Power calculation from E and H field

Following from the previous post above. The user provided me with some assistance however I am still a bit unclear on how to apply the equations provided. Could someone please assist me in determining if the way I calculated the power received from the RFID tag is correct?

Ex = 0, Ey = 0, Ez = 149 (V/m)

Hx = 0.06, Hy = 0.834, Hz = 0 (A/m)

S = E X H = (-124.27 ; 8.94 ; 0)

|S| = 124.59

P = Aperture area x |S| x cos(theta)

P = 0.013539 x 124.59 x cos(38.54) = 1.32W

The aperture area is 0.013539 meters^2.

The angle was calculated using the picture attached. Is this the correct way of calculating the angle?

enter image description here

  • 2
    \$\begingroup\$ The area is defined by the aperture of the antenna and not some simple physical measurement. Go google antenna aperture. \$\endgroup\$ – Andy aka Feb 14 at 15:39
  • \$\begingroup\$ @Andyaka the aperture area was calculated using the frequency and gain of the antenna \$\endgroup\$ – Joey Feb 14 at 15:44
  • 2
    \$\begingroup\$ Ok my mistake. I think you need to make that clearer in your question. \$\endgroup\$ – Andy aka Feb 14 at 15:50
  • \$\begingroup\$ @Andyaka I updated the question. Is my working out correct? \$\endgroup\$ – Joey Feb 14 at 16:00
  • \$\begingroup\$ It hasn’t updated yet but I expect someone will point out if not. \$\endgroup\$ – Andy aka Feb 14 at 16:03

The definition of the aperture of the antenna is

The aperture is defined as the area, oriented perpendicular to the direction of an incoming electromagnetic wave, which would intercept the same amount of power from that wave as is produced by the antenna receiving it.


So if you know the aperture of the antenna, you already know, by definition, the area which, when multiplied by the intensity of the electromagnetic wave, gives the power received by the antenna.

If the antenna isn't oriented perpendicular to the incoming wave, you'll need to multiply by an additional factor to account for that. If you know the radiation pattern of the antenna, you can calculate the orientation factor from that.

The \$\cos\theta\$ factor I used in the previous answer assumes the antenna acts more or less like an actual aperture --- that its directive gain falls off to zero when oriented parallel to the incoming wave. If your antenna is isotropic (for example), then this is a completely wrong assumption. In general you should use the actual radiation pattern of your antenna to find the directive gain for this calculation.

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  • \$\begingroup\$ From the picture the antenna is not orientated perpendicular to it. So I included the cos(theta) factor to account for this. And the theta was calculated has shown in the picture. The RFID TAG is parallel to the longest side of the container and the angle was thus calculated. Is this calculation correct? \$\endgroup\$ – Joey Feb 14 at 17:01
  • \$\begingroup\$ If you're going to use \$\cos\theta\$ as an approximation, you should take \$\theta\$ as the angle to the normal, not the angle you showed. \$\endgroup\$ – The Photon Feb 14 at 17:03
  • \$\begingroup\$ So just take 90-38.45 degrees? \$\endgroup\$ – Joey Feb 14 at 17:04
  • \$\begingroup\$ Yes, but I realized I don't know the actual main lobe direction of your antenna, so maybe it's something else. \$\endgroup\$ – The Photon Feb 14 at 17:10
  • \$\begingroup\$ It's just a simulation for now so I assumed the main lobe direction is at 0 degrees. Upon practical testing I will see how much the deviation is from the simulations and will then account for the main lobe direction. Thank you for the feedback. \$\endgroup\$ – Joey Feb 14 at 17:14

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