404 BELL SYSTEM TECHNICAL JOURNAL 



size have been standardized. For broad band carrier systems, the 

 compactness of channel separating filters is largely due to the volume 

 economies introduced by molybdenum-permalloy coils. 



APPENDIX 



The following formulae illustrate the essential steps in selecting the 

 size and permeability of an annular core best suited for a coil having 

 a desired set of characteristics. For sake of simplicity, they assume 

 throughout a coil of arbitrarily chosen proportions, in which all 

 dimensions bear fixed ratios to the mean core diameter, and approxi- 

 mating those that are practicable from a manufacturing standpoint. 

 The core is assumed to be rectangular in section. It is assumed that 

 wire of any diameter can be used and that the winding efficiency is 

 independent of the wire diameter. Any inductance due to air space 

 outside of the core is neglected. Because of these simplifications, the 

 expressions are of somewhat restricted applicability. However, they 

 yield solutions for optimum permeability and corresponding values of 

 Q and core size which are sufficiently accurate for most practical 

 purposes. 



The inductance in henrys due to a core of permeability n, and mean 

 diameter d cm., wound with N turns of wire is 



(1) L = I iVW X 10-9. 



If the coil is wound with wire of resistivity pe ohm-cm., with winding 

 efficiency 5 (i.e., the ratio of copper area to total available winding 

 area), the direct current resistance in ohms will be 



... „ 19pcL X 10^ 



The maximum flux density due to sine wave measuring current of 

 effective value / amperes is 



(3) -^^ - T \ M' ■ 



In terms of the hysteresis loss coefficient k^ = /xa, the modulation 

 factor thus becomes ^^ 



(4) m = 



or 



£3 ^hBm ^k^I SfiL X 10^ 



£1 IOtt 257r \ d^ 



(5) d'^3fxLX10'(^Y- 



