Editing Log-periodic antenna (section)

== Basic concept ==

The LPDA normally consists of a series of [[dipole antenna|half wave dipole]] "elements" each consisting of a pair of metal rods, positioned along a support boom lying along the antenna axis. The elements are spaced at intervals following a logarithmic function of the [[frequency]], known as ''d'' or ''sigma''.  The length of the successive elements and the spacing between them gradually decrease along the boom. The relationship between the lengths is a function known as ''tau''. ''Sigma'' and ''tau'' are the key design elements of the LPDA design.<ref>[http://www.salsburg.com/Log-Periodic.pdf The Log-Periodic Dipole Array"]</ref><ref name=d>{{Cite web|url=http://www.ewh.ieee.org/soc/es/Nov1998/13/LPARRAY/LPDA.HTM|archive-url=https://archive.today/20141005152354/http://www.ewh.ieee.org/soc/es/Nov1998/13/LPARRAY/LPDA.HTM|url-status=dead|archive-date=October 5, 2014|title=Log Periodic Dipole Array (LPDA)|website=[[IEEE]]}}</ref>  The [[radiation pattern]] of the antenna is unidirectional, with the [[main lobe]] along the axis of the boom, off the end with the shortest elements.  Each dipole element is [[resonance|resonant]] at a [[wavelength]] approximately equal to twice its length. The [[bandwidth (signal processing)|bandwidth]] of the antenna, the [[frequency]] range over which it has near-maximum [[antenna gain|gain]], is approximately between the [[resonant frequency|resonant frequencies]] of the longest and shortest elements.

Every element in the LPDA antenna is a [[driven element]], that is, connected electrically to the [[feedline]]. A parallel wire [[transmission line]] usually runs along the central boom, and each successive element is connected in ''opposite'' [[phase (waves)|phase]] to it. The feedline can often be seen zig-zagging across the support boom holding the elements.<ref name=d/>  Another common construction method is to use two parallel central support booms that also acts as the transmission line, mounting the dipoles on the alternate booms. Other forms of the log-periodic design replace the dipoles with the transmission line itself, forming the log-periodic zig-zag antenna.<ref>[http://www.google.ca/patents/US3355740 "Log-periodic zig zag antenna"], US Patent 3355740</ref> Many other forms using the transmission wire as the active element also exist.<ref>[http://www.ece.illinois.edu/about/history/antenna/photos.html Photo Archive Of Antennas], Illinois Historic Archive</ref>

The [[Yagi–Uda antenna|Yagi]] and the LPDA designs look very similar at first glance, as they both consist of a number of dipole elements mounted along a support boom. The Yagi, however, has only a single [[driven element]] connected to the transmission line, usually the second one from the back of the array, the remaining elements are [[parasitic element|parasitic]]. The Yagi antenna differs from the LPDA in having a very narrow bandwidth.

In general terms, at any given frequency the log-periodic design operates somewhat similar to a three-element Yagi antenna; the dipole element closest to resonant at the operating frequency acts as a driven element, with the two adjacent elements on either side as director and reflector to increase the gain, the shorter element in front acting as a director and the longer element behind as a reflector. However, the system is somewhat more complex than that, and all the elements contribute to some degree, so the gain for any given frequency is higher than a Yagi of the same dimensions as any one section of the log-periodic. However, a Yagi with the same number of elements as a log-periodic would have ''far'' higher gain, as all of those elements are improving the gain of a single driven element. In its use as a television antenna, it was common to combine a log-periodic design for VHF with a Yagi for UHF, with both halves being roughly equal in size. This resulted in much higher gain for UHF, typically on the order of 10 to 14&nbsp;dB on the Yagi side and 6.5&nbsp;dB for the log-periodic.<ref>{{cite book |url={{GBurl|id=jDCs1Ckne_EC|pg=PA177}} |page=178 |title= Computational Electromagnetics for RF and Microwave Engineering |first=David |last=Davidson |publisher=Cambridge University Press |date=2010|isbn=978-1-139-49281-2}}</ref> But this extra gain was needed anyway in order to make up for a number of problems with [[UHF television broadcasting#UHF vs VHF|UHF signals]].

The log-periodic shape, according to the IEEE definition,<ref>"''Log-periodic antenna'' Any one of a class of antennas having a structural geometry such that its impedance and radiation characteristics repeat periodically as the logarithm of frequency." (see ''The new IEEE Standard Dictionary of Electrical and Electronics Terms'', 1993 ⓒ IEEE.) </ref><ref>"''Log-periodic antenna'' Any one of a class of antennas having a structural geometry such that its impedance and radiation characteristics repeat periodically as the logarithm of frequency." (see Acknowledgments, and footnote in page 1), ''Self-Complementary Antennas―Principle of Self-Complementarity for Constant Impedance''―, by Mushiake, Yasuto, Springer-Verlag London Ltd., London, 1996.</ref> does not align with broadband property for antennas.<ref>Mushiake, Yasuto, "Constant-impedance antennas", ''J. IECE Japan'', 48, 4, pp. 580-584, April 1965. (in Japanese).</ref><ref>{{cite journal|last=Mushiake|first=Yasuto|url=http://www.sm.rim.or.jp/~ymushiak/sub.non-const.htm|title=Log-periodic structure provides no broad-band property for antennas|journal=J. IEE Japan |volume=69 |issue=3 |page=88 |date=March 1949 |publisher=Sm.rim.or.jp |access-date=15 January 2014}}</ref> The broadband property of log-periodic antennas comes from its [[self-similarity]]. A planar log-periodic antenna can also be made [[self-complementary antenna|self-complementary]], such as logarithmic [[spiral antenna]]s (which are not classified as log-periodic ''per se'' but among the [[frequency independent antennas]] that are also self-similar) or the log-periodic toothed design. Y. Mushiake found, for what he termed "the simplest self-complementary planar antenna," a driving point impedance of [[Impedance of free space|η<sub>0</sub>]]/2=188.4&nbsp;Ω at frequencies well within its bandwidth limits.<ref>{{cite journal|last=Mushiake|first=Yasuto|url=http://www.sm.rim.or.jp/~ymushiak/sub.docu.1.htm##%% |title=Origination of self-complementary structure and discovery of its constant-impedance property|journal=J. IEE Japan|volume=69 |issue=3 |page=88 |date=March 1949 |lang=ja |publisher=Sm.rim.or.jp |access-date=31 January 2014}}</ref><ref>{{cite web|last=Mushiake|first=Yasuto|url=http://www.sm.rim.or.jp/~ymushiak/sub.sca.htm|title=Infinite freedom |publisher=Sm.rim.or.jp |access-date=15 January 2014}}</ref><ref name="Rumsey Frequency">Rumsey, V. H., ''Frequency independent antennas'', Academic Press, New York and London. 1966. [p. 55]</ref>
{{multiple image
| align    = center
| direction = horizontal
| header   =
| image1   = Schwarzbeck UHALP 9108 A.jpg
| caption1 = Log-periodic antenna, 250&ndash;2400 MHz
| width1   = 200
| image2   = VHF UHF LP-antenna closeup.JPG
| caption2 = Log-periodic mounted for vertical polarization, 140&ndash;470&nbsp;MHz
| width2   = 150
| image3   = Log periodic VHF TV antenna 1963.jpg
| caption3 = LP television antenna 1963. Covers 54&ndash;88&nbsp;MHz and 174&ndash;218&nbsp;MHz. Slanted elements were used because on the upper band they operate at the third harmonic.
| width3   = 262
| image4   = Log-periodic monopole antenna.png
| caption4 = Wire log-periodic monopole antenna
| width4   = 202
}}