# When designing antennas which speed of light should be used?

When calculating "antenna element length" should we use the speed of light in the "medium between transmitter and receiver (antenna)" or the speed of light in the "element material"? (for example speed of light in air vs speed of light in Aluminum)

• not sure light propagates in aluminum… do you mean speed of the EM wave? Jun 24 at 3:14
• Yes, You know speed of light is typically used to express the speed of EM radiation/ radio waves. It is true that aluminium is very opaque to frequencies of light. Of course I mean radio waves. Jun 24 at 3:38
• Without Details , I think we should use both , which-ever is appropriate in which-ever formula & a certain formula may use both at the same time. If you have a certain formula to share , then that might use either , where we might have a confusion & this Question can be Answered more Correctly.
– Prem
Jun 24 at 14:29

The speed of EM propagation in a metal antenna is not the same as c in free space, it is always slower. This requires that the physical length of a dipole antenna be shortened, compared to the free-space wavelength of the signal to which it is tuned.

This is true for the feedline between the antenna and the transmitter as well, and when a tuned feedline is used to optimize antenna performance, this slower velocity must be taken into account, and the feedline length be shortened accordingly.

Both effects can be described in the antenna world in terms of something called the velocity factor, which is the percentage by which c is reduced in a feedline or antenna. That factor is also the percentage by which the antenna's physical length must be shortened to match up with the incident waves.

• But velocity factor is not just the ratio of wavelengths in vacuum and in the material, it should take into account both, depending on how much the field strength gets concentrated inside the antenna vs the surrounding vacuum. This is somewhat similar to computation of eigenmodes of optical fibers, where the wave is partially in the cladding, which affects the wavelength in longitudinal direction for a given frequency. Jun 24 at 17:01
• Yes, but what does happen actually? Whether EM wave propagates inside the antenna (conductor) or does EM waves in air induce electric currents inside the metal? I asked this because in practice generic antenna formulations use only c for their calculations. Because in aluminium EM radiation only travel 30% slower, elements should be significantly reduced in length. But I didn't see this in simple antenna formulas that I have seen. Jun 25 at 5:37

There are two effects, and they're tricky.

1. Dielectric material in the antenna's vicinity slows down the light in that material. But, since we usually don't have an antenna fully embedded in dielectric material, that means that the speed of light is different at different places, complicating the analysis.

2. The field at the ends of antenna elements isn't simple. The ends effectively have capacitance, which makes their "electrical length" longer than their physical length. If you like, you may consider this a concentration of displacement current that extends the physical current beyond the ends.

Note that radio waves don't propagate in metals, so at radio frequencies there is no speed of light in aluminum. A wire may guide an external radio wave, but the wave isn't present inside the wire.

• Part 1 amounts to: what you really want isn't the speed of light in the antenna material or the far-field medium, it's the speed of light in whatever's in the near field, weighted by... field strength probably... if the near-field isn't filled with one homogeneous material. Jun 24 at 21:52
• +1 from Niels. -.. .. . .-.. ... NN Jun 24 at 22:55

Definitely the speed of light in which the waves will be propagating.

• What is your opinion on the other answers posted? They are indicating that the speed of EM waves in antenna material should be taken into account too. Jun 25 at 8:10