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# electromagnetism question

## electromagnetism question

(OP)
I am currently working on a project and I have a problem i am not sure how to solve. I have two NRF2401AG 2.4 GHz transceiver with an omnidirectional antenna. Those 2 transceivers are located on point "X" and point "Y" respectively. I need to compute the distance between point "X" and point "Y" (distance between both transceivers).
Is it possible to use the Poynting Theorem to calculate this distance? i mean, I know the TX power and the RX power aswell, and i could use the formula
Prx=(Ptx*G)/(4*pi*R^2) .... where Prx is the RX power, Ptx is the TX power, and G is the TX antenna gain.
I also thought of the possibility of sending a signal and compute the time it takes to get to the receiver...but i do not know how to do that.

### RE: electromagnetism question

Is this schoolwork? Student posting is not allowed.

### RE: electromagnetism question

(OP)
no, it's not school work, i am a graduate telecommunications engineer.

### RE: electromagnetism question

Well, then you need to come up with what the actual requirements are.  Considering the difficulties in accurately measuring antenna gain, as well as amplifier gain, as well as potential issues with near-field interactions, as well as potential issues with ground effects, that seems like a long-shot for analysis.  Actual testing would be far easier, since you only need to measure the change in signal as a function of distance, although, time of day, circuit temperature, etc., all affect the noise of the system.

Why can't you use GPS?

### RE: electromagnetism question

(OP)
Because it's a small scale project. The maximum distance measured would be 10 or 15 feet. And its a 2 dimensional project, i only have coordinates on the X and Y plane, i do not consider the Z plane.

### RE: electromagnetism question

I pretty guessed that.  However, the round trip time for a 15-ft separation is 30 ns, which means that your circuit latencies will dominate the measurement.  Obviously, it can be done, but it's a big chunk of development.

Another option is to buy/rent a variant of total station, which would be a theodolite and laser rangefinder.  You can get rangefinders accurate to a few millimeters, which can only be matched by a high-performance differential GPS.

Frankly, you hanve't really given any information that precludes using a 25-ft tape measure, which is both cheap and accurate.

### RE: electromagnetism question

This sort of question (radio-location within a reasonably small arena) has been asked about a half-dozen times in as many months on Eng-Tips. You might want to search around.

Signal strength is not a reliable method of measuring distance. There are too many variables besides distance. For example, antenna gain is not really a constant (example '2.4dBi'), but is typically a complex function of azimuth and elevation.

### RE: electromagnetism question

Since you are working in a plane, the antenna is presumably a vertical dipole and therefore there is no problem with directivity errors. The attenuation with distance will depend on the presence or absence of a ground plane and the uniformity of whatever this plane is. The key is calibration. If you go to a known distance and calibrate you will then get accurate answers at this distance, assuming a uniform ground plane. Calibration at extra points gives better accuracy elsewhere.

### RE: electromagnetism question

It depends on what sort of accuracy is required. If you bring along the error budget (+/- 0.1 dB here, +/- 0.1 dB there) at each step of the system design process, you'll see why 1/R^2 methods are so rarely used for navigation. The 1/R^2 method is sometimes used for estimating galactic distances to stars. But I'm struggling to think of any practical radio location system where that method is used. Every radio location system that I'm familiar with is based on time of flight, or intersection of bearings.

### RE: electromagnetism question

You can get accuracy by calibrating your answer with measurements and using a lookup table. Accuracy in a very friendly environment (air or anechoic chamber) would probably be only a foot or two in a 15 foot distance.

One system I worked on uses the changing amplitude measurement to approximate distance to a target.

Aircraft Storm Scopes listen to radiation from lightning to assess distance to a storm based on amplitude alone.

In general, it's not accurate, but amplitude alone can be useful. Especially if you set up an array and take amplitude data from every sensor.

kch

### RE: electromagnetism question

"Aircraft Storm Scopes listen to radiation from lightning to assess distance to a storm based on amplitude alone."

When these sorts of StormScope(TM) systems first started to appear, I was naturally very curious how they estimated the distance to each stroke (because it seemed obvious to me that it was not a trivial method - in other words, I couldn't figure it out!).

Azimuth is of course very easy using normal DF techniques. Trivial.

But since the strength of lighting strokes varies widely, signal strength alone would be a very poor indicator of accurate distance (certainly not commensurate with the distance resolution of the lovely graphical display).

That left me with a mystery to be investigated. So, at the time, I looked it up. The explanation that I found at the time mentioned something about measuring the signal at different frequencies and that the DIFFERENCE in those signals somehow related to the distance (accurately).

Tonight I found a related patent with more details:
http://www.freepatentsonline.com/5541501.html

"...determine the range of a lightning stroke by utilizing two narrow frequency bands in the field emanated by the lightning stroke and relying on the relationship between the energy levels detected in these bands to determine range."

(There may be other patents and perhaps other concepts.)

So, these sort of aircraft StormScope systems use something much more subtle than just plain amplitude (1/R^2) to estimate distance.

But there may be inexpensive pocket-size lightning detectors that provide only a rough indication using nothing but amplitude. But they'd probably have something like a crude three step display for 'approximate distance'.

### RE: electromagnetism question

Seems amplitude comparison of a lightning strike at frequencies higher than 2 and less than 5 gives a fixed  distance from the lightning strike.

kch

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