Dave Shrader wrote:
Ian White, G3SEK wrote:
Dave Shrader wrote:
If the Yagi is to be tuned for MAXIMUM gain, and that is the
objective, then Ro will be the lowest value at resonance.
That's an interesting assertion. Do you have further evidence for
it?
(Apologies for the delay in replying to this, Dave. I've been away from
the computer for two weeks.)
I've been away from Yagis for many years. But, maximum gain requires
maximum radiation which requires maximum current which requires lowest
radiation resistance. Twenty years ago, or so, Ro of 15 to 20 ohms was
common in high gain Yagis wher Gamma matching was used to raise the
impedance to approximately 50 ohms. A slight reduction in gain allows
Ro of close to 50 ohms.
Kraus, Antennas, McGraw-Hill 1950, Chapter 11 provides the analysis for
a simple 2 element 'Yagi' type array. In written terms, the driving
point, feed point, resistance, ignoring losses, is the radiation
resistance of the driven element minus the ratio of the mutual
impedance to the self impedance of the parasitic elements. Far field
gain is maximized by a term where the input power is divided by the net
impedance of the driven element minus the net impedance contributed by
the parasitic elements.
Conclusion, maximum gain, in any configuration [3 element, 4 element,
etc.], requires lowest Rr produced by highest mutual coupling.
This is stretching a simplified theoretical case, way beyond the point
where it ceases to apply.
I agree that the maximum *theoretical* gain - ignoring losses - is
achieved when the element currents are as high as possible, and the
feedpoint resistance is as low as possible. This also requires that the
element spacing is as close as possible... which leads to the
interesting conclusion that a compact beam should have more gain than a
full-sized one!
In practice, of course, this doesn't happen. The reason is that losses
can *never* be ignored in this particular problem. As the element
currents rise and the feedpoint impedance drops, the I^2*R losses in the
elements and the matching losses to 50R rapidly overtake any theoretical
increase in gain.
This means that high-gain beams with deliberately high element currents
are only a theoretical curiosity. The underlying theory has a valid
place in academic textbooks such as Kraus, but it isn't relevant to
practical antenna engineering. (Even superconducting elements and
matching circuits wouldn't make such antennas practical.)
Also, it isn't correct to apply generalizations about 2- and 3-element
yagis to a long, multi-element yagi. In particular, the first 2 or 3
elements of a long yagi cannot be considered in isolation from all the
other elements.
It is true that gain optimization in multi-element yagis tends to reduce
the feedpoint impedance towards 15-20R, but this is a remote side-effect
of all the other design parameters. A low feedpoint impedance certainly
isn't a desirable design aim in itself, because it leads to significant
matching losses and a reduction in the SWR bandwidth.
Numerous designers have found that when they are getting close to a
gain-optimized design, it is usually possible to raise the feed
impedance back towards 50R by inserting an additional first director
with a very close spacing ahead of the driven element. (This technique
may have been developed after you ceased to take a close interest in
yagi design, Dave.)
The close-spaced first director is mostly an impedance-changing device,
and it has relatively few side-effects on the overall gain and pattern.
With a multi-element yagi, it is usually possible to take out most of
these side-effects in the next round of optimization. The result is a
yagi that can be fed directly from 50R coax (through a balun) which
eliminates matching losses and greatly improves the SWR bandwidth. If
the re-optimization is done well, any decrease in gain is almost
undetectable in simulation, and completely undetectable on the air.
--
73 from Ian G3SEK 'In Practice' columnist for RadCom (RSGB)
http://www.ifwtech.co.uk/g3sek