Magnetic materials in alternating fields

Since // is small, from Fig. 9.5 5m (= tan 1 (//V/( )) is also small and therefore the voltage leads the current by nearly 90°. 

The mean power P dissipated over a cycle of period x is the mean value of the product of the current and the in-phase voltage component U-t, i.e. 

In the pot-cores used in inductors (see Section 9.5.1) for LC filter circuits, the fields are low enough for /T and tan i)m to vary only gradually with the field and the ratio (tan 5m)//T is sensibly constant. These cores are designed with small gaps of variable width so that their effective permeability can be adjusted in accordance with Eq. (9.12). If /tr 3 1 Eq. (9.12) can be expressed in complex form to take account of losses and rearranged to give 

Since low loss is essential in pot-core applications, tan2(5m C 1 and can be neglected. Separating real and imaginary parts then gives 

20) shows that, for a small gap and at low field strengths, the ratio (tan 5)/ p of a high-permeability low-loss material is independent of the gap width and is therefore a useful material constant in the pot-core context. It is often referred to as the magnetic loss factor but is clearly quite different in character from the dielectric loss factor (see Section 2.7.2). It indicates that a reduction in permeability due to the introduction or enlargement of a gap is accompanied by a proportionate reduction in tan (5m (or increase in Qm). 

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