282 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1953 



METHODS OF INDUCTANCE ADJUSTMENT 



The fact that ferrites can be molded in a variety of shapes, can be 

 machined, and can be used with discrete air gaps permits considerable 

 freedom in the mechanical methods that can be used to provide contin- 

 uous adjustability of inductance. Whether the need is for factory ad- 

 justment to prescribed values or for adjustment after the coil is as- 

 sembled in its equipment, the basic methods are the same. 



We have noted, in (4) that the inductance of a magnetic core coil is 

 given by 



L = ^ (4) 



in which A; is a constant depending on the units used, and the other four 

 quantities are design variables. Any of these, or any combinations of 

 them, can be manipulated to produce variations in the inductance. 

 They are: length of magnetic path, l\ cross section of magnetic path, A\ 

 nimaber of turns, iV; and effective permeability, \i. There is an additional 

 variable hidden by the formula's assumption that perfect coupling exists 

 among all the turns in the winding. Inductance can be adjusted by chang- 

 ing the coupling between parts of the winding. Each of these five var- 

 iables, which are of widely differing practical value, will be commented 

 upon at least briefly. 



1. Adjustment of Inductance by Change in Magnetic Path Length, I 



Adjustment by a change in I without an accompanying change in 

 /x requires that the air gap also be changed since the effective permeability 

 is a function of the ratio of the air gap dimensions to those of the total 

 structure. 



^ " 1 , Q (44) 



1 + Mm - 



a 



where m m = permeability of the core material 



g — ratio of the length of air gap to total length, I 



a — ratio of effective cross section of gap to core cross section, A. 



It would be mechanically possible to design an adjustable inductor 

 of this sort but it is unlikely that there would be any practical advantage 

 in maintaining constant permeability over the adjusting range. On the 



