Final answer:
The standard reference antenna for directive gain is the half-wave dipole antenna, which is used as a comparison baseline due to its well-understood radiation pattern and gain.
Step-by-step explanation:
The standard reference antenna for the directive gain is a half-wave dipole antenna, not a half dipole antenna. The half-wave dipole antenna is often used as a reference because it has a well-known radiation pattern and gain, making it a good baseline for comparing other antennas.
Directive gain, which is sometimes just called gain, quantifies the directionality of an antenna's radiation pattern. It represents how well the antenna directs the energy in comparison to a standard reference antenna. When compared with a half-wave dipole, the gain of another antenna is given in dipole gain units (dBi).
Antenna design is crucial for directing radio waves into desired patterns. For example, Figure 27.29 illustrates that microwave transmission antennas exhibit a spreading of the beam due to diffraction, which is inversely proportional to the diameter of the antenna expressed by the relation 1.22 λ/D.
An antenna size that is one-fourth the wavelength of the emitted radiation, as stated in the question, would be the most efficient for a broadcast antenna with one end on the ground. This is equivalent to the fundamental resonant mode of an air column closed at one end, where the length of the column is one-fourth of the wavelength of the resonant frequency.