The answer is 3 mW.

Any version of EZNEC can be used to do this calculation. The demo
program will yield slightly less accurate results because of the limited
number of segments(*).

I modeled two vertical wires, 1 meter high and 1 mm diameter, spaced 1
km apart, at 20 MHz, over perfect ground. The reported feedpoint
impedance varies with segmentation, from 1.988 - j952.3 ohms at 10
segments/wire to 1.72 - j882 ohms at 100 segments/wire. Accuracy is
likely to degrade with a larger number of segments, since even 100
results in segment length/diameter ratio less than NEC recommendations.
I used 100 segments/wire for the test.

One of the choices in EZNEC of far field strength reporting is in V/m at
1 kW input and 1 km distance. For this antenna, EZNEC reports 300.8 V/m
(RMS) at ground level.

EZNEC also permits setting a fixed power input, so this was set to 1 kW.
The resulting source voltage and current are 21270 V. and 24.12 A.
respectively.

A load of 1.72 + j882 ohms was placed at the base of the second
vertical. EZNEC reports a power of 3.234 mW being dissipated in this load.

Care has to be used when analyzing the current induced in one antenna by
another which is distant using numerical calculations. Errors can occur
due to truncation and other causes when the ratio of distances between
the two antennas is great relative to the segment lengths or to segment
distances within one of the antennas. However, EZNEC gets virtually
identical results when using mixed and double precision NEC-2
calculating engines, which indicates that the limit hasn't been reached
and that numerical problems aren't occurring. (Another check which can
be done is to reduce the distance between antennas by a factor of two.
The power in the load resistance should increase by a factor of four.)

Another critical matter is the setting of the load reactance. The
reactance is many times larger than the resistance, so a slight error in
setting its value will result in a large difference in load current and
therefore load dissipation. For example, if the segmentation is changed
from 100 to 50 segments/wire and no other change is made to the model,
the reported load power becomes 0.3917 watts. The reason is that the
reported source impedance is now 1.756 - j891.4 ohms, while the load is
still 1.72 + j882 ohms. Changing the load to the proper conjugately
matched value of 1.756 + 891.4 ohms returns the load power to the
correct value of 3.24 mW.

All given, I'd trust the reported load power to be easily within 10% of
the theoretically correct value.

(*) Results for 10 segments/wire are 1.988 - j952.3 ohms for the source
impedance, 300.71 V/m field strength at 1 km for 1 kW, and 3.24 mW in a
conjugately matched load impedance in the distant vertical.

Roy Lewallen, W7EL

Roy Lewallen wrote:
. . .
Another critical matter is the setting of the load reactance. The
reactance is many times larger than the resistance, so a slight error in
setting its value will result in a large difference in load current and
therefore load dissipation. For example, if the segmentation is changed
from 100 to 50 segments/wire and no other change is made to the model,
the reported load power becomes 0.3917 watts. . . .

Correction: That should be 0.3917 mW. The error doesn't alter the
conclusion.

Roy Lewallen, W7EL

Roy,

My program requires antenna gains relative to isotropic to be entered.
To help discover where I was going wrong a numerical type program was
needed. Numerical programs do not need the intervention of fallible
human ideas about isotropes, mirror images and ground reflections.

I did not realise that EZNEC has the ability to calculate voltages and
currents induced in elements miles away from the radiating element.

But having the correct answer, I still have a problem. Praps you can
help me to solve it.

Staying with the same example of -

Frequency = 20 MHz.
Tx power = 1000 watts.
Distance = 1 kilometre.
Rx antenna height = 1 metre.
Rx antenna Rin = 1.944 ohms, including wire resistance.
Rx antenna -jXin is not needed.
Field strength = 300 millivolts per metre.

According to You, Terman and other Bibles, Volts induced in the 1
metre high antenna = 300 millivolts.

So we have a generator with open-circuit volts of 300 mV, with an
internal resistance of 1.944 ohms, with an Rx load resistance also of
1.944 ohms (which is in excellent agreement with EZNEC).

