Interesting observations.

The 2:1 swr points are only being mentioned to show that the bandwidth is
narrowing with increasing number of radials. That makes sense.

What doesn't make sense is the increasing feedpoint Z at resonance in
response to increasing radial numbers. There could be some minor trimming,
but 3 or 4 ohms reactance is probably close enough...the antenna is near
resonance and the resistive component is not likely to change much by
trimming the last 3 or 4 ohms of reactance out. The problem is, I can't
explain the the 65 ohm feedpoint impedance.

Most installations, start with a Z too high (because it includes ground
losses), and as radials are added, the feedpoint Z drops (as the loss
resistance disappears). This is the classical 1/4w ground mounted vertical
case. You know when to stop adding radials when the measured feedpoint
impedance at resonance is equal to the Z of the antenna over a "perfect"
ground.

Another way to accomplish the same thing is to keep adding radials until the
2:1 vswr bandwidth no longer narrows. I think I'm approaching that right
now.

The anomaly I'm trying to deal with is why the feedpoint Z has increased as
I went from 0 to 2, to 4, to 8 radials, when it should have decreased. I
wouldn't care a whit, if the terminal (end point) feedpoint Z was 65 ohms
resistive with no reactive component.

This is a technical element that I want to understand...no further changes
are likely to make any real difference in performance. What is it Johnny
Cochran said, "If the data don't fit, I just won't quit."? vbg

73,

....hasan, N0AN
"Ham op" wrote in message
...
If your antenna is over a PERFECT ground, an EM mirror, then the mutually
coupled impedance between the antenna and it's image antenna gets to be a
bit difficult to calculate or estimate. The Apex and it's image are 80
feet apart. That is 107 degree spacing, and the ends are 77 degrees apart.
The mutual impedance along the length of the antenna changes due to the
difference in phase shift.

Change from perfect reflecting ground to 'real' ground with varying
conductivity and permittivity as a function of length, width and depth and
the problem becomes much more complicated.

Your measurements, in your location, with your installation indicate, to
me, that your 8 radial solution is starting to converge to best solution.
I say this for two reasons. Your 2:1 VSWR bandwidth is narrow and your Z
is approaching 73 ohms.

I would use the eight radial solution and trim the antenna length to your
desired center frequency. Remember, a 2:1 VSWR indicates that 90% of your
energy is going into the antenna.

For the best analysis of your installation, the soil characteristics would
have to be known and controlled for several wavelengths square and
approximately 1/4 wavelength deep. Your radials [counterpoise] are
simplifying and stabilizing your solution.

Roy Llewellen is much better qualified than I to proceed deeper into the
EM Physics regarding all the possible interactions. If the science of
what's happening is your interest then contact Roy off-line [Roy, sorry to
volunteer you without your consent]. If a brief understanding of possible
contributing EM effects is your desire, then I hope this contributes to
your understanding.

Ham Op

hasan schiers wrote:

Question: Where was I taking my measurements.

I started out at the actual feedpoint...then put in about 55' of LMR-400,
and started a new set of measurements in the shack. Here is the latest
data:

Radials 2:1 Fo 2:1 BW Z VSWR @ Fo
0 3340 3522 3920 580 36,0 1.3
2 3354 3524 3774 420 45,0 1.0
4 3419 3533 3741 322 60,1 1.2
8 3445 3550 3742 297 65,4 1.3

The formatting is bad, but in order, left to right:

Number of Radials
Lower 2:1 vswr point
Resonant Freq point
Upper 2:1 point
Bandwidth in kilohertz
Impedance as shown on the MFJ 269 at resonance.

I'm a bit confused by the rising feedpoint impedance with increasing
number of radials. That seems backwards to me.

73,

...hasan, N0AN

VSWR shown by MFJ 269 at resonance
"Ham op" wrote in message
...

At what point in the system are you making your measurements?

hasan schiers wrote:


45' high, 25.8 sloping wire at the top, 29 feet high at the far end. #12
THHN Insulated copper wire, stranded.

Predicted Radiation Resistance: 25.8 ohms, very good ground (rich
pastoral, midwest).

With no radials, I get a flat 50 ohm match at 3595 khz. Obviously this
would indicate ground losses of approximately 25 ohms, if I'm thinking
about this right. Also, predicted efficiency would then be 50 %
(25/(25+25), indicating a 3 dB loss. Forgetting about fresnel region
losses, this seems to be better than I had expected. 2:1 vswr bandwidth
is very broad....broader than what I get with EZnec 4.x with a 25 ohm
load in the base.

