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

"hasan schiers" wrote (I'm still waiting for
clarification on your formula, btw)

====================================

There's a mistake in the formula. I copied it incorrectly from my old
notebook.

The wavelength Lambda doesn't come into it. No wonder you asked what
units Lambda is in.

The correct, more simple, formula is -

RadRes = 18 * ( 1 - Cos( 180 * H / ( H + L ) ) ohms,

Where H = Height, L = Length of horizontal section, and the angle is
in degrees.

Your antenna is 45 feet high and 70.8 feet overall length. (It doesn't
matter what the measurement units are. It's just a ratio.)

And so your radiation resistance, at 1/4-wave resonance, is 25.4 ohms,
give or take a few ohms.

The only thing I'm unhappy about is making impedance measurements at
the other end of 55 feet of coax. You need to know the exact Zo and
velocity factor and length of this cable, plus some accurate
calculations. The technique is fraught with error.

Get your hand-held antenna analyser right to the bottom end of the
antenna wire, on the R + jX range, and immediately adjacent to the
focal point of the radials. And hope you don't get interference from
the local, high power, MF broadcast station. But you are already aware
of this and I mention it for the benefit of the lurkers.

I assume you measure SWR only to estimate antenna bandwidth. At the
other end of 55 feet of coax anything can happen to SWR. But if
bandwidth decreases as the number of radials increases then at least
it is going in the right direction. I don't think you will squeeze any
other information out of it.
----
Reg, G4FGQ

Hasan,

If you download program ENDFEED and insert details of your antenna and
ground radials system, you will find the impedances closely agee with
what you actually get. (I'm always very happy when this happens.)

Enter the exact 80-meter band frequency at which you have found your
own antenna to be 1/4-wave resonant. Then slightly prune antenna
height until the program says the antenna is 1/4-wavelength long. Very
likely your antenna horizontal section is sloping.

As a final check, do with the program what you have done with your own
antenna, and subtract the RF ground resistance from the antenna input
resistance to give the radiation resistance. (The radiation
resistance is not displayed by the program although, obviously, it is
used internally.)

The primary purpose of the program is to calculate the L and C values
of three different impedance-matching networks (tuners), which you may
find useful. Radiating efficiency is also calculated and displayed.

Download ENDFEED, an old program of mine, from website below.
----
.................................................. ..........
Regards from Reg, G4FGQ
For Free Radio Design Software go to
http://www.btinternet.com/~g4fgq.regp
.................................................. ..........

Final Measurements:

I added 8 more radials this evening for a total of 16.

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

8 3460 3564 3801 341 40,0 1.2 (at antenna)

16 3524 3580 3800 276 31,0 1.7 (at antenna)

Fo is the resonant freq, 2:1 are the lower and upper 2:1 vswr frequency
points.
BW is the 2:1 SWR Bandwidth in Khz.
Z is the R +/- j impedance read from an MFJ-269 antenna analyzer at the
feedpoint.

Since the radiation resistance of the antenna is known to be 25.4 ohms:

Efficiency with 8 radials: 25.4/40 = 63.5% or ground loss = 1.97 dB
Efficiency with 16 radials: 25.4/31 =81.9% or ground loss = 0.86 dB

Additional info, 2:1 VSWR Bandwidth in Khz:

0 Radials = 580 khz
8 Radials = 341 khz
16 Radials = 275 khz

So, both "traditional" considerations of a 1/4 wave vertical have now been
satisfied:

Increasing the number of radials decreased the feedpoint Z, approaching the
nominal 25.4 ohms radiation resistance of the antenna.

Increasing the number of radials from 0 to 8 to 16, narrowed the bandwidth
from 580 to 341 to 276 khz respectively.

The SWR at resonance is worse with 16 radials than with 0 radials (higher
ground losses mask the reactance at the feedpoint)

16 Radials over very good Iowa black loam yields an efficiency of
approximately 82%, and I see no reason to further increase the number of
radials to recover .86 dB...and of course, it would probably require
doubling the radial number yet again, to 32 to get half way there.

I'm now satisfied that the antenna behaves as expected and that the numbers
are credible, but not absolute.

Time to play on the air some more. So far it is getting out very well.

Thanks to all of you for your input, I've learned a lot by playing. The TLE
on-line calculator is a jewel! EZNEC 4.1 got me in the ballpark. The three
most valuable lessons learned: beware of an unintentional 1/4 wave
transformer (coax); Reg's clever formula for calculating radiation
resistance of an inverted L, using simple trig functions, and 16 radials on
80m are quite sufficient OVER MY TYPE OF SOIL.

