I 



FERRITE CORE INDUCTORS 271 



current losses in ferrite are extremely small. Second, the introduction of 

 the transistor has created many new applications for inductors for use 

 at very low power levels, and with proportionately lower hysteresis 

 losses. For this condition we have, from (14) 



^ = rt/ + ^'^ (IS) 



Solving for the value of /x, /Xopt. , w^hich will yield the lowest dissipation 

 dD ^ l_ 



and 



^°pt- =" ^ 71/3J1/2 • C17) 



It may be noted from (16) and (17) that the optimum permeability 

 is that which wall result in the dc resistance and residual loss being equal. 



2. DC Resistance and Hysteresis Loss Predominate 



This condition, while it does not often apply to conventional size 

 inductors for transmission networks, may occur when miniaturization 

 of coils is contemplated. It will be noted from (14) that hysteresis is the 

 only core loss component that is dependent on the volume of the core. 

 We have, from (14) 



h 1. 3/2 r 1/2 . 



The optimum permeability and dissipation factor derived from this 

 equation are 



Z><.p.. = [(3/2)^'^ + (2/3)"1 Y'^ff ■ ^^^ 



Inspection show^s that 



(a) The optimum permeability is such that the ratio of dc resistance 

 to hysteresis loss is 3/2. 



