If there are two resonant (λ/2) electric dipoles parallel to the z-axis
separated by a distance d of 63 mm on the x-axis (and thus both are on y=0).
If both dipoles are excited by a, equal in amplitude and phase, harmonic signal
with frequency 2400 MHz
How would the E- and H-plane normalised antenna pattern, maxima, minima and sidelobes look like ?
So far I know for a single dipole, but have no idea of this configuration?
Just add up the patterns from the two antennas taking into account the phase difference due to the different distances from each antenna that are due to the different directions. The phase difference is 2 pi (63 mm sin theta)/wavelength. Add up the square roots of the power as vectors differing in direction by the angle given above, then square the new length. Take off 3 dB because each antenna has only half the total power available. There may be some reaction between the antennas (one receiving the other)that will affect their match, which will need to be corrected, or this will lower the gain.
Look up Antennas by Krauss. That has a good treatment of simple array antennas such as yours. Mr White's answer highlights some of the problems though.
The separation between 2 antenna is half the wave length (wave length at 2400 MHz is 125 mm), it will have maxima in Y direction off set from origin by 32.5 mm (line of maxima will pass through middle point of tho antenna. Minima in X direction in X-Y plane (Non zero). As distance between two antenna is quarter wave length, the no of lobes will quarter per quabrant (i. e. With a Maxima in parallel Y axis, it will have reduction in power in X-Y plane to wards X axis in a quadrant and then mirror image for other qudrant/s)
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