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Date: Sat, 13 Jul 2013 12:35:46 +0200
From: Pieter-Tjerk de Boer <ptdeboer@cs.utwente.nl>
To: rsgb_lf_group@blacksheep.org
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Subject: Re: Fwd: Re: LF: VK1OD's analysis of the MiniWhip antenna
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On Fri, Jul 12, 2013 at 12:38:28AM +0200, Stefan Sch=E4fer wrote:

> When thinking about the sketch you recently attached (here attached aga=
in),
> would you agree that here the shape of the probe is not irrelevant? I m=
ean, a
> round plate which is in a horizontal position to ground should cause le=
ss
> potential difference (signal level) then a vertical thin wire with the =
same
> capacity.

No, I think the shape is mostly irrelevant, as long as the size is small
compared to the wavelength.
What is relevant is the average height of the probe, for some suitable
definition of "average".
This was also demonstrated by Roelof by his experiment with a horizontal
and vertical whip, reported on this maillinglist in his mail of July 5th.

> I try to compare it to a TX antenna. I see the TX antenna as a capacito=
r
> against ground. But the imaginary E field lines that go directly to gro=
und are
> "useless", except for reduction of the needed L for resonance. This can=
 be
> described as a fixed capacitor parallel to the loading coil. Ony the fi=
eld
> lines that make a faaaaaaaar way will cause something that is described=
 by a
> radiation resistance.
> So back to the mini whip, the often stated 4 pF must be against "someth=
ing
> useful", which is not the grounded pole. It must catch some of the fiel=
d lines
> of the distant transmitter. And if the E fields of your sketch are from=
 this
> transmitter it must be useful to cross as many as possible of the =E4qu=
ipotential
> lines, i.e. a long thin vertical wire should result in more signal volt=
age as a
> plate near the pole.

It is physically impossible for the probe to cross multiple equipotential
lines.
Each equipotential line corresponds to a different potential. If several
of them were to cross the same piece of metal, there would be a potential
difference, i.e., a voltage, over the metal. That clearly can't be true,
assuming it is a good conductor (and still in the static approximation,
i.e., small compared to the wavelength).
What will happen instead, is that _one_ equipotential line will hit the
probe, and the others will bend around it, just like they bend around the
pole.

Note (or recall) that the electrical field lines are perpendicular to the
equipotential lines.

I (also) find it hard to make the connection between this reasoning about
the mini-whip, and an LF transmit antenna. But I think that is mostly due
to the fact that for the analysis of the mini-whip, we can use the static
approximation (it would in theory work all the way down to DC), and that
won't suffice for considering the radiation efficiency of the transmit
antenna.

Still, there is some analogy. If you put a large grounded conductor near
an LF transmit antenna, you have more capacitance but not more radiation.
Similarly, a large grounded conductor near the mini-whip probe will
increase its capacitance, but it will also distort the field (similar to
how the pole distorts the field), moving the equipotential lines "upward"
and thus putting the probe at a potential closer to ground.

73, Pieter-Tjerk, PA3FWM