MAGNETIC SHIELDING OF TRANSFORMERS 423 



where a Is the radius and d the thickness in cm. k is given by 



where/ is frequency in cycles and p is resistivity in ohms per centimeter 

 cube. At low frequencies (12) reduces to 



l+,-l![!^10- 



(14) 



which is good up to about 10^ cycles. The direction of the disturbing 

 magnetic field in (12) and (14) has been assumed perpendicular to 

 the axis of the cylinder. 



Other formulse which take into account both conductivity and 

 permeability are also given in King's article. They are, however, 

 rather complicated and require elaborate calculations. 



Mr. S. A. Schelkunoff in an article in the October 1934 issue of the 

 Bell System Technical Journal has derived formula? which are com- 

 paratively simple although they take into account both conductivity 

 and permeability. His treatment is quite different from that presented 

 above and his results are expressed in terms of radial impedances. 

 For an infinitely long cylindrical shield the diameter of which is large 

 compared to the radial thickness of the shield the shielding efficiency, 

 S, is given by 



S^R-^A. (15) 



In this formula R is the sum of the reflection losses at the surfaces of 

 the shield. We have 



R=T.20 logio ■ " T ' db, (16) 



n=l 4 I ^„ I 



where kn is the ratio of the radial impedance in the first medium to 

 that in the second. That is, 



kn = ^- (17) 



The radial impedance for a good dielectric is given by 



Z — livfixpi ohms. (18) 



For a metal 



Z = ^3^'. (19) 



