A Yagi-Uda array, commonly known simply as a Yagi antenna, is a directional antenna consisting of a driven element (typically a dipole or folded dipole) and additional parasitic elements (usually a so-called reflector and one or more directors). Yagi-Uda antennas used for amateur radio are sometimes designed to operate on multiple bands.
These elaborate designs create electrical breaks along each element (both sides) at which point a parallel LC (inductor and capacitor) circuit is inserted. The reflector element is slightly longer (typically 5% longer) than the driven dipole, whereas the so-called directors are a little bit shorter.
The lengths of the directors are smaller than that of the driven element, which is smaller than that of the reflector(s) according to an elaborate design procedure. These elements are usually parallel in one plane, supported on a single crossbar known as a boom.
This so-called trap has the effect of truncating the element at the higher frequency band, making it approximately a half wavelength in length. At the lower frequency, the entire element (including the remaining inductance due to the trap) is close to half-wave resonance, implementing a different Yagi-Uda antenna.
This design achieves a very substantial increase in the antenna's directionality and gain compared to a simple dipole. Yagi-Uda antennas are directional along the axis perpendicular to the dipole in the plane of the elements, from the reflector toward the driven element and the director(s). Typical spacings between elements vary from about 1/10 to 1/4 of a wavelength, depending on the specific design.
There are no simple formulas for designing Yagi-Uda antennas due to the complex relationships between physical parameters such as element length, spacing, and diameter, and performance characteristics such as gain and input impedance. But using the above sort of analysis one can calculate the performance given a set of parameters and adjust them to optimize the gain (perhaps subject to some constraints).