THE FIELD DISPLACEMENT ISOLATOR 895 



with ferrite height reduction. It is not inconsistent therefore to choose 

 600 oersteds for the full height analysis in contrast to the value deter- 

 mined from the experiment. 



V. SCALING 



Once the optimum set of parameters has been decided upon for a 

 given frequency range (e.g., 5,925-6,425 mc/sec, 5 = 0.180", b = 0.074", 

 ( = 5", h = 0.550", 4wMs = 1,700 gauss, Hoc = 660 oersteds) it is a 

 simple matter to scale these parameters to other frecpency ranges. From 

 Maxwell's equations: 



Curl H = icceE + gE 



Curl^ = -iwT-H 



where T is the permeability tensor, and g is the conductivity in mhos/ 

 meter. The first of Maxwell's equations suggest that frequency scaling 

 may be accomplished by permitting both the curl and the conductance 

 to grow linearly with respect to frequency. The curl, which is a spatial 

 derivati^'e operator, may be made to increase appropriately by shrinking 

 all dimensions by a 1/co factor, which will keep the field configuration 

 the same in the new scale. 



Having imposed this condition on the first equation we must satisfy 

 the second of Maxwell's equations by causing 7" to remain unchanged 

 with frequency. T is a tensor given as follows for a cartesian coordinate 

 system: 



(Hr ikr 0\ 



-ikr Mr (V— 1) 



1/ 



for a magnetizing field in the z direction. The components may be ex- 

 panded in the following fashion: 



Mr = 



4 



X 



^ ^ (V— 2) 



h = 



CO 



m - ^ 



