What type of radiation pattern is created by two 1/4-wavelength vertical antennas spaced 1/2-wavelength apart and fed in phase?
Why With two verticals fed in phase, a point broadside (perpendicular to the line joining them) is equidistant from both elements, so the signals arrive in step and add for maximum radiation. Off the ends of the array, the extra travel to the far element is the full 1/2-wavelength spacing, which is 180 degrees of phase, so the two signals cancel and produce deep nulls. The result is a two-lobe figure-eight pattern broadside to the array axis.
Watch out The end-fire figure-eight is what you get from the same 1/2-wavelength spacing when the elements are fed 180 degrees out of phase, and a cardioid comes from 1/4-wavelength spacing with a 90 degree phase difference.
In phase equals broadside; out of phase equals end-fire. 1/4-wave spacing plus 90 degrees equals cardioid.