Contributors to the Wikipedia
article on the YagiUda antenna credit Japanese professor Shintaro Uda primarily
for the antenna's development, with Hidetsugu Yagi having played a 'lesser role."
Other sources assign the primary role to Yagi. Regardless, history  and this article's
author, rightly or wrongly, has decreed that this highly popular design be referred
to commonly as the Yagi antenna and not the Uda antenna. I don't recall seeing advertisements
for 'Uda' television or amateur radio antennas. Harold Harris, of Channel Master
Corporation, does a nice job explaining the fundamentals of the Yagi antenna.
The Yagi Antenna
By Harold Harris, Channel Master Corp.
Fig. 1  A fiveelement Yagi using a 3conductor, 600 ohm
folded dipole. Feed points are in the lower conductor of the folded dipole.
Fig, 2  How the center conductor can be removed from folded
dipole in order to permit its utilization as a connecting rod in stacking.
Fig. 3  Stacked fiveelement Yagi antennas with center
conductors removed from folded dipoles and used to provide halfwave stacking.
Fig. 4  Types of dipole antennas. See text.
Fig. 5  Method of choosing correct quarterwave transformer
to match 600 ohm line to the commonlyused 300 ohm line.
Fig. 6  Common method of stacking two Yagis at a half wave.
See text for details.
Fig. 7  (A) Two 3·conductor folds spaced a onehalf wave.
(B) The two folds with center conductor removed preliminary to using conductors
as stacking rods. (C) The two folds used as conventional folded dipoles with the
center conductors used as connecting rods.
Fig. 8  Characteristic impedance versus spacing of commonlyused
conductors.
Fig. 9  (A) Schematic of Fig. 6 with impedance values
included. (B) Schematic showing resultant impedance of two 300 ohm Yagis stacked
using 3/8 inch rods spaced at 3 inches (325 ohms). (C) Schematic and problem: Find
antenna impedance value required to match 300 ohm line when stacked with 3/8 inch
rod spaced at 3 1/4 inches (350 ohms).
One of the best TV fringe area antennas. Article covers methods of stacking and
details of how to obtain correct antennareceiver impedance match.
The emergence of the Yagi antenna as one of the most popular television receiving
antennas for use in the fringes of one or twochannel service areas has been one
of the most interesting antenna developments of the year.
The Yagi antenna was developed by Hidetsugu Yagi, a Japanese physicist, and,
ironically, it found widespread use against the Japanese as a mobile radar antenna
during World War II.
The unique feature of the Yagi antenna is that only one element is driven and
the one or more elements in the field of the driven element are parasitically excited.
Due to length and spacing, these parasitic elements act as directors or reflectors.
The term "Yagi" was originally used to designate any antenna using a parasitic element
but present terminology applies to antennas having two or more parasitic elements.
The success of the Yagi as a television receiving antenna has been somewhat dimmed
by the difficulty involved in stacking commercial models so that the additional
gain contributed by the second bay can be fully realized.
Since the problem lies chiefly with impedances it might be well to review the
characteristics of the various dipoles used in Yagi antennas.
In a simple folded dipole (Fig. 4B) the current divides equally between
the two conductors. Thus, at the feed point only one half the current is flowing
that would flow in a straight dipole being fed with the same power. Since the impedance
varies with the square of the current the reduction of the current by half means
that the impedance is raised four times.
A straight dipole (Fig. 4A) has an approximate impedance of 75 ohms thus
the twoconductor folded dipole has an impedance of 300 ohms. In a threeconductor
folded dipole (Fig. 4C) the current is reduced to onethird at the feed point
and thus the impedance is raised nine times or to approximately 600 ohms.
In the folded dipole using conductors of different diameters (Fig. 4D)
if the driven conductor is the smaller of the two, a larger percentage of the current
flows in the conductor having the greatest diameter. The current at the feed point
is reduced by factors relating to the ratio of the diameters and the spacing between
them.
In any parasitic array the addition of reflectors or directors lowers the antenna
input impedance. In general, each additional parasitic element reduces the impedance
still further. The amount of the reduction depends chiefly on the spacing between
the added element and the fed dipole. It will thus be seen that the use of a straight
dipole in a Yagi array consisting of three or more closespaced elements is not
practical in television receiving applications since in this instance the impedance
might drop to as low as 25 ohms. In most Yagi arrays the addition of more than three
directors no longer affects the impedance adversely since the distance between he
additional director and the driven element is too great for coupling. There is an
advantage to be realized in the form of increased directivity.
The use of a 300 ohm folded' dipole in a television receiving Yagi is preferred
over a straight dipole because the higher input impedance comes close to matching
the popular 300 ohm transmission line.
It must be emphasized that the reduction in antenna impedance depends equally
on spacing and the number of parasitic elements. As a matter of fact, a widespaced,
fiveelement Yagi can have a higher impedance than a closespaced, threeelement
Yagi.
From a practical standpoint and for mechanical considerations, the cross arm
on television receiving Yagis is usually restricted to a half wavelength, particularly
on the low band. This, in turn, means close coupling between the elements and, therefore,
a low impedance results. In most commercial Yagis a dipole having an impedance of
approximately 600 ohms is required. This value is usually obtained in a fiveelement
television receiving Yagi by using one of two types of dipoles. One type is the
threeconductor folded dipole (Fig. 4C) which has an impedance of approximately
600 ohms. The second arrangement utilizes the two diameter folded dipole (Fig. 4D)
which should have a ratio of 3 to 1 in order to provide the desired 600 ohm impedance.
