## loop inductance

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• Hi group, I here have a loop with the following data: 375 windings of 0.15 mm enamelled copper wire on a 1.35 x 1.35 m wooden square. The windings fill a cross
Message 1 of 18 , Nov 1, 2005
Hi group,

I here have a loop with the following data:

375 windings of 0.15 mm enamelled copper wire on a 1.35 x 1.35 m
wooden square.
The windings fill a cross section of app 4 by 4 mm
'Air core'

Now for the problem:
calculating the inductance gives something like 3 mH
measuring inductance gives 1.5 H

Now this is a bit too big of a difference to believe in.

What would you expect for such a loop? Based on measurement or
calculation? How?

btw: the loop construction is inspired by Renatos minimal ulf
receiver - the one with the geese on vlf.it :-)

thanks for help
Walter
• Hi Walter, well first what frequency was your tester measuring at ?? If this is not remote from the self resonant frequency you will get silly answers. The
Message 2 of 18 , Nov 1, 2005
Hi Walter, well first what frequency was your tester measuring at ?? If this
is not remote from the self resonant frequency you will get silly answers.
The problem is that the loop is not pure inductance

For instance there will be a lot of stray (inter-turn) capacitance. Use
Reg's program for a first estimate of the inductance then measure it, if
possible, at several frequencies or measure the resonant frequency. If you
plot the parallel capacitance and the resonant frequency, you can find the
self resonant frequency, and the get a better feel for it. It looks like the
stray capacitance is cancelling out about 1.5mH at the measurement
frequency. My guess is you dont want a measuring frequency of much more than
1kHz.

Cheers de Alan G3NYK

----- Original Message -----
From: "karula4711" <fedderwi@...>
To: <VLF_Group@yahoogroups.com>
Sent: 01 November 2005 17:50
Subject: [VLF_Group] loop inductance

> Hi group,
>
> I here have a loop with the following data:
>
> 375 windings of 0.15 mm enamelled copper wire on a 1.35 x 1.35 m
> wooden square.
> The windings fill a cross section of app 4 by 4 mm
> 'Air core'
>
> Now for the problem:
> calculating the inductance gives something like 3 mH
> measuring inductance gives 1.5 H
>
> Now this is a bit too big of a difference to believe in.
>
> What would you expect for such a loop? Based on measurement or
> calculation? How?
>
> btw: the loop construction is inspired by Renatos minimal ulf
> receiver - the one with the geese on vlf.it :-)
>
> thanks for help
> Walter
>
>
>
>
>
>
>
>
>
>
>
> Post message: VLF_Group@yahoogroups.com
> Subscribe: VLF_Group-subscribe@yahoogroups.com
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contains all of the days comments. Simply send an e-mail to the list owner
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>
• Walter, Ummm... you have very high permeability air!! Can you send me some?? Like Alan said, the measurement needs to be done at a different frequency. My gut
Message 3 of 18 , Nov 1, 2005
Walter,

Ummm... you have very high permeability air!! Can you send me some??

Like Alan said, the measurement needs to be done at a different
frequency. My gut feeling is that it needs to be done at the power grid
frequency. You are probably picking up a high enough amplitude of 50Hz
energy to upset your instrument's calibration.

I also think you may be better off estimating the inductance based on
resonating the loop with a known value capacitor then looking for
noise "bands" (not discrete frequencies) in the output. Calculate the
inductance based on the resonance roughly centered in the band with the
lowest frequency range.

73,

'Bear' NH7SR
• Hi Alan, ... Thanks for your fast reply. Where to find Reg s program ? Things look much better now that I found a slight ommission in my calculation. Now
Message 4 of 18 , Nov 1, 2005
Hi Alan,

> Use Reg's program for a first estimate

Things look much better now that I found a 'slight ommission'
in my calculation. Now things fit together. The computation of
L gives 0.7 H which is close enuff to the measured value given the
approach used.

The lumped parameter diagram of the loop I used for measuring
was (look at it in a monospaced font)

----------------
| |
L | | -
| - C
R | | |
| |
-------------------

Now R is the resistance of the wire, about 2kO and easy to measure.
the resonant frequency is around 1 kHz, go well below it so you
can forget C, put another R in series with the loop, measure the
voltages across the loop, across the external R, do a little math and
out comes L. :-)
Then go well above the resonant frequency and get C. All this is
proven approach and verified with known L and C components.

