Antenna Length vs Frequency

During the course of my CCNA Wireless, I have become increasingly confused about the relation of length and frequency, and thanks to the community of experts on LinkedIn that confusion was cleared up quite quickly, so I thought I would share my understanding on this blog.

I remember in high school physics, when learning about how to generate a wave, one of the key determining factors was the antenna length – the length of the antenna had to match the wavelength (which can be folded nicely to 1/2, 1/4 wavelength etc) – It’s quite logical; Wireless Communication and Sound have a lot in common, and in order to change the note of a length of vibrating material, you change the length.

For example – I always remember this one from an exam in my SATS, grab your nearest ruler and hold it with the end on a desk, and the length hanging over the desk, then twang it.

Change the length of the ruler, you get a different note.

Why? Well, the reason is that the difference in the length of the ruler which is not supported by the table means the it can vibrate up and down less or more (Longer means it can move more freely, and shorter means it can move less) – the amount the ruler moves up and down is its oscillation – and the number of oscillation per second (Hz) is the frequency of the note you hear. The exact same applies to most musical instruments – in a piano its a small hammer hitting strings of different lengths and thicknesses, on a guitar its a finger changing the length of a string – it all applies. The key is that each sound is being generated by an input making an object oscillate at its resonating frequency.

So, back to the subject – how does this apply to wireless networking?

Well, a radio signal being emitted by an antenna is most effective at its resonating frequency. There’s a formula for working this out:

Wavelength (Lambda) = Wave Velocity (v in meters per second) / Frequency (f in Hz)

The Wave Velocity, is the same for the vast majority of cases – it’s the speed of light in a vacuum: 299792458 m/s.

So, for 2.4GHz channel 1, with a centre frequency of 2412 MHz, the Wavelength is 12.43cm (rounded).

A good and easy calculator can be found here.

Now, as you know, a radio can change frequency, just like a speaker can produce sounds of different notes – well the logic is exactly the same. Now, unlike a ruler, guitar or piano, the determining factor for a frequency with a speaker or antenna is the frequency of the current generated to the radiating element.
To generate a wave at 2412 MHz, the radio generates an Alternating current at 2412 MHz, which reaches the antenna and leaks into the air. Picture it like this, instead of your finger making the ‘twang’ its AC – that current is set by a radio, so an antenna tuned to that exact frequency would be most effective, but a radio tuned to operate at the entire 2.4GHz band can still leak frequencies for each channel, it just can’t do it at is optimum.

Just to finalize, don’t forget a heck of a lot of engineering has gone into the radios and the antenna design over decades which ensures these things can jump frequency as effectively as possible, just like a speaker can effectively produce many crisp and clear sounds – but even with speakers you still get Tweeters and Subs, as some frequencies are far better produced on devices which resonate closer to their intended frequency, for the same reason the majority of 2.4GHz and 5GHz radios are separate radiating elements, even with dual band sometimes its just 2 antenna of different characteristics crammed into one aerial!

To summarise – a wave forms better when it matches the physical characteristics of the wave, but it’s not the be all and end all.