This means one of two things to me:

Either my ground losses are much higher than the 25 ohms I'm indirectly
calculating, or I have made some sort of conceptual error in thinking
about what the implications are of a 25 or 26 ohm feedpoint. All my
references point toward a 25 ohm radiation resistance for my 42'
vertical x 25.8 ft inverted L (with sloping top wire instead of flat top
wire). What is wrong with my logic here? If the R(rad) is 25 ohms, and I
measure a flat VSWR (on two other meters) at 3600 khz, then isn't the
remaining 25 ohms, ground loss?

I also show about 37 ohms resistance and 0 ohms reactance at 3600 khz
with my MFJ-269, which is really confusing, in that if I have 25 ohms
for Rrad, then I have 13 ohms of ground losses. Further, 37 ohms is
around 1.3 to 1. So I have two other vswr meters showing 1:1 at 3600,
and the MFJ showing 37 ohms. This is a pretty large percentage
difference.

I would be inclined to believe the 25.8 ohms predicted by both EZnec 4
and the Low Band DX'rs Handbook. In any case, I'll put out 4 radials
tomorrow morning and repeat all my measurements, looking for narrowing
bandwidth and lowered input Z as my ground losses decrease.

Ultimately, I'm going to put down 16, 66' radials, in steps of four,
taking measurements of input Z (mfj-269) and vswr bandwidth for 2:1, at
0,4,8 and 16 radials. I'll report what happens as I go along.

Anywho, without any radials at all there are quite a few distant signals
on 80m this evening, that are consistently louder on the newly
installed inverted L, than on my Carolina Windom at 45'. Most signals as
one pans the band, are louder (at 2 hours after sunset) on the C. Windom
than on the radial-less inverted L, but ones from several states away
are equal or better on the radial-less inverted L. Both seem to make
good sense at this point. I sure will be interested to see the effects
of 4 and then 8 and on up radials, but that is going to take a few days,
because I don't want to make radial changes unless I have access to low
angle signals, which only happens at night or just before sunrise.

Tomorrow is radial day. I will be laying out 4 radials 65' long to begin
with. I have resistance and reactance measurements every 50 khz as a
baseline, before installing radials. 4 in the early morning, 4 more just
before sunset, then 4 more the next morning, and the final 4 the next
evening. #14 THHN stranded insulated copper wire for the radials, btw.

Depending on what I end up seeing for "effect" I'll go to 24 or 32
radials by winter....but only if the improvement is both measurable and
"observable on the air"...radials are a pain in the rear (or more
accurately, the knees) to put in.

What fun!

...hasan, N0AN

Hasan,

I think you are measuring the input impedance of an Inverted-L against
a system of ground radials.

You are trying to estimate the input resistance of the ground radials
by subtracting the CALCULATED radiation resistance of the Inverted-L
from the measured antenna input resistance.

Excellent, there is no better way of doing it!

First of all, the overall length of the antenna must be 1/4-wavelength
resonant at the testing frequency such that its input impedance is
PURELY RESISTIVE. The measured input resistance, of course, will be
greater than the calculated radiation resistance referred to its base.
The difference between them is the required input resistance of the
ground radials.

The hard part of the exercise is calculating the radiation resistance
referred to the base of the Inverted-L. The radiation resistance is a
very complicated function of the dimensions, overall length and
height, of the antenna.

However, for the purposes of estimating ground loss resistance, (it
changes with rainfall and temperature of the season), the following
approximation for radiation resistance is good enough.

RadRes = 18 * ( 1 - Cos( Theta ) ) ohms,

where Theta is an angle = 180 * H / ( H + L ) / Lambda degrees,

H = height of vertical portion of Inverted-L,
L = length of horizontal portion of Inverted-L
and Lambda is the free-space wavelength.

This formula applies ONLY when L+H is 1/4-wave resonant. Which is the
condition under which you are working if you are doing the job
correctly.

You will not find the formula in the books of bible-writer Terman.
Nor in any of the works of the other regular gurus. If you ask from
where it came from, it came from one of my old notebooks and I worked
it out for myself, years back.

Bear in mind it is only an approximation. It would take 6 months to
work out how precisely accurate it is and I don't have the time. But
it's as least as accurate as you can make impedance measurements. I
do hope I have copied it out correctly.

