1158 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER, 1953 



Such cores find an important application in memory circuits employed 

 in connection with digital computers. Suitably cut ferrite single crystals 

 also exhibit rectangular loops when properly annealed.^ 



Initial permeability of ferrites has a wide range of values depending 

 upon the material under consideration. It may be as low as 4 for magne- 

 tite and as high as 3,000 for manganese-zinc ferrites. Curie temperature 

 (the temperature above which the material no longer exhibits ferro- 

 magnetic properties) is around 80°C for the high permeability MnZn 

 materials and is several hundred degrees C for the low permeability 

 nickel ferrite. Resistivity also depends upon the composition of the 

 material. Typical data gives values of 100 ohm-cm for a MnZn ferrite 

 and 10® ohm-cm for a NiZn ferrite. The commonly used metallic magnetic 

 materials have resistivities of the order of 10""^ ohm-cm. As mentioned 

 above, this much higher resistivity is the feature of ferrites which makes 

 possible their application at frequencies where ordinary metallic ma- 

 terials are generally not usable. At dc the dielectric constant of ferrites 

 is high. Determination of dielectric constant is rather difficult, but the 

 best measurements to date indicate values of from 10 to 30. 



IV. LOW FREQUENCY PHENOMENA (0 tO 1 mc) 



A convenient and commonly used method of determining low fre- 

 quency characteristics of magnetic materials consists in making bridge 

 measurements of inductance (L) and effective series resistance (R) of a 

 uniform winding placed on a toroidal core of the material. Subtraction 

 of the dc winding resistance gives a value of resistance (Rm) which 

 represents the core loss in the material. Permeability may be calculated 

 from the inductance measurements. The method of analysis described 

 by Legg** may be applied to powdered or laminated alloys. The method 

 consists essentially in determining the coefficients in the equation 



Rm = cixfL + auBmJL -f c/x/L, (1) 



where Bm is maximum flux density, ju is permeability, / is frequency, and 

 c, a and c are constants. For alloys in laminated or powder form these 

 constants are associated respectively with eddy current, hysteresis, and 

 residual losses. From measurements of L and Rm at two or more fre- 

 quencies with a fixed flux density, jB„, and two or more values of flux 

 density at a fixed frequency, /, the coefficients e, a and c can be deter- 

 mined by solving the simultaneous equations obtained from equation (1). 

 Equation (1) is equally applicable to the ferrites at frequencies below 

 that at which domain wall resonance and dimensional effects (discussed 

 in Sections VI and VII) begin to appear. This frequency, which is some- 



