As far as I understand, and antenna like a simple dipole has a circular radiation pattern at the 2 edges, so the physical aperture in this case is circular.

$${A = \pi * r^2}$$

Where r is the radius of the circle surrounding the dipole, or basically r is the length of 1 rod of the dipole.

Then we have the gain formula:

$${G = 10* \log_{10} ( \frac{\eta * 4 * \pi * A }{\lambda ^2 } )}$$

Where eta is the efficiency, and A is the aperture calculated above.

So can we use the following formula to calculate the gain of an antenna?

$${G = 10* \log_{10} ( \frac{\eta * 4 * \pi^2 * r^2 }{\lambda ^2 } )}$$

  • \$\begingroup\$ What do you mean by aperture. My version of aperture involves wavelength. \$\endgroup\$
    – Andy aka
    Jun 10, 2017 at 12:19
  • \$\begingroup\$ @Andyaka I meant physical apperture which is defined by the smallest circle surrounding the antenna. There is also the "antenna aperture" definition which contains also the nearby area where the current can couple to other objects and relay the signal to the antenna. \$\endgroup\$
    – Louis J.
    Jun 11, 2017 at 13:04
  • \$\begingroup\$ what happens if I increase the aperture size what is the effect on gain/directivity?? PS sorry....i can't comment this post, i don't have 50 point \$\endgroup\$
    – user193562
    Jul 26, 2018 at 8:28

1 Answer 1


In many antenna designs, such as a dipole, the physical aperture has no direct correlation to directivity and therefore gain of the antenna. For example, a 1/2 wavelength dipole has a gain of 1.65 while an extremely short dipole, say 0.05 wavelengths long, has a gain of 1.5 at the same frequency. You may not be able to effectively drive the short dipole but its directivity is nearly the same.

So I hope you can see that your premise of starting with the physical aperture is the wrong approach. In fact, no receive antenna can have current induced in it by a plane wave that is more than about 0.16 wavelengths away. You may find it helpful to study Effective Aperture, directivity, and efficiency. A classic book in this field was written by John Kraus. You may also find some suitable texts published by ARRL.

  • \$\begingroup\$ I assumed that the antenna is perfectly aligned, like in plane of sight. The efficiency is a parameter in the formula above, so what is exactly the problem with that? \$\endgroup\$
    – Louis J.
    Jun 11, 2017 at 13:00
  • \$\begingroup\$ " For example, a 1/2 wavelength dipole has a gain of 1.65 while an extremely short dipole, say 0.05 wavelengths long, has a gain of 1.5 at the same frequency." Yes that is the definition of efficiency, if a shorter dipole can just be as good as a long one, then that means that the short one is more efficient, so the efficiency parameter will vary according to that. There is nothing wrong with my formula if we look at it from this point of view. \$\endgroup\$
    – Louis J.
    Jun 11, 2017 at 13:07
  • \$\begingroup\$ No that is not the definition of efficiency - it is an exemplification of directivity. Efficiency of an antenna is defined as Radiation_Resistance/(Radiation_Resistance+Resistive_Losses). Directivity times Efficiency = Gain. Regarding your assertion of alignment, this is always the case when discussing antenna gain. \$\endgroup\$
    – Glenn W9IQ
    Jun 11, 2017 at 15:56

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