By the way, as the number of your radials increases and the ground
loss resistance gets very low, don't be surprised if you calculate
negative values of ground loss resistance.
----
Reg, G4FGQ

I'm calculating as we speak, thanks tip, I'll see if the numbers line up.
Also, I'm going out to the feedpoint to do some measurements as the 55' of
coax is transforming the impedance at the feedpoint. Gotta beat the
misquitoes, the come in swarms at local sunset. 73

....hasan, N0AN

45 high by 25.8 feet are the antenna dimensions.
BTW is lambda in meters (free space wavelength)? I got something on the
order of 11.28 ohms, but that was with a new calculator that I'm not sure of
the precedence of operations in. Very fancy, but completely backwards from
all the other calcs I had previously owned. No wonder it was cheap.
"Reg Edwards" wrote in message
...
Hasan,

I think you are measuring the input impedance of an Inverted-L against
a system of ground radials.

You are trying to estimate the input resistance of the ground radials
by subtracting the CALCULATED radiation resistance of the Inverted-L
from the measured antenna input resistance.

Excellent, there is no better way of doing it!

First of all, the overall length of the antenna must be 1/4-wavelength
resonant at the testing frequency such that its input impedance is
PURELY RESISTIVE. The measured input resistance, of course, will be
greater than the calculated radiation resistance referred to its base.
The difference between them is the required input resistance of the
ground radials.

The hard part of the exercise is calculating the radiation resistance
referred to the base of the Inverted-L. The radiation resistance is a
very complicated function of the dimensions, overall length and
height, of the antenna.

However, for the purposes of estimating ground loss resistance, (it
changes with rainfall and temperature of the season), the following
approximation for radiation resistance is good enough.

RadRes = 18 * ( 1 - Cos( Theta ) ) ohms,

where Theta is an angle = 180 * H / ( H + L ) / Lambda degrees,

H = height of vertical portion of Inverted-L,
L = length of horizontal portion of Inverted-L
and Lambda is the free-space wavelength.

This formula applies ONLY when L+H is 1/4-wave resonant. Which is the
condition under which you are working if you are doing the job
correctly.

You will not find the formula in the books of bible-writer Terman.
Nor in any of the works of the other regular gurus. If you ask from
where it came from, it came from one of my old notebooks and I worked
it out for myself, years back.

Bear in mind it is only an approximation. It would take 6 months to
work out how precisely accurate it is and I don't have the time. But
it's as least as accurate as you can make impedance measurements. I
do hope I have copied it out correctly.

By the way, as the number of your radials increases and the ground
loss resistance gets very low, don't be surprised if you calculate
negative values of ground loss resistance.
----
Reg, G4FGQ

On Sat, 3 Sep 2005 09:27:52 -0500, "hasan schiers"
wrote:

Question: Where was I taking my measurements.

I started out at the actual feedpoint...then put in about 55' of LMR-400,
and started a new set of measurements in the shack. Here is the latest data:


Radials 2:1 Fo 2:1 BW Z VSWR @ Fo

Hassan,

Where are the radials (above ground, buried, how far)?

I think you told us that they radial wire is insulated, is that
correct?

Why did you choose 66' long radials?

Owen
--

Owen,

Wire is laying on the ground, insulated, as it doesn't make any difference
and lasts longer. 66' is 1/4 wave at 80m which is always a safe starting
point. I probably could shorten them and do more. I intend to put in at
least 8 more for a total of 16.

I found out why the input Z was going up as I put more radials in...I was
measuring at the end of 55' of LMR-400 (as opposed to the measurements I
took when I was outside originally tuning the antenna.), and that was acting
as a 1/4 wave transformer.

I just went outside and connected through an 18 inch jumper to the MFJ-269
and got the following measurements:

2:1 VSWR Low freq Point: 3460 khz
2:1 VSWR Hi freq Point: 3801 khz
2:1 VSWR Bandwidth: 341 khz
Fo (Resonant freq) = 3560 khz, 40 ohms resistive, 0 ohms reactance

3500 32,9 1.6
3550 38,0 1.0
3600 44,9 1.2
3650 52,19 1.4
3700 57,30 1.6
3750 63,35 1.8
3800 69,39 2.0

Above table: freq, R,+/- j, VSWR, all taken from the MFJ-269

If the radiation resistance is 26 ohms and I measure 38 ohms feed impedance
at resonance, then apparently I have 12 ohms of ground loss, for an
efficiency of:

26/(26+12) or 26/38 = 68%

At least, that's where I'm at for the moment. Time for another 8 radials.

