRL, 1986, maps these trade-offs element by element.)
Trim it like you would in the field
Someone cut this wire long on purpose. Hoist it at the height shown, read the analyzer, and trim toward the target frequency. Cuts are permanent. If you overshoot, you can splice wire back on, but splices cost points, as they cost you a soldering iron and a ladder trip in real life. The goal is 1.5:1 at the target, or within 5% of the best this install can reach when the height and soil make 1.5:1 impossible. Fewer cuts score higher: every number on the analyzer comes from the same moment-method solver as the rest of the lab.
How the solver works
Each wire is cut into short straight segments and the current along it is expanded in overlapping triangle functions. Requiring the total electric field along every wire to vanish, except across a 1 V gap at the feedpoint, gives a matrix equation that is solved directly (complex LU). The feed impedance is the gap voltage divided by the computed gap current; the pattern is the sum of every segment's radiation; gain is referred to the input power, so for these lossless wires it equals directivity. Perfect ground is an exact image; real ground adds the Sommerfeld half-space correction, as NEC-2 does for its GN 2 ground. This is the same family of method as NEC-2 and MININEC.
| Validation case | This solver | Reference |
|---|---|---|
| Half-wave dipole, free space: resonant length | 0.4757 λ | 0.4741 λ (NEC-2) |
| … feed resistance at resonance | 71.95 Ω | 71.89 Ω (NEC-2); about 73 Ω (textbook, infinitely thin) |
| … gain | 2.14 dBi | 2.14 dBi (NEC-2); 2.15 dBi (textbook) |
| Quarter-wave monopole on perfect ground: R at resonance | 35.98 Ω | about 36 Ω, half the dipole (textbook) |
| … gain at the horizon | 5.15 dBi | 5.15 dBi (textbook); 5.19 dBi (NEC-2, quarter wave) |
| Dipole ½ λ over perfect ground: takeoff, gain | 30.0°, 8.45 dBi | 30° (image theory), 8.45 dBi (NEC-2) |
| Dipole ½ λ over average ground: takeoff, gain | 28.3°, 7.21 dBi | 28°, 7.27 dBi (NEC-2 Sommerfeld, GN 2) |
| 3-element Yagi, free space: gain, front-to-back | 7.80 dBi, 15.9 dB | 7.85 dBi, 17.3 dB (NEC-2) |
- Thin-wire limits (NEC-2 modeling guidelines): segment length at most 0.1 λ (the lab uses λ/40, or λ/24 in fast mode), segment length at least 8 wire radii, wire radius at most λ/100. Out-of-range models are clamped and the readout says so.
- Wire antennas are #14 AWG copper (1.63 mm). Yagi elements use radius λ/1000; verticals 1 in tube on HF and 1/8 in rod on VHF.
- Not modelled in the antenna solution: conductor and insulation loss, and the transmission-line effect of a feed line's outer shield. Feed-line loss is computed separately in the Feedline tab, from the makers' attenuation tables and the full lossy-line transformation. A ground-mounted vertical's radial-field loss is added from published measurements (see below).
AccuracyHow accurate is this lab?
Every row below was built exactly as the lab builds it (#14 copper wire, λ/40 segments) and run through NEC-2 (PyNEC 2.3.4, the nec2++ engine) with its Sommerfeld-Norton ground, GN 2. Ground is average (εr 13, σ 0.005 S/m) unless noted. Lab and NEC-2 are different codes: where they differ, the last column says which one moves when the wire is cut finer.
