Gain
The gain of a rectangular microstrip patch antenna with air dielectric can be very roughly estimated as follows. Since the length of the patch, half a wavelength, is about the same as the length of a resonant dipole, we get about 2 dB of gain from the directivity relative to the vertical axis of the patch. If the patch is square, the pattern in the horizontal plane will be directional, somewhat as if the patch were a pair of dipoles separated by a half-wave; this counts for about another 2-3 dB. Finally, the addition of the ground plane cuts off most or all radiation behind the antenna, reducing the power averaged over all directions by a factor of 2 (and thus increasing the gain by 3 dB). Adding this all up, we get about 7-9 dB for a square patch, in good agreement with more sophisticated approaches (see Balanis, p. 841, for more details).
A typical radiation pattern for a linearly-polarized 900-MHz patch antenna is shown below. The figure shows a cross-section in a horizontal plane; the pattern in the vertical plane is similar though not identical. The scale is logarithmic, so (for example) the power radiated at 180° (90° to the left of the beam center) is about 15 dB less than the power in the center of the beam. The beam width is about 65° and the gain is about 9 dBi. An infinitely-large ground plane would prevent any radiation towards the back of the antenna (angles from 180 to 360°), but the real antenna has a fairly small ground plane, and the power in the backwards direction is only about 20 dB down from that in the main beam.
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