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I designed the same slot shape in different sizes of patch and ground plane and got on different results I want to know what the effect of size the patch and ground on the performance of antenna clearly.
Ground plane size affects the antenna performance like gain, radiation pattern and efficiency. As a rule, the ground plane should extend beyond the edges of the patch by at least 2-3 times the board thickness for proper operation. A ground plane that is too small will result in a reduced front to back ratio. Making the ground plane larger also increases the gain, but as the ground plane size increases, diffraction near the edges plays less of a role and increasing the size of an already “large” ground plane has very little effect on gain. Ground plane size has less influence on resonant frequency.
You noted that the patterns of a patch antenna change with ground plane size. I have never found a "clear" description but have observed that as ground plane size increases the variation in patch performance stabilizes. As one would expect front to back ratio also increases. Everyone wants smaller antennas and often neglects the size of the ground plane. I have found that until the ground is a couple of wavelengths if not larger the antenna characteristics can change considerably.
I prefer to deal with this using a good (e. g. expensive) analysis software tool in conjunction with the fabrication of several prototypes.
The usual complaints are: With the ground plane the antenna is too big.
The software is too expensive.
It is taking too ling to develop.
The materials are too expensive.
The antenna will probably work as expected, that is the good part.