View source for Yagi–Uda antenna

{{Short description|Type of radio antenna}}
[[File:UHF TV Antenna 001.JPG|thumb|A modern high-gain UHF Yagi [[television antenna]] with 17 directors, and one reflector (made of four rods) shaped as a [[corner reflector antenna|corner reflector]]]]
[[File:Yagi TV antenna 1954.png|thumb|Drawing of Yagi–Uda [[very high frequency|VHF]] [[television antenna]] from 1954, used for analog channels 2–4, 54–72&nbsp;MHz (U.S. channels). It has five elements: three directors (''to left'') one reflector (''to right'') and a driven element which is a [[folded dipole]] (''double rod'') to match the 300&nbsp;Ω [[twin lead]] feedline. The beam direction (direction of greatest sensitivity) is to the left.]]
A '''Yagi–Uda antenna''', or simply '''Yagi antenna''', is a [[directional antenna]] consisting of two or more parallel [[Antenna (radio)#Resonant antennas|resonant]] antenna elements in an [[Antenna array#Types|end-fire array]];<ref name="Graf">{{cite book
| last1  = Graf
| first1 = Rudolf F.
| title  = Modern Dictionary of Electronics
| publisher = Newnes
| date   = 1999
| edition = 7
| pages  = 858
| url    = https://books.google.com/books?id=AYEKAQAAQBAJ&q=yagi+antenna&pg=PA858
| isbn   = 0080511988
}}</ref> these elements are most often metal rods (or discs) acting as [[half-wave dipole]]s.<ref name="wiseGEEK">{{cite web
| title = What Is a Yagi Antenna?
| work = wiseGEEK website
| publisher = Conjecture Corp.
| date = 2014
| url = http://www.wisegeek.net/what-is-a-yagi-antenna.htm
| access-date = 18 September 2014}}</ref> Yagi–Uda antennas consist of a single [[driven element]] connected to a radio [[transmitter]] or [[radio receiver|receiver]] (or both) through a [[transmission line]], and additional ''[[passive radiator]]s'' with no electrical connection, usually including one so-called ''reflector'' and any number of ''directors''.<ref name="wiseGEEK" /><ref name="Balanis">{{cite book
| last1  = Balanis
| first1 = Constantine A.
| title  = Modern Antenna Handbook
| publisher = John Wiley and Sons
| date   = 2011
| pages  = 2.17–2.18
| url    = https://books.google.com/books?id=UYpV8L8GNCwC&q=%22Yagi-Uda&pg=SA9-PA9
| isbn   = 978-1118209752
}}</ref><ref name="Wolff">{{cite web
| last = Wolff
| first = Christian
| title = Yagi Antenna
| work = Radar Basics
| publisher = Radartutorial.eu
| date = 2010
| url = http://www.radartutorial.eu/06.antennas/an08.en.html
| access-date = 18 September 2014}}</ref> It was invented in 1926 by [[Shintaro Uda]] of [[Tohoku University|Tohoku Imperial University]], [[Japan]],<ref name="Uda1925" /> with a lesser role played by his boss [[Hidetsugu Yagi]].<ref name="Uda1925">{{cite journal | last = Uda | first = S. | title = On the Wireless Beam of Short Electric Waves | journal =The Journal of the Institute of Electrical Engineers of Japan| pages = 1128 | publisher = Institute of Electrical Engineers of Japan |date=December 1925 | url = https://books.google.com/books?id=UyECngEACAAJ }} (This was the preface and notice in advance for a series of eleven papers, of the same title, by Uda, between 1926 and 1929, on the antenna. However, it seems that Uda's pre-announcement caused his invention to lose its [[Novelty (patent)|novelty]] and become unpatentable. He would not have been informed by Professor Yagi about those.)</ref><ref name="Yagi1926">{{cite journal | last1 = Yagi | first1 = Hidetsugu | last2 = Uda | first2 = Shintaro | title = Projector of the Sharpest Beam of Electric Waves | journal = Proceedings of the Imperial Academy| volume = 2 | issue = 2 | pages = 49–52 | publisher = Imperial Academy |date=February 1926 | url = http://www.wa5vjb.com/references/Yagi1926.pdf | doi = 10.2183/pjab1912.2.49| access-date = 11 September 2014| doi-access = free }}</ref>
Reflector elements (usually only one is used) are slightly longer than the driven dipole and placed behind the driven element, ''opposite'' the direction of intended transmission. Directors, on the other hand, are a little shorter and placed in front of the driven element ''in'' the intended direction.<ref name="Wolff" /> These parasitic elements are typically off-tuned short-circuited dipole elements, that is, instead of a break at the feedpoint (like the driven element) a solid rod is used. They receive and reradiate the radio waves from the driven element but in a different [[phase (waves)|phase]] determined by their exact lengths. Their effect is to modify the driven element's [[radiation pattern]]. The waves from the multiple elements [[Superposition principle|superpose]] and [[interference (wave motion)|interfere]] to enhance radiation in a single direction, increasing the antenna's [[antenna gain|gain]] in that direction.
