# Wave collapse vs. Friis transmission equation

1. Aug 23, 2008

### Antenna Guy

If waves collapse upon detection, how is it that the Friis transmission equation yields accurate results?

Regards,

Bill

2. Aug 23, 2008

### Marty

Hi Bill

I'm going to quote from Wikipedia here:

"The ideal conditions are almost never achieved in ordinary terrestrial communications, due to obstructions, reflections from buildings, and most importantly reflections from the ground. One situation where the equation is reasonably accurate is in satellite communications when there is negligible atmospheric absorption; another situation is in anechoic chambers specifically designed to minimize reflections."

I just want to point out that Wikipedia says you can use this formula in outer space or in anechoic chambers. It says nothing about applying it at the atomic level. In fact, you can find all kinds of references where they use the cross sectional area of the atom when calculating things like the photoelectric effect.

3. Aug 24, 2008

### Antenna Guy

The common theme in the above is multipath (or, in the case of obstructions, no/limited direct path between apertures). Other non-ideal conditions involve losses, but these can be accounted for. The Friis transmission equation has been used in a number of less-than-ideal situations with reasonable results.

The crux of the question was to determine if the notion of wave collapse is consistent (on a macroscopic scale) with how spherical waves propogate. In my experience, reception in one direction has no impact on gain in other directions (at least not until diffraction effects begin to fill in the shadow at somewhat larger R). If a spherical wave were to collapse when received, I would expect gain in all directions about the source to be affected by the missing component of the radiated wave spectrum.

Basically, the Friis transmission equation suggests to me that the receive antenna can only capture a fraction of the wave energy that is available - not all of it. For example: in the case of two ideal isotropic radiators, the gains can be replaced with unity, and the formula reduces to the path loss (aka "spreading factor"). Thus, the Friis transmission equation appears to contradict the hypothesis of wave collapse (wherein the energy is either recieved in total, or it isn't).

Regards,

Bill

4. Aug 29, 2008

### Antenna Guy

In the interest of provoking some conversation on this topic, I'd like to expand upon what "gain" in the Friis transmission equation is.

An antenna's gain is comprised of two parts:

1) Directivity
2) Losses

Losses apply equally in all directions, and directivity relates the radiated power density in a particular direction to that of an isotropic source radiating the same power. Because of reciprocity, the relative strength of a signal received from from a particular direction is directly related to the antenna's ability to radiate a signal of the same frequency in the same direction.

For all intents and purposes, the directivity of an antenna must be related to the probability that a particular photon will be observed in a given direction relative to the source.

Returning to the original question: How is it that what supposedly must hold at infinitesimal scale does not hold at macroscopic scale?

Regards,

Bill

5. Aug 30, 2008

### Marty

Don't you mean it the other way around? The Friis equation applies at the macroscopic scale but not when applied the capture of single photons?

6. Aug 30, 2008

### Antenna Guy

If you take the limit as R approaches zero, the Friis equation has the power received going to infinity for any transmitted power - which implies that there is some minimum radius at which the formula can be applied.

Conversely, I don't know of any maximum radius at which wave collapse might occur, but it does not appear valid to assume that any such radius would be in the range where the Friis transmission equation can be applied.

Regards,

Bill