....hasan, N0AN

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

If you download program ENDFEED and insert details of your antenna and
ground radials system, you will find the impedances closely agee with
what you actually get. (I'm always very happy when this happens.)

16 radials on
80m are quite sufficient OVER MY TYPE OF SOIL.

...hasan, N0AN

============================

So much for B.L & E !
----
Reg.

OUCH!

(Flame suit on)

"Reg Edwards" wrote in message
...
16 radials on
80m are quite sufficient OVER MY TYPE OF SOIL.

...hasan, N0AN

============================

So much for B.L & E !
----
Reg.

Hassan Schiers wrote:
"--and 16 radials on 80m are quite sufficient over my type of soil."

Glancing at Fig. 2.17 on page 119 of Laport`s "Radio Antenna
Engineering" shows that BL&E would agree.

1000 watts into a 90-degree vertical with 16 radials will produce about
160 mv/m at one mile. Perfection is only about 190 mv/m. 85% should be
close enough to perfection, unless you are a broadcaster or the FCC
enforcing its rules on a broadcaster.

Best regards, Richard Harrison, KB5WZI

Outstanding, Reg. Your formula for Rrad agrees completely with the graph in
Devoldere's book. I will make a special effort to copy the formula down
correctly and put it in the subdirectory of my hard disk that has all your
other programs.

I already figured out the 1/4 wave transformer problem, so I went out in
measured again directly (18" jumper) the feedpoint impedance and got much
more realistic readings.

I recall from reading some of your other posts when people were wringing
their hands about what antenna they could put up in a given circumstance.
You advised the inverted L in the garden. When I started work on this
project (whose goal was a decent DX antenna for 80m), I thought of your
comments on many occasions.

As you noted, I'm doing the 2:1 VSWR bandwidth measurements strictly to look
for the point of diminishing returns on laying the radial field. It is quite
clear at this point that 8 is not quite enough, but 16 should be more than
adequate to get me within 1 dB of the idea.

It has been a fun experiment so far, and an enlightening discussion. Thanks
so much for your formula and other comments. Most helpful.

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

"hasan schiers" wrote (I'm still waiting for
clarification on your formula, btw)

====================================

There's a mistake in the formula. I copied it incorrectly from my old
notebook.

The wavelength Lambda doesn't come into it. No wonder you asked what
units Lambda is in.

The correct, more simple, formula is -

RadRes = 18 * ( 1 - Cos( 180 * H / ( H + L ) ) ohms,

Where H = Height, L = Length of horizontal section, and the angle is
in degrees.

Your antenna is 45 feet high and 70.8 feet overall length. (It doesn't
matter what the measurement units are. It's just a ratio.)

And so your radiation resistance, at 1/4-wave resonance, is 25.4 ohms,
give or take a few ohms.

The only thing I'm unhappy about is making impedance measurements at
the other end of 55 feet of coax. You need to know the exact Zo and
velocity factor and length of this cable, plus some accurate
calculations. The technique is fraught with error.

Get your hand-held antenna analyser right to the bottom end of the
antenna wire, on the R + jX range, and immediately adjacent to the
focal point of the radials. And hope you don't get interference from
the local, high power, MF broadcast station. But you are already aware
of this and I mention it for the benefit of the lurkers.

I assume you measure SWR only to estimate antenna bandwidth. At the
other end of 55 feet of coax anything can happen to SWR. But if
bandwidth decreases as the number of radials increases then at least
it is going in the right direction. I don't think you will squeeze any
other information out of it.
----
Reg, G4FGQ

"Reg Edwards" wrote in message
...

"I assume you measure SWR only to estimate antenna bandwidth. At the
other end of 55 feet of coax anything can happen to SWR. But if
bandwidth decreases as the number of radials increases then at least
it is going in the right direction. I don't think you will squeeze any
other information out of it."

Boy, Reg, that last sentence describes EXACTLY what I have been attempting
to do, squeeze the last bit of information or inference that I can make of
the data collected. Your formula works perfectly for me, giving the same
results on this fancy new calculator. It is formula based (which I am not
used to), so the data entry is backwards from what I'm used to (RPN). Once I
entered your formula into the calculator just as you show it, left to right,
it produced the expected 25.4 ohms. That is one handy formula indeed! Who
knows the boundary limits for its accuracy, (only the creator would know
that), but in the case of my particular antenna, it is right on the money
and agrees with the "book" based graph that gave me the original value of 25
ohms for a 0.16 wavelength high quarter wave inverted L. It's nice to have
convergence!

....hasan, N0AN