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I am designing a PIFA antenna in CST microwave studio. I have found something peculiar that I do not quite understand. My antenna resonates at 1.6 GHz, and when the substrate (FR4) is very thin (0.5 mm), I get an S11 of about -20 dB. The realized gain at this frequency is -12.5 dB. If I make the substrate thicker, the S11 resonance gets worse, and the gain gets better. For example, making it 3 mm (instead of 0.5 mm), the S11 went to -4, and the gain went to -6.

Can anyone explain why this is? I thought realized gain takes into account mismatch loss, meaning S11 should be a factor. If the S11 gets worse, how is the realized gain getting better??

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  • \$\begingroup\$ I think I might have gotten it, or at least I have gotten closer. It seems like while the S11 goes down, the radiation efficiency goes up. But this confuses me because I would think the radiation efficiency is directly related to the S11. I guess the efficiency goes up more than the S11 goes down, thereby making the realized gain go up. \$\endgroup\$
    – user41178
    Commented Apr 7, 2017 at 14:35
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    \$\begingroup\$ When you say "the S11 resonance" what are you talking about? You never said before that you saw resonant behavior in the S11 spectrum? Sharing the S11 vs frequency curve would probably make it more clear. Also what do you mean by "realized gain"? Antenna gain doesn't mean the same thing as gain does for N-port devices. Again, some charts of your results and a diagram of your simulation setup might make it more clear what you're asking about. \$\endgroup\$
    – The Photon
    Commented Apr 7, 2017 at 14:42
  • \$\begingroup\$ Yes that is a good idea. I will do that later today. What I mean is, the antenna radiates at 1.6 GHz, therefore there is a resonance dip at 1.6 GHz in the S11 response because the power at that frequency is not being reflected. Realized gain is related to the power SENT to the antenna, where gain is related to the ACCEPTED power of the antenna. So realized gain takes into account the mismatch loss at the antenna feed. \$\endgroup\$
    – user41178
    Commented Apr 7, 2017 at 14:51

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An antenna's realized gain is the antenna gain reduced by power lost to reflections at the antenna feed. The antenna gain is the product of efficiency and directivity:

$$G_R = \left(1-\left|S_{11}\right|^2\right)E_A D$$

If \$|S_{11}|\$ increased, but realized gain also increased, that implies that one of the other factors improved. I would normally think that since you didn't improve the conductivity of copper or reduce the dielectric losses of your substrate, the efficiency term most likely didn't change much. So it's most likely that directivity improved.

But something still doesn't quite add up. -20 dB is really a very good \$S_{11}\$ magnitude, indicating a very well matched antenna. And the \$D\$ term is always greater than 1 (since any change from perfect isotropic radiation increases \$D\$). So the -12.5 dB realized gain in your first measurement indicates a very poor efficiency value.

It seems likely there is some subtlety to setting up the realized gain measurement in the simulator. Perhaps some signal is being reflected back into high order wave guide modes, or into guided waves in the board substrate, and these are not being measured as part of the reflected wave or the radiated wave, resulting in very poor efficiency.

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