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Basic Shielding Mechanisms for Conduit Enclosing Dipole Sources and Net Current Sources

J. F. Hoburg

September 12, 2000

Prepared for Larry Maltin, President, Amuneal Manufacturing Corporation

Introduction

This report describes the fundamental issues that govern shielding of magnetic fields by conduit, both for sources composed of multiple conductors carrying zero net current and for sources that carry net current.

The current in any set of conductors that are collinear can be thought of as a superposition of two components:

  1. a “dipole” component, wherein individual conductors carry currents at different phases, but the total current in all conductors is zero.  This kind of current distribution produces magnetic fields as a result of the spatial separation of the individual conductor axes.  It includes two-wire and three-wire combinations.
  1. a “net current” component, describing a non-zero sum of currents in the individual conductors.  This component of current can be thought of as a single line current in the geometric center of a two-wire or three-wire combination.

In general, an actual current distribution in a set of collinear conductors includes components of both kinds; we consider such a distribution to be a superposition because the shielding characteristics of the surrounding conduit are different for the two components.  The two sections below describe basic shielding characteristics of conduit for dipole and net current contributions respectively.

Dipole sources

A dipole source within a surrounding conduit is portrayed in Figure 1 below.  The two wires in the figure can alternatively be three wires, corresponding to a three-phase source.  What is of fundamental importance is that the individual conductors have axes that are spatially separated from one another, and the sum of currents in all conductors is zero.  Any nonzero net current is considered to be a separate source, as described in the section that follows this section.  The conduit can be conducting, ferromagnetic, or both.  For example, if it is steel, it is both ferromagnetic and conducting.

In general, the dipole field induces both free and magnetization currents in the conduit.  These induced sources do not involve any net current within the conduit.  Both kinds of induced source are distributed sinusoidally as a function of angular position.  The resultant total field in the region outside the conduit is reduced in magnitude (shielded) at each point in space; the ratio of shielded field magnitude to unshielded field magnitude is the shielding factor s, which is determined by the radii, permeability and conductivity of the conduit.

                       

Figure 1.  Conduit surrounds a two-wire dipole source, carrying zero net current.  The basic shielding mechanisms apply to both two-wire and three-wire sources.

The basic physical mechanisms (induced current and flux shunting) for this kind of shielding are described in:

“Principles of quasistatic magnetic shielding with cylindrical and spherical shields”, J. F. Hoburg, IEEE Transactions on Electromagnetic Compatibility, 37, 4, November, 1995, pp. 574-579.

A computational algorithm to compute the shielding factor for a specific cylindrical shield, or for any number of layers of shielding material is described in:

"A computational methodology and results for quasistatic multilayered magnetic shielding", J. F. Hoburg, IEEE Transactions on Electromagnetic Compatibility, 38, 1, February, 1996, pp. 92-103.

Comparisons of shielding factors computed using this algorithm with measured shielding factors using cylindrical shields fabricated at Amuneal are described in:

"Comparisons of measured and calculated power frequency magnetic shielding by multilayered cylinders", J. F. Hoburg, B. A. Clairmont, D. W. Fugate and R. J. Lordan, IEEE Transactions on Power Delivery, 12, 4, October, 1997, pp. 1704-1710.

The fundamental point here is that shielding by conduit of dipole sources is determined by the radii and material characteristics of the shielding material, and no electrical contact between the source currents and the conduit is needed in order for this mechanism to operate.

Net current sources

Net current in a single wire or in multiple wires with collinear axes within conduit are described by a wire along the axis of a surrounding cylinder.  As in the prior section, the conduit can be conducting, ferromagnetic, or both.  In contrast with dipole sources, an essential question for this kind of source is: “Where does the current return?”  Two different situations have fundamentally different characteristics with respect to the shielding characteristics of the conduit:

a.      If the net current source is electrically connected to the conduit through the load, then the current returns through the conduit, then no net current is enclosed by a circular contour in the shielded air space outside the conduit.  This situation is portrayed in Figure 2 below.  In this case, the magnetic flux density around the wire is terminated by the return current in the conduit, and the magnetic flux density in the air space outside the conduit is completely reduced to zero.  (Complete shielding is really only achieved if the net current is exactly along the center line of the conduit; any asymmetry in the net current source leads to a corresponding small asymmetric field outside the conduit.  But, for practical purposes, the conduit completely contains the field in the same way that coaxial cable contains a magnetic field, completely shielding the outside region from the field due to net current.)

 

Figure 2.  Conduit surrounds a source carrying nonzero net current.  Through a connection at the load, the current returns in the conduit.  The resultant field due to net current is confined to the region inside the conduit, and the outer air region is completely shielded.

b.     If the net current source is not electrically connected to the conduit, then the current returns outside the conduit (typically in a neutral return conductor or in ground paths).  This situation is portrayed in Figure 3 below.  Because the conduit carries no net current, it provides no shielding, and the field outside it is the same as if it were not present.  (This statement is exactly true if the net current is exactly along the center line of the conduit; asymmetry in the net current source can lead to local distortion in the field outside in the region near the conduit.  But, for practical purposes, the conduit is completely ineffective in shielding the field due to net current.)

 

Figure 3.  Conduit surrounds a source carrying nonzero net current.  Because the conduit is not connected to the source current, it carries no net current.  The resultant field due to net current is unaltered by the conduit, and the outer air region is not shielded.

Conclusion

Magnetic shielding is most commonly thought of in the context of shielding materials that are electrically separated from the conductors that serve as primary sources of the fields.  For conduit surrounding source conductors, if there is no electrical connection between the source conductors and the conduit, there is no shielding effect exterior to the conduit for net currents, whereas the conduit does shield contributions from balanced current source conductors whose axes are separated.  By contrast, if the conduit is electrically connected to the source conductors through the load, it completely shields net current contributions.

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