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A Yagi-Uda antenna is familiar as the commonest kind of terrestrial TV antenna to be found on the rooftops of houses. It is usually used at frequencies between about 30MHz and 3GHz, or a wavelength range of 10 metres to 10 cm. (There are some obsessional amateur radio enthusiasts who construct Yagi-Uda antennas for the 80 metre wavelength band. This is rather impractical as spacing them from the ground by more than half a wavelength is difficult.) The rod lengths in a Yagi-Uda are about a half wavelength each, and the spacings of the elements are about 1/3 of a wavelength. This puts the overall sizes of Yagi-Udas in the ranges
freq transverse length length length dimension 3 elements 5 elements 15 elements (lambda/2) 30MHz 5 metres 6 metres 13 metres 47 metres 100MHz 1.5 metres 1.8 metres 3.9 metres 14 metres 300MHz 50 cm 60 cm 1.3 metres 4.7 metres 1GHz 15 cm 18 cm 39 cm 1.4 metres 3GHz 5 cm 6 cm 13 cm 47 cm
From this table one can get a very good idea of the approximate frequency of the link by looking at the antenna from afar.
A diagram of a 7 element Yagi-Uda layout is given here:-
There are three kinds of elements (or rods) mounted on a longitudinal connecting bar or rod. It doesn't matter if this connecting rod conducts, as it is orientated at right angles to the currents in the elements, and to the radiating electric fields; it supports little or no current, and does not contribute to the radiation. It does not matter what it is made of other than that it should have good structural properties. If it is made of conducting metal as are the elements, it can be connected electrically to the directors and to the reflector (but not to the driven element) without disturbing any of the properties of the antenna.
The three types of element are termed the driving element, the reflector(s) and the director(s). Only the driving element is connected directly to the feeder; the other elements couple to the transmitter power through the local electromagnetic fields which induce currents in them. The driving element is often a folded dipole, which by itself would have a driving point impedance of about 300 ohms to the feeder; but this is reduced by the shunting effect of the other elements, so a typical Yagi-Uda has driving point impedance in the range 20-90 ohms.
The maximum gain of a Yagi-Uda is limited to an amount given approximately by the gain of a dipole (1.66 numerical) times the total number of elements. Why is the power gain proportional to the total number of elements? Well, in an end-fire array of N elements the gain is proportional to N. Consider N isotropic sources, all phased such that the field contributions in the end-fire direction from each element all add up in phase in the far field. The field strength (E-field or H-field) of the sum of the phasors will be N times the field from a single element, so the radiated power density, which is proportional to the square of the fields, will be N^2 times larger. However, the total POWER delivered to the N elements will be N times larger than that delivered to a single element, so the power gain in the far field is (N^2)/N = N . Now this argument becomes suspect when the radiation resistance of an element in the array is different from the radiation resistance of an isolated element, for it is the currents in the elements which contribute to the far field strengths. In a longish Yagi-Uda, however, the end elements will not see a very different environment for the addition of an element in the middle of the directors, and the elements in the middle of the directors are not much affected by how long the array may be. Thus, as a rough "rule of thumb", the factor N (which is empirically about right) may be justified theoretically.
Many people believe that the gain of a Yagi-Uda rises proportional to the boom length, rather than the number of elements. These two criteria boil down to the same thing for "sensible element spacings". Clearly, taking the reductio-ad-absurdum of a three element yagi with indefinitely increasing element spacing, the gain will not rise as the spacing is increased, beyond a certain amount. On the other hand, placing a great many elements within a short boom length can plainly be seen not to increase the gain.
Thus, a single element has maximum gain 1.66 = 2.2dBi, a driving element with a single reflector has maximum gain 3.3 (numerical) or 5.2dBi, a three element antenna consisting of a single director, driving element, and reflector has maximum gain about 5 (numerical) or 7dBi and a 15 element Yagi-Uda with 13 directors has maximum gain about 25 (numerical) or 14dBi. There may be compromises in the design to achieve the required front/back ratio, driving point impedance, and bandwidth, so the gains may be somewhat less than these numbers in a practical antenna.
