# Friis Free Space Equation for Received Power

According to Friis Equation the received power is directly proportional to the square of the wavelength or inversely proportional to square of the frequency. But is this not misleading. There is nothing in free space that would cause higher loss at higher frequency. The lower received power is only because the antenna size is smaller at higher frequency. In fact if the antenna aperture is maintained received power would increase with increasing frequency?

Does this make sense? Look at this post.

• Sure, if you make the antenna gains bigger (making aperture bigger) then this effect cancels out. Dec 3, 2021 at 11:39
• There's a quite long answer to this topic here: space.stackexchange.com/questions/36521/… Dec 3, 2021 at 11:40
• The lowered receive power assumes that the antenna is the same size - has the same aperture, at the two frequencies. For a given size aperture, the beamwidth narrows as the frequency increases, and so the receive power (uW/cm^2) increases proportionally. Dec 3, 2021 at 11:52
• @SteveSH correction: the receive power decreases (not inceases) proportionally as frequency increases. Dec 3, 2021 at 13:14
• Yasir if we're done here and you are happy with my answer you should follow the guidelines here and complete this session by accepting my answer. If you still have something that needs explaining, please add a comment under my answer. Dec 17, 2021 at 13:40

If the antenna aperture is maintained received power would increase with increasing frequency? Does this make sense?

Yes it makes sense. The effective aperture is also a measure of the antenna's gain so, if the frequency were (say) 1 GHz and the gain was 0 dBi (the same as an ideal isotropic antenna) then the aperture area is 0.007152 m². If the antenna gain were 10 dBi then the aperture area is 0.071521 m² i.e. ten times the power gain equates to ten times the area of the aperture.

There's nothing unusual about that when you consider the the Friis equations are considering a transmit antenna that can emit power in all directions (i.e. isotropic) and, that at any distance (radius r) from that antenna, you can encircle it with a sphere of radius r. Thus, if you could count the number of watts crossing that sphere's boundary it would equal the number of watts at any other size of sphere.

The total watts passing through the sphere's surface don't change but the sphere's surface area grows with 4πr². Hence, if the aperture remains the same size for a given sphere radius, then the received power has got nothing to do with the frequency of the transmitted wave.

So, if you want to counter the effects of a larger frequency, you must make your transmit and receive antennas have a bigger aperture. This can be done of course by increasing the gain of the antenna.

Having said that, making a half wave dipole have higher gain usually means replacing it with a Yagi Uda Antenna like this: - Image taken from this Yagi Uda antenna calculator and note that the gain (dBd) is relative to a dipole antenna and not relative to an isotropic antenna.

What you get with more antenna gain solves the conundrum of lower signal strength at increasing frequencies (due to natural aperture reductions) but, the down side is that the antenna is very directional. And, it's very directional because all the transmit power has been compressed from a sphere (as in an isotropic antenna) into a few degrees of arc. What you gain in one direction, you lose out on in all the other directions: - Image from here