60 BELL SYSTEM TECHNICAL JOURNAL 



expression for power loss,^* computing the loss in a ring of thickness 

 dyl2, and integrating from di to Jo yields an expression for core 

 resistance identical with (33), (34) and (35) except that the terms con- 

 taining a or X must be multiplied by the factor d'^/dido. It appears that 

 radial thickness of the core affects only that part of the loss which 

 depends upon the variation of permeability with H or B. 



In preparing a test core, a compromise must be struck between the 

 radial thickness, diameter, and axial height, so as to secure the desired 

 cross-sectional area without excessive length of copper winding. 

 The laminations of the core must be well insulated from each other. 

 They should be of uniform thickness, which should be known accu- 

 rately. A good technique used with material in the form of ribbon or 

 tape, consists of winding it tightly in several layers upon a cylindrical 

 mandrel and providing insulation against eddy current straying by 

 dusting the strip with finely powdered alumina while winding. Such 

 insulation is found to withstand the high temperatures ordinarily 

 used in heat treating the core. In order to eliminate the airgap in 

 this type of core, the inside end of the tape may be brought out, 

 folded over, and welded to the outside end, before annealing the core. 

 The use of 50 turns of tape or more in a spiral core reduces the airgap 

 effect to a negligible amount so that welding the tape ends is not 

 necessary. A mandrel diameter should be selected large enough to 

 make the ratio Ad/d^ quite small. Thus, a 9 cm. mandrel, wound to a 

 depth of 1 cm., gives a core in which the magnetizing force decreases 

 about 20 per cent from the inside diameter to the outside, while the 

 correction term decreases the effective diameter about 0.4 per cent 

 below the mean diameter. The correction to the permeability 

 variation term is d^/dtdo — 1.002. 



The completed core, if strain sensitive, can be protected from the 

 mechanical stresses of handling and winding by mounting it in a loose 

 fitting toroidal box upon which the test windings are applied. Such 

 spacing helps to decrease distributed capacitance, but even more 

 important is sectionalizing, or bank winding of the coil. Types of 

 insulation and windings depend upon the loss characteristics of the 

 core. In general, lower loss characteristics in the core require higher 

 quality windings, to permit measurements at higher frequencies. 



SYMBOLS 

 a Hysteresis resistance coefficient. 

 a I Hysteresis loop area; = ^aBm^ = 4TrW. 



=1 W. Cauer, Arch. f. Eleklrolechnik 15, 308 (1925). 



