MAGNETIC SHIELDING OF TRANSFORMERS 427 



wall of which is P. When the air-gap is equal to P, the thickness of 

 the two cylinders is zero, and hence the shielding efficiency is zero. 

 The air-gap is so located that the radii of the two cylinders are in 

 geometric progression. 



Experimental Data 



From the discussion under "Theory" it is evident that although the 

 equations (2 to 11 inch) were derived with the assumption of a steady 

 magnetic field the above calculated values apply equally well to an 

 alternating magnetic field if the effective permeability is used. How- 

 ever, the results are far from sufficient to determine the shielding 

 efficiency of a magnetic shield for a transformer. The shielding due 

 to the eddy currents, iei (see Fig. 1), is not included. To include 

 this the formulae (12) to (20) inclusive must be used. The equations 

 have been derived with the assumption that the length of the cylinders 

 is infinite. In practical applications this is obviously not so. Covers, 

 however, approximately counterbalance the effect of the finite length 

 of the cylinders. The magnetic core of the transformer also materially 

 affects the shielding efficiency. In connection with such factors as 

 these which would be very laborious to treat theoretically some 

 experimental information will now be given. The frequency range of 

 the disturbing magnetic field was limited to from 50 to 4000 cycles. 



The shielding efficiency has previously been defined as follows: 



Shielding Efficiency = 20 logio He/Hi. (1) 



From the standpoint of the shielding of transformers we are primarily 

 interested in the reduction of the transformer terminal voltage which 

 is caused by the disturbing magnetic field. For this reason it will be 

 found convenient to define the shielding efficiency in connection with 

 transformers in decibels as follows : 



Shielding Efficiency = 20 logio Ee/Ei, (21) 



where Ee is the terminal voltage due to the disturbing magnetic field 

 with the shield removed and Ei the corresponding voltage with the 

 transformer inside the shield. In addition, Ee and Ei are restricted 

 to the maximum terminal voltages, with respect to position, that is, 

 the transformer is assumed to be in that angular position with respect 

 to the direction of the magnetic field, in which the maximum terminal 

 voltage is obtained. With an unshielded shell type transformer, for 

 example, this position would be that in which the axis of the winding 

 coincides with the direction of the disturbing magnetic field. This 

 restriction is necessary for the definition (21) to be of any value. 



