Antenna design guide

An antenna resonates when its length is a set fraction of the wavelength it works on. The wavelength is the speed of light divided by the frequency, and the speed of light is exactly 299 792 458 m/s by definition. At 98 MHz the wavelength is 3.06 m; at 2442 MHz it is 122.8 mm. That one ratio is why an FM aerial is longer than a broom handle and a Wi-Fi antenna fits inside a router.

A real element comes out a little shorter than the free-space fraction. Current cannot flow off the end of a wire, so the ends behave like a small capacitor and the wire looks electrically longer than it is. The ARRL's cutting rules allow for this: 468 ÷ f(MHz) feet for a half wave and 234 ÷ f(MHz) feet for a quarter wave (ARRL). That works out to 95.2 % of the free-space length. Thicker elements need a little more shortening, so treat the rule as a starting length and trim to it.

A dipole is two equal legs fed in the middle. At half a wavelength the current is zero at the tips and largest at the feed, and the feed impedance is close to 73.1 Ω, nearly all of it radiation resistance (C. A. Balanis). That resistance is the useful part: the power fed into it leaves as radio waves.

The dipole radiates most broadside to the wire and nothing along it. Seen from the side the pattern is a figure of eight. The half-power beamwidth, the angle between the two directions where the power is half (−3 dB) of the peak, is 78° (C. A. Balanis). Stand the dipole upright and that becomes an even ring all round the horizon, which is why vertical dipoles and ground planes are the usual choice for a base station that talks in every direction.

Gain compares an antenna's strongest direction with a reference. dBi uses an isotropic source, an imaginary point that radiates equally in every direction. dBd uses the half-wave dipole, which is 2.15 dBi above isotropic, so dBd = dBi − 2.15. A seller's "5 dB" antenna is 2.85 dBd if they meant dBi, which is why a missing i or d in a listing matters.

An antenna has no amplifier in it. It gains in one direction only by giving up others. A short dipole already shows 1.76 dBi, the half-wave dipole 2.15 dBi. A quarter-wave monopole over an infinite, perfect ground plane reaches 5.15 dBi, because all its power goes into the upper half of space (C. A. Balanis). Over four short radials there is no such bonus; plan on roughly dipole gain. For a beam, Kraus's rule of thumb turns the two beamwidths into gain: D ≈ 41 253 ÷ (θE × θH) (J. D. Kraus and R. J. Marhefka). A beam 60° wide each way gives about 10.6 dBi; 30° each way gives 16.6 dBi.

What gain buys you is range. In free space the received power falls with the square of the distance, so each extra dB of gain stretches the range by a factor of 10^(dB ÷ 20). Six dB is ×2.00, and 10 dB is ×3.16. Gain counts at both ends of the link, so adding it to the receiver helps exactly as much as adding it to the transmitter.

Frequency matters as well. Between two isotropic antennas 1 km apart, ITU-R P.525 gives a free-space loss of 85.1 dB at 433.92 MHz and 100.2 dB at 2442 MHz (Recommendation ITU-R P.525-4). The air is not absorbing more. The difference, 15.0 dB, comes from the smaller wavelength: a smaller antenna catches less of the wave. Directional antennas, which are easy to make at 2.4 GHz because they stay small, are how Wi-Fi links get that loss back.

Hobby radios, modules and coax are built for 50 Ω. When the antenna's feed impedance Z differs, part of the power reflects back down the cable. The reflection coefficient is Γ = (Z − 50) ÷ (Z + 50), and everything an antenna analyser shows comes from it: SWR = (1 + |Γ|) ÷ (1 − |Γ|), return loss = −20 log |Γ| and mismatch loss = −10 log (1 − |Γ|²) (C. A. Balanis).

The numbers explain two habits. A plain dipole on 50 Ω coax shows SWR 1.46 and loses 0.16 dB, so builders feed it straight with no matching network. A quarter-wave vertical with its radials flat sits near 36.5 Ω, SWR 1.37; sloping the radials down raises the feed impedance toward 50 Ω (ARRL), which is why the build below droops them.

A low SWR matters more for the transmitter than for the lost tenth of a dB. Many small RF stages are only rated into a load near 50 Ω, and the reflected power ends up as heat in the output transistor. At SWR 3 a quarter of the power comes back.

Our take: aim for SWR under 1.5 at the frequency you use and stop there. Below that, the remaining loss is under 0.2 dB, far smaller than a few metres of thin coax at 866 MHz or above.

A straight antenna sends out a wave whose electric field lies along the wire. The receiving antenna picks up only the part of that field lying along its own wire, so the power falls as cos² of the angle between them (C. A. Balanis). At 30° the loss is 1.2 dB, at 45° it is 3.0 dB, and at 75° it is 11.7 dB. At 90° it is complete in theory; in practice reflections let a little through.

A handheld module with its whip upright talks well to a vertical ground plane and badly to a horizontal dipole. A circularly polarised antenna such as the axial-mode helix avoids the tilt problem, at a fixed cost of 3.0 dB into a straight antenna. The helix and the 2.4 GHz builds are on our Wi-Fi antennas page.