At a meeting of the RSGB at Sandown Park Racecourse on 21 Feb 1999 I looked at a stand advertising a 9 element Yagi-Uda antenna with a stated gain of "11.4 dBd" or 11.4dB over the gain of a single dipole. We note that the array factor for this antenna is limited to the number of elements, in this case 9, and so we would expect the maximum gain to be 10log9 or 9.54 dBd. If we add the gain of the dipole elements over isotropic as about 2.2dBi we are limited in gain to at most 11.8 dBi. So we deduce that the people advertising this antenna were either misinformed, or they didn't appreciate the difference between dBd and dBi.
Of course, a naive comparison between a simple dipole antenna and a Yagi-Uda just substitutes one for the other, and then the "gain" may be measured from some field strength measurements on boresight. However, since the radiation resistances will be different, and recalling that the definition of relative gain is the ratio of radiated power levels in a certain direction produced by two antennas having the same TOTAL ACCEPTED INPUT POWER, there is a potent source of confusion here. This is because the antenna is connected via a feeder to a transmitter whose output level may be determined in terms of the voltage at its terminals. Thus for the same transmitter and feeder, the accepted powers for the two antennas may be quite different. If one assumes they are the same, one makes an error in deducing the gain figure from the field strength measurements.
To broadband a Yagi-Uda, sometimes the individual elements are split into two in an approximation to a primitive "biconical antenna". An example is shown here; this shows part of a UHF television receive Yagi-Uda to cover a fractional bandwidth of around 30 percent. It is vertically polarised.
and here is a horizontally polarised example....
The objective of the design is to make a "travelling wave" structure with currents in the elements all contributing to the far field in the forward direction. The contributions are designed to add up in phase in the forward direction, and to cancel in the reverse direction. The director elements are cut shorter than the driving element, which is itself a little shorter than a half wavelength at the design frequency. The reflector is cut to be about a half wavelength and it is longer than the driving element, and spaced closer than are the directors. The directors present a capacitative impedance, acting like two lengths of open circuit transmission line each a little shorter than a quarter wavelength to a hypothetical generator at the centre formed from the "induced emf" set up by the impinging fields. See the SMITH chart . Similarly, the reflector presents an inductive impedance to a hypothetical emf generator at its centre. The effects of the spacings and the current progressive phase shifts mean that the contributions of the current in the various elements to the radiated fields all add up in phase.
For a closely spaced driving element and parasitic element, isolated from each other as far a electrical conduction currents are concerned, the currents are oppositely directed as can be seen in the discussion on folded dipoles with the folds cut off. As the spacing is increased, the currents remain oppositely directed until when the spacing is a half-wavelength, the contributions to the far field add up in phase in the "endfire direction", as can be seen from the discussion on array antennas.
If the director elements are cut a little short, their self-impedance is capacitative and they have to be spaced a little closer than a half-wavelength in order to maintain equality of phase in the radiation contribution with the wave arriving from the previous director. The currents in successive elements thus roughly have the pattern
....up down up down up down ......
but will all be very nearly equal in magnitude to each other. There is also some progressive phase shift as the wave advances, caused by the fact that the directors are cut short (capacitative).
The field pattern on the yagi directors therefore advances as a travelling wave in the forward direction, with wavelength approximately equal to three director spacings. This can be seen in the table at the top of this page; at 30MHz the wavelength (lambda) is 10 metres so for a 15 element Yagi array, the length given as 47 metres is nearly five wavelengths, or 15 elements divided by 3.
So the travelling wave structure supports a non-attenuating wave in the forward direction, and the currents in the directors are all approximately the same size, although with a progressive phase delay. It is for this reason that, for moderate numbers of elements, the forward gain is proportional to the number of elements.