The only obstacle was the difference between calculation and
measurement.

But sometimes you need to put the question to the group in order to

Walter
• Hi bear, that was exactly what my stomach *) told me: don t believe this high value of the inductance! But it seems to be right. I found some slight
Message 5 of 18 , Nov 1, 2005
Hi bear,

that was exactly what my stomach *) told me: don't believe this high
value of the inductance!
But it seems to be right. I found some 'slight ommission' in my
calculation which in fact made me disregard most of the flux. So now
that this is corrected the calculation says 0.7 H which is close
enuff given the crude approach I used.

This high value is mostly due to the very thin wire. Close to it's
surface there is lot of flux. If you increase wire diameter this goes
down.

Considering the hi perm air: you missed your chance! We have the
remnants of your last hurricane here now. Didn't you note the
rapid increase in inductance while the hurricane passed along?

Walter

+) don't know if this applies to Americans as well. But Germans
have a feeling about something without knowing exactly they say:
'aus dem Bauch' so your belly tells you what to believe
• Hi bear, that was exactly what my stomach *) told me: don t believe this high value of the inductance! But it seems to be right. I found some slight
Message 6 of 18 , Nov 1, 2005
Hi bear,

that was exactly what my stomach *) told me: don't believe this high
value of the inductance!
But it seems to be right. I found some 'slight ommission' in my
calculation which in fact made me disregard most of the flux. So now
that this is corrected the calculation says 0.7 H which is close
enuff given the crude approach I used.

This high value is mostly due to the very thin wire. Close to it's
surface there is lot of flux. If you increase wire diameter this goes
down.

Considering the hi perm air: you missed your chance! We have the
remnants of your last hurricane here now. Didn't you note the
rapid increase in inductance while the hurricane passed along?

Walter

+) don't know if this applies to Americans as well. But Germans
have a feeling about something without knowing exactly they say:
'aus dem Bauch' so your belly tells you what to believe
• ... OOOOkay, I replaced the spaces by dots due to some fancy formatting Yahoo elects when redisplaying the message. ? Walter
Message 7 of 18 , Nov 1, 2005
>....----------------
>..............|....|
>..........L..|.|...-
>..............|....-.C
>..........R..|.|...|
>..............|....|
>.-------------------

OOOOkay, I replaced the spaces by dots due to some fancy
formatting Yahoo elects when redisplaying the message.

?

Walter
• Walter, Here s the URL for a power grid frequency inductance measuring setup... This is the first
Message 8 of 18 , Nov 1, 2005
Walter,

Here's the URL for a power grid frequency inductance measuring
setup...

<http://www.oz.net/~coilgun/theory/measureinductance.htm>

This is the first time I have ever heard of the flux being higher
close to the surface of a thin wire vs a thicker wire. Sounds like it
might be related to skin effect. Where did you get the info on that??

The hurricane didn't pass close enough to me to notice any increase
in local air permeability. I'll have to keep my eyes open for some
North Pacific storms and have my jar ready <G>

Ayah... "gut feeling" is a fairly common term in the U.S. Those with
more refined sensibilities refer to it as "visceral sensation".

73,

'Bear' NH7SR
• Hi Walter try http://www.btinternet.com/~g4fgq.regp/ I think the program is RJELOOP3 Ah yes there is nothing like trying to explain a problem, even to someone
Message 9 of 18 , Nov 1, 2005
Hi Walter try
http://www.btinternet.com/~g4fgq.regp/
I think the program is RJELOOP3

Ah yes there is nothing like trying to explain a problem, even to someone
yourself !!

