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directivity simly varies with size of antenna.
You can have a look on small antennas fudamental limits regarding relations between antenna size and other parameters for a better view.
anybody knows what is the microstrip antenna gain of remote car keys?
i wonder how they fit a practically short microstrip antenna to radiate at 315/433mhz freq inside remote car keys .... any ideas?
(sorry might be out of topic already)
The gain of a microstip patch depends also on the substrate thickness (and dielecric constant), size of GND.
A small GND would broaden the beam significantly (a patch on a key holder is not a patch anymore - since the gnd is probably very small) so the gain is smaller
a thin patch does not exceed 5.5 dB (32 mil think on 5880)
a thick patch (air instead of dielectric) can indeed reach 8 dB
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