Also called a [[beam antenna]]<ref name="Wolff" /> and [[Antenna array#parasiticarray|parasitic array]], the Yagi is widely used as a [[directional antenna]] on the [[high frequency|HF]], [[very high frequency|VHF]] and [[Ultra high frequency|UHF]] bands.<ref name="Balanis" /><ref name="Wolff" /> It has moderate to high [[antenna gain|gain]] of up to 20&nbsp;[[decibel|dBi]],<ref name="Balanis" /> depending on the number of elements used, and a [[front-to-back ratio]] of up to 20&nbsp;dB. It radiates [[linear polarization|linearly polarized]]<ref name="Balanis" /> radio waves and is usually mounted for either horizontal or vertical polarization. It is relatively lightweight, inexpensive and simple to construct.<ref name="Balanis" /> The [[bandwidth (signal processing)|bandwidth]] of a Yagi antenna, the [[frequency]] range over which it maintains its gain and [[Antenna (radio)#Impedance matching|feedpoint impedance]], is narrow, just a few percent of the center frequency, decreasing for models with higher gain,<ref name="Balanis" /><ref name="Wolff" /> making it ideal for fixed-frequency applications. The largest and best-known use is as rooftop terrestrial [[television antenna]]s,<ref name="Balanis" /> but it is also used for point-to-point fixed communication links,<ref name="wiseGEEK" /> radar,<ref name="Wolff" /> and long-distance [[shortwave]] communication by broadcasting stations and [[radio amateurs]].<ref name="wiseGEEK" />
== Origins ==
[[File:FuG 220 and FuG 202 radar of Me 110 1945.jpg|thumb|upright|Quartet of two-dipole Yagi arrays (''Hirschgeweih'') of the German [[Lichtenstein radar#FuG 220 Lichtenstein SN-2|FuG 220 VHF-band radar]] on the nose of a late-World War II [[Messerschmitt Bf 110|Bf 110]] night fighter aircraft]]
The antenna was invented by [[Shintaro Uda]] of [[Tohoku University|Tohoku Imperial University]], [[Japan]],<ref name="Uda1925" /> in 1926, with a lesser role played by  [[Hidetsugu Yagi]].<ref name="Yagi1926" /><ref name="Sarkar">{{cite book | last1  = Sarkar | first1 = T. K. | last2  = Mailloux | first2 = Robert | last3  = Oliner | first3 = Arthur A.| title  = History of Wireless | publisher = John Wiley and Sons | date = 2006 | pages  = 462–466 | url    = https://books.google.com/books?id=NBLEAA6QKYkC&q=Uda+Yagi&pg=PA465 | isbn = 0471783013 |display-authors=etal |author-link1=Tapan Sarkar |author-link2=Arthur A. Oliner}}</ref>
However, the name ''Yagi'' has become more familiar, while the name of Uda, who applied the idea in practice or established the conception through experiment, is often omitted. This appears to have been due to the fact that Yagi based his work on Uda's pre-announcement<ref name="Uda1925" /> and developed the principle of the absorption phenomenon Yagi had announced earlier.<ref name="Yagi1925">{{cite journal | last1 = Yagi | first1 = Hidetsugu | title = On the Measurement of Natural Frequency of Coils with Ultra-radio Waves | journal = The Journal of the Institute of Electrical Engineers of Japan | volume = 45 | issue = 446 | pages = 783–787 | publisher = The Institute of Electrical Engineers of Japan | language = Japanese |date=September 1925 | url = https://www.jstage.jst.go.jp/article/ieejjournal1888/45/446/45_446_783/_article/-char/en | doi = 10.11526/ieejjournal1888.45.783 | access-date = 3 December 2022 | doi-access = free }}</ref> Yagi filed a patent application in Japan on the new idea, without Uda's name in it, and later transferred the patent to the [[Marconi Company]] in the UK.<ref>{{cite web|url=http://www.sm.rim.or.jp/~ymushiak/sub.hist.corner.htm###|title=Y. Mushiake, '"Notes on the History of Yagi-Uda Antenna."''' IEEE Antennas and Propagation Magazine'', Vol. 56, No. 1, February 2014. pp. 255-257. |publisher=Sm.rim.or.jp |access-date=4 July 2014}}</ref> Incidentally, in the US, the patent was transferred to [[RCA|RCA Corporation]].<ref name="Milestones_1924" />
Yagi antennas were first widely used during [[World War II]] in [[radar]] systems by Japan, Germany, the United Kingdom, and the United States.<ref name="Sarkar" />  After the war, they saw extensive development as home [[television antenna]]s.
==Description==
[[File:Yagi 3 element.svg|thumb|left|Yagi–Uda antenna with a [[passive radiator|reflector]] (''left''), half-wave driven element (''centre''), and [[passive radiator|director]] (''right''). Exact spacings and element lengths vary somewhat according to specific designs.]]
