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Variable Inductor Help

Discussion in 'Electronic Design' started by amdx, Apr 18, 2007.

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  1. amdx

    amdx Guest

    Does the orientation of flux affect the saturation?

    Please see attached picture at ABSE.
    Subject: Variable Inductor Help
    My thought is to build a variable inductor by installing a toroid in the gap
    of a potcore. The potcore would then have near normal ungapped inductance.
    However when the toroid is saturated (by turns installed on the toroid) it
    would be invisible and act like a gap. Hopefully this effect could be
    modulated by the amount of current through the turns on the toroid.The
    problem I have is the orientation of the flux, the potcore center flux is
    vertical and the toroid is horizontal. Any thoughts?

  2. Wimpie

    Wimpie Guest

    Hello Mike,

    Basically the principle will work. When you saturate the toroidal
    core, the permeability of the toroid will reduce, for all directions
    of flux. Because the toroid's winding will take some space, the
    overall permeability of the pot core will be less.

    I see some things that you have to bear in mind. Because of the DC
    winding on the toroid, the flux of that pot core will also go through
    the copper. Although virtually no EMF is induced in the DC winding,
    there will be eddy current loss in the DC winding, because of the flux
    through the pot core (that must also go through the copper. Probably
    you inductor will have somewhat more losses (depending on frequency
    and thickness of wire and volume of wire of DC winding).

    There will be some small coupling between the winding on the pot core
    and the winding on the toroid. That is because of some flux goes
    through the air in the middle of the toroid. Whether this is a
    problem, depends on the application. With proper winding technique,
    you can avoid this.

    By having the inductance control flux spatially 90 degrees with
    respect to the AC flux, I believe your AC inductor will be more linear
    (provided AC flux << DC flux). I haven't measured this.

    Best regards,

  3. Wimpie

    Wimpie Guest

    Hello Mike,

    I forgot to mention that I see no link to the image.

    Best regards,

  4. amdx

    amdx Guest

    Hi Wim,
    The picture is posted in alt.binaries.schematics.electronic.
    Thanks, Mike
  5. whit3rd

    whit3rd Guest

    No, magnetization is a VECTOR and it doesn't matter that the
    circumferential field is saturated (maximum magnetization in the
    theta direction) because the pot core induces a magnetization in
    the axial direction (tilts the magnetization from full-amplitude
    in the theta direction, i.e. gives a component at right angles).

    So, without changing the magnitude of magnetization, the direction
    can change. This means the axial component of magnetization
    responds to the applied field, and that means the toroid is fully
    magnetically active, just like it wasn't saturated by its winding.

    Energy conservation suggests that this would cause some
    coupling of the windings at saturation (regardless of the geometric
    shape of the windings, which do not couple magnetically).
    It might generate some interesting harmonics of the drive
  6. amdx

    amdx Guest

    Hi Whit,
    I think you said it won"t work.
    Work with me here to help me understand what you said above.

    I thought the magnetic domains would be locked in position by the dc and the
    flux within the potcore would not be able to move them around, and this
    would result
    in a lower AsubL.
    Oh, I think I just gained some insight. As you said it's a VECTOR so the
    do move.
    It would seem to me that being a vector that the domains have a limited
    and not a full 180* swing each half cycle. Wouldn't this limited swing
    the AsubL?
    I don't know where to go with that.

    Thanks for the input and anything more you can add,
  7. Paul Mathews

    Paul Mathews Guest

    It seems to me that you can minimize the coupling between the flux in
    the main core and the windings of the toroid by positioning all of the
    toroid windings well away from the main core. If this seems like an
    impossibility, note that only a portion of the toroid needs to be
    placed in the gap. You could have a relative large toroid, with only a
    small part of its circumference inserted into the gap. This also
    allows you to reduce the remaining air gap to almost zero. Given
    sufficient DC in the toroid windings to saturate the core, there
    should be very little coupling. On the other hand, with reduced dc
    bias, I'd expect some coupling again.
    Paul Mathews
  8. Wimpie

    Wimpie Guest

    Hello Whit,

    Assume the DC driving field is horizontally directed, the AC field is
    vertical and the magnetic material is anisotropic but non-linear.

    Magnetization is a vector and has a maximum (non-linear system). If
    you assume the DC (horizontal) field infinite, a finite AC field will
    not be able to change the angle of the resultant field, hence the
    direction of the magnetization vector. So there will be 0 contribution
    of the magnetic material to the AC field.

    In general, once the core has been saturated (by the DC field), , the
    vertical polarization component is inversely proportional to the DC
    field (assuming AC field << DC field).

    It is therefore very likely that a variable inductor can be made based
    on Mike's description. Whether this inductor is technically/
    commercially the best solution is another question.

    Best regards,

  9. whit3rd

    whit3rd Guest

    In the large-signal regime, yes, it gets reduced. In the small-signal
    model, however, the derivative of the total magnetization
    with respect to small axial field is zero, so the axial field
    isn't coupled to the total magnetization. The second derivative
    does not vanish, so the even harmonics (second harmonic)
    of the exciting signal do show significant effect.

    The toroid winding current creates a second harmonic of the potcore
    drive, SO one can imagine using wide-dynamic-range sensing
    of that second harmonic to measure the toroid current. A sensor
    based on this effect could measure microamps to kiloamps in
    this way (which is way cooler than using op amps and resistors).

    A physics lab needed lots of high voltage; they built a four-arm
    transformer core, sawed a gap in one arm and wound a secondary
    on it, then overdrove the other three arms with three-phase power.
    The saturation at peaks caused current in the secondary at
    3x the powerline frequency (and the secondary then drove a
    Cockroft-Walton rectifier). They made megavolts at respectable
    current that way.

    The power company hated it. The power factor was dreadful,
    and (at that time) the customer wasn't liable to pay extra on account
    of the line losses that resulted. That little billing issue has been
    resolved nowadays, so you know this is an OLD story.
  10. whit3rd

    whit3rd Guest

    In analogy, a taut string resists sideways deflection; still, a piano
    string at nearly full stress allowable for steel DOES deflect when
    the little felt hammer hits it.

    In particular, the quantity of interest is the axial component of the
    magnetization, and NOT the angle (which is, in the small-angle
    sine/tangent approximation, the ratio of the axial and toroidal
    As a small axial addition to the magnetization vector does not (to
    first order) increase the magnetization amplitude, so saturation
    doesn't prevent axial magnetization.

    Taking the toroidal field to a large number reduces the angle (as you
    say) without reducing the axial component (so it doesn't change
    the result).
  11. Wimpie

    Wimpie Guest

    Hi Whit,

    As the contribution of the absolute magnetization (= length of vector)
    does not change in the saturated regime, reduction of angle, gives
    proportional reduction of vertical (axial magnetization). Am I wrong?

    Best regards,

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