Alan

----- Original Message -----
From: "karula4711" <fedderwi@...>
To: <VLF_Group@yahoogroups.com>
Sent: 01 November 2005 17:50
Subject: [VLF_Group] loop inductance

> Hi group,
>
> I here have a loop with the following data:
>
> 375 windings of 0.15 mm enamelled copper wire on a 1.35 x 1.35 m
> wooden square.
> The windings fill a cross section of app 4 by 4 mm
> 'Air core'
>
> Now for the problem:
> calculating the inductance gives something like 3 mH
> measuring inductance gives 1.5 H
>
> Now this is a bit too big of a difference to believe in.
>
> What would you expect for such a loop? Based on measurement or
> calculation? How?
>
> btw: the loop construction is inspired by Renatos minimal ulf
> receiver - the one with the geese on vlf.it :-)
>
> thanks for help
> Walter
>
>
>
>
>
>
>
>
>
>
>
> Post message: VLF_Group@yahoogroups.com
> Subscribe: VLF_Group-subscribe@yahoogroups.com
>
> Members may request the option of receiving just one e-mail per day which
contains all of the days comments. Simply send an e-mail to the list owner
(VLF_Group-owner@yahoogroups.com) requesting digest mode.
>
>
>
>
>
>
• Hi Walter, The inductance of the square loop will be close to L ~= 2 * Mu * N^2 * D * (arcsinh(D/w) - 1) / pi where Mu = 4 * pi * 10^-7 N = Number of turns D =
Message 10 of 18 , Nov 1, 2005
Hi Walter,

The inductance of the square loop will be close to

L ~= 2 * Mu * N^2 * D * (arcsinh(D/w) - 1) / pi

where

Mu = 4 * pi * 10^-7
N = Number of turns
D = length of a side (metres)
w = Wire diameter (metres)
pi = 3.14159

and arcsinh is the inverse hyperbolic sin function.

For N=375, D=1.35, w=0.00015, we get

L ~= 2 * 4 * pi * 10^-7 * 140625 * 1.35 * (9.798 - 1) / pi

~= 1.34 Henries.

--
Paul Nicholson
http://www.abelian.demon.co.uk/
--
• Hello Paul, it s funny. Every day I learn a new coil calculation formula, and they are always different... Being inspired by your own experiments about VLF
Message 11 of 18 , Nov 2, 2005
Hello Paul,
it's funny. Every day I learn a new coil calculation formula, and they are
always different...
ionosphere, on the 23 October at night I recorded my first LEP on the
transmitter of Le Blanc that is at 234 km from my place in Bordeaux
(France).

You can see that at : http://www.enseirb.fr/~alves/LEP23oct05_20h26UTC.jpg

The software is the demo version of skypipe, so I used the soundcard of my
laptop.

I used a tuned 1500 turns home made ferrite coil, a upconverter to 3.5 MHz
and an home made direct conversion receiver...It works good and I can tune
from 7 to 20 kHz, I can even here Alpha but I have to go out from the
buildings (Yes I'm in the city center !)

Thanks, from Thierry.
• hello everyone, i would like to know if someone is using the raven software from the cornell university, especially the mac version, eventually some report.
Message 12 of 18 , Nov 2, 2005
hello everyone,
i would like to know if someone is using the raven software from the
cornell university, especially the mac version, eventually some
report.

thanks!

fg
--
Flavio Gori
NASA - INSPIRE Project, Inc.
European Coordinator
http://image.gsfc.nasa.gov/poetry/inspire

http://www.LoScrittoio.it
Edizioni in Rete
LoScrittoio.it@...

American Geophysical Union (A.G.U.) Member

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• ... Bear, sorry for this late answer. ... Not skin effect. Take a long straight wire carrying some current I. The ring integral of H around the wire (for
Message 13 of 18 , Nov 5, 2005
--- In VLF_Group@yahoogroups.com, "Michael Hebert" <qrpbear@y...> wrote:
>
Bear,

>This is the first time I have ever heard of the flux being higher
> close to the surface of a thin wire vs a thicker wire.

Not skin effect. Take a long straight wire carrying some current I.

The ring integral of H around the wire (for instance on a circular
path) equals I.
Now do this calculation just outside the wire. Thin wire -> less
way round it, but integral has to be the same -> H increases. Look at
Paul Nicholsons formula for L. It contains the wire diameter for
exactly this reason. Every basic text book on Maxwells has the pictures
and formulas.

Don't mix things. The field we talk about is the one generated by the
current in the wire. If you place the loop into some field coming from
elsewhere (and leave the ends open) there is no concentration of flux
close to thin wires or something like that.