This is the old "how to build a ground plane antenna" project, redone with the numbers shown. It suits the 433.92 MHz modules (the remote-control transmitters and the cheap superhet receivers) and, scaled, any band in figure 1. You need a chassis-mount SO-239 or N socket with four corner holes, about 1 m of 1.5 to 2 mm copper or brass wire, solder and a short length of 50 Ω coax.

1. Cut the radiator long, 173 mm (5 % over the rule, about the radial length), and solder it into the socket's centre pin, straight up.
2. Cut 4 radials of 173 mm, the full free-space quarter wave. Bolt or solder one to each corner hole, so they are 90° apart.
3. Bend each radial down to 45°. Its tip ends 122 mm below the socket, and opposite tips sit 244 mm apart.
4. On an antenna analyser (a NanoVNA does this well), find the SWR dip. At 173 mm it should sit near 413.26 MHz, below the band.
5. Trim the radiator a millimetre or two at a time. Each millimetre moves the dip up by about 2.64 MHz. Stop when the dip sits on 433.92 MHz, which should be close to 164 mm.
6. If the lowest SWR is still above 1.5, change the droop: steeper raises the feed impedance, flatter lowers it. Then trim the radiator again.

With no analyser, cut straight to 164 mm and accept the rule. A receiver will not notice a few megahertz of error, and a low-power transmitter module copes with the small mismatch. Mount the antenna clear of metal by at least a quarter wave (173 mm here) and run the coax straight down between the radials.

Most hobby links need either all-round coverage or reach in one direction. Work down the chart; the first yes usually decides it.

For 866 MHz LoRa modules a quarter-wave whip is 87 mm, short enough to stand straight up from the board. For FM broadcast reception a half-wave dipole is 1.46 m tip to tip, which fits on a wall or under a roof. Our FM transmitter page covers the transmitting side of that band.

• Always cut long and trim. You can take metal off an element; you cannot put it back.
• Check whether a gain figure is dBi or dBd before you compare two antennas. The difference is 2.15 dB.
• Measure SWR with the antenna in its final place. Nearby metal, walls and your own hand shift the dip.
• Keep both ends of a link on the same polarisation. A 45° tilt alone costs 3.0 dB.
• At 866 MHz and above, a short run of good coax matters more than a perfect SWR; thin cable can lose more than the mismatch ever will.
• A module's spring or wire antenna is tuned for one band. Don't cut it down; move the module or use a better external antenna.

• Frequency and periodFrom 433.92 MHz to a 691 mm wavelength.
• ResonanceWhy an element cut to the wrong length stops working.
• Impedance matchingWhy the feed has to look like 50 Ω.
• The decibelAdding gain and loss along a link.
• Skin effectWhy only the surface of the wire carries RF current.
• Wi-Fi antennasBiquad, double biquad, can and helix for 2.4 GHz.
• Antennas sectionEvery antenna build on the site.

• C. A. Balanis, Antenna Theory: Analysis and Design, 4th ed., Wiley 2016 (§2.12 polarisation loss factor |cos ψp|²; §2.13 reflection coefficient, VSWR and mismatch loss; §4.5 short dipole D = 1.5; §4.6 half-wave dipole Rr ≈ 73 Ω, D = 1.643 (2.15 dBi), half-power beamwidth 78°; §4.7 λ/4 monopole over an infinite ground plane Rr ≈ 36.5 Ω, D = 3.286 (5.15 dBi))
• ARRL, The ARRL Antenna Book for Radio Communications, 24th ed., 2019, chapters on dipoles and vertical antennas (practical half-wave length 468 / f(MHz) ft and quarter-wave 234 / f(MHz) ft for wire elements; radials sloped downward raise a ground plane’s feed impedance from about 36 Ω toward 50 Ω)
• J. D. Kraus and R. J. Marhefka, Antennas for All Applications, 3rd ed., McGraw-Hill 2002, chapter 2 (directivity from the two principal half-power beamwidths: D ≈ 41 253 / (θE° × θH°), an upper estimate that ignores side lobes)
• Recommendation ITU-R P.525-4, Calculation of free-space attenuation (2019) (free-space basic transmission loss L = 32.4 + 20 log f(MHz) + 20 log d(km) dB, between isotropic antennas)
• BIPM, The International System of Units (SI Brochure), 9th ed., 2019 (speed of light in vacuum c = 299 792 458 m/s, exact)

Checked on 19 October 2026. Our own choices: 98 MHz for the FM band, 433.92 MHz and 866 MHz for the hobby modules, 2442 MHz for 2.4 GHz Wi-Fi, 4 radials at 45° for the build, beams of 60° × 60° and 30° × 30°, and a 1 km path for the loss comparison. Gains are for lossless antennas; real ones lose a little in the metal and the feed. This page rebuilds an older ElectronicsInfoline article of the same title and folds in the old ground-plane project; none of their text is reused.