Theory of Operation
Consider a Yagi-Uda consisting of a reflector, driven element and a single director as shown here. The driven element is typically a λ/2 dipole or folded dipole and is the only member of the structure that is directly excited (electrically connected to the feedline). All the other elements are considered parasitic. That is, they reradiate power which they receive from the driven element (they also interact with each other).
One way of thinking about the operation of such an antenna is to consider a parasitic element to be a normal dipole element with a gap at its center, the feedpoint. Now instead of attaching the antenna to a load (such as a receiver) we connect it to a short circuit. As is well known in transmission line theory, a short circuit reflects all of the incident power 180 degrees out of phase. So one could as well model the operation of the parasitic element as the superposition of a dipole element receiving power and sending it down a transmission line to a matched load, and a transmitter sending the same amount of power down the transmission line back toward the antenna element. If the wave from the transmitter were 180 degrees out of phase with the received wave at that point, it would be equivalent to just shorting out that dipole at the feedpoint (making it a solid element, as it is).
The fact that the parasitic element involved isn't exactly resonant but is somewhat shorter (or longer) than λ/2 modifies the phase of the element's current with respect to its excitation from the driven element. The so-called reflector element, being longer than λ/2, has an inductive reactance which means the phase of its current lags the phase of the open-circuit voltage that would be induced by the received field. The director element, on the other hand, being shorter than λ/2 has a capacitive reactance with the voltage phase lagging that of the current. If the parasitic elements were broken in the center and driven with the same voltage applied to the center element, then such a phase difference in the currents would implement an end-fire phased array, enhancing the radiation in one direction and decreasing it in the opposite direction. Thus one can appreciate the mechanism by which parasitic elements of unequal length can lead to a unidirectional radiation pattern.
Read more about this topic: Yagi-Uda Antenna
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