shown in Fig. 3 [1]. The inner characteristics of the equivalent model are expressed in terms of permeability and conductivity. In a 2-D model, some reasonable assumptions can be made for simplicity. First, we assume that all regions extend infinitely in the x-direction, whereas the primary extends infinitely in the y-direction; the primary moves in the x-direction. Secondly, the physical constants of the regions are homogeneous, isotropic, and linear, and variations in the z-direction are ignored. Thirdly, all the currents flow only in the z-direction. Moreover, the secondary consists of a back-iron and an aluminum-conducting plate (Fig. 2) with permeability identical to that of air. On the other hand, the permeability of back-iron is considered as infinity.
In practice, the back-iron is usually not laminated, and hence its conductivity is directly adopted. In addition, it is assumed that current does not exist in region 1 and 4 due to high permeance. Moreover, since the primary is typically laminated, its conductivity can be ignored. From Maxwell’s equations, the governing equation of the
analysis model in Fig. 3 is derived as (1); further, from the above assumptions, the magnetic vector potential can be expressed as (2) Therefore, (1) can be rewritten as (3)