Hi Dan,
I can see where you've reached your conclusion, but your comment that
"Rudy seems to say..." is a good qualifier.
Let's get back to basics, say with a classic 1/4 WL vertical. The
theoretical impedance against an in infinite ground is 36 ohms. From
free space modeling, one quickly realizes that this is nothing more half
of a free space dipole, which it is. Next, power being fed into the base
is simply: P = I squared X R radiation, at resonance. Very simply, more
current means more power. Now with any radial system, screen, or ground
rod, or counterpoise, that current into the base HAS to come from the
ground system. There can be NO discontinuity here...it's not
electrically possible.
Now let's look at the ELECTRICAL length of a radial. The one given is
that the far end is open-circuited, I think we all agree so far...That
means that for standing wave purposes, current here must be zero (the
wire stops!), so impedance is highest. At the antenna end of the radial,
impedance reaches a minimum at 1/4 ELECTRICAL WL, and increases back to
the reflected maximum at 1/2 ELECTRICAL W/L. Notice please that
ELECTRICAL WL is extended by Vp, same as shortening a PHYSICAL piece of
coax to make a phasing line or tuned stub. To recap this, the impedance
presented at the antenna end of a radial varies from a minimum at 1/4
ELECTRICAL WL to a maximum at 1/2 ELECTRICAL WL. (And multiples of these
lengths, of course).
The error of your conclusion comes from the fact that Rudy is comparing
equal currents INTO the radials, Which means that the POWER into the
antenna is NOT constant. POWER is at a minimum to achieve the fixed
current value at 1/4 WL, and goes to a maximum at 1/2 WL. A verification
is when he increases radial length and the current maximum becomes
greater than at the base of the antenna....more power into the antenna,
more power in the radial standing wave current peak, and more losses.
In our real world, our transmitters/amplifiers are fixed in power
output, not infinitely variable, so as the combined vertical/ground
system impedance goes up, current decreases. Recall, radiated power is P
= I squared X R radiation. This obviously reaches a minimum as the
impedance hits it's maximum, at 1/2 ELECTRICAL WL. Rudy's
summations/conclusions reflect this.
Sorry for being so long-winded.
Brian K8BHZ
On 10/26/2017 11:47 PM, Dan Maguire via Topband wrote:
K8BHZ wrote:
The length to avoid is nothing more than a half wavelength, which translates
the same impedance from end to end
i.e., the high Z open end translates to a high Z antenna base end. This results
in minimum radial current.
I'm not so sure I buy that and I don't think N6LF does either. If you look at the
section "An Explanation for the Dips in Ga" (Part 1, QEX pg 40) in Rudy's
document
http://rudys.typepad.com/files/qex-mar-apr-2012.pdf
you'll find this: ["L" is the variable for radial length]
<quote N6LF>
... For the same current at the feed point, with longer radials the currents are much
higher as we go out from the base. We would expect these higher currents to increase
both E and H-field intensities at ground level under the radials. ... Since the power
dissipation in the soil will vary with the square of the field intensity, it’s
pretty clear why the efficiency takes such a large dip when the radials are too long.
</quote>
So Rudy seems to be saying that the increased loss is due to higher radial
currents, not minimum radial currents.
Below is a different animation, this time showing E-field intensity
as the radial length changes. For this animation the radial height was
10 ft so the dip occurs at ~0.45 WL (frame 9). That corresponds to the
highest radial current and the max E-field.
Dan, AC6LA
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