[fourier54]

How can an equation that does not represent a balance of energy violate energy conservation?

With path loss equation I assume you refer to Friis equation which is just the ratio of power received at an antenna to power given to the transmitter. It is correct and does not violate conservation of energy since it says nothing about the power not received at the receiver

[nestes]

What they're saying is that the geometrical interpretation of an outwardly expanding spherical shell of power shouldn't depend on frequency. In this respect they are correct and they have a good intuition for the problem.

Now here's the catch: If the receive area were not changing as a function of frequency when the receive antenna gain is kept constant (it does), this would break physics (it doesn't). However, the effective area of an antenna with fixed gain varies as 1/lambda^2. In effect the geometric interpretation is still correct, but the variation of antenna area with gain resolves the seeming paradox and saves physics.

[fourier54]

> the geometrical interpretation of an outwardly expanding spherical shell of power shouldn't depend on frequency

I think nobody says that is does. I believe the problem is to call Friis transmission equation "Free-space loss". Actually the Friis formula is composed of 3 terms: the receiving and transmitting antennas gain and the actual free space loss which has the 1/R^2 dependency (which actually isn't a "loss" in energy balance terms, since it's not lost energy, just energy not received at a certain point, so we could argue about that term too...)