The reflector has an induced current in it that contributes a wave in the backwards direction that just cancels the backward wave from the driven element. Only a little power is radiated backwards. The net power radiated by the reflector current has to go somewhere, so it appears as a contribution in the forward direction. The length and the spacing of the reflector have a strong influence on the residual backward radiation from the Yagi-Uda. Typically the reflector will be spaced by 1/8 to 1/4 of a wavelength, and the directors by about 1/3 wavelength each.
The array factor gain of a Yagi-Uda is therefore limited to the number of elements, and the element gain is that of a dipole of length about half a wavelength, which is 1.66.
Therefore the maximum gain we can reasonably expect from the Yagi-Uda is 1.66 times the number of elements, over isotropic, (or just a factor [equal to the number of elements] over the gain of a single half-wave dipole).
The properties of a receive-mode Yagi are relatively uncritical. The bandwidth and VSWR preformance matters less than the gain of the antenna and its discrimination against unwanted signals. However, for a transmit Yagi such as is commonly used by Hams and short-wave broadcasters, the accepted power depends critically on getting a good match to the feed. This will vary across the band, and is susceptible to variations in local environment and geometry distortions.
The lore of the Yagi designer has it that the gain of a Yagi is governed more by the overall boom length than by the number of elements. For an HF Yagi, the boom length can be a critical design factor, and the Ham is usually seeking to optimise the forward gain, the front-to-back ratio, and the construction techniques required. Yagis having thick rod elements (in terms of a wavelength) are better-behaved than those made from thin wires.
The gain of a Yagi-Uda is only moderate, but for the frequency range given above it is cheap and relatively simple to build. It is reasonably tolerant to variations in construction, and indeed, many Yagi-Uda designs have been arrived at by cut and try empirical methods. This is why antenna design is often seen as a black art. With proper numerical simulation, useful improvements have been made to the empirical designs. Trade-offs may be made between the various factors, such as bandwidth, impedance, front-to-back ratio, gain, sidelobe performance, and ease of mounting. A vertically polarised Yagi-Uda often is mounted on the top of a vertical conducting mast which, being in the near field, and also polarisation- matched, will modify the electrical properties. There is less of a problem with mounting a horizontally polarised Yagi-Uda.
For moderately long Yagis with several directors, the reflector spacing and size has little effect on the forward gain, providing that there IS a reflector, but being close to the driving element it has a strong effect on the front-to-back ratio and on the driving point impedance of the antenna. The driving element has of course a big effect on the impedance of the structure and it can be tuned to make this impedance nearly real. The directors form the majority of the travelling wave structure and amply repay care in design.
As with all antenna simulation exercises, it is very easy to fall into the trap that one can calculate properties which one cannot reliably measure. It is therefore questionable as to the utility of such calculations at present. There are a large number of parameters to be chosen by the designer; the individual spacings, lengths, and diameters of the elements give three adjustable parameters per element.
There is a fashion in 1999 to write simulation papers (for the academic journals on antennas), which are unsupported in any way by measurements. As a warning to the reader, if you see an antenna design based on simulation only, and unsupported by any experimental verification, it is wise to be very skeptical about its applicability to a real antenna construction, and you should certainly not believe the performance figures it quotes for such an antenna, without investigating the performance further.
There are many published "cookbook" style designs for Yagi-Uda antennas. Often these have been arrived at by empirical "cut-and-try" methods, or else simulations. If one plays around with the lengths and spacings of the elements, using different tube diameters, with, for example, a NEC simulation package one rapidly realises that it is much easier to make a Yagi-Uda structure which has broadside boresight max-gain directions than it is to make an endfire Yagi-Uda. There are many more combinations of parameters which give broadside main beams than give end fire main beams. One deduces from this observation that many, if not most, practical Yagi-Uda antennas do not work "as advertised" or "as desired", particularly if the build process departs from the exact specifications. Caveat emptor!