How does the ground plane size affect the gain and radiation pattern of a monopole antenna?

The ground plane size significantly affects the gain and radiation pattern of a monopole antenna because the monopole relies on the ground plane to create an image of itself (forming the equivalent of a dipole) and to provide a reference for the return current. With an infinite ground plane: the monopole produces a pattern identical to one half of a dipole pattern, with maximum radiation along the ground plane (at the horizon for a vertical monopole), 3 dBi gain for a quarter-wave monopole (equivalent to 5.15 dBi dipole divided by 2 for the half-space). With a finite ground plane: the ground plane edges act as secondary radiating sources (the currents flowing on the ground plane surface terminate at the edges and create diffracted waves). These edge diffraction effects cause: pattern ripple (amplitude oscillations in the elevation pattern caused by interference between the monopole radiation and the edge diffraction), elevated beam peak (the pattern maximum shifts upward from the horizon by approximately 20-40 degrees for ground planes smaller than approximately 2 lambda diameter), reduced gain (the peak gain decreases by 1-3 dB for ground planes smaller than 1 lambda diameter compared to the infinite case), and back radiation (some energy radiates below the ground plane through edge diffraction). The minimum ground plane size for reasonable performance is approximately 0.25 lambda radius (0.5 lambda diameter), which gives approximately 0 dBi gain with a significantly elevated beam. A 1 lambda radius ground plane provides approximately 2-3 dBi gain with the beam peak approximately 20 degrees above the horizon. A 2-3 lambda radius ground plane approaches the infinite ground plane performance.