Walter
• Walter, I must admit that I am still confused about the idea of flux being higher close to the surface of thin vs thick wire. The strength of the field
Message 14 of 18 , Nov 6, 2005
Walter,

I must admit that I am still confused about the idea of flux being
higher close to the surface of thin vs thick wire. The strength of
the field developed around the wire is related to the current through
the wire whether the current is steady-state or time-varying. Since a
thin wire has a higher resistance vs a thick wire the thicker wire
should be capable of generating a stronger field. Or, conversely,
delivering a greater current into a given load resistance when
exposed to a time-varying magnetic field.

BTW, an inconclusive but interesting experiment conducted last
night...

I tried taping a sheet of CoNetic mumetal material to the inside
surface of a portion of one of my degaussing coil loops following the
curvature of the loop. The loop turns running across the center of
the long dimension of the sheet (roughly 10" X 15" and .003" thick).
There was an approximately 20% increase in signal strength noted with
the sheet in place vs without it. This makes me curious about the
potential performance of a loop constructed in the manner of Renato's
Minimal ELF Loop but with a layer or two of Metglas placed in the
wire-duct channel before the wire is added. The Metglas would have to
be insulated from itself to avoid creating a shorted turn but that is
easy to do. Of course it is also possible that the increase was due
to the sheet acting as one plate of a capacitor.

BTW #2... I am convinced of the virtue of using a balanced input
instrumentation amps vs an OP27 C2V converter show a significant
reduction (on the order of 20+dB) in the level of even order
harmonics of the power grid. I suspect the same principle would apply
in conjunction with voltage-probe sensors. In any case, the odd order
harmonics tend to be cleaner and easier to deal with than the even
order garbage.

73,

'Bear' NH7SR
• ... Imagine two straight wires having round cross sections and the second wire having twice the diameter of the first. Further imagine there are equal currents
Message 15 of 18 , Nov 6, 2005
Michael Hebert wrote:

>I must admit that I am still confused about the idea of flux being
>higher close to the surface of thin vs thick wire. The strength of
>the field developed around the wire is related to the current through
>the wire whether the current is steady-state or time-varying. Since a
>thin wire has a higher resistance vs a thick wire the thicker wire
>should be capable of generating a stronger field. Or, conversely,
>delivering a greater current into a given load resistance when
>exposed to a time-varying magnetic field.
>
>
Imagine two straight wires having round cross sections and the second
wire having twice the diameter of the first. Further imagine there are
equal currents flowing along those wires. Outside the wires the magnetic
fields' intensities vary according to exactly the same rule (which is
inversely proportional with the distance between center axis of the
wire and the location of the measurement). With regard to the magnetic
field the two wires differ only in the fact that a measurement can be
taken closer to the wire's center axis with the thinner wire only and
that means that the field strength at the surface is greater with the
thinner wire.

Peter
• Thanks, Peter, a picture in words makes all the difference 73, Bear NH7SR
Message 16 of 18 , Nov 6, 2005
Thanks, Peter, a picture in words makes all the difference <G>

73,

'Bear' NH7SR
• ... Peter, The wording of your explination implies that if it were possible to make a magnetic field strength reading inside the thicker wire, then it would be
Message 17 of 18 , Nov 10, 2005
--- In VLF_Group@yahoogroups.com, Peter Schmalkoke
<peter.schmalkoke@a...> wrote:
>
> Imagine two straight wires having round cross sections and the second
> wire having twice the diameter of the first. Further imagine there are
> equal currents flowing along those wires. Outside the wires the magnetic
> fields' intensities vary according to exactly the same rule (which is
> inversely proportional with the distance between center axis of the
> wire and the location of the measurement). With regard to the magnetic
> field the two wires differ only in the fact that a measurement can be
> taken closer to the wire's center axis with the thinner wire only and
> that means that the field strength at the surface is greater with the
> thinner wire.
>
> Peter
>

Peter,
The wording of your explination implies that if it were possible to
make a magnetic field strength reading inside the thicker wire, then
it would be the same in the middle of the twice as thick wire as it is
at the surface of the thinner wire.

