Frank wrote:
....
Using NEC 2 I found out, the hard way, that maximum pick-up takes place off
the ends of the loop. Given these constraints: With a field strength of
5.5 V/m, the voltage across the 50 Ohm resistor is 0.091 V RMS, or an
antenna factor of 35.1 dB. Within 0.4 dB of Owen's results.


I have modified my EZNEC model to irrradiate the loop from an exciter
dipole at some distance. I have tried it with the exciter at 100m and
200m distance, I get AF=35.69 and 35.72 dB respectively (against 36.1
from the Mathcad model). I note that if you report on the so called near
field values too close to the loop, the results are effected by the loop.

I note that the Matchcad model estimates the inductance slightly higher
than EzNEC, and others have suggested to me that the Lw term in the
Matchcad model is a double up, that the Ll term fully accounts for the
inductance of the loop. Removal of the Lw term results in an AF of
35.8dB, which is closer to the EzNEC prediction.

Has anyone views of whether Lw should not be included?

The currents in my model vary slightly, here is the current report:

Frequency = 7.1 MHz

Wire No. 1:
Segment Conn Magnitude (A.) Phase (Deg.)
1 W4E2 4.0E-6 -137.0
2 4.0E-6 -137.7
3 4.0E-6 -138.1
4 4.0E-6 -138.4
5 4.0E-6 -138.5
6 4.0E-6 -138.4
7 4.0E-6 -138.1
8 4.0E-6 -137.5
9 W2E1 4.0E-6 -136.8

Wire No. 2:
Segment Conn Magnitude (A.) Phase (Deg.)
1 W1E2 4.1E-6 -136.0
2 4.1E-6 -135.1
3 4.1E-6 -134.2
4 4.1E-6 -133.4
5 4.2E-6 -132.5
6 4.2E-6 -131.7
7 4.2E-6 -130.8
8 4.3E-6 -130.0
9 W3E1 4.3E-6 -129.2

Wire No. 3:
Segment Conn Magnitude (A.) Phase (Deg.)
1 W2E2 4.3E-6 -128.4
2 4.3E-6 -127.8
3 4.4E-6 -127.4
4 4.4E-6 -127.2
5 4.4E-6 -127.1
6 4.4E-6 -127.2
7 4.4E-6 -127.4
8 4.3E-6 -127.9
9 W4E1 4.3E-6 -128.5

Wire No. 4:
Segment Conn Magnitude (A.) Phase (Deg.)
1 W3E2 4.3E-6 -129.3
2 4.3E-6 -130.1
3 4.2E-6 -130.9
4 4.2E-6 -131.8
5 4.2E-6 -132.6
6 4.1E-6 -133.5
7 4.1E-6 -134.3
8 4.1E-6 -135.2
9 W1E1 4.1E-6 -136.1



Owen

I have written a deck for NEC2 which uses and incident plane wave as the
excitation scenario.

The deck:

CMSmall square untuned loop
CMEXTENDED THIN WIRE KERNEL USED
CM1. FREE SPACE
CE2. Plane wave excitation
GW 1 9 -0.25 0 1 -0.25 0 1.5 .0007
GW 2 9 -0.25 0 1.5 +0.25 0 1.5 .0007
GW 3 9 +0.25 0 1.5 +0.25 0 1 .0007
GW 4 9 +0.25 0 1 -0.25 0 1 .0007
GE 1
EK
FR 0 1 0 0 7.1
EX 1 1 1 0 90 0 0 0 0 0
LD 4 1 1 1 50 0
GN -1
XQ
EN

I get an antenna factor of 35.8dB/m by multiplying the current in wire
1, seg 1 (the location of the 50 ohm load) by 50 ohms, and taking
-20*log of that voltage.

Owen

PS: This won't work if you are working with one of the original column
formatted Fortran inputs, but it does work with nec2++ (
http://www.si-list.org/NEC_Archives/swindex.html )

It is futile to accept Mathcad or any other program as being the Bible
unless one is sure that the underlying reasoning, by the user, is
correct.

Validity of the results are dependent solely on the user, plus the
possible uncertainty of program bugs.
----
Reg, G4FGQ

Reg Edwards wrote:
It is futile to accept Mathcad or any other program as being the Bible
unless one is sure that the underlying reasoning, by the user, is
correct.

Validity of the results are dependent solely on the user, plus the
possible uncertainty of program bugs.

Well, perhaps the validity of the model, which leads me to...

