Contributors to the Wikipedia article on the
Yagi-Uda 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.

One of the best TV fringe area antennas. Article covers methods
of stacking and details of how to obtain correct antenna-receiver
impedance match.

Fig. 1. A five-element Yagi using a 3-conductor,
600 ohm folded dipole. Feed points are in the lower conductor
of the folded dipole.

The emergence of the Yagi antenna as one of the most popular
television receiving antennas for use in the fringes of one
or two-channel 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.

Fig, 2. How the center conductor can be removed
from folded dipole in order to permit its utilization as a connecting
rod in stacking.

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.

Fig. 3. Stacked five-element Yagi antennas
with center conductors removed from folded dipoles and used
to provide half-wave stacking.

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 two-conductor folded dipole has an impedance
of 300 ohms. In a three-conductor folded dipole (Fig. 4C) the
current is reduced to one-third at the feed point and thus the
impedance is raised nine times or to approximately 600 ohms.

Fig. 4. Types of dipole antennas. See text.

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 close-spaced 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.

Fig. 5. Method of choosing correct quarter-wave
transformer to match 600 ohm line to the commonly-used 300 ohm
line.

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 wide-spaced, five-element Yagi can have
a higher impedance than a close-spaced, three-element Yagi.

Fig. 6. Common method of stacking two Yagis
at a half wave. See text for details.

From a practical standpoint and for mechanical considerations,
the cross arm on television receiving Yagis is usually restricted
to a half wave-length, 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 five-element television receiving Yagi
by using one of two types of dipoles. One type is the three-conductor
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 five-element 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 five-element 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.

Fig. 7. (A) Two 3·conductor folds spaced
a one-half 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.

In pursuing this topic, it is first necessary to discuss
the characteristics of the linear quarter-wave transformer.
The characteristics of this quarter-wave 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 quarter-wave 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.

Fig. 8. Characteristic impedance versus spacing
of commonly-used conductors.

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 quarter-wave
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 commonly-used 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.

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).

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 three-conductor 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 tip-to-tip distance of the fold is one half-wave, 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 January 10, 2016/p>