On Thu, 18 Mar 2004 09:04:40 -0600 (CST),
(Richard Harrison) wrote:

Richard Clark wrote:
"How many pF capacitance in your top hat?"

How many degrees in your vertical?
What`s the ground system?
What`s the periphery of your vertical?
What`s the surge impedance of your vertical?
What other loading are you using ?

ON4UN works examples in the 2nd edition of "Low-Band DXing". His
examples happen to have slightly more than 100 pF when there`s no
loading coil. I`ve seen other top loading capacitance values of 100-500
pF.

ON4UN`s capacitance hat, as used with a 40-foot vertical pipe on 160
meters which has a 166-microhenry loading coil at the top, has 43 pF.

XL must equal Xc in the antenna circuit because the antenna must be
resonant to maximize current and radiation.

The 19th edition of the ARRL Antenna Book says on page 6-36:
"For estimating the capacitance of a T antenna made of wires, an
approximation is to use 6 pF per meter for vertical wires, and 5 pF per
meter for horizontal wires." With parallel wires, the total capacitance
must be discounted when the wires are close together.

Best regards, Richard Harrison, KB5WZI

Hi Richard,

I didn't expect any actual, literal, quantitative response from Yuri,
nor from many others than yourself for that matter.

I would offer that this "capacitive" top hat is another one of those
matters taken on faith, and when that faith is disturbed, then heads
bury into the sand.

For one, accepting that a capacitor that encompasses significant
wavelength dimensions is a travesty of logic in its own right. Trying
to maintain that logic is humorous by the contortions of the faithful.

Some of your numbers above are very suspect on the simple computation
of capacitance if we allow that it is done for DC or low frequency
(like 60Hz) AC. Specifically:
ON4UN works examples in the 2nd edition of "Low-Band DXing". His
examples happen to have slightly more than 100 pF when there`s no
loading coil. I`ve seen other top loading capacitance values of 100-500
pF.
This must contain some rather elaborate, undisclosed presumptions that
sorely tax real implementations. I've dwelt on this waiting for
someone to hit the trip wire.

This all began with the innocent observation, obtained through
nebulous sources:
"The last description I saw of a quarter wave antenna was that of a
parallel circuit. Isn`t that basically how a capacity hat shortens an
antenna, by increasing the parallel capacitance?"

It is tempting to equate the large top hat structure to the plate of a
capacitor. It serves such a metaphor so well by abstraction. That
is, a lot of conductive surface (or at least by the suggestion of the
skeleton of a disk) suspended above earth (presumably the other plate
to complete this circuit).

The first and obvious problem is that it is too big to qualify as just
a capacitor. The neophyte typically ignores the caution of not
treating large structures as lumped elements (or vise-versa).

If we were to dismiss this warning entirely, that is proceed as the
neophyte, and employ the DC or low AC analysis of a significantly
sized hat, what would its capacitance be? However, this is getting
the cart before the horse. To this point scribblers to this forum
really don't even consider how much capacitance (still talking this DC
or low AC stuff) a monopole offers. As I have a prospective design
for 40M in mind, I will start it off with a 2.54cM tube, 11.1M tall.
I will then decimate its length to add top hats to return the
structure to its former resonant frequency (7.1MHz). Right out of the
gate at its full height, the whip shows all of 4.99pF to earth around
it. I will crop it 25% to 8.4M (4.80pF); and 45% to 6.15M (4.58pF);
and 67% to 3.66M (4.21pF).

Do we use a solid disk, or a skeleton? The practical problem is no
one builds a solid disk for HF. To obtain that several hundred
picoFarads elevated, say, 10M above earth, would lead to a nightmare
sized disk. Hence surface area plummets and so does this capacitance.
However, for the sake of argument, we will maintain the diameter, but
approximate it through a skeleton of 16 spokes of #8 wire (even here,
far more aggressive than many neophyte's efforts).

Lop off 25% of that radiator and resonance shifts to another, higher
frequency. We can add a top hat to accomplish this, and for that
missing 25% we will find a top hat of 12.5 cM diameter will do this
job. Now how much capacitance does that represent? In this case
0.011pF. How much is missing? In this case 0.19pf about 20 times
more than what the hat offers.

Lop off 45% of that radiator and resonance shifts to an even higher
frequency. We can add a larger top hat to return to that original
frequency, and for that missing 45% we will find a top hat of 2 M
diameter will do this job. Now how much capacitance does that
represent? In this case 0.24pF. How much is missing? In this case
0.41pf (about 2 times more than what the hat offers).

Lop off 67% of that radiator and resonance shifts to an even higher
frequency. We can add a very much larger top hat to return to that
original frequency, and for that missing 67% we will find a top hat of
7 M diameter will do this job. Now how much capacitance does that
represent? In this case1.37pF. How much is missing? In this case
0.78pf (about 2 times less than what the hat offers).

Given the quid pro quo, the numbers reveal a very strong nonlinearity
for a resonance equation that is solidly ratio metric. That is to
say: halve the inductance, then double the capacitance. This can be
observed to occur NOWHERE except by accident at one point (I will
leave this to the student to discover that propitious combination).

This logic of "capacitance" grows even more absurd if one simply takes
Reggie's former blighted thread about the inductance of a dipole and
employs the low frequency capacitance and inductance to discover that
by those values his 40M dipole resonates at 95MHz (unless it is
hanging 4 inches off the ground perhaps).

Giving such values to large structures is a fantasy.

73's
Richard Clark, KB7QHC