{{Antennas|expanded=Common Types}}
The Yagi–Uda antenna typically consists of a number of parallel thin rod elements, each approximately a half wave in length. Rarely, the elements are discs rather than rods. Often they are supported on a perpendicular crossbar or "boom" along their centers.<ref name="wiseGEEK" />  Usually there is a single dipole [[driven element]] consisting of two collinear rods each connected to one side of the transmission line, and a variable number of [[parasitic element]]s, ''reflectors'' on one side and optionally one or more ''directors'' on the other side.<ref name="wiseGEEK" /><ref name="Balanis" /><ref name="Wolff" />  The parasitic elements are not electrically connected to the transmission line and serve as [[passive radiator]]s, reradiating the radio waves to modify the [[radiation pattern]].<ref name="wiseGEEK" />    Typical spacings between elements vary from about {{frac|1|10}} to {{frac|1|4}} of a wavelength, depending on the specific design. The directors are slightly shorter than the driven element, while the reflector(s) are slightly longer.<ref name="Wolff" />  The [[radiation pattern]] is unidirectional, with the [[main lobe]] along the axis perpendicular to the elements in the plane of the elements, off the end with the directors.<ref name="Balanis" />
Conveniently, the dipole parasitic elements have a [[node (physics)|node]] (point of zero [[radio frequency|RF]] [[voltage]]) at their centre, so they can be attached to a conductive metal support at that point without need of insulation, without disturbing their electrical operation.<ref name="Wolff" /> They are usually bolted or welded to the antenna's central support boom.<ref name="Wolff" /> The most common form of the driven element is one fed at its centre so its two halves must be insulated where the boom supports them.
The gain increases with the number of parasitic elements used.<ref name="Wolff" /> Only one reflector is normally used since the improvement of gain with additional reflectors is small, but more reflectors may be employed for other reasons such as wider bandwidth.  Yagis have been built with 40 directors<ref name="Balanis" /> and more.<ref>''[https://www.arrl.org/files/file/Antenna%20Book%20Supplemental%20Files/23rd%20Edition/Archibald%20VE1FA%20-%20Ultra%20Light%20Yagi%20-%20March%202016%20TCA.pdf]'', VE1FA transatlantic Yagi</ref>
The [[Bandwidth (signal processing)|bandwidth]] of an antenna is, by one definition, the width of the band of frequencies having a gain within 3&nbsp;dB (one-half the power) of its maximum gain. The Yagi–Uda array in its basic form has a narrow bandwidth, 2–3 percent of the centre frequency.<ref name="Wolff" /> There is a tradeoff between gain and bandwidth, with the bandwidth narrowing as more elements are used.<ref name="Wolff" /> For applications that require wider bandwidths, such as [[terrestrial television]], Yagi–Uda antennas commonly feature trigonal reflectors, and larger diameter conductors, in order to cover the relevant portions of the VHF and UHF bands.<ref name=hdtvprimer>[http://www.hdtvprimer.com/antennas/types.html Common TV Antenna Types]</ref> Wider bandwidth can also be achieved by the use of "traps", as described below.
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 circuit|LC]] ([[inductor]] and [[capacitor]]) circuit is inserted. 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. Using a second set of traps, a "triband" antenna can be resonant at three different bands. Given the associated costs of erecting an antenna and [[Antenna rotator|rotator]] system above a tower, the combination of antennas for three amateur bands in one unit is a practical solution. The use of traps is not without disadvantages, however, as they reduce the bandwidth of the antenna on the individual bands and reduce the antenna's electrical efficiency and subject the antenna to additional mechanical considerations (wind loading, water and insect ingress).
==Theory of operation==
[[File:Two meter yagi.jpg|thumb|right|upright=1.2|A portable Yagi–Uda antenna for use at 144&nbsp;MHz (2&nbsp;m), with segments of yellow tape-measure ribbon for the arms of the driven and parasitic elements.]]
Consider a Yagi–Uda consisting of a reflector, driven element, and a single director as shown here. The driven element is typically a [[Dipole antenna#Half-wave antenna|{{frac|1|2}}''λ'' 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, but this mutual coupling is neglected in the following simplified explanation, which applies to [[Near and far field|far-field]] conditions.
