WimRFP
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Very likely your example antenna doesn't use a perfect conducting infinite ground, and then you don't have the +3 db gain increase.
Other thing, they state the gain for one value of elevation (or theta angle), maybe the gain is higher at somewhat higher elevation (lower theta). This happens frequently with small ground planes.
Best you can do is to get more details about the radiation pattern you provided (that is actual antenna geometry with ground plane and dielectrics if present, and check their definition of gain as you know that there can be some confusion).
Other thing, they state the gain for one value of elevation (or theta angle), maybe the gain is higher at somewhat higher elevation (lower theta). This happens frequently with small ground planes.
Best you can do is to get more details about the radiation pattern you provided (that is actual antenna geometry with ground plane and dielectrics if present, and check their definition of gain as you know that there can be some confusion).