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loop inductance

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  • karula4711
    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
    • Alan Melia
      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
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        >
        >
        >
        >
        >
      • Michael Hebert
        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
        • karula4711
          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

            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 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
            find your own mistakes ....

            Walter
          • karula4711
            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
            • karula4711
              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
              • karula4711
                ... 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
                • Michael Hebert
                  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
                  • Alan Melia
                    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
                      who does not understand what you are talking about, to help you solve it
                      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.
                      > Yahoo! Groups Links
                      >
                      >
                      >
                      >
                      >
                      >
                    • pan@abelian.demon.co.uk
                      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/
                        --
                      • thierry alves
                        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...
                          Being inspired by your own experiments about VLF observation of the
                          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.
                        • FLAVIO GORI
                          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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                          • karula4711
                            ... 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,
                              sorry for this late answer.

                              >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
                            • Michael Hebert
                              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
                                preamp with loop sensors. Comparisons made using INA217 and AD620
                                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
                              • Peter Schmalkoke
                                ... 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
                                • Michael Hebert
                                  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
                                  • vlf_ddd
                                    ... 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).

                                      To magnify your illustration, consider three wires (one with radius =1
                                      , 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.

                                      Wire radius = 1
                                      ___ 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

                                      Wire radius = 2
                                      ___ 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

                                      Wire radius = 4
                                      ___ 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
                                    • Peter Schmalkoke
                                      ... 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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