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Simple Mutual Inductance Experiment

  1. Apr 17, 2007 #1
    Hello All,

    I did a simple mutual inductance experiment recently which involving two coils (5 turns each) in series with a high frequency signal (MHz range) running through them.

    One coil is directly connected to function generator via a co-axial cable, and the other coil is connected to the probe of the oscilloscope to see the received signal.

    The questions that I am gonna ask are based on my "wierd" observation, as I could not find any theory to explain the obsercations:

    1. The phase shift: according to the thoery, the received signal should always be in-phased or 180 degrees out of phase compare to the reference signal from the signal generator(depends how you connect the probe and the earth), but the signal shows from the oscilloscope seems like there is always a certain amount of phase shift (20-30 degrees)...

    2. Sensitivity changes: when I swap the position of the probe and the earth connection for the receiving coil, all I should observe should be the 180 degree phase change only. However, the sensitivity of the coil changes as well...i.e. the coil does not pick up the signal as sensitive as before (or sensitivity increase if we swap it back...)

    3. The natural resonance frequency is around 13 MHz, if I vary the frequency from 11MHz to 14MHz, I can observe another 180 degree phase shift as well while the driving frequency pass through the resonance...

    I hope someone could help me to find out the theories to explain above phenomenons, or maybe there are some system setup errors...don't know...I hav been struggle into it for so long...

    Thank you for your time!
  2. jcsd
  3. Apr 17, 2007 #2


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    Staff: Mentor

    First of all, you are getting some capacitive signal coupling between the coils, and that is confusing your measurements. You need to put some grounded electrostatic shielding between the two coils in order to confine the coupling to just the flux coupling. This capacitive coupling is what is giving you strange results when you swap which end of the pickup coil is grounded.

    Are you using one channel of the 'scope to monitor the drive coil, and the other to monitor the pickup coil?

    BTW, you need to be careful how you make the grounded electrostatic shield between the two coils. You don't want it to become a shorted turn and kill all the flux coupling.... Can you think of ways that you can make a good electrostatic shield and still allow flux past it?
  4. Apr 17, 2007 #3
    What you observed is very normal. The weirdness has to do with the effect of the transmission line (coax) and source and load impedances.

    What is the generator's output impedance (I'm assuming 50 Ohm)?

    What is the coax characteristic impedance (I'm assuming 50 Ohms)?

    1. The load impedance is your coil on one end of the coax which is definetely introduces impedance mismatch which results in different phase shift, and voltage, when referenced to generator without coax.

    2. Not sure about this one, but it is likely something is canceling the flux lines when you swap out the position of the coil.

    3. Obviously the turns of the coil act like a capacitor so every coil has its own capacitance as well. Capacitance and inductance leads to only one thing, resonance.
  5. Apr 17, 2007 #4
    Thank you, berkeman and waht:

    Yes, I am using one channel of the 'scope to monitor the drive coil (as the reference), and the other to monitor the pickup coil?

    about the electrostatic screening...it should be placed in between the coils right? to prevent the coupling...do you think a magnetic screening is necessary as well (of course...it must be placed outside the system...)

    and for my third questions...it is the phase shift that is worrying me...is it normal to observe such a phase shift when varying the frequency around the resonance...?

    Thank you guys again!
  6. Apr 17, 2007 #5


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    The electrostatic screen needs to be a grounded piece of metal (you can use copper tape or shim brass if either one is handy -- aluminum foil is hard to make reliable contact with), which does not act like a shorted turn. So for example, you can make a ring of metal foil that is the same diameter as your coils but wider (in the polar direction) so that it is a good shield, with a hole in the middle and a narrow cut out of the side to make like a "C" shape. Minimize the width of the cut-out section, so that you don't still have a lot of E-field capacitive coupling from coil-to-coil.

    As for resonance phase shifts, I honestly don't know. I try not to have my transformers resonate..... :-) But considering how the current will mostly be going into the LC tank at resonance, and not generating much flux (I think?), I could see how weird things would happen there.
  7. Apr 18, 2007 #6
    Thanks for all your guys help...