From which, power generated in the receiver = 11.6 milliwatts

BUT THIS IS SIX DB GREATER THAN THAT CALCULATED BY EZNEC.

From other considerations, and taking EZNEC's small errors into
account, it is EXACTLY 6.02 dB too large.

THE CALCULATION WOULD BE CORRECT IF THE VOLTAGE INDUCED IN THE
RECEIVING ANTENNA WAS EXACTLY HALF OF THE FIELD STRENGTH.

OR THE FIELD STRENGTH FROM THE 1KW TRANSMITTER WAS EXACTLY HALF OF THE
BIBLICAL VALUE OF 300 mV.

Where or how is the above calculation going wrong? A factor of 2 is
involved somewhere.

Thanks for your time and patience.
----
Reg, G4FGQ.

On Fri, 9 Dec 2005 03:43:27 +0000 (UTC), "Reg Edwards"
wrote:

Where or how is the above calculation going wrong? A factor of 2 is
involved somewhere.

Thanks for your time and patience.

Asking for another chin lifted for the sucker punch? Reggie, this is
precious.

"A factor of 2 is involved somewhere?"

First place I would look is at the coltage actually applied to the
receiver. If the antenna intercepts 1 volt per meter in a 1-meter
antenna, only 0.5 volt is applied to the receiver. The other 0.5 volt is
lost to reradiation in a matched antenna system.

Best regards, Richard Harrison, KB5WZI

Reg Edwards wrote:
Roy,

My program requires antenna gains relative to isotropic to be entered.
To help discover where I was going wrong a numerical type program was
needed. Numerical programs do not need the intervention of fallible
human ideas about isotropes, mirror images and ground reflections.

I did not realise that EZNEC has the ability to calculate voltages and
currents induced in elements miles away from the radiating element.

There's a limit because of numerical precision, which I cautioned about
in my last posting. But this problem is within its capabilities.

But having the correct answer, I still have a problem. Praps you can
help me to solve it.
. . .

Yes, I'm very interested by the apparent contradiction. But I'm also
seemingly getting some contradictory answers -- I'll have something to
offer after I get it sorted out.

Roy Lewallen, W7EL

The reason for the contradiction is that I got the first result of 1
volt for the base of a 1 meter vertical wire above perfect ground in a 1
V/m field by using NEC with a plane wave excitation source which
produced a 1 V/m plane wave field. The 3 mW value I got later for Reg's
model was obtained by generating a 1 V/m field by putting a conventional
source at the base of a second short vertical. And what I've now
determined after a considerable amount of experimentation is:

The current reported by NEC-2 or NEC-4 to be induced in a wire (or the
voltage in its center or between base and ground) by an impinging field
created by another antenna is exactly half the value it is when the same
field is created instead by an NEC plane wave excitation source, when a
ground plane is present. This doesn't occur in free space models, which
seem to produce correct results.

Unless there's some problem with interpreting the meaning of the plane
wave source's field value, it looks like this is a bug in NEC-2 and
NEC-4. I've posted a query on a mailing list frequented by the real
experts at using these programs, and I'll report back what I find out
from them.

We really need a sound theoretical basis for deciding what the value of
induced current or voltage should be, for a final determination of which
answer is right and which is wrong. I'll try to take a good look at that
tomorrow.

But in the meantime, we do know that the field strength generated by a
short vertical with a source at its base is being reported correctly by
NEC. NEC programs have been used very widely for determining induced
currents and field strengths, and my guess is that the plane wave
excitation feature is relatively rarely used, and less so over ground.
Consequently, I'll put my money on the result obtained by exciting a
second antenna to generate the field rather than on the plane wave
excitation source result.

If this conjecture is correct, then I was wrong when I said in an
earlier posting that the voltage at the base of a one meter wire over
ground was one volt when exposed to a one V/m field -- it should be 0.5
volt. I got the 1 volt result by using an NEC plane wave excitation
source -- ironically, after first verifying that I got the known
theoretical result in free space. And my more recent posting giving the
power in Reg's example antenna load as 3 mW rather than 12 is correct.