One way of thinking about the operation of such an antenna is to consider a parasitic element to be a normal dipole element of finite diameter fed at its centre, with a short circuit across its feed point. The principal part of the current in a loaded receiving antenna is distributed as in a center-driven antenna. It is proportional to the effective length of the antenna and is in [[Phase (waves)|phase]] with the incident electric field if the passive dipole is excited exactly at its resonance frequency.<ref name="King">{{cite book
| last1  = King
| first1 = Ronold W. P.
| title  = The Theory of Linear Antennas
| publisher = Harvard University Press
| date   = 1956
| page  = 568
| isbn   = 9780674182172
}}</ref> Now we imagine the current as the source of a [[power wave]] at the (short-circuited) port of the antenna. As is well known in [[transmission line]] theory, a short circuit reflects the incident voltage 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 up the transmission line back toward the antenna element. If the transmitted voltage wave were 180&nbsp;degrees out of phase with the received wave at that point, the superposition of the two voltage waves would give zero voltage, equivalent to shorting out the dipole at the feedpoint (making it a solid element, as it is). However, the current of the backward wave is in phase with the current of the incident wave. This current drives the reradiation of the (passive) dipole element. At some distance, the reradiated electric field is described by the far-field component of the radiation field of a [[Dipole Antenna#Dipole variations|dipole antenna]]. Its phase includes the propagation delay (relating to the current) and an additional 90&nbsp;degrees lagging phase offset. Thus, the reradiated field may be thought as having a 90&nbsp;degrees lagging phase with respect to the incident field.
Parasitic elements involved in Yagi–Uda antennas are not exactly resonant but are somewhat shorter (or longer) than {{frac|1|2}}''λ'' so that the phase of the element's current is modified with respect to its excitation from the driven element. The so-called ''reflector'' element, being longer than {{frac|1|2}}''λ'', has an inductive [[Electrical reactance|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 phase delay is thus larger than 90&nbsp;degrees and, if the reflector element is made sufficiently long, the phase delay may be imagined to approach 180&nbsp;degrees, so that the incident wave and the wave reemitted by the reflector [[Wave interference|interfere]] destructively in the forward direction (i.e. looking from the driven element towards the passive element). The ''director'' element, on the other hand, being shorter than {{frac|1|2}}''λ'', has a capacitive reactance with the voltage phase lagging that of the current.<ref name="Kraus">{{cite book
| last1  = Kraus
| first1 = John D.
| last2 = Carver
| first2 = Keith R.
| title  = Electromagnetics
| publisher = McGraw-Hill
| date   = 1973
| page  = 681
| isbn   = 9780070353961
}}</ref> The phase delay is thus smaller than 90&nbsp;degrees and, if the director element is made sufficiently short, the phase delay may be imagined to approach zero and the incident wave and the wave reemitted by the reflector interfere constructively in the forward direction.
Interference also occurs in the backward direction. This interference is influenced by the distance between the driven and the passive element, because the propagation delays of the incident wave (from the driven element to the passive element) and of the reradiated wave (from the passive element back to the driven element) have to be taken into account. To illustrate the effect, we assume zero and 180&nbsp;degrees phase delay for the reemission of director and reflector, respectively, and assume a distance of a quarter wavelength between the driven and the passive element. Under these conditions the wave reemitted by the director interferes destructively with the wave emitted by the driven element in the backward direction (away from the passive element), and the wave reemitted by the reflector interferes constructively.
In reality, the phase delay of passive dipole elements does not reach the extreme values of zero and 180&nbsp;degrees. Thus, the elements are given the correct lengths and spacings so that the radio waves radiated by the driven element and those re-radiated by the parasitic elements all arrive at the front of the antenna in-phase, so they superpose and add, increasing signal strength in the forward direction. In other words, the crest of the forward wave from the reflector element reaches the driven element just as the crest of the wave is emitted from that element. These waves reach the first director element just as the crest of the wave is emitted from that element, and so on. The waves in the reverse direction [[destructive interference|interfere destructively]], cancelling out, so the signal strength radiated in the reverse direction is small. Thus the antenna radiates a unidirectional beam of radio waves from the front (director end) of the antenna.
==Analysis==
While the above qualitative explanation is useful for understanding how parasitic elements can enhance the driven elements' radiation in one direction at the expense of the other, the assumption of an additional 90&nbsp;degrees (leading or lagging) phase shift of the reemitted wave is not valid. Typically, the phase shift in the passive element is much smaller. Moreover, to increase the effect of the passive radiators, they should be placed close to the driven element, so that they can collect and reemit a significant part of the primary radiation.
<gallery widths="330px" heights="300px">
Yagi antenna animation 16 frame 1.6s.gif|How the antenna works. The radio waves from each element are emitted with a phase delay, so that the individual waves emitted in the forward direction ''(up)'' are in phase, while the waves in the reverse direction are out of phase. Therefore, the forward waves add together, ([[constructive interference]]) enhancing the power in that direction, while the backward waves partially cancel each other ([[destructive interference]]), thereby reducing the power emitted in that direction.
Yagi en.svg|Illustration of forward gain of a two element Yagi–Uda array using only a driven element (left) and a director (right). The wave (green) from the driven element excites a current in the passive director which reradiates a wave (blue) having a particular phase shift (see explanation in text, note that the dimensions are not to scale with the numbers in the text). The addition of these waves (bottom) is increased in the forward direction, but leads to partial cancellation in the reverse direction.
