MEASUREMENT OF DIELECTRIC AND MAGNETIC PROPERTIES 435 



Now (12) may be written in terms of the normalized applied static field 

 as 



Xma ± Ks = , , ^ (18) 



0" ± 1 



Comparison with (11) shows that the functional dependency of the 

 effective parameters Xms and «« on the applied field H ^ is identical to 

 Polder's relations for Xm ± k. This permits plotting Xms ± Ks versus H z 

 and relabeling the coordinates x,„ ± k and H^ , provided that Polder's 

 equations hold exactly. It would appear however that one of the reasons 

 for measuring ferrite parameters is the fact that Polder's equations are 

 known to be approximations which do not always hold and which are 

 subject to many restrictions as pointed out earlier in this paper. Sum- 

 ming up, one may say that measurements of the parameters of a small 

 ferrite sphere lead to excellent results in terms of effective quantities 

 Xms and Ks as a function of the applied static field, but may only be 

 approximations when interpreted in terms of the intrinsic parameters 

 Xm and K. 



3.2 The Thin Disc Method 



The use of a thin disc rather than a small sphere as a cavity perturba- 

 tion eliminates most of the difficulties enumerated in the previous sec- 

 tion because the intrinsic parameters Xm ± k are measured directly. 

 Placing a thin disc against the endwall of a cylindrical TEm mode 

 cavity (Fig. 3) and observing the splitting of the resonance frequency 

 and change in 1/Q as before one obtains the following relationships 

 (see Appendix for derivation) 



' ixm'Ri ± k'R,) (19) 



Aco+ 1 Xo i 



ooo 



4 L^ 



^ I ^ ixJ'R. ± x"R^ (20) 



The ciuantity / denotes the thickness of the disc, and Ri and R2 are func- 

 tions of the geometry which take into account that the RF magnetic 

 field is not constant over the face of the disc. A plot of Rx and Ri versus 

 the ratio of disc diameter to cavity diameter (Fig. 4) shows that the 

 functions are closely equal for disc diameters less than \D. This implies 

 circular polarization of the magnetic field in this region whereas the 

 field becomes elliptically polarized as one approaches the outer diameter 

 of the cavity. It might be argued that the disc should be small enough 



