Multi element antennas like LPDA (log periodic dipole antennas) have the advantage that they can work over a wide range of frequencies.
An antenna has a fixed length which is calculated experimentally to maximize the radiation. It follows therefore that an antenna designed this way will work on a limited range of frequencies. Or only the one it is designed for.
When you combine multiple such elements you increase the range of frequencies that the antenna can handle. Each element maximizes the radiation for a particular frequency.
This feature is incredibly useful in cellular technologies, for example, that have to transmit over a set of frequencies.
Conversely an LPDA can also function as a receiver for a frequency range. Single LPDA receiving many frequencies.
However not all elements can radiate on all frequencies. In these cases the elements that do radiate are called active elements those that don't are passive.
Passive elements can act as reflectors, increasing the gain of the antenna and make the system directional.
Therefore an LPDA is used in cases where we want a directional antenna to work on a wide range of frequencies.
References
http://www.antenna-theory.com/antennas/wideband/log-periodic-dipole.php
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