</gallery>
A more realistic model of a Yagi–Uda array using just a driven element and a director is illustrated in the accompanying diagram. The wave generated by the driven element (green) propagates in both the forward and reverse directions (as well as other directions, not shown). The director receives that wave slightly delayed in time (amounting to a phase delay of about 45° which will be important for the reverse direction calculations later). Due to the director's shorter length, the current generated in the director is advanced in phase (by about 20°) with respect to the incident field and emits an electromagnetic field, which lags (under far-field conditions) this current by 90°. The net effect is a wave emitted by the director (blue) which is about 70° (20°&nbsp;-&nbsp;90°) retarded with respect to that from the driven element (green), in this particular design. These waves combine to produce the net forward wave (bottom, right) with an amplitude somewhat larger than the individual waves.
In the reverse direction, on the other hand, the additional delay of the wave from the director (blue) due to the spacing between the two elements (about 45° of phase delay traversed twice) causes it to be about 160° (70°&nbsp;+&nbsp;2&nbsp;×&nbsp;45°) out of phase with the wave from the driven element (green). The net effect of these two waves, when added (bottom, left), is partial cancellation. The combination of the director's position and shorter length has thus obtained a unidirectional rather than the bidirectional response of the driven (half-wave dipole) element alone.
{{anchor|Mutual_impedance}}
[[File:Zij-en.png|thumb|right|Mutual impedance between parallel <math>\scriptstyle{{\lambda \over 2}}</math> dipoles not staggered as a function of spacing. Curves '''Re''' and '''Im''' are the resistive and reactive parts of the mutual impedance. Note that at zero spacing we obtain the self-impedance of a half-wave dipole, 73&nbsp;+&nbsp;j43&nbsp;Ω.]]
When a passive radiator is placed close (less than a quarter wavelength distance) to the driven dipole, it interacts with the [[near and far field|near field]], in which the phase-to-distance relation is not governed by propagation delay, as would be the case in the far field. Thus, the amplitude and phase relation between the driven and the passive element cannot be understood with a model of successive collection and reemission of a wave that has become completely disconnected from the primary radiating element. Instead, the two antenna elements form a coupled system, in which, for example, the self-impedance (or [[radiation resistance]]) of the driven element is strongly influenced by the passive element. A full analysis of such a system requires computing the ''mutual impedances'' between the dipole elements<ref>Principles of Antenna Theory, Kai Fong Lee, 1984, John Wiley and Sons Ltd., {{ISBN|0-471-90167-9}}</ref> which implicitly takes into account the propagation delay due to the finite spacing between elements and near-field coupling effects. We model element number ''j'' as having a feedpoint at the centre with a voltage ''V''<sub>j</sub> and a current ''I''<sub>j</sub> flowing into it. Just considering two such elements we can write the voltage at each feedpoint in terms of the currents using the mutual impedances ''Z''<sub>ij</sub>:
: <math> V_1 = Z_{11} I_1 +  Z_{12} I_2 </math>
: <math> V_2 = Z_{21} I_1 +  Z_{22} I_2 </math>
''Z''<sub>11</sub> and ''Z''<sub>22</sub> are simply the ordinary driving point impedances of a dipole, thus 73&nbsp;+&nbsp;j43&nbsp;ohms for a half-wave element (or purely resistive for one slightly shorter, as is usually desired for the driven element). Due to the differences in the elements' lengths ''Z''<sub>11</sub> and ''Z''<sub>22</sub> have a substantially different reactive component. Due to reciprocity we know that ''Z''<sub>21</sub> = ''Z''<sub>12</sub>. Now the difficult computation is in determining that mutual impedance ''Z''<sub>21</sub> which requires a numerical solution. This has been computed for two exact half-wave dipole elements at various spacings in the accompanying graph.
The solution of the system then is as follows. Let the driven element be designated 1 so that ''V''<sub>1</sub> and ''I''<sub>1</sub> are the voltage and current supplied by the transmitter. The parasitic element is designated 2, and since it is shorted at its "feedpoint" we can write that ''V''<sub>2</sub>&nbsp;=&nbsp;0. Using the above relationships, then, we can solve for ''I''<sub>2</sub>  in terms of ''I''<sub>1</sub>:
: <math>0 = V_2 = Z_{21} I_1 +  Z_{22} I_2 </math>
and so
: <math>I_2 = - {Z_{21}  \over Z_{22}}  \, I_1 </math>.