Up to now we have considered some of the problems involved in the design of a
television receiving Yagi. In many cases, however, the gain realized by the fiveelement
Yagi is insufficient for fringe areas. The small amount of gain obtained by adding
more directors is not worthwhile. The most common procedure, then, is to stack these
fiveelement Yagis. It is the specific purpose of this article to point out why,
in most cases, this is an unprofitable and an inefficient procedure. A Yagi that
matches a 300 ohm line as a single bay cannot be stacked and still match a 300 ohm
line unless certain changes are made.
In pursuing this topic, it is first necessary to discuss the characteristics
of the linear quarterwave transformer. The characteristics of this quarterwave
section of parallel wire transmission line are such that it has the property of
matching unlike impedances so that there is no electrical discontinuity in the system
in which it is incorporated. This characteristic is effective only for the frequency
at which the transformer equals one quarter wavelength. The formula for determining
the desired impedance for the quarterwave matching transformer is:
where: Z_{M} is the unknown matching impedance
Z_{I} is the input impedance, and
Z_{O} is the output impedance.
As an example, let's determine what impedance is necessary to match 300 ohms
to 600 ohms in the problem of Fig. 5.
These particular values were chosen for this problem because they are the ones
involved when stacking two Yagis each having an impedance of 300 ohms. The problem
involves the antennas shown in Fig. 6 and its schematic representation with
the values superimposed in Fig. 9A.
Each antenna must have its impedance stepped up to 600 ohms at the junction point
where the 300 ohm line to the set is connected. The two transformed impedances of
600 ohms each are in parallel. Paralleling these impedances gives an impedance of
300 ohms at the junction point, the exact impedance required to match the 300 ohm
transmission line.
At first glance the problem appears simple. It would seem that all that is necessary
is to use two sets of 425 ohm quarterwave matching transformers to stack the two
300 ohm Yagis. However, let us first consider how the characteristic impedance of
parallel wire transmission is determined. The formula is:
Z = 276 log 10 (2S/d)
where: S is the spacing between conductors, and d is the diameter.
In other words, the impedance depends on the diameter and spacing. Bear in mind
that practically every commercial stacked Yagi is claimed to match 300 ohm line
and uses 3/8 or 1/2" tubing for matching bars. These bars are usually spaced 3"
apart. The chart of Fig. 8 shows the characteristics or surge impedances of
the most commonlyused transmission line conductor sizes at various spacings.
In order to stack 300 ohm Yagis it is necessary to use 425 ohm transmission line.
In order to obtain a 425 ohm impedance using 3/8 " line, the spacing should be approximately
6 1/2". In order to get 425 ohms using 1/2" tubing, the spacing should be approximately
10".
Since most commercial television receiving Yagis use 3/8" tubing spaced at 3",
let's check the chart to determine the surge impedance of this line. The chart shows
that the impedance is approximately 325 ohms. The schematic diagram of Fig. 9B
shows that a 325 ohm transformer is tied to each 300 ohm Yagi, resulting in two
parallel impedances of 350 ohms or a net impedance of 175 ohms at the junction point.
Thus, the two single bay Yagis which match the 300 ohm line present a 2 to 1
mismatch under ordinary methods of stacking. Two solutions to this problem are possible.
First, it is possible to use 425 ohm stacking harnesses constructed of wire. Referring
to the chart of Fig. 8, it will be seen that for a 425 ohm line at 3" spacing
#6 wire must be used. Second, the impedance of each Yagi can be lowered so that
the 3/8" matching bars, with their characteristic impedance of 350 ohms, can be
used to present two parallel impedances of 600 ohms.
Schematically, Fig. 9C, the problem is as follows:
If we can lower the impedance of the Yagi to approximately 200 ohms when stacking,
this 200 ohm impedance will be transformed to 600 ohms by the 3/8" tubing matching
bars. The two 600 ohm impedances in parallel result in a perfect 300 ohm match to
the transmission line.
The Channel Master Corp. has achieved these results by means of a mechanical
arrangement. To obtain a total impedance of 300 ohms in a single bay Yagi, a threeconductor
folded dipole is used. The 600 ohm impedance of the element is reduced to 300 ohms
by the proper choice of spacing of the parasitic elements. See Fig. 1.
The bottom section of the fold contains the feed points, for the following reasons.
In stacking this Yagi the impedance is dropped to 200 ohms by removing the center
conductor of the folded element, making it a conventional folded dipole. Since the
tiptotip distance of the fold is one halfwave, the removal of the center conductor
yields a pair of 3/8" quarter wave connecting bars. The same process is repeated
on the other Yagi and a full set of connecting rods is obtained. (Fig. 2) These
are then used to connect the two Yagis as shown in Fig. 3. The result is a
Yagi which provides a perfect match to 300 ohm line either in its single or stacked
version. In this way the full value of stacking is realized and an additional gain
of 3 db is obtained.
Posted March 4, 2020 (updated from original post on 1/10/2016)
