# Why is “wavelength” used as a unit for the length of an antenna?

We often refer to antenna size relative to wavelength. For example: a 1/2 wave dipole is approximately half a wavelength long. Wavelength is the distance a radio wave travels during one cycle. (Here)

Why is antenna length measured in terms of wavelength? Wavelength is not even a universal unit or SI unit. Wavelength is not a fixed constant and varies from wave to wave. So why is an antenna measured in terms of wavelength?

There are formulae for calculating antenna length in metres (here) but why are antenna lengths not described in metres in the first place, and why do we have to use formulae to convert wavelength to metres? What is the importance of wavelength as a unit of antenna length?

• Which gives you more information "a 15m antenna" or "a quarter wavelength dipole for 50MHz" ? – PlasmaHH May 17 '18 at 15:03
• Because a 10m antenna for the AM band is short but a 1m antenna for UHF is long. – Brian Drummond May 17 '18 at 15:04
• Because the properties of an antenna are largerly determined by its size expressed in wavelengths. Note that the size expressed in wavelengths is a (dimensionless) ratio, hence it is even more fundamental than some value expressed in an (arbitrary!) SI unit. – Wouter van Ooijen May 17 '18 at 15:12
• Antenna transmission line properties and inductance correction factor but depends on wave ratios and 1/sqrt(dielectric constant) * 3e8 m/s – Tony Stewart Sunnyskyguy EE75 May 17 '18 at 17:33

Antennas are designed for operation at a specific frequency, and the physical dimensions of an antenna scale with the design frequency. In the case of a dipole antenna, things like the antenna gain and directivity depend on the length in wavelengths, known as the electrical length. So if you know the antenna is, for example, a 1/2 wave dipole, you know immediately what the gain, directivity, and radiation pattern look like. If the length was specified in meters, then you would have to also know the design frequency so you can calculate the electrical length in wavelengths in order to determine the antenna characteristics. Also, it is possible to use electrical lengthening techniques which make the antenna behave electrically like it's longer than its physical length, complicating things when you know only the physical length but not the electrical length.

I will note that it is conventional for some antenna types to specify the size in wavelengths, and for others in meters. For example, dipole antennas are very commonly specified in terms of their electrical length in wavelengths, while dish antennas are commonly specified by their diameter in meters.

• Maybe convert "1/4 wave dipole" to "1/4 wave monopole" for strictest accuracy. – Andy aka May 17 '18 at 17:13
• Good point, fixed – alex.forencich May 17 '18 at 17:50
• A dish is not an antenna -- it is a concentrating reflector. It's diameter is independent of frequency (although its material is not). – amI May 17 '18 at 22:04
• @aml A dish is an aperture antenna, and the gain of a dish at a fixed diameter is absolutely dependent on the frequency, as with any other antenna. – alex.forencich May 18 '18 at 2:28
• Another "electrical lengthening technique" is fractal design. Often used in cell phones and portable wifi devices. en.wikipedia.org/wiki/Fractal_antenna – DaveM May 18 '18 at 2:47

Not only is it best practice to state the length in $\lambda$ it's also important to specify the type i.e. monopole or dipole for instance. Consider a monopole and look at the impedance it presents to the circuit it attached to: -

A typical quarter wave monopole has zero reactance (magenta line) and has a radiation resistance of about 37 ohms (although it's a tad difficult to get a precise value from the graph above). If this were a half wave dipole it would have double the radiation resistance of a quarter wave monopole so, just saying a 10 metre antenna tells you nothing that is import for the designer.

But monopoles can be short and specifying one that is one-tenth $\lambda$ is useful to know because a designer would be able to estimate at its optimum frequency it would be capacitive at -j500.

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Actually this is a very basic question about high frequency (HF) applications. If one is talking about HF, the wavelength is short in comparison to the transmission line, which is the case in an antenna. The wavelength is given by $$\lambda = \frac{c}{f}\,.$$ The frequency $f$ is the operating frequency. The propagation speed $c$ is given by $$c= \frac{1}{\epsilon_0\epsilon\cdot\mu_0\mu}\,.$$ If we have free space, $\epsilon$ and $\mu$ are one and $c$ simplifies to the speed of light $c_0$. If there is dielectric material, in whicht a wave propagates, the speed of the wave is dependent on these two parameters ($\epsilon$, $\mu$).

So the quantity of how the wave is propagating is important in the design of an antenna. With the wavelength $\lambda$, one can directly see, which dimensions the antenna has, without further calculations.

$I$ shows the current distribution and $V$ the voltage distribution over a half-wave dipole antenna. So one can see that $\lambda=2\pi$, where $2\pi$ is one period of the voltage/current distribution. The current distribution over the dipole plays an important role e.q. for the radiation pattern. So it makes sense to give the quantity $\lambda$ to directly have a feeling for the current distribution over the piece of wire.

Furthermore, the wavelength is just a length, so its quantity is given in SI units, for example meter $$[\lambda] = \mathrm{m} \,.$$

Just as PlasmaHH commented, the properties of an antenna are dependent on its wavelength. This wavelength is frequency dependent. So you can have two antennas with the same length with both a different impedance matching for two different frequencies, so one of the antennas could be a full wavelength antenna for frequency 1 while the other one may be a quarter wavelength antenna for frequency 2.

In Antenna basic concepts they'll explain the difference between different antenna lengths:

1/4 wave: A single radiating element approximately 1/4 wavelength long. Directivity 2.2 dBi, 0 dBd. Loaded 1/4 wave

1/2 wave: A single radiating element 1/2 wavelength long. Directivity 3.8 dBi, 1.6 dBd. A special design is the end fed 1/2 wave.

• Re "... its wavelength": the antenna or the radio wave? If the antenna, how can an antenna have a wavelength? – Peter Mortensen May 18 '18 at 16:40

Wavelength is not a fixed constant and varies from wave to wave. So why is an antenna measured in terms of wavelength?

What is the importance of wavelength as a unit of antenna length?

Because different wavelengths(frequencies) require different length antennas. Size of antenna must be very closely tuned to the length of the wave it's supposed to work with.

There are formulae for calculating antenna length in metres (here) but why are antenna lengths not described in metres in the first place, and why do we have to use formulae to convert wavelength to metres?

Where do you start when you're building an antenna? You start with "what wavelength(frequency) will it operate on?". Therefore you start with wavelength and that is your entry data. So the formulae are designed to work this direction: you enter wavelength (or frequency) and it tells you required dimensions of your antenna.

You never start with meters and ask "what frequency will it operate on?" (except those rare cases when you find some old junk in the attic and try to figure out what the hell it is)

Antenna design described in absolute units would be locked-in to just one frequency, therefore (almost) useless for anyone who needs another frequency.