Reg, I mentioned in an earlier post that I was concerned about the
estimate of the loop inductance. It was suggested to me that the Lw term
that I included because it was in a prof's lecture notes was a double
up, and that the La term sufficiently estimates the inducance of the loop.

Searching the net suggests that there is some degree of black magic or
black art in estimating inductance of such things, and that Grover and
Terman had a view on it, but the formula I used seems to be commonly
used by online calculators and perhaps a more modern view.

Can you (or others) throw any light on the most appropriate formula for
estimation of the inductance of a square loop of about the size in the
model (0.5m sides, ~2mm dia copper wire).

I do recall that you said what I have done is too complicated and it can
be done with a hand calculator... but I would like to find an expression
for the inductance of the loop that will be accepted generally as the
best estimate withing the other constraints of the model and construction.

All constructive help appreciated.

Owen

Owen wrote:
Reg Edwards wrote:

It is futile to accept Mathcad or any other program as being the Bible
unless one is sure that the underlying reasoning, by the user, is
correct.

Validity of the results are dependent solely on the user, plus the
possible uncertainty of program bugs.


Well, perhaps the validity of the model, which leads me to...

Reg, I mentioned in an earlier post that I was concerned about the
estimate of the loop inductance. It was suggested to me that the Lw term
that I included because it was in a prof's lecture notes was a double
up, and that the La term sufficiently estimates the inducance of the loop.

Searching the net suggests that there is some degree of black magic or
black art in estimating inductance of such things, and that Grover and
Terman had a view on it, but the formula I used seems to be commonly
used by online calculators and perhaps a more modern view.

Can you (or others) throw any light on the most appropriate formula for
estimation of the inductance of a square loop of about the size in the
model (0.5m sides, ~2mm dia copper wire).

I do recall that you said what I have done is too complicated and it can
be done with a hand calculator... but I would like to find an expression
for the inductance of the loop that will be accepted generally as the
best estimate withing the other constraints of the model and construction.

All constructive help appreciated.

Owen

Hi, Owen -

I don't know if the following posts will be of any help at all.

Subjects:
Wheeler's 1982 formulas verified
Wheeler's 1982 formulas verified - Wheeler.gif
Another solenoid inductance calculation - Solenoid.zip

group:
alt.binaries.schematics.electronic

Good luck.

John

"Owen" wrote
Reg, I mentioned in an earlier post that I was concerned about the
estimate of the loop inductance.

Owen,

The HF inductance of a square loop is -

L = 0.8 * H * ( Ln( 4 * H / D ) - 1.467 ) microhenries,

where H is length of one side,

and D is diameter of circular conductor,

both dimensions are in metres.

There are half a dozen other formulas which at first appear to be
different from the above but can be mathematically transformed to be
identical. And then there are imperial and metric units.

I got it out of one of one of my old notebooks. It's what I use in my
programs. I think I stole it from Terman. And Terman stole it from
Grover. So it's sure to be accurate enough for anything you are ever
likely to use it for.

It is obviously an approximation because when a large conductor
diameter is comparable with a very short length of side, the
inductance has a negative value.

As a sanity check, compare it with whatever formula you have used up
to now.
----
Reg, G4FGQ

Reg Edwards wrote:
"Owen" wrote

Reg, I mentioned in an earlier post that I was concerned about the
estimate of the loop inductance.


Owen,

The HF inductance of a square loop is -

L = 0.8 * H * ( Ln( 4 * H / D ) - 1.467 ) microhenries,

where H is length of one side,

and D is diameter of circular conductor,

both dimensions are in metres.


Though it looks a little different, that formula will always produce
exactly the same results as the one that I have used.

There are half a dozen other formulas which at first appear to be
different from the above but can be mathematically transformed to be
identical. And then there are imperial and metric units.

I got it out of one of one of my old notebooks. It's what I use in my
programs. I think I stole it from Terman. And Terman stole it from
Grover. So it's sure to be accurate enough for anything you are ever
likely to use it for.

I looked in Terman, but didn't find it, and still can't. I might be blind!

I got it from http://emcsun.ece.umr.edu/new-induct/ but it obviously
shares the same root as yours. They attribute it to Grover.


It is obviously an approximation because when a large conductor
diameter is comparable with a very short length of side, the
inductance has a negative value.

Understood.


As a sanity check, compare it with whatever formula you have used up
to now.

See above. I think you are telling me I should be confident I am sane.
If it was just that easy!

Now I just have to find someone with access to an OATS to measure one of
these things.

Thanks Reg...

Owen