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If the transmitter and receiver are placed one centimeter apart, what would be the power at the receiving end if the tranmission power is 1dBm?

Consider an omnidirectional antenna. And if it is a directional antenna, how could I calculate based on the VSWR and directivity? I just want to know if the inverse square law can be applied here.

I am doing a study in which I used a stub antenna. The antenna is operating at 950MHz. The datasheet of the antenna is unknown. When gone through VNA S11[dB] is -20dB which conveys that 0.99mW is radiated from the transmitter, whereas the received power is -20dB which is 0.01mW. I placed both the antennae adjecent, still I didn't achieve. Here's the link to earlier discussion.

Now I am trying to calculate the maximum and least possible powers to complete my work.

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    $\begingroup$ At what frequency? The inverse square law only works in the far field. 1 cm would be far field from about 10 GHz up. If the antennas are directive then you might need to be further / higher frequency. $\endgroup$ – tomnexus Jan 7 at 10:50
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    $\begingroup$ @tomnexus at 950MHz. It is a quarterwave antenna, actually a stub antenna. I don't know anything about the antenna i bought, since i got it from a vendor who has no clue about it. I observed the S11 characteristics through which I am concluding. Here's the link to earlier discussion(physics.stackexchange.com/questions/451648/…). Now I am trying to calculate the maximum and least possible powers to complete my work. $\endgroup$ – shiva Jan 7 at 11:12
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    $\begingroup$ Please edit your question to include all of the information, rather than putting it only in comments. $\endgroup$ – Kevin Reid AG6YO Jan 7 at 16:41
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    $\begingroup$ @KevinReidAG6YO I did edit the description... Please let me know if I need to change the question too. $\endgroup$ – shiva Jan 7 at 17:13
  • $\begingroup$ Hi Shiva, Good. I did a little editing, as far as I could tell from what you are asking. $\endgroup$ – Mike Waters Jan 7 at 17:22
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A couple of observations based on your post here and Physics SE.

Your choice of antennas is a significant compromise. These are not balanced antennas so your coaxial cables will easily function as part of the antenna. This will cause stray RF and it will alter the receive and transmit patterns of the antennas. You would have more predictable results with a balanced antenna, such as a half wave, center fed dipole, and ensuring that your feedline length is an odd multiple of 1/4 of wavelength of 950 MHz. The directionality and impedance of the center fed, half wavelength dipole is well understood and documented.

The intent of your experiment is not completely clear. If you are trying to determine the effect of the sample on the attenuation or reflection of RF, you should position your antennas at least 1 wavelength (~0.318 meters) apart and insert your sample material mid position. You can calculate the amount of transmit power required by using a link budget calculator based on your receiver sensitivity, the antenna spacing, and the gain of the antennas. For dipole antennas, you can estimate the gain to be 2.15 dBi each. As a rough calculation, if your receiver has a -107 dBm (1 $\mu$V at 50 ohms) sensitivity, the minimum transmit power would be approximately -90 dBm. You can of course determine this experimentally by simply stepping down the transmit power until the receiver no longer registers a signal and then bring it back up just a bit.

Your test fixture should be in an anechoic chamber in order to eliminate unwanted reflections and standing waves. If you fail to take this step, you will likely find the results of your experiment to be inconsistent and unrepeatable.

The screen shot you showed of the VNA in the Physics SE link shows that you have the bandwidth of your VNA set much too wide. You should have it set to perhaps +/- 50 kHz of the carrier frequency instead of multiple harmonics as shown. This will allow you to more easily see the effects of the change of scattering parameters on the plot.

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    $\begingroup$ this study is intended to characterise transmission medium to calculate its dielectric properties. So here I am new to radio physics experimental setup. Firstly we don't have anechoic chamber where this VNA is located. Secondly ,I have a doubt, if there is a signal of 5GHz from wifi would that be reflected in this spectrum or gain bandwidth. And as you said the minimum distance should be the length of wavelength the least to get substantial gain. I'll try that. $\endgroup$ – shiva Jan 7 at 17:20
  • $\begingroup$ @shiva In your comment here you referenced a 5 GHz signal but in your comments to your question, you said 950 MHz. Could you please clarify? $\endgroup$ – Glenn W9IQ Jan 7 at 17:48
  • $\begingroup$ It is a quarter wave antenna and I don't know whether it is a monopole or dipole, the vendor calls it stub, in the discussion in PhysicsSE, you can see there is graph, in which we can observe that there is -30dBm peak at 5GHz, which is approx 0.0001 mW. And the band is broad when compared to other peaks. I am asking is this the outcome of 5GHz WiFi transmission in the surroundings. $\endgroup$ – shiva Jan 7 at 18:33
  • $\begingroup$ @shiva You are seeing the VNA sweep through a wide range of frequencies. It generates each frequency in order to measure the associated scattering parameters. The antennas will work to some degree at other select frequencies. I think this is what you are seeing on the display. $\endgroup$ – Glenn W9IQ Jan 7 at 19:52
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At a distance of 1 cm and a frequency of 950 MHz, the two antennas will be coupled substantially by the near field, and so the inverse square law is not applicable. Furthermore the inverse square law only works for point sources, and at these distances it is grossly inaccurate to approximate the antennas as points.

The actual power coupling will be highly dependent on the precise geometry of each antenna involved. I'm afraid no precise answer is possible without either performing an empirical measurement or modelling.

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