DESIGN OF SMALL IRON-CORED CHOKES AND TRANSFORMERS 



a choke or the primary winding of a transformer contains a direct component 

 which is not balanced out, as happens in, e.g., a single-sided instead of a 

 push-pull output stage, the iron experiences a mean magnetization, or bias, 

 towards saturation and the permeabihty is found to be reduced : this causes 

 a similar reduction in the self inductance. The remedy is to include an air 



r+/?, 



■Ri/n'^ ' 



V-(R,/n^)/(R,/nV'-r3, 



IS equivalent 

 to 



IS approximately 

 equivalent to 



Figure 22.7 



gap in the magnetic circuit, which increases the absolute reluctance of the 

 magnetic circuit and hence reduces the polarizing flux which is the cause of 

 the trouble. The consequent improvement in permeability reduces the incre- 

 mental reluctance of the iron and, if the air gap is not too great, actually 

 reduces the net incremental reluctance of the whole magnetic circuit. It is on 

 the incremental reluctance that the inductance depends (Figure 22.8): the 



No air gap 



I With air 

 I gap 



Figure 22.8. With no air gap a given mmF produces a flux proportional to OP, representing 

 a certain reluctance. The incremental reluctance is proportional to the reciprocal of the slope 

 of yy, and is large. Introducing an air gap reduces the flux from OP to OQ, an increase in 

 absolute reluctance ; but the core material comes out of saturation, xx is steeper than yy, 



representing a fall in incremental reluctance 



problem is to know how great the air gap ought to be. Fortunately the 

 answer may be easily found from a design procedure due to Hanna^. A 

 Hanna design curve for A4 Ferroxcube which is suitable for any value of 

 ^max below 1,000 gauss is given in Graph 34. The method is to choose a 

 core and to work out 



LP 



V 



where L is the inductance required in henries, / is the polarizing current in 

 milliamps and v is the volume of the core in cm^, then on the graph mark 

 off on the curve a point opposite the value of LPfv just found. This point 



313 