This is the current induced in the parasitic element due to the current ''I''<sub>1</sub> in the driven element. We can also solve for the voltage ''V''<sub>1</sub> at the feedpoint of the driven element using the earlier equation:
:<math>\begin{align}
V_1 &= Z_{11} I_1 + Z_{12} I_2 = Z_{11} I_1 - Z_{12}{Z_{21} \over Z_{22}} \, I_1 \\
&= \left( Z_{11} - {Z_{21}^2 \over Z_{22}} \right) I_1
\end{align}</math>
where we have substituted ''Z''<sub>12</sub> = ''Z''<sub>21</sub>. The ratio of voltage to current at this point is the ''driving point impedance Z<sub>dp</sub>'' of the 2-element Yagi:
: <math> Z_{dp}= V_1 / I_1 = Z_{11}  -  {Z_{21}^2  \over Z_{22}}  </math>
With only the driven element present the driving point impedance would have simply been ''Z''<sub>11</sub>, but has now been modified by the presence of the parasitic element. And now knowing the phase (and amplitude) of  ''I''<sub>2</sub> in relation to ''I''<sub>1</sub> as computed above allows us to determine the radiation pattern (gain as a function of direction) due to the currents flowing in these two elements. Solution of such an antenna with more than two elements proceeds along the same lines, setting each ''V''<sub>j</sub>&nbsp;=&nbsp;0 for all but the driven element, and solving for the currents in each element (and the voltage ''V''<sub>1</sub> at the feedpoint).<ref>{{cite book |url=http://www.sm.rim.or.jp/~ymushiak/sub.yubook.htm |title=Yagi-Uda Antenna |author1=S. Uda |author2=Y. Mushiake |publisher=The Research Institute of Electrical Communication, Tohoku University |location=Sendai, Japan |date=1954}}</ref> Generally the mutual coupling tends to lower the impedance of the primary radiator and thus, [[Dipole antenna#Folded dipole|folded dipole]] antennas are frequently used because of their large radiation resistance, which is reduced to the typical 50 to 75 Ohm range by coupling with the passive elements.
[[File:Yagi uda antenna.jpg|thumb|upright|Two Yagi–Uda antennas on a single mast. The top one includes a corner reflector and three stacked Yagis fed in phase in order to increase gain in the horizontal direction (by cancelling power radiated toward the ground or sky). The lower antenna is oriented for vertical polarization, with a much lower resonant frequency.]]
==Design==
There are no simple formulas for designing Yagi–Uda antennas due to the complex relationships between physical parameters such as
* element length and spacing
* element diameter
* performance characteristics: gain and input impedance
However using the above kinds of iterative analysis, one can calculate the performance of a given a set of parameters and adjust them to optimize the gain (perhaps subject to some constraints). Since with an {{math|''n''}} element Yagi–Uda antenna, there are {{math|2''n''&nbsp;−&nbsp;''1''}} parameters to adjust (the element lengths and relative spacings), this iterative analysis method is not straightforward. The mutual impedances plotted above only apply to {{math|''λ''/2}} length elements, so these might need to be recomputed to get good accuracy.
The current distribution along a real antenna element is only approximately given by the usual assumption of a classical standing wave, requiring a solution of [[Hallen's integral equation]] taking into account the other conductors. Such a complete exact analysis, considering all of the interactions mentioned, is rather overwhelming, and approximations are inevitable on the path to finding a usable antenna. Consequently, these antennas are often empirical designs using an element of [[trial and error]], often starting with an existing design modified according to one's hunch. The result might be checked by direct measurement or by computer simulation.
A well-known reference employed in the latter approach is a report published by the United States National Bureau of Standards (NBS) (now the [[National Institute of Standards and Technology]] (NIST)) that provides six basic designs derived from measurements conducted at 400&nbsp;MHz and procedures for adapting these designs to other frequencies.<ref>[http://tf.nist.gov/general/pdf/451.pdf ''Yagi Antenna Design'', Peter P. Viezbicke, National Bureau of Standard Technical Note 688, December 1976]</ref> These designs, and those derived from them, are sometimes referred to as "NBS yagis."
By adjusting the distance between the adjacent directors it is possible to reduce the back lobe of the radiation pattern.
==History==
The Yagi–Uda antenna was invented in 1926 by [[Shintaro Uda]] of [[Tohoku University|Tohoku Imperial University]],<ref name="Uda1925" /> [[Sendai]], [[Japan]], with the guidance of [[Hidetsugu Yagi]], also of Tohoku Imperial University.<ref name="Yagi1926" /> Yagi and Uda published their first report on the wave projector directional antenna. Yagi demonstrated a [[proof of concept]], but the engineering problems proved to be more onerous than conventional systems.<ref name=Brown138>Brown, 1999, p. 138</ref>
Yagi published the first English-language reference on the antenna in a 1928 survey article on short wave research in Japan and it came to be associated with his name. However, Yagi who provided the conception which was originally vague expression to Uda, always acknowledged Uda's principal contribution towards the design which will currently be recognized as the [[reduction to practice]], and if the [[Novelty (patent)|novelty]] is not considered, the proper name for the antenna is, as above, the Yagi–Uda antenna (or array).
