I. IntroductionThis paper examines the non-linear behavior of integrated magnetics used in Linear Level Control (LLC) converters . Due to the non-linear behavior of the magnetics, implementation of magnetic integration needs to be carefully considered . The saturation of magnetics is normally not a concern in high voltage input applications [1], but becomes a serious issue when designing the low voltage input and high power applications . The inserted magnetic integration has been categorized into two types according to the position of their magnetic insertions . The inserted magnetic structure MIO as presented in [1], and MIP structure introduced in [2] . They performs poorly in high power and low voltage input applications over add-on type of magnetic integration structure [3] .A brief discussion of these two categories is presented . The completed analysis and simulation results, using the 3-Dimensional (3-D) Finite Element Method (FEM), will be presented in the full paper .
II. Consideration of Magnetic Saturation in Integrated MagneticsA . Equivalent circuit model for Integrated Magnetics For a conventional transformer, the leakage inductance is linear, there is no saturation phenomenon due to the air medium has no limit on the amount of flux it can handle . However, when a specific inductance is required in the resonant circuitry, the enormous magnetizing current required for circuit operations might causes inefficiencies in the designated power applications . The power loss becomes very large since the winding loss is proportional to the current square . For this reason, the magnetic material is normally utilized as the electro-magnetic force conduction medium, which generates the same magnetic force but requires less excitation current compare to the air medium . In the traditional magnetic design process, engineers tend to assume a linear characteristic of the magnetics used for the ease of calculations . However, due to the inherent non-linear characteristic of the magnetic material, the resonant inductor L s , and the magnetizing inductor L p in the LLC equipvalent circuitry need to be treated carefully to avoid saturation operations . B . Numerical EM Computation for Integrated Magnetics The nonlinear magnetic field of the magnetic integration can be described by the following equation, ,×ν,×A -J = 0 ( 1 ) where A is the magnetic vector potential, v is the reluctivity and J is the current density, which includes exciting current density and eddy current density . The energy function is generalised from linear techniques . Galerkin's method is used to discretize the governing equation . A system matrix equation can be obtained from (1) and rewritten as shown in (2), where the matrix [S] is the global coefficient matrix . [M] is the frequency harmonic matrix, [K] is the related current density and G is the weighted residual . G = [S]{K}+[M]{A}-{K} ( 2 )
III. Analysis and Simulation ResultsTo examine the non-linear phenomenon of magnetic integration further, a case study example of 350W LLC converter is ...