Traditionally, magnetic fields have been conceptualized as lines of flux (f) emanating from magnetic poles. Since then, magnetic systems of units have been developed, each with a particular purpose. Let us review two of these systems and see how they interrelate.

Magnetic parameters include field intensity (H) , flux (f) and flux density (b). The flux density and field intensity are related by

b=mH,

where m is the permeability of the material.

In the CGS system of units, b is expressed in Gauss, Maxwells/cm² or lines /cm² while H is expressed in Oersteds. The permeability of free space, m₀, equals one. Thus in free space, b=H, and their units are occasionally interchanged. This CGS system is very popular in transformer and shield design.

In the rationalized MKS system of units, the permeability of free space, m₀, is equal to 4px10^-7. The flux, f, is expressed in Webers. The flux density, b, is expressed in Webers/meter² or Tesla and the field intensity is expressed in Amperes/meter. The RMKS system is used in radio frequency field measurements, and it is popular because it makes conversion between electrical and mechanical units very easy. Table 1 may be utilized to convert between RMKS and CGS units.

Magnetic shielding can be achieved by either containing the magnetic flux lines within a restricted area, converting the stray magnetic energy into heat or reflecting the magnetic field. At low frequencies, stray magnetic fields are often just contained, while at high frequencies, all three methods are utilized. Since this paper deals with low frequency stray fields, only the containment method is discussed.

The object of containment is to surround a stray magnetic radiation source with a material that exhibits a very high relative permeability with respect to that of air. This provides a low resistance continuous path for the stray flux lines to follow. Magnetic resistance is known as Reluctance, Â. The highest permeability materials contain 80% nickel and exhibit relative permeabilities in

excess of 300,000; however, the permeability of these materials is high at low flux densities and quickly reduces to a low value at moderate flux densities. Lower permeability materials such as soft iron and steel retain their permeabilies at relatively high flux densities but require thicker sections than high permeability materials to achieve the same shield effectiveness at low flux densities.

Double shielded enclosures are sometimes utilized to take advantage of these properties. For instance, the shield material closest to the high field level is often of a low permeability steel, while the material farthest from the high field level is of a high permeability, 80% nickel material.

Shield effectiveness or attenuation, a, is defined as the ratio of the field intensities, H, on each side of the shield. The units are dimensionless and can be expressed logarithmically in db.

The shield effectiveness or attenuation, a, of a continuous spherical shield can be calculated by the formula

a=mt/D

where m is the relative permeability of the material at the flux density, t is the thickness of the shield and D is the diameter of the sphere. Both t and D should be expressed in the same units. In a long shielding cylinder, with the field direction normal to the axis of the cylinder, half of the above attenuation can be theoretically achieved.

The flux density in the material can be determined by utilizing the following formula

b=.4pDH₀/t

where b is the flux density in Gauss and H₀ is the external field intensity in Oersteds. b vs H curves or m vs b or H curves can be utilized to determine the permeability of a particular material in the magnetic field.

Thus, surrounding stray magnetic radiation with a high permeability material in a continuous void free package should provide significant attenuation. However, very few applications would allow void free packaging because it is usually necessary to fabricate the enclosure with seams and to provide access for repair and maintenance. Additionally, holes must be provided for input and output wires and terminations.