That 1/4 wave transformer (55' of LMR-400 between feedpoint and shack) that
Tom, W8JI, pointed out, makes a big difference in my confusion...at least it
all makes sense now.

73,

....hasan, N0AN
"Owen Duffy" wrote in message
...
On Sat, 3 Sep 2005 09:27:52 -0500, "hasan schiers"
wrote:

Question: Where was I taking my measurements.

I started out at the actual feedpoint...then put in about 55' of LMR-400,
and started a new set of measurements in the shack. Here is the latest
data:


Radials 2:1 Fo 2:1 BW Z VSWR @ Fo

Hassan,

Where are the radials (above ground, buried, how far)?

I think you told us that they radial wire is insulated, is that
correct?

Why did you choose 66' long radials?

Owen
--

Reg, et al, yes, you have what I'm doing correctly. I just went out to the
feedpoint and made measurements. Here's what I found. (I'm still waiting for
clarification on your formula, btw)


I found out why the input Z was going up as I put more radials in...I was
measuring at the end of 55' of LMR-400 (as opposed to the measurements I
took when I was outside originally tuning the antenna.), and that was acting
as a 1/4 wave transformer.

I just went outside and connected through an 18 inch jumper to the MFJ-269
and got the following measurements:

2:1 VSWR Low freq Point: 3460 khz
2:1 VSWR Hi freq Point: 3801 khz
2:1 VSWR Bandwidth: 341 khz
Fo (Resonant freq) = 3560 khz, 40 ohms resistive, 0 ohms reactance

3500 32,9 1.6
3550 38,0 1.0
3600 44,9 1.2
3650 52,19 1.4
3700 57,30 1.6
3750 63,35 1.8
3800 69,39 2.0

Above table: freq, R,+/- j, VSWR, all taken from the MFJ-269

If the radiation resistance is 26 ohms and I measure 38 ohms feed impedance
at resonance, then apparently I have 12 ohms of ground loss, for an
efficiency of:

26/(26+12) or 26/38 = 68%

At least, that's where I'm at for the moment. Time for another 8 radials.

That 1/4 wave transformer (55' of LMR-400 between feedpoint and shack) that
Tom, W8JI, pointed out, makes a big difference in my confusion...at least it
all makes sense now.

73,

....hasan, N0AN
"Reg Edwards" wrote in message
...
Hasan,

I think you are measuring the input impedance of an Inverted-L against
a system of ground radials.

You are trying to estimate the input resistance of the ground radials
by subtracting the CALCULATED radiation resistance of the Inverted-L
from the measured antenna input resistance.

Excellent, there is no better way of doing it!

First of all, the overall length of the antenna must be 1/4-wavelength
resonant at the testing frequency such that its input impedance is
PURELY RESISTIVE. The measured input resistance, of course, will be
greater than the calculated radiation resistance referred to its base.
The difference between them is the required input resistance of the
ground radials.

The hard part of the exercise is calculating the radiation resistance
referred to the base of the Inverted-L. The radiation resistance is a
very complicated function of the dimensions, overall length and
height, of the antenna.

However, for the purposes of estimating ground loss resistance, (it
changes with rainfall and temperature of the season), the following
approximation for radiation resistance is good enough.

RadRes = 18 * ( 1 - Cos( Theta ) ) ohms,

where Theta is an angle = 180 * H / ( H + L ) / Lambda degrees,

H = height of vertical portion of Inverted-L,
L = length of horizontal portion of Inverted-L
and Lambda is the free-space wavelength.

This formula applies ONLY when L+H is 1/4-wave resonant. Which is the
condition under which you are working if you are doing the job
correctly.

You will not find the formula in the books of bible-writer Terman.
Nor in any of the works of the other regular gurus. If you ask from
where it came from, it came from one of my old notebooks and I worked
it out for myself, years back.

Bear in mind it is only an approximation. It would take 6 months to
work out how precisely accurate it is and I don't have the time. But
it's as least as accurate as you can make impedance measurements. I
do hope I have copied it out correctly.

By the way, as the number of your radials increases and the ground
loss resistance gets very low, don't be surprised if you calculate
negative values of ground loss resistance.
----
Reg, G4FGQ

On Sat, 3 Sep 2005 09:27:52 -0500, "hasan schiers"
wrote:

Question: Where was I taking my measurements.

