NEC-LIST: A question about yagis raised by Zvi Frank

Dear NEC-list Members,

About a week ago Zvi Frank put out a message looking for a design for
a UHF yagi which would produce a gain of 14 - 15 dBi. The purpose of
this contribution is to point him in the direction of such and to make
a few of comments about it.

In 1966 I produced an extensive design table for yagis of between 3
and 10 elements. It was published in an Australian journal, which
unfortunately is not to be compared with the front page of The New
York Times, and so it became known to only a relative few. However in
1985 it was reprinted in an IEEE publication making it much more
widely available. The reference to that reprinting is IEEE Antennas &
Propagation Society Magazine, Vol. 27, No. 3, pp 11-13, June 1985. It
provides all the yagi design tables which originally appeared in
H. E. Green, "Design Data for Short and Medium Length Yagi-Uda
Arrays", Institution of Engineers, Australia, Electrical Engineering
Transactions Vol. 2, No.1, pp 1-8, March 1966.

This design table relates only to uniform yagi arrays, i.e. arrays in
which all directors have the same length and spacing. However, within
that constraint, the yagis in the table are optimum in the sense that
they produce maximum gain while at the same time having a real input
impedance. Normally these radiation resistances are much less than is
required to conveniently match any readily available transmission
line. This is correctable by using a folded dipole with the
appropriate impedance transformation ratio and the original 1966 paper
also included an easy to use folded dipole design table which covered
all standard tube and rod sizes used in Imperial (inch) unit
countries, of which Australia was then one. However, this was not
included in the A&P Newsletter reprint.

The way in which a uniform yagi works is this. The driven element and
reflector act to launch a wave onto the director string, which acts as
a slow wave structure, off the end of which it is radiated into
space. Since the launcher is not perfect but radiates part of its
input power directly, the pattern produced is the interference between
this direct radiation and that from the slow wave structure. The
upshot of all this though is that once the director string becomes
long enough to support a fully formed travelling slow wave, not much
more gain is to be had by adding more, i.e. the gain is asymptotic
with the number of directors. It is therefore hard to get a gain much
in excess of 14 - 15 dBi with any uniform array, about the figure that
Frank says he wants.

The 1966 table was generated on an IBM 7090 machine, truly a giant for
its day though of trivial capability by modern standards. Although I
did not appreciate it at the time, the process I used was really a
method of moments solution with piecewise sinusoidal basis
functions. At that time Harrington's classic book was still a bit into
the future and little or nothing about moment methods had appeared in
the literature. The formulas I used to generate the off diagonal
(mutual ) terms in the impedance matrix were derived from some work
published by P. S. Carter in 1932! That the solution is a method of
moments solution was demonstrated in a later paper of which I was a
co-author. Unfortunately this too was published in an Australian
journal and has not been reprinted else where. The reference is
N. Longsomboon, H. E. Green and J. D. Cashman, "Numerical Optimisation
of Yagi-Uda Arrays", Proc IREE (Australia), Vol. 38, No. 11, pp
169-176, November 1977.

This paper is interesting as in it we set out to better the gains
obtainable from uniform yagis by allowing the interelement spacings to
vary and not constraining the directors all to have the same
length. The method used was to take a uniform array from the table
previously referred to and use a Nelder and Mead simplex algorithm to
systematically adjust it for improved performance. In this way it is
possible to squeeze 1 - 2 dBi more gain out of the array, largely by
cleaning up its side lobe structure. (It is an interesting example of
the synergy of science to relate that when Nelder and Mead devised
their algorithm they were working at the National Vegetable Research
Station in the United Kingdom.) This paper did not attempt production
of a design table but used a few representative cases as illustrations
of the power of the method. The other thing that was not done was to
investigate the bandwidth over which optimised performance was
maintained; in percentage terms, I suspect that it would be small.

There are, of course, always some imponderables which it is impossible
for anyone producing a design table to know. One is whether the
intending constructor will use rods or tubes (which effects the end
cap capacitance and therefore the effective length of the member) and
another is the sort of central support boom that will be used. The
result is that any array constructed from the table normally needs a
bit of experimental trimming to get quite the stated
performance. However. at least with uniform arrays, this is not
difficult. Experience has shown that if the parasitic elements are
adjusted to achieve the published front-to-back ratio, something close
to the proper settings will have been obtained. The other notable
thing about yagis is the relative insensitivity of the pattern to
small changes in the length of the driven element. It is therefore
possible to tune the driven element to resonance (purely real input
impedance) without upsetting the rest of the array.

I have two last comments. One is that over time things tend to keep
getting re-invented as the contributions of one generation get buried
from the eyes of the next deep in the bowels of the literature. There
must be a lot of useful stuff lying about in various places if we
could only find it. The other concerns the physics of the yagi array,
that it operates as a slow wave structure. None of this is, of course,
brought out in a numerical solution, which just spurts out a series of
highly correct numbers from a machine. A penalty which I believe we
pay for both this increased accuracy and the ability to tackle
problems of a complexity which in former times it would not have been
possible to manage is perhaps a more superficial understanding of
what's actually happening inside the "box".

Maybe all this is a bit more than Zvi Frank was expecting when he put
out his call, but I hope that he and perhaps some others will find it
useful.

Harry E. Green,
Adjunct Research Professor,
Institute for Telecommunications Reseaerch

Tuesday 20 April @ 10.55 am (local time)
Received on Tue Apr 20 1999 - 05:50:27 EDT