"Roy Lewallen" wrote
Sorry, there's no theoretical basis for declaring what the "best balance"
of those parameters is. So there's no theoretical basis for deciding what
the feedpoint impedance will be for the "best balance".
But. . .
If the Yagi impedance is very low, it indicates very strong coupling
between elements and high element currents. This indicates a sharply tuned
antenna which might have high gain if the losses are minimized, but also
narrow bandwidth. This is a common result of trying to squeeze too much
gain from too small an antenna. To understand why, try googling "super
gain" or "supergain" antennas or look this topic up in an antenna text.
If the Yagi impedance is high -- close to that of a dipole -- it means
that there's very little coupling from the driven element to the parasitic
elements. Consequently, the parasitic elements won't have much current
with which to produce fields, and they won't do much. The antenna won't
have much gain relative to a dipole, and its pattern won't be much
different from a dipole.
So while a Yagi having an impedance outside very roughly the 25 - 35 ohm
range can still perform well in one or more respects, you should look
carefully at it to see what tradeoffs have been made.
When we design antennas, we try to optimize the design for desired gain,
F/B, bandwidth. The impedance is secondary consideration, we can match it to
the feedline, but any transformation, matching adds losses. All the
parameters are interdependent and we can always try to aim for the best
desired compromise. In a typical Yagi, as Roy indicated we end up with range
of impedances that are appropriate for particular design.
I realized that Yagi has low impedance and I generally do not like any
matching and introducing unnecessary loses. The way for maximum gain, clean
pattern, great F/B, 50 ohm feedpoint impedance and no matching gizmos to me
was to go Quad and Quad/Yagi element combinations. Quads have higher
impedance and by adding elements, the impedance would drop to around 50
ohms.
My design goals were to in order of priorities: close to 50 ohms impedance,
best possible clean pattern and F/B, broad bandwidth and maximum gain. I
prefer better pattern over max gain. In order to get max gain one can tweak
the design for about +- 1 dB, while differences in major vs. minor lobes can
be in order of 10s dBs, which means much better S/N ratio and capability to
dig weak signals.
The results was series of designs from 3 el Quad, through 5 el. Razor (3Q, 2
Y), to 7 (8, 10 ) element Razors with log cell driven element and quad and
yagi parasitic elements, while achieving 50 ohm feedpoint.
I would not claim that 50 ohm was the indicative of best performance design
and should be considered "rule" for design, but that I managed to optimize
the arrays for best performance and minimum loses while achieving 50 ohms.
Later, when I wanted to further improve the designs or check them in
software modeling (the original designs were done on 2m antenna test range)
and started with 3 el Quad comparison and optimization, the results were off
and I did not get the chance to go back and follow the process in soft and
hard modeling and see where the discrepancies are.
Pictures of my 15m 7 el. stacked Log Razors are at
http://www.k3bu.us/razor_beams.htm
showing the 7 el. design having Yagi Reflector, Quad Reflector, dual Quad
driven log cell, Quad Director and two Yagi directors. Impedance was 50 ohms
and SWR 1:1.1 at the band edges. In real life, the Razors were head and
shoulders above the Yagi variety and helped me to cream bunch of world
records from VE3BMV.
So I guess the lesson is, one can achieve desired compromise and use any of
the design parameters as priority and work around, but there are limitations
as what would be the results. Back to Yagi, as Roy outlined, You could have
50 ohm dipole like Yagi (lousy F/B and gain, but "good" impedance and match)
or great pattern and gain at the price of lower impedance and some lossy
matching, which still outweighs the former.
73 Yuri, K3BU