MEASUREMENT OF DIELECTRIC AND MAGNETIC PROPERTIES 433 



field //° 



and observing that the RF components of M and IT (denoted by lower 

 case letters) are related in a cylindrical coordinate system by 



7 • 7 



nir = Xms'lr " JkJ10 



me = jKjir + -Kmshe 



Placing the small ferrite sphere close to the endwall of the cavity (Fig. 2) 

 and observing the splitting of the resonance into two frequencies co± 

 (related to the positive and negative circularly polarized modes) and the 

 two changes in 1/Q of the cavity after application of a static magnetic 

 field in the axial direction leads to two measurable quantities 



Acoj. = ojd — coj. frequency shift 



A(l/Q)^ = l/Q± — l/Qo change in internal Q of the cavity 



where coo and Qo are resonance freciuency and Q of the empty cavity. 

 It can be shown that real and imaginary part of Xms and Ks can be ob- 

 tained fromf 



^^'^^ = 0.6982 )i ■ ii (x./ ± ./) (7) 



COo 



7)2 L 



Xo do 



3 



3 



A(l/Q)± = 0.6982 ^ • ^ (xms" ± Ks") (8) 



The quantities do , D, and L are the sphere diameter, cavity diameter 

 and length respectively, Xo is the wavelength in free space associated with 

 COo . In order to obtain the intrinsic parameters Xm and k from (7) and 

 (8) one may use the relationships'" 



Il° =^ H + M/S (9) 



3(xm ± k) . . 



Xms db /Cs = -— (10) 



Xm ± K + 3 



\ * *-♦ - 4-» 



sphere to the applied field by writing — B = MsH^ where jus may be designated the 



Mo 

 external relative permeabilitj^ tensor. It can be readily shown that Waldron'sre- 



suits are in agreement with ours if one notes that (2/3)xms = ms — 1- We found 

 that the use of the effective susceptibility tensor Xms is much to be preferred over 

 Us because it simplifies notation and interpretation of experimental results in terms 

 of the intrinsic quantities X"> and k. 



t Equations (7) and (8) are identical to Artman and Tannenwald's^ expressions, 

 if 47r2Z)V(13.56 + irWyi^) is substituted for Xo^. 