[[File:Nakajima J1N1-S Gekko land based night fighter at the Steven F. Udvar-Hazy Center.jpg|thumb|A [[Nakajima J1N]]1-S night fighter with quadruple Yagi radar transceiver antennas]]
The Yagi was first widely used during [[World War II]] for airborne [[radar]] sets, because of its simplicity and directionality.<ref name=Brown138/><ref>Graf, Rudolf F. (June 1959). [https://books.google.com/books?id=0dsDAAAAMBAJ&pg=PA214 "Make Your Own UHF Yagi Antenna".] ''Popular Mechanics'', pp. 144–145, 214.</ref> Despite its being invented in Japan, many Japanese radar engineers were unaware of the design until late in the war, partly due to rivalry between the Army and Navy. The Japanese military authorities first became aware of this technology after the [[Battle of Singapore]] when they captured the notes of a British radar technician that mentioned "yagi antenna". Japanese intelligence officers did not even recognise that Yagi was a Japanese name in this context. When questioned, the technician said it was an antenna named after a Japanese professor.<ref>[https://books.google.com/books?id=MgpWAAAAMAAJ&q=yagi+singapore 2001 IEEE Antennas and Propagation Society International Symposium By IEEE Antennas and Propagation Society. International Symposium.]</ref><ref>{{cite journal |last1=Sato |first1=Gentei |title=A Secret Story About the Yagi Antenna |journal=IEEE Antennas and Propagation Magazine |date=June 1991 |volume=33 |issue=3 |pages=7–18 |doi=10.1109/74.88216 |bibcode=1991IAPM...33R...7S |s2cid=8215383 |url=http://w5sc.org/wp-content/uploads/2020/01/Secret-story-about-Yagi.pdf |access-date=14 October 2022}}</ref><ref group=N>This story is analogous to the story of American intelligence officers interrogating German rocket scientists and finding out that [[Robert Goddard]] was the real pioneer of rocket technology even though he was not well known in the US at that time.</ref>
[[File:ASV Mk II radar transmitter antenna on Bristol Beaufort.jpg|left|thumb|Close-up of Yagi arrays of the [[ASV Mark II radar]] fitted beneath a [[Bristol Beaufort]] aircraft for [[anti-submarine warfare]]]]
A [[Horizontal polarization|horizontally polarized]] array can be seen on many different types of WWII aircraft, particularly those types engaged in maritime patrol, or night fighters, commonly installed on the lower surface of each wing. Two types that often carried such equipment are the [[Grumman TBF Avenger]] carrier-based [[US Navy]] aircraft and the [[Consolidated PBY Catalina]] long range patrol seaplane. Vertically polarized arrays can be seen on the cheeks of the [[P-61]] and on the [[nose cone]]s of many WWII aircraft, notably the [[Lichtenstein radar]]-equipped examples of the German [[Junkers Ju 88]]R-1 [[fighter-bomber]], and the British [[Bristol Beaufighter]] night-fighter and [[Short Sunderland]] flying-boat. Indeed, the latter had so many antenna elements arranged on its back – in addition to its formidable turreted defensive armament in the nose and tail, and atop the hull – it was nicknamed the ''fliegendes Stachelschwein'', or "Flying Porcupine" by German airmen.<ref>[https://books.google.com/books?id=9LVOSdGUGPkC&dq=%22Flying+Porcupine%22&pg=PA5 The Sunderland flying-boat queen, Volume 1 By John Evans, Page 5]</ref> The experimental ''Morgenstern'' German AI VHF-band radar antenna of 1943–44 used a "double-Yagi" structure from its 90° angled pairs of Yagi antennas formed from six discrete dipole elements, making it possible to fit the array within a conical, rubber-covered plywood radome on an aircraft's nose, with the extreme tips of the ''Morgenstern's'' antenna elements protruding from the radome's surface, with an [[NJG 4]] [[Junkers Ju 88|Ju 88]]G-6 of the wing's staff flight using it late in the war for its Lichtenstein SN-2 AI radar.<ref>{{cite web |url=http://www.hyperscale.com/images/aims_48D001%201%20-%203.jpg |title=HyperScale 48D001 Ju 88 G-6 and Mistel S-3C Collection decals  |publisher=Hyperscale.com |access-date=15 April 2012}}</ref>
[[File:Montreal-tower-top.thumb2.jpg|thumb|22{{math|}}0px|A three-element Yagi–Uda antenna used for long-distance ([[skywave]]) communication in the [[shortwave]] bands by an [[amateur radio]] station. The longer ''reflector'' element (''left''), the [[driven element]] (''centre''), and the shorter ''director'' (''right'') each have a so-called ''trap'' (parallel [[LC circuit]]) inserted along their conductors on each side, allowing the antenna to be used on more than one frequency band.]]