I started out at the actual feedpoint...then put in about 55' of LMR-400,
and started a new set of measurements in the shack. Here is the latest data:

Radials 2:1 Fo 2:1 BW Z VSWR @ Fo
0 3340 3522 3920 580 36,0 1.3

Ok, you have figured out the coax transforms the impedance. If indeed
the Z at the generator end of the coax was 36+j0 (ie it was resonant
at that point), then I make the load Z ~ 62-j5.

This will confuse your efforts to infer an effective ground system
impedance, and losses.

Another point to consider, instruments like you are using (in my
experience) are more accurate near to 50+j0, and you may get better
results by bulking up the feedpoint Z with a known fixed resistor to
exploit the better measurement accuracy around 50+j0.

Owen
--

On Sat, 03 Sep 2005 23:49:14 GMT, Owen Duffy wrote:


Ok, you have figured out the coax transforms the impedance. If indeed
the Z at the generator end of the coax was 36+j0 (ie it was resonant
at that point), then I make the load Z ~ 62-j5.

Sorry that should have been 69-j7 (above calc was for one of your
other figures, 40+j0).

Owen
--

On Sat, 3 Sep 2005 09:50:43 -0500, "hasan schiers"
wrote:

I do have correlation now. The vswr meters and the mfj all read the same
resonant frequency now, Wes. See my post that shows the data for 0,2,4,8
radials. While a given absolute value might be in error (a certainty due to
inexpensive instruments), the trend is sound for bandwidth, but a bit
strange for feedpoint impedance. (BW is narrowing but input Z is going up,
with increasing numbers of radials.)

Ideas?

Well, I think that you're expecting the thing to behave just like a
monopole but it's not a monopole.

When I model your configuration (except for insulation) I get a
resonant freq of 3.573 MHz and R = 23.3 ohm over a Mininec Pastoral
ground.

Making it a full height monopole it must be 67' high and the feedpoint
R = 37.

I believe that I read elsewhere that you are taking data at the input
end of a coax line. Unless you have characterized the line and are
backing out its effects you are going to remain mystified.

Also it you have any other antennas in the area that can be an issue.

I'm a believer in modeling but unless -everything- is accounted for,
reality and the model won't correlate.

For example, I have a Cushcraft AV-80 vertical that I've used as a
test bed. This is a 2" diameter, 36' high pipe with four 3' top hat
wires. Cushcraft supplied a base-loading coil, which is not used.
The antenna is ground-mounted on a 16" square aluminum plate with
sixteen 50' radials. Installing radials at this location is a
"sticky" proposition and the soil is best characterized as sand
(decomposed granite actually).

I have measured the base impedance with both an HP8405 Vector
Voltmeter and coax bridge that was calibrated with an open-short-load
(OSL) method as well as a much faster N2PK vector network analyzer,
calibrated the same way. All measurements were taken at the base of
the antenna. This is an on again off again project (currently off)
with the goal of determining the effectiveness of the radial field.

The data are very repeatable and believed to be correct; however, I
cannot construct a model that replicates the physical antenna. For
example the curve on the Smith chart of the measured data has a little
bump in it and the resonant frequency is slightly off from the model.
The "bump" isn't a full-blown resonance loop, but it looks like it's
trying. Here is a plot from 1.5 to 15 MHz. The resonant freq is 5.5
MHz.

http://users.triconet.org/wesandlinda/Vertical_Z.gif

As you can see from the photo, there several other "verticals" in the
vicinity as well as my 45' foot tower with beam and wire dipoles 90'
away.

http://users.triconet.org/wesandlinda/Vertical_4.jpg

Yep! A question remains for modelling. Is the value for Source Data in EZnec
4.x directly correlated to the Rrad? My EZnec model (a modified ARRL
Inverted L with radials), shows:

Frequency = 3.6 MHz

Source 1 Voltage = 25.65 V. at 4.18 deg.
Current = 1 A. at 0.0 deg.
Impedance = 25.58 + J 1.872 ohms
Power = 25.58 watts
SWR (50 ohm system) = 1.958 (25 ohm system) = 1.081

Is that 25.58 ohms the same 25 ohms from the graph of Devoldere's book, or
is it simply a coincidence?

I have attached my *.ez file, if it makes it through the usenet group.


