ELECTRIC WAVE FILTERS 277 



the portion "B" of Li is equal to K'^Lu Now let a current A be as- 

 sumed to be flowing in L, and, A in L2^ ^The mutual inductance be- 

 tween the coil and the shield is - K^JLiLi. If ei is the voltage drop 

 across the portion "B" of Li 



\ex = jcoK'^LJi — jccK^LiL-,l2 



from which 





Suppose i?2 = 0, which would be the case if the shield were made 

 of a perfect conductor. Then ex = 0. If, however, R^ is assumed to 

 be infinite, ei = IjjwK^Li, the voltage which would appear if the shield 

 were not present. Since the portion " B " of Li is the only inductance 

 coupled with the shield, it is the only source of a field which might ex- 

 tend beyond the shield. Therefore, when R2 is 0, and ex the voltage 

 across "B" is also 0, there is no energy in the field, and it obviously 

 cannot make coupling with anything beyond the shield. This condi- 

 tion would obtain for perfect shielding, but R2, of course, is never zero 

 in practice. 



When i?2 is finite, "ei," the voltage across "B" is finite, and a certain 

 amount of energy is transferred to the equivalent circuit of the shield. 

 Part of this energy is dissipated in the equivalent resistance of the 

 shield, and the remainder is stored in the field of the equivalent induc- 

 tance. 



The reactance, or "j" term of Equation 1 is a measure of the energy 

 stored in the shield and is, therefore, also a measure of the field which 

 may exist outside the shield. As the flux is proportional to the am- 

 pere-turns, and the reactance is proportional to the square of the turns, 

 the square root of the ratio of this reactance value when i?. is infinite 

 to its value when R2 is finite is the average ratio of the flux (po with 

 no shield present to the flux <p, with the shield present. 



1 



where P = -^ 

 L2 



^!~Vi?2^+ W" v+l^' ^^^ 



The efficacy of the shielding in reducing the external field is therefore 

 seen to be dependent upon the frequency, and a parameter "P," the 

 ratio of resistance to inductance of the shield itself. As the voltage in- 

 duced in some coil beyond the shield is proportional to the flux, the 