| Antenna | Lab Z, gain | NEC-2 Z, gain | Notes |
|---|---|---|---|
| 80 m dipole at 35 ft (0.13 λ) | 54.8 + j25.1 Ω, 6.12 dBi | 55.0 + j26.7 Ω, 6.12 dBi | v2.99.411 read 1 dB high at this height |
| 40 m dipole at 35 ft | 84.5 + j14.3 Ω, 5.97 dBi | 84.9 + j16.0 Ω, 5.97 dBi | Poor ground: 80.1 + j8.1 vs 80.5 + j9.8 Ω |
| 20 m dipole at 50 ft | 71.8 + j7.4 Ω, 7.46 dBi | 72.7 + j9.2 Ω, 7.43 dBi | |
| 40 m dipole at 0.05 λ (7 ft) | 56.9 + j13.2 Ω, 0.40 dBi | 55.8 + j14.9 Ω, 0.51 dBi | Lowest height checked |
| 40 m inverted-V, apex 35 ft | 67.5 + j18.9 Ω, 5.37 dBi | 67.8 + j12.9 Ω, 5.38 dBi | NEC-2 needs a short feed wire at the apex; at λ/160 the two agree within 1.2 Ω |
| 40 m folded dipole at 35 ft | 340.8 + j53.1 Ω, 5.95 dBi | 342.3 + j64.4 Ω, 5.94 dBi | X converges: 1.9 vs 3.5 Ω at λ/160 in free space |
| 20 m 3-element Yagi at 50 ft | 37.9 + j0.6 Ω, 12.70 dBi | 37.4 + j3.0 Ω, 12.74 dBi | F/B in free space 15.9 vs 17.3 dB; NEC-2 alone gives 16.6–18.4 dB as segments go from 11 to 121 |
| 40 m end-fed half-wave at 30 ft, 0.05 λ counterpoise | 2868 − j654 Ω, 6.10 dBi | 2748 − j77 Ω, 6.08 dBi | The high-impedance end is the hardest point to model; at λ/120: 2881 − j729 vs 2883 − j440 Ω |
| G5RV at 35 ft, 20 m (flat-top / after 31.3 ft line) | 105.4 − j50.9 / 105.1 − j45.2 Ω | 106.6 − j48.8 / 106.3 − j43.2 Ω | SWR on 50 Ω: 2.6 vs 2.6 |
| G5RV at 35 ft, 80 m (flat-top / after line) | 26.2 − j408.5 / 14.4 + j27.8 Ω | 27.3 − j416.0 / 14.7 + j23.7 Ω | SWR 4.6 vs 4.2: a tuner is needed either way |
| 20 m ground plane, base 0.5 λ, four 45° radials | 51.1 + j1.6 Ω, 0.78 dBi | 45.8 − j0.7 Ω, 1.34 dBi | The worst row. A 1 in radiator joins #14 radials, and NEC-2's guidelines warn against big radius steps at a junction; with equal radii the codes agree within 3% |
Method
- Thin-wire method of moments (triangle basis, Galerkin testing, reduced kernel), the family of NEC-2 (Burke and Poggio, Numerical Electromagnetics Code (NEC) — Method of Moments, NOSC TD 116, 1981).
- Real ground: the field reflected by a uniform lossy earth is the Sommerfeld integral (A. Sommerfeld, Annalen der Physik 28, 1909), split into TE and TM plane waves (K. A. Michalski and J. R. Mosig, IEEE Trans. Antennas Propag. 45(3), 1997). As in NEC-2's GN 2, a quasi-static image is taken out exactly and the smooth remainder is tabulated and interpolated. With perfect-ground coefficients the integrals reproduce the exact image field to six digits.
- Reference: PyNEC 2.3.4 (nec2++). A 40 m dipole from 0.05 to 1 λ over average and poor ground agrees within 2% in R, 2 Ω in X and 0.11 dB in gain; the regression test pins 30 such cases.
- Ground-mounted vertical: radiation resistance from the solver over a perfect radial field, plus a ground-loss resistance from N6LF's measured feed resistance with 4–64 radials at 7.2 MHz (R. Severns, QEX Jan/Feb 2009 pp. 48–52, Mar/Apr 2009 pp. 29–32), scaled to other soils and bands with the Wait–Pope surface-impedance model (Appl. Sci. Res. B 4, 1954). Brown, Lewis and Epstein (Proc. IRE 25(6), 1937) set the 120-radial reference. Read the 4–8 radial values as ±50%.
What is not modelled
- Coax shield currents. The feed line is ideal. Common-mode current on the outside of the shield makes the coax part of the antenna, which changes the feed impedance and the pattern; that is why the lab recommends a choke (ARRL Antenna Book, on baluns and common-mode current). On an end-fed half-wave the coax is often the counterpoise.
- Nearby objects. Towers, gutters, trees, house wiring and other antennas are absent.
- Wire and insulation loss. Wires are lossless. NEC-2 with copper wire loss (its LD 5 card) gives 0.07 dB less gain for the 40 m dipole at 35 ft, 0.16 dB for the 80 m dipole and 0.08 dB for the 40 m end-fed. Insulated wire resonates lower and must be cut shorter (ARRL Antenna Book).
- Tapered Yagi tubing. Elements are uniform wires of radius λ/1000. Real telescoping elements need a taper correction (D. Leeson, W6NL, Physical Design of Yagi Antennas, ARRL, 1992), so use these lengths for learning, not for cutting aluminium.
- Real soil. The earth is flat and uniform with textbook constants (ARRL Antenna Book ground-constants table). Real soil is layered and changes with moisture and frequency: N6LF measured σ ≈ 0.015 S/m, εr ≈ 30 at his site (QEX Jan/Feb 2009), three times the “average” conductivity.
- The 49:1 unun and the G5RV line are ideal and lossless, and coax loss is not included, so the SWR at the rig will usually read lower than the lab's.