I am looking for a formula for near field power density from a dipole antenna antenna. Is cylindrical model is sufficient? Do I have to consider ground reflection too? Please share your ideas?


It is accepted that an EM wave doesn't properly form in the near field because the E and H fields are not properly aligned. Therefore you cannot consider a near field signal as a power. Here's a simple illustration: -

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As for trying to understand or predict the E and H fields closeby, this is quite difficult. Here is an article from wiki that might help you understand. Here is an extract concerning the near field: -

Near-field diffraction

In contrast to the far-field, the diffraction pattern in the near-field typically differs significantly from that observed at infinity and varies with distance from the source. In the near-field, the relationship between E and H becomes very complex. Also, unlike the far-field where electromagnetic waves are usually characterized by a single polarization type (horizontal, vertical, circular, or elliptical), all four polarization types can be present in the near-field. The "near-field" is a region in which there are strong inductive and capacitive effects from the currents and charges in the antenna that cause electromagnetic components that do not behave like far-field radiation. These effects decrease in power far more quickly with distance than do the far-field radiation effects. Non-propagating (or evanescent) fields extinguish very rapidly with distance, which makes their effects almost exclusively felt in the near-field region. Also, in the part of the near-field closest to the antenna (called the "reactive near-field", see below), absorption of electromagnetic power in the region by a second device has effects that feed-back to the transmitter, increasing the load on the transmitter that feeds the antenna by decreasing the antenna impedance that the transmitter "sees". Thus, the transmitter can sense when power is being absorbed in the closest near-field zone (by a second antenna or some other object) and is forced to supply extra power to its antenna, and to draw extra power from its own power supply, whereas if no power is being absorbed there, the transmitter does not have to supply extra power.

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  • \$\begingroup\$ I understand. But if you put a another receiving dipole antenna in the near field, it will generate voltage and current. Do you know what the equations are for that? \$\endgroup\$ – user72035 Sep 13 '15 at 14:46
  • \$\begingroup\$ As I said above, the derivation of these sorts of formulas are at best a weak approximation based on the simplest type of antennas. In the near field it is better to study the biot savart law - this is a really simple law that predicts the flux density in space from a simple conductor. Once the conductor becomes a circular coil it gets more complex (and solvable) but anything more complex (like a square section coil) has mathematical integrations that I don't think have solutions. I have used an excel spreadsheet to numerically solve this type of problem in the past but there are better tools. \$\endgroup\$ – Andy aka Sep 13 '15 at 14:55
  • \$\begingroup\$ This website is calcutating near filed power density. Any idea what formula are they using? hintlink.com/power_density.php \$\endgroup\$ – user72035 Sep 13 '15 at 20:08
  • \$\begingroup\$ That is not a proper near field calculator. Although it will accept a distance of zero at small distances from the antenna it will be totally wrong. That calculator probably uses the Friis equations for far field transmission powers. Listen to what I told you in my 1st paragraph - if powers are mentioned then it's not a near field calculation even if the online calculator permits zero length. The Friis equations permit zero length but it would also be pointless to do so. \$\endgroup\$ – Andy aka Sep 13 '15 at 20:17
  • \$\begingroup\$ If you read the links to that calculator you would find this document: transition.fcc.gov/Bureaus/Engineering_Technology/Documents/… - apparently it contains the equations used in the website. \$\endgroup\$ – Andy aka Sep 13 '15 at 20:20

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