I work on a program that simulates the wave propagation of high frequency electromagnetic waves (2.4 or 5 GHz Bands) in 3D. I use a ray launching approach, where the emitted rays approximate the electromagnetic waves, which carry the transmission power of a particular wave in dBm as an attribute. The user is able to import a csv list which holds the angles of the vertical and horizontal radiation pattern (polar diagram) and the corresponding values for the actual transmitted power from the antenna in dBm.

My question is now, how can I calculate the values in that list in respect to a given radiation pattern of an antenna? Or in other words, how can I calculate the real transmitted power of an antenna in respect to a given radiation pattern in the horizontal and vertical planes?

Thanks in advance and sorry for the bad English.

Update 1

The picture below shows an example for a radiation pattern that I want to use. With this pattern and the transmitting power of the transmitting antenna (In the case of 2.4 GHz Wireless LAN thats 20 dBm respectively 100 mW) I want to calculate the real outgoing power of the antenna in respect to the given angles (λ or φ) shown in the radiation pattern.

So my calculation would look something like this(?):

Poutgoing = 20 dBm * PdirectionDependentGainFactor(λ)

enter image description here source: http://www.mpantenna.com/antenna-gain-and-radiation-patterns/

  • \$\begingroup\$ I‘m not sure if I understand your question correctly. Could you show us an example of an antenna radiation pattern that you would like to calculate? Radiation patterns often show the gain of an antenna in dBi, which is relative to a spherical emitting antenna (which does not exist). You would need the input power and the efficiency of the antenna to calculate radiated power. \$\endgroup\$ Commented Aug 29, 2018 at 19:25
  • \$\begingroup\$ Thanks for your reply, I've updated the question and hope that it's now more understandable what I try to achieve. \$\endgroup\$
    – Jupp Otto
    Commented Aug 30, 2018 at 11:32
  • \$\begingroup\$ Yes, you are quite there: Your radiation diagram shows the gain, so the antenna losses are part of that diagram. I propose simple addition of the logarithmic parts, so: EIRP = Pin + Pgain. (EIRP is the usual term for what you called Poutgoing). If you further subtract the damping losses per distance, you get the radiation power at a given distance in dBm. (Edit: in my first comment I wrote „gain“ where it should be „directivity“) \$\endgroup\$ Commented Aug 30, 2018 at 15:23

1 Answer 1


The parameter I was looking for is the EIRP which gives us the radiated power in direction of the maximum antenna gain in dBm or mW.

enter image description here

source: http://cdn.everythingrf.com/live/erp_eirp_formula.PNG

The EIRP can also be calculated for any other direction if you take the loss in dB from the radiation pattern. These values are measured in dB and they are relative to the antenna gain. So if you take the picture from Update 1, the antenna gain at 30° would be decreased about 4.5 dB. The directive antenna gain at 30° would be -1.5 dBi (3 bBi which is the max gain of the anetnna - 4.5 dB).
Now you can do the calculation of the EIRP by insert the -1.5 dBi for the variable Ga.

  • \$\begingroup\$ I'm very unsure about your calculation example and the related picture. In the picture it is written 3dB max. gain, but in the graph I can not see where this 3dB max gain direction is. The graph has its maximum at 0dB gain at 0°/180°. What do you think? \$\endgroup\$ Commented Aug 31, 2018 at 16:00
  • \$\begingroup\$ The values you see in the radiation pattern are relative to the max gain of 3dBi. So all loss values are relative to the max dBi level (3 dBi = 0 dB in the pattern). \$\endgroup\$
    – Jupp Otto
    Commented Aug 31, 2018 at 16:08
  • \$\begingroup\$ Ok, after checking the datasheet of that antenna, I agree with you. \$\endgroup\$ Commented Aug 31, 2018 at 16:09

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