MEASUREMENT OF DIELECTRIC AXD MAGNETIC PROPERTIES 437 



we do not recommend this method for measurement of resonance Une- 

 width. The greatest advantage of the thin disc method Hes in its abihty 

 to explore the region below resonance where many ferrite devices operate. 

 It will be noted that this region is wider for the disc than for a small 

 sphere or for a thin cyhnder magnetized normal to its axis. Using Kittel's 

 relations we find the field in the ferrite at which resonance occurs for a 

 given saturation magnetization and operating frequency 



„ _ CO jj _ oi _ M^ fj - ^ —^^' roi^ 



•"res — j r -nres — i T o -"res — i T —pT \^'~) 



ITI ItI 3 \y\ 2 



Thin Disc Small Sphere Thin Cylinder 



It is seen that for some materials a small sphere or a thin cylinder may 

 be at resonance even before it is saturated. 



4. METHODS FOR MEASURING THE DIELECTRIC PROPERTIES 



In principle the electric susceptibility x* may be measured with any 

 of the three sample shapes discussed above provided the sample is 

 placed into a region of maximum electric and vanishing magnetic field, 

 e.g., the center of a TEm mode cylindrical cavity. A simple computation 

 shows that a small sphere located at the center of the cavity produces a 

 frequency shift and change in 1/Q as follows: 



^ = 4.189 -i^-4i (22) 



OJo 



x/ + 3 D^L 



A(l/Q) = 25.136^-^,.^ (23) 



In actual measurements it is found that the dielectric constant is not 

 entirely independent of the diameter of the sphere, and that the measure- 

 ment of the loss factor Xe" is difficult because the change in \/Q is very 

 small. An additional inherent difficulty of this method is the fact that 

 (22) is rather insensitive to large values of Xe as are frequently encoun- 

 tered with ferrites. Again the thin disc method permits greater ease of 

 measurement, larger effects, and a simpler relationship between the ob- 

 served quantities and x« • We find (see Appendix A) 



^ = X.- ^ R, (24) 



COo Li 



A(l/Q) = 2x;' I R, (25) 