This is not true, as the behavior the magnetic field vs. distance
inside the condutor is different from that outside the conductor.
Ampere's Law states that the magnetic field intensity is proportional
to the ENCLOSED current. Inside the conductor, not all of the current
is enclosed. Therefor the magnetic field inside the larger conductor
will be less than that in the smaller conductor, even for the same
distance from the center of the conductor (outside the conductor H is
proportional to 1/r, while inside the conductor it is proportional to
r/(R^2), where r is the distance from the center of the conductor and
R is the radius of the conductor (and a constant for a given
conductor) - note that the two equations produce equal answers at the
surface of the conductor).

, one with radius 2, and one with radius 4) and five distances (.5, 1,
2, 4, and 8). Then, sellect a current that produces unity H field at
the surface of the smallest conductor (2pi/uo). The data below (why
can't we insert a table) shows the relative H field at the five locations.

___ r = 0.5 ___ H = 0.5 (inside wire)
___ r = 1.0 ___ H = 1.0 (surface of wire)
___ r = 2.0 ___ H = 0.5 (outside wire)
___ r = 4.0 ___ H = 0.25
___ r = 8.0 ___ H = 0.125

___ r = 0.5 ___ H = 0.125
___ r = 1.0 ___ H = 0.25 (inside wire)
___ r = 2.0 ___ H = 0.5 (surface of wire)
___ r = 4.0 ___ H = 0.25 (outside wire)
___ r = 8.0 ___ H = 0.125

___ r = 0.5 ___ H = 0.03125
___ r = 1.0 ___ H = 0.0625
___ r = 2.0 ___ H = 0.125 (inside wire)
___ r = 4.0 ___ H = 0.25 (surface of wire)
___ r = 8.0 ___ H = 0.125 (outside wire)

From this it becomes obvious that not only is the H field more intense
at the surface of the smaller wires, but also the peak H field
intensity never gets as high inside a larger wire as it is at the
surface of a smaller wire.

(ok, a pictures worth a thousand words, after typing all this, found
these two web pages that illustrates most of the above...
http://www.phys.uri.edu/~gerhard/PHY204/tsl243.pdf
http://www.phys.uri.edu/~gerhard/PHY204/tsl244.pdf
Notice the graph on the second page showing linier increase insider
wire and 1/r decrease outside of wire. Also looks like may H's should
have been B's).

ddd
• ... I do absolutely agree with you, ddd. I didn t mean to make any statement about the magnetic field inside the conductor, but apparently forgot to emphasize
Message 18 of 18 , Nov 10, 2005
vlf_ddd wrote:

> Peter,
> The wording of your explination implies that if it were possible to
> make a magnetic field strength reading inside the thicker wire, then
> it would be the same in the middle of the twice as thick wire as it is
> at the surface of the thinner wire.
> This is not true, ...

I do absolutely agree with you, ddd.
I didn't mean to make any statement about the magnetic field inside
the conductor, but apparently forgot to emphasize this. My consider-
ations only referred to the outside field, which is the only region
of significance when regarding inter-winding coupling and its effect
on the resulting inductivity of a multi-turn loop -- which was the
initial subject of this discussion.

The effect of wire thickness on the resulting inductivity becomes
pretty obvious, if the wire thickness comes close to the order of the
winding diameter. Then the windings' center lines must inevitably be
separated so far from each other, that the magnetic coupling between
them must be significantly reduced.

I think the implications of a thick wire on the sensitivity of such a
'coil' are these:
1 The induced voltage does not change, although the inductivity is
clearly reduced.
2 The maximum current through a shortened 'coil' of thicker wire is
larger, although the enclosed area in 2D-view is the same.
3 The combined result of the points 1 and 2 is: The maximum real
power, that can be drawn from the thick wire 'coil', is larger.
4 Point 3 is not only due to the lower resistive loss with a thick
wire, but also due to the lower inductivity, which goes along with
a larger effective volume of such a spatially bigger coil.
5 Point 4 also means that a larger spacing between the windings of
a thin wire 'coil' must also result in greater output power --
again due to the larger effective volume.

As far as I can remember, both the volume of magnetically energized
space and the effective volume of air-cored 'coils' (like solenoids,
multi-turn loops, and combined loops) have never been subjects on this
list before, but I think they are concepts worth to be considered.

Regards, Peter
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