In telecommunication, a log-periodic antenna (LP, also known as a log-periodic array) is a broadband, multi-element, unidirectional, narrow-beam antenna that has impedance and radiation characteristics that are regularly repetitive as a logarithmic function of the excitation frequency. The individual components are often dipoles, as in a log-periodic dipole array (LPDA). Log-periodic antennas are designed to be self-similar and are thus also fractal antenna arrays. The log periodic antenna was invented by Dwight E. Isbell, Raymond DuHamel and variants by Paul Mayes. U of I had patented the Isbell and Mayes-Carrel antennas and licensed the design as a package exclusively to JFD electronics in New York. Lawsuits regarding the antenna patent which the UI Foundation lost, evolved into the Blonder-Tongue doctrine. This precedent governs patent litigation. 
It is normal to drive alternating elements with 180° (π radians) of phase shift from one another. This is normally done by connecting individual elements to alternating wires of a balanced transmission line.
The length and spacing of the elements of a log-periodic antenna increase logarithmically from one end to the other. A plot of the input impedance as a function of logarithm of the excitation frequency shows a periodic variation.
This antenna design is used where a wide range of frequencies is needed while still having moderate gain and directionality. It is sometimes used for a (VHF/UHF) television antenna. 
Popular Amateur radio variations
The HB9CV is a very popular two-element beam which can be considered as a log-periodic dipole array with only two elements. Antenna Design Details
This is a beam antenna which for a given boom length gives a higher gain than a Yagi antenna, it is a log-periodic where only two elements are driven with a series of parasitic elements (directors) in front of the smaller of the two driven elements.
The driven elements are folded dipoles which are linked by a length of balanced twin-lead feed line. The polar plots of the ZL special and the HB9CV are heart shaped (cardioid) while the typical Yagi antenna has a large forward lobe and a smaller back lobe.
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