Antenna Basics: Wavelength, Dipole Length, Gain and VSWR
An antenna converts guided electrical energy in a cable into electromagnetic waves in space, and back again at the receiver. For a hobbyist building a 433 MHz link or a student studying wave propagation, a few ideas cover most practical needs: how antenna length relates to wavelength, what gain in dBi means, why polarisation matters, and how to tell whether the antenna is matched to its cable.
This tutorial gives the formulas and worked numbers so you can cut a working dipole for any frequency and interpret the VSWR reading from an antenna analyser.
Wavelength and Frequency
lambda = c / f c = 3 x 10^8 m/s (speed of light in free space) Shortcut: lambda (m) = 300 / f (MHz)
| Frequency | Wavelength | Half wave | Quarter wave |
|---|---|---|---|
| 98 MHz (FM broadcast) | 3.06 m | 1.53 m | 0.77 m |
| 433 MHz (ISM) | 0.693 m | 34.6 cm | 17.3 cm |
| 866 MHz (LoRa, India) | 0.346 m | 17.3 cm | 8.7 cm |
| 2.4 GHz (Wi-Fi, Bluetooth) | 12.5 cm | 6.25 cm | 3.1 cm |
These are free-space values. Real antennas are cut slightly shorter, as explained below.
The Half-Wave Dipole
A half-wave dipole is two equal conductors fed at the centre, with a total length close to half a wavelength. It is resonant, so its input impedance is almost purely resistive, about 73 ohms in free space. Because the wire has finite thickness and fringing fields at the ends, the resonant length is a few percent shorter than lambda/2. A common practical formula for thin wire dipoles uses a factor of about 0.95:
Practical dipole total length: L (m) = 0.95 x 150 / f (MHz) = 143 / f (MHz) Each arm = L / 2 Example: 433 MHz L = 143 / 433 = 0.330 m -> each arm 16.5 cm Example: FM band at 98 MHz L = 143 / 98 = 1.46 m -> each arm 73 cm
The Quarter-Wave Monopole
Replace one arm of the dipole with a ground plane and you get a quarter-wave monopole, the familiar whip on a radio module. The ground plane acts like a mirror, supplying the missing half. Its feed impedance is about half that of the dipole, around 36 ohms, and it needs a ground plane at least roughly a quarter wavelength across, or radial wires, to work properly.
Monopole length ~ 0.95 x 75 / f (MHz) = 71.5 / f (MHz) metres 433 MHz: 71.5 / 433 = 0.165 m (16.5 cm) 866 MHz: 71.5 / 866 = 0.083 m (8.3 cm)
Radiation Pattern, Directivity and Gain
An antenna does not create power; it redirects it. A dipole radiates most strongly broadside to the wire and not at all off its ends, giving a doughnut-shaped pattern. Gain compares the peak radiation with a reference.
| Term | Meaning |
|---|---|
| dBi | Gain relative to an ideal isotropic antenna that radiates equally in all directions |
| dBd | Gain relative to a half-wave dipole; dBi = dBd + 2.15 |
| Directivity | How concentrated the pattern is, ignoring losses |
| Gain | Directivity multiplied by radiation efficiency |
| Beamwidth | Angle between the half-power (-3 dB) points of the main lobe |
| Front-to-back ratio | Main lobe strength compared with the opposite direction, for directional antennas like Yagis |
A half-wave dipole has a gain of 2.15 dBi. A Yagi with several directors might give 10 dBi or more, but only in one direction; a patch antenna is typically a few dBi to around 8 dBi depending on design. Higher gain always means a narrower beam.
Polarisation
The electric field of the wave points along the antenna element. A vertical whip produces vertical polarisation. If the receiving antenna is rotated 90 degrees, the theoretical coupling falls to zero; in practice reflections leave some signal, but losses of 20 dB or more are common. Keep both ends of a link with the same polarisation.
Matching: Reflection Coefficient, VSWR and Return Loss
Most radio modules and coaxial cables are 50 ohms. If the antenna impedance differs, part of the power reflects back towards the transmitter.
Reflection coefficient: Gamma = (ZL - Z0) / (ZL + Z0) VSWR = (1 + |Gamma|) / (1 - |Gamma|) Return loss (dB) = -20 log10 |Gamma| Mismatch loss (dB) = -10 log10 (1 - |Gamma|^2)
Worked Example: Dipole on 50 Ohm Coax
ZL = 73 ohm, Z0 = 50 ohm Gamma = (73 - 50) / (73 + 50) = 23 / 123 = 0.187 VSWR = 1.187 / 0.813 = 1.46 Return loss = -20 log10(0.187) = 14.6 dB Mismatch loss = -10 log10(1 - 0.035) = 0.16 dB
A VSWR of 1.46 wastes only 0.16 dB, which is negligible. As a rough guide, VSWR under 1.5 is very good and under 2 (about 0.5 dB mismatch loss) is acceptable for most hobby links. A VSWR of 3 means about 25 percent of power is reflected, roughly 1.25 dB lost, and some transmitters reduce power or risk damage.
Common Mistakes
- Cutting a dipole to exactly 300/(2f) and wondering why it resonates low.
- Using a quarter-wave whip without any ground plane, so the coax shield becomes part of the antenna.
- Mounting the antenna inside a metal enclosure or flat against a PCB ground pour.
- Mixing vertical and horizontal polarisation between the two ends of a link.
- Quoting gain in dBi for one antenna and dBd for another in the same calculation.
Summary
Wavelength in metres is 300 divided by frequency in MHz. A practical half-wave dipole is about 143/f(MHz) metres long, has roughly 73 ohms impedance and 2.15 dBi gain; a quarter-wave monopole is half that length over a ground plane. Gain only reshapes the pattern, and polarisation must match. Check matching with Gamma and VSWR: a dipole on 50 ohm coax gives VSWR about 1.46 and loses only 0.16 dB. These gains and losses feed directly into the link budget, covered next.