From my other more recent posts on the topic, you can see that I went back
out to the feedpoint with an 18" jumper and remeasured and the results are
quite "traditional".

If one can believe the graph in the latest version of Devoldere's "Low-Band
DXing", an inverted L like mine withe a .16 wavelength vertical portion and
the horizontal or vee'd portion making of the remainder to achieve
resonance, the Rrad should be about 25 ohms. Since the Z at resonance at the
feedpoint with 8 radials 66 feet long shows 38 ohms, it would appear I have
something like 13 ohms of ground return loss. This would represent an
efficiency of 67% or a loss of 1.7 dB. I'm thinking another 8 radials should
get me closer to about 1 dB of loss, at which point, I think I'll be tired
of cutting slits in the lawn. vbg

I did use an on-line TLE calculator to correct for the 55' of LMR-400, and
doing that yielded readings virtually identical to those I measured at the
feedpoint through my 18" jumper.

So, all in all, things worked as they should What got me confused was not
considering that I had a quarter wave transformer after I moved into the
shack to measure, and it was inverting my readings. Made me real queasy
there for a while.

Thanks to all for taking the time to provide ideas and answers. Tom and a
few others caught the 1/4 wave transformer problem...and after all, that was
my real question. I had no doubt that I was seeing an improvment in
efficiency by adding radials (as the 2:1 BW was steadily decreasing with
increasing radials)...I just couldn't get my head around the 60 ohm, ever
increasing values of Z in the shack. All I can say now is, "DUH!"

The sun has set....it's time to make instant switching comparisons between
my 45' high dipole and the new Inverted L. Last night and this morning it
appeared (although I didn't have a lot of data points yet), that stations
1500 km were much stronger on the inverted L than they were on the dipole,
including a 59+ report from an LU early this morning.

Thanks again, Wes (and all the others who commented). It has been fun
working through the process. Now it's time to chase DX.

....hasan, N0AN
"Wes Stewart" wrote in message
...
On Sat, 3 Sep 2005 09:50:43 -0500, "hasan schiers"
wrote:

I do have correlation now. The vswr meters and the mfj all read the same
resonant frequency now, Wes. See my post that shows the data for 0,2,4,8
radials. While a given absolute value might be in error (a certainty due
to
inexpensive instruments), the trend is sound for bandwidth, but a bit
strange for feedpoint impedance. (BW is narrowing but input Z is going up,
with increasing numbers of radials.)

Ideas?

Well, I think that you're expecting the thing to behave just like a
monopole but it's not a monopole.

When I model your configuration (except for insulation) I get a
resonant freq of 3.573 MHz and R = 23.3 ohm over a Mininec Pastoral
ground.

Making it a full height monopole it must be 67' high and the feedpoint
R = 37.

I believe that I read elsewhere that you are taking data at the input
end of a coax line. Unless you have characterized the line and are
backing out its effects you are going to remain mystified.

Also it you have any other antennas in the area that can be an issue.

I'm a believer in modeling but unless -everything- is accounted for,
reality and the model won't correlate.

For example, I have a Cushcraft AV-80 vertical that I've used as a
test bed. This is a 2" diameter, 36' high pipe with four 3' top hat
wires. Cushcraft supplied a base-loading coil, which is not used.
The antenna is ground-mounted on a 16" square aluminum plate with
sixteen 50' radials. Installing radials at this location is a
"sticky" proposition and the soil is best characterized as sand
(decomposed granite actually).

I have measured the base impedance with both an HP8405 Vector
Voltmeter and coax bridge that was calibrated with an open-short-load
(OSL) method as well as a much faster N2PK vector network analyzer,
calibrated the same way. All measurements were taken at the base of
the antenna. This is an on again off again project (currently off)
with the goal of determining the effectiveness of the radial field.

The data are very repeatable and believed to be correct; however, I
cannot construct a model that replicates the physical antenna. For
example the curve on the Smith chart of the measured data has a little
bump in it and the resonant frequency is slightly off from the model.
The "bump" isn't a full-blown resonance loop, but it looks like it's
trying. Here is a plot from 1.5 to 15 MHz. The resonant freq is 5.5
MHz.

http://users.triconet.org/wesandlinda/Vertical_Z.gif

As you can see from the photo, there several other "verticals" in the
vicinity as well as my 45' foot tower with beam and wire dipoles 90'
away.

http://users.triconet.org/wesandlinda/Vertical_4.jpg