I'll post more as I find out more.

Roy Lewallen, W7EL

I've received an authoritative answer about NEC plane wave excitation.
When a 1 V/m incident plane wave is specified via a plane wave source
and a ground plane is present, the field strength at all points is 2
V/m, not 1 V/m as I had assumed. The rationale is that the "incident
wave" is reflected by the ground plane, doubling its strength.

The conclusions from this are that:

1. NEC reports that the voltage from the base of a 1 meter electrically
short vertical wire to perfect ground in the presence of a 1 V/m field
is 0.5 volt, not 1 volt as I said in my earlier posting in response to a
question by Reg. I apologize for the error.

2. The power intercepted by the matched dipole in the problem recently
posed by Reg is approximately 3 mW, not 12. The EZNEC calculation I
described, which does not use a plane wave source, is correct. The same
result can be obtained with NEC by using two antennas as in EZNEC, or
with a 212 V/m (peak, equal to 150 V/m RMS) plane wave source which
produces a 300 V/m RMS field at the loaded antenna.

This is a good place to give an additional caution to people using NEC
for calculations. NEC uses peak, not RMS values for all voltages and
currents. Power results will be off by a factor of two or four if a user
mistakenly assumes RMS values. EZNEC uses RMS values throughout. When
Reg posed the dilemma about the factor of four disparity in reported
powers, my first thought was that this was the cause. As it turned out,
it wasn't, but caution is needed. Results should always be given a
reality check, as Reg has done. Any model -- and this doesn't exclude
the mathematical models we often consider "theory" -- can be subject to
many errors, including but not limited to misapplication,
misinterpretation, and limitations of an approximation or numerical
calculation.

Roy Lewallen, W7EL

On Fri, 09 Dec 2005 11:45:32 -0800, Roy Lewallen
wrote:


2. The power intercepted by the matched dipole in the problem recently
posed by Reg is approximately 3 mW, not 12. The EZNEC calculation I
described, which does not use a plane wave source, is correct. The same
result can be obtained with NEC by using two antennas as in EZNEC, or
with a 212 V/m (peak, equal to 150 V/m RMS) plane wave source which
produces a 300 V/m RMS field at the loaded antenna.

To a certain extent, this comes back to a decision about whether
ground reflection contributes to the received power, and you are
saying that NEC assumes it does under plane wave excitation in
presence of a ground plane.

In "running the numbers", I note that the radiation resistance
indicated by NEC for a short dipole in free space is quite different
to that predicted by Kraus for a dipole with uniform current,
(Rr=80*pi()**2(L/Lambda)**2)!

Owen
--

Owen Duffy wrote:
. . .
In "running the numbers", I note that the radiation resistance
indicated by NEC for a short dipole in free space is quite different
to that predicted by Kraus for a dipole with uniform current,
(Rr=80*pi()**2(L/Lambda)**2)!

The only way to achieve uniform current on a short dipole is with large
capacity hats at the ends of the dipole. Otherwise, the current tapers
nearly linearly from a maximum at the center to zero at the ends. If
you'll look closely at Kraus' figure of the short dipole he analyzes,
you'll see that it has capacity hats. Nearly all other authors analyze
just a straight wire which doesn't have those hats, and consequently
linear rather than uniform current distribution. And of course get quite
a different result.

I'll bet you didn't include large capacity hats in your model. I haven't
tried it, but you should get results much closer to Kraus' if you do.
NEC analysis gives radiation resistance very close to theoretical when
analyzing a plain straight wire dipole, but this isn't what Kraus does
in his book. It is interesting, though, to see how much effect the wire
diameter has on the impedance, and that the wire has to be very thin
indeed to approach the theoretical impedance for an infinitesimally thin
dipole.

Roy Lewallen, W7EL