780 BELL SYSTEM TECHNICAL JOURNAL 



terial in respect to its freedom from harmonic production may be 

 determined by a consideration of the circuit problem. The third 

 harmonic driving e.m.f. is obtained from the last section as 



£3 = pnAa<i.IP\Q)-\ 



^n^A (45) 



in which n represents the number of turns enclosing the core of area 

 A, d\s the mean diameter of the toroidal core and ao2 is the hysteresis 

 coefficient. 



Suppose that we have to design a coil of fixed inductance in which 

 the harmonic is to be a minimum, so that 



L = K^^ = const. (46) 



We proceed to the consideration of a number of special cases subject 

 to condition (46). 



Case 1 — L Fixed, n Variable. From (46) 



n = const. (-^)'^ 



which may be substituted in (45) to give 



Hence in a coil of fixed inductance, fixed core area, and fixed core 

 diameter, minimum harmonic voltage is produced with a material 

 for which 002/^'^'^ is minimum. 



Case 2 — L Fixed, A Variable. From (46) 



A = const. djU' fjL, 



which, upon insertion in (45), yields 



£3=^^% (48) 



a IX 



in which the modulated voltage varies linearly with a 02//^. 



Case 3 — L Fixed, d Variable. By a similar procedure, we obtain an 

 expression for the generated third harmonic voltage 



For further work we suppose the coil reactance considerably greater 