After World War II, the advent of [[television broadcasting]] motivated extensive adaptation of the Yagi–Uda design for rooftop television reception in the [[very high frequency|VHF]] band (and later for [[Ultra high frequency|UHF]] television) and also as an [[FM broadcasting|FM radio]] antenna in fringe areas. A major drawback was the Yagi's inherently narrow bandwidth, eventually solved by the adoption of the wideband [[log-periodic dipole array]] (LPDA). Yet the Yagi's higher gain compared to the LPDA makes it the best for [[Broadcast range#Edge-of-range issues|fringe reception]], and complicated Yagi designs and combination with other antenna technologies have been developed to permit its operation over the broad [[Television channel frequencies|television bands]].
The Yagi–Uda antenna was named an [[List of IEEE milestones|IEEE Milestone]] in 1995.<ref name="Milestones_1924">{{cite web |url=https://ethw.org/Milestones:Directive_Short_Wave_Antenna,_1924 |title=Milestones:Directive Short Wave Antenna, 1924 |work=[[Engineering and Technology History Wiki]] |date=December 2022 |publisher=IEEE |access-date=1 December 2022}}</ref>
== See also ==
* [[Antenna (radio)]]
* [[Antenna array]]
* [[Numerical Electromagnetics Code]]
* [[Radio direction finder]]
* [[Radio direction finding]]
==Notes==
{{reflist|group=N}}
==References==
;Citations
{{Reflist}}
;Bibliography
* Brown, Louis (1999). [https://books.google.com/books?id=wpFMWeLmp4cC ''A radar history of World War II: technical and military imperatives'']. CRC Press. {{ISBN|0-7503-0659-9}}
* S. Uda, "High angle radiation of short electric waves".  ''[[Proceedings of the IRE]]'', vol. 15, pp.&nbsp;377–385, May 1927.
* S. Uda, "Radiotelegraphy and radiotelephony on half-meter waves". ''Proceedings of the IRE'', vol. 18, pp.&nbsp;1047–1063, June 1930.
*  J. E. Brittain, Scanning the Past, Shintaro Uda and the Wave Projector, Proc. IEEE, May 1997, pp.&nbsp;800–801.
* H .Yagi, {{doi-inline|10.1109/JPROC.1997.649674|Beam transmission of ultra-shortwaves}}, Proceedings of the IRE, vol. 16, pp.&nbsp;715–740, June 1928.  The URL is to a 1997 IEEE reprint of the classic article.  See also {{doi-inline|10.1109/JPROC.1997.649661|Beam Transmission Of Ultra Short Waves: An Introduction To The Classic Paper By H. Yagi}} by [[David M. Pozar|D.M. Pozar]], in [[Proceedings of the IEEE]], Volume 85,  Issue 11,  Nov. 1997 Page(s):1857–1863.
* "[http://ieee.cincinnati.fuse.net/reiman/05_2004.htm Scanning the Past: A History of Electrical Engineering from the Past]". Proceedings of the IEEE Vol. 81, No. 6, 1993.
* Shozo Usami and Gentei Sato, "[https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=958785 Directive Short Wave Antenna, 1924]". IEEE Milestones, IEEE History Center, IEEE, 2005.
* {{cite journal|title=Conceptualizing engineering as a science: Hidetsugu Yagi as a promoter of engineering research|url=https://repository.kulib.kyoto-u.ac.jp/dspace/handle/2433/250442?locale=en|publisher=Philosophy and History of Science, Kyoto University|author=Toma KAWANISHI|journal=Philosophy and History of Science Studies |issue=14|date=7 April 2020|volume = 14|pages=1–24|doi = 10.14989/250442}}
* {{cite journal |last1=Griffiths |first1=Hugh |title=The Yagi Antenna |journal=IEEE Aerospace and Electronic Systems Magazine |date=1 January 2022 |volume=37 |issue=1 |pages=4–5 |doi=10.1109/MAES.2021.3127141 |publisher=IEEE |s2cid=245708628 |url=https://ieeexplore.ieee.org/document/9670003 |access-date=12 December 2022}}
==External links==
{{Commons category|Yagi-Uda antennas}}
* [http://www.dxzone.com/the-true-story-of-yagi-antenna/ Yagi-Uda antenna History]". History of antenna invention and its patents.
* D. Jefferies, "[http://www.ee.surrey.ac.uk/Personal/D.Jefferies/yagiuda.html Yagi-Uda antennas] {{Webarchive|url=https://web.archive.org/web/20051225230930/http://www.ee.surrey.ac.uk/Personal/D.Jefferies/yagiuda.html |date=2005-12-25 }}". 2004.
* [https://patents.google.com/patent/RU2453955C2/en 'Yagi–Uda emitter used for AESA(active electronically scanned array)' low-frequency radars] patents.google.com
* [http://yagi-uda.com/ Yagi-Uda Antenna]. Simple information on basic design, project and measure of Yagi–Uda antenna. 2008
* [http://www.antenna-theory.com/antennas/travelling/yagi.php Yagi-Uda Antennas] www.antenna-theory.com
* [https://www.wa2ooo.com/yagistrikesback.html Yagi Antenna calculator and computer designs 2020]"
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