MAGNETIC SHIELDING OF TRANSFORMERS 419 



the ratio between the reluctance of the magnetic path in the walls 

 around the case and the path through the interior of the case depends 

 upon the size of the case. Also, any openings in the case will obviously 

 affect its shielding efifiiciency. 



When a magnetic transformer core is placed inside the case, the 

 reluctance through the interior of the case will decrease and the 

 shielding efficiency of the case will also decrease. It is therefore 

 evident that with one type of magnetic core a case might have a 

 different shielding efficiency than with another. 



To obtain general mathematical relations between the shielding 

 efficiency and the various factors mentioned above is very difficult. 

 By making some simplifying assumptions, however, relations can be 

 obtained that will be useful from a practical standpoint, although 

 they will necessarily be somewhat limited in application. 



A great deal of work on the shielding efficiency of shields constructed 

 of different magnetic materials has been done by various investigators.* 

 Except in a few of the more recent papers,! consideration has been 

 restricted to a steady, uniform, magnetic field where no eddy currents 

 are produced and where, therefore, the shielding is due entirely to the 

 magnetic properties of the material. They have also usually limited 

 themselves to spherical and cylindrical shields. The cylinders have 

 been considered of infinite length with the direction of the disturbing 

 magnetic field perpendicular to the axis of the cylinder. However, 

 with cylinders of finite length they have found that for moderate 

 shielding efficiencies, at points inside a c^^linder at a distance from 

 the end equal to its diameter the shielding efficiency is approximately 

 that of an infinite cylinder. The ratio between the shielding efficiency 

 of a cylinder and that of a sphere, the radii of the two, the permeability, 

 the thickness and construction of the walls being the same, varies 

 from approximately 4 : 3 in favor of the sphere for very thin shells 

 to 9 : 8 in favor of the cylinder for very thick shells. This gives some 

 idea of how the shape of the shield affects the shielding efficiency. 



Investigations by the various investigators referred to above show 

 that the shielding efficiency of two or more concentric cylinders or 

 spheres may be vastly greater than that of one cylinder or sphere, 

 the amount of magnetic material being the same. They have given 

 mathematical relations between the shielding efficiency, the permea- 

 bility and the mechanical dimensions of both spheres and cylinders. 

 Although these relations have been derived for a steady magnetic 

 field, they may also be applied with certain limitations to an alternating 



* See Bibliography. 



t Tfie most important exceptions are articles No. 18, 19, 21, and 28 in the 

 Bibliography. 



