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# 26th Idea [Friis law]

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#### g86

##### Full Member level 4
friis law

Assume a Tx-Rx system at frequency f where two antennas (with gain G1 and G2) are there with zero reflection, 100% efficiency and no sidelobes. The distance between the two is say d. Tx antenna generats a very sharp pencil beam and Rx antenna apertue is large enough to receive all radiation transmitted. Now apperently if we transmit 1 watt we will receive the same. Now the question is how can we represent this by Friis law.

:!: :idea: :?:

friis law

This law, like many others, is based on approximations and assumptions that are valid for the usual cases of practical situations. Taking them to limits that make these assumptions and approximations false will produce false calculated results.

One example of this would be to use such a large gain at each end of your imiganary link that the formula predicts more received power than the transmitter output.

friis law antenna

Am I violating any assumptions made by Friis?

:!: :idea: :?:

flatulent said:
This law, like many others, is based on approximations and assumptions that are valid for the usual cases of practical situations. Taking them to limits that make these assumptions and approximations false will produce false calculated results.

One example of this would be to use such a large gain at each end of your imiganary link that the formula predicts more received power than the transmitter output.

wiki friis law

You are not. In the optical region it is possible for all of the transmitted energy to be focused (like a laser beam) so that it strikes a photodetector.

The practical problem in your microwave case is the construction of such large diameter antennas and the tolerances of the surfaces. I know of cases where there was consideration of raising the operating frequency of a RADAR in the hopes of getting better angle resolution. The surface of the antenna reflector was so wobbly that when they connected higher frequency electronics to it the resolution declined because of the beam broadning.

I have vague memories of reading the derivation of the power picked up by a dipole where it was shown that in the perfectly matched case half of the energy went into the load and the other half was re-radiated. If this is a true memory, you will get at most half of the transmitted power at the receiver.

friisâ€™s law

So, where the catch is? Dose it mean in such cases 1/d^2 proportionality wont work?

Basically these methods are to be used to transfer solar power by solar satellites.

:!: :idea: :?:

flatulent said:
You are not. In the optical region it is possible for all of the transmitted energy to be focused (like a laser beam) so that it strikes a photodetector.

The practical problem in your microwave case is the construction of such large diameter antennas and the tolerances of the surfaces. I know of cases where there was consideration of raising the operating frequency of a RADAR in the hopes of getting better angle resolution. The surface of the antenna reflector was so wobbly that when they connected higher frequency electronics to it the resolution declined because of the beam broadning.

I have vague memories of reading the derivation of the power picked up by a dipole where it was shown that in the perfectly matched case half of the energy went into the load and the other half was re-radiated. If this is a true memory, you will get at most half of the transmitted power at the receiver.

satellite

Right. The 1/ d squared is for the case when only part of the wave front is captured.

For your satellite system, the pointing problem will be large. Many years ago there was a project to power small airplanes that used electric motors. Microwave signals were sent to them. It never worked properly.

Re: 1/d squared

But I know that plane worked even I know one professor who was ther in that project in japan. Even they are testing two solar satellites.

:!: :idea: :?:

flatulent said:
Right. The 1/ d squared is for the case when only part of the wave front is captured.

For your satellite system, the pointing problem will be large. Many years ago there was a project to power small airplanes that used electric motors. Microwave signals were sent to them. It never worked properly.

Two different airplanes

There must have been several groups doing the microwave powered airplane at different times. The one I know about was 40 years ago. It was not economical.

Re: Two different airplanes

This is very current research what I mentioned and they used a moving microwave beam to power a plane. But question is why such beem does not follow 1/d^2 law? Where is the problem?

:!: :idea: :?:

flatulent said:
There must have been several groups doing the microwave powered airplane at different times. The one I know about was 40 years ago. It was not economical.

need data

What distance law do the measurements plot out to?

On the satellite power collection, there has been the objection that if the pointing became defective the high power microwave beams would be pointed at cities and damage the health of the people and possibly start fires.

Re: need data

flatulent said:
On the satellite power collection, there has been the objection that if the pointing became defective the high power microwave beams would be pointed at cities and damage the health of the people and possibly start fires.

A 10 GW power transfer has already been tested using 1 km radius antenna. I know about all helth things and this seems to be a good non conventional energy resource but not a very good option.

:!: :idea: :?:

book reference

The book Introduction to Communication Science and Systems by Pierce and Posner have a passing reference to this on page 15. They give the name of Rudolf Kompfer and his calling this effect the Hertzian Cable.

IMHO use of multi GW microwave beam from space to earth to transfer solar energy is a bit utopistic. Maybe one can get it to work, but the dangers are obvious and the economy of such arrangement is questionable. How much energy (and money) is needed to lift that satellite up to the skies? How about maintenance costs?

Therefore the question has exellent theoretical relevance, and maybe even several practical implementations. But -- for energy transfer from a satellite???

I have also seen somewhere a proposal to tap the ionosphere directly by two enormous conductors. One should use some kind of nuclear device to ionize the air in two columns and extract the power from those..... I think those devices could be a bit nasty, too. Think for example a poor bird or airplane flying into the "conductor" -- or a satellite to the residual beam in the space. (Also the microwave beam solution might cook birds or damage airplanes).

About a receiving dipole radiating 50% back to space: I think one might be able to construct a microwave "black object" which do not radiate out any remakable fraction of the incoming energy? Just a thought!

horns

I suspect that horns would not reflect. Also there is the conversion efficiency of going from solar to electric to microwave.

Here on earth the most efficient solar converters go directly to heat with nearly 100% efficiency compared to 18% or so for solar cells.

About the 1/d^2 law, let think in optics.
The power density (measured in W/m^2) decreases as 1/d^2 along a beam, where d is measured from the focal point (a point from which the beams adjacent to the current beam seem to come from).
But the total power picked by your receiving antenna is the integral of that power density over its effective area. If this antenna picks all the beam it is true that it receives all the power regardless of d: at little distance it picks a narrow pencil of high power density, and at greater distance the pencil is wider but it has less power density.
Regards

Z

If you know the E and B vectors of the radiation (E perpendicular to B for plane waves), you can determine the radiation vector S, which is proportional to ExB. The effective radiant flux can easily be calculated by integrating the inproduct of the surface normal n and S.

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