    Does anyone know whether there is any good EM field simulation software that can simulate this kind of experiment? (preferbly freeware...but commercial package is also fine...)?

    All I want to do is to compare my observation with the theorectical result......

  8. Apr 18, 2007 #7


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  9. Apr 19, 2007 #8
    You started with simple idea to experiment magnetic coupling between two coils but all parasitics complicated problem. Actually you should study coupled resonators or mutually coupled resonance circuits to understand problems.

    For simulation of this circuits you may use Microcap9 Demo www.spectrum-soft.com . Using K element (coupling factor) you can define coupling between two or more coils and with AC Analisys you will get amplitude and phase responces of test circuit.
  10. Apr 19, 2007 #9
    Thanks guys..

    Yes...I have tried both QuickField and MagNet...but the bad things about student version is that there is always a node limitation...and doesn't have AC analysis function...i am downloading Microcap9 Demo and see whether it will be better!

    Actually the aim of my experiment is to observe whether there is any signal amplitude or phase change at the receiver coil when I insert any conductive object between two coils...(due to eddy current)...I just didn't expect that this can give me so much headache...haha!

    Um..borber...can you please tell me more detail about what I need to study? or do you have any good reference material for me?


  11. Apr 19, 2007 #10
    Well this things about coupled resonators are standard topics in analog electronics under linear analysis.
  12. Apr 25, 2007 #11
    Quote from Berkeman:
    ( So for example, you can make a ring of metal foil that is the same diameter as your coils but wider (in the polar direction) so that it is a good shield, with a hole in the middle and a narrow cut out of the side to make like a "C" shape. Minimize the width of the cut-out section, so that you don't still have a lot of E-field capacitive coupling from coil-to-coil.

    Sorry Berkeman...I don't quite understand your description about constructing a proper electric screening, can you please explain it more carefully for me? Thanks..

    I am now trying to use a sheet of tin-foil to wrap around my coil...then attach it to ground...don't know whether it is a good way of electric screening...

  13. Apr 25, 2007 #12


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    Staff: Mentor

    Okay, let's say you have two coils, each about 4cm in diameter, and spaced 1cm apart. You want to electrostatically shield them from each other, without affecting the B-field coupling between them.

    So you make a conductive disk about 6cm in diameter, put it between them and parallel to the coils, and ground the shield disk. Except, if it's a full disk, then eddy currents can flow around the disk (in the same direction as the coil windings), which generates a back-EMF and interferes with the B-field coupling. So you need to break the conductive path around the disk, so that the eddy currents cannot flow.

    To do this, you need to at least cut a slot in the disk from the center point out to the edge. It doesn't matter much where the cut is, as long as it goes all the way from the center point out to the edge.

    But you are still left with places where you can get smaller eddy current circles near the middle part of the disk, so to prevent this, you can cut out the cener part of the shield disk. So you are left with a ring, say the part of the disk from radius 4cm to 6cm, with a slot cut in it at one point to keep it from being a shorted turn between the two coils.

    Does that make more sense?
  14. Apr 26, 2007 #13
    Thanks Berkeman! I wil try it now!

    I actually just come out with an idea...if I use a thin co-axial cable to wind a coil (since my coil is only 5 turns, the size shouldn't be a problem..) Do you think that wil make a good electric screening as well? of course the outer shield of co-axal cable must be grounded as well...

    And also, for your screening, do you think a metal sheet between the coils will be enough fro preventing direct coupling? if i put more than 1 sheets around the coils, will it work better....or you think it will decrease the magnetic coupling as well?

    Thank you for your time!
  15. Apr 26, 2007 #14


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    You can use coax, but you need to cut the shield at one point, or you will have an effective shorted turn that will zero out the external B field. You can also use a metal sheet, but again you have to cut it as I described above to eliminate eddy currents and the resulting shorted turn effect.
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