Design of magnetic component is a key factor in achieving high frequency, high power-density converters. Planar magnetics are widely used in bias power supplies for the benefits of low profile and their compatibility with printed-circuit boards (PCB). The coupled inductors with winding layers sandwiched between two core plates are studied in this dissertation in order to model the self-inductance, winding loss, and core loss.

The most challenging task for the plate-core inductor is to model the magnetic field with finite core dimensions, very non-uniform flux pattern, and large fringing flux. The winding is placed near the edge of the core to maximize the energy within the limited footprint and the amount of energy stored outside the core volume is not negligible. The proportional-reluctance, equal-flux (PREF) model is developed to build the contours with equal amount of flux by governing the reluctance of the flux path. The shapes of the flux lines are modeled by different functions that guided by the finite-element simulation (FES). The field from the flux lines enables calculation of inductance, winding loss, and core loss, etc.

The inductance matrix including self-inductance and mutual inductance of a coupled inductor is important for circuit simulation and evaluation. The derivation of the inductance matrix of inductors with plate-core structure is described in Chapter 2. Two conditions are defined as common-mode (CM) field and differential-mode (DM) field in order to compute the matrix parameters. The proportional-reluctance, equal-flux (PREF) model introduced is employed to find the CM field distribution, and the DM field distribution is found from functions analogous to that of a solenoid's field. The inductance calculated are verified by flex-circuit prototypes with various dimensions, and the application of the inductance model is presented at the last with normalized parameters to cover structures within a wide-range.

In circuit where coupled inductors are used instead of transformers, the phase shift between the primary and secondary side is not always 180 degrees. Therefore, it is important to model the winding loss for a coupled inductor accurately. The winding loss can be calculated from the resistance matrix, which is independent of excitations but only relates to the frequency and geometry. The methodology to derive the resistance matrix from winding losses of coupled inductors is discussed. Winding loss model with 2D magnetic field is improved by including the additional eddy current loss for better accuracy for the plate-core structures. The resistance matrix calculated from the model is verified by both measurement results and finite-element simulation (FES) of coupled-inductor prototypes.

Accurate core loss model is required for designing magnetic components in power converters. Most existing core loss models are based on frequency domain calculation and they cannot be implemented in SPICE simulations. The core loss model in the time domain is discussed in Chapter 5 for arbitrary current excitations. An effective ac flux density is derived to simplify the core loss calculation with non-uniform field distribution. A sub-circuit for core loss simulation is established in LTSPICE that is capable of being integrated to the power stage simulation. Transient behavior and accurate simulation results from the LTSPICE matches very well with the FES results.

An equivalent circuit for coupled windings is developed for inductors with significant fringing effect. The equivalent circuit is derived from a physical model that captures the flux paths by having a leakage inductor and two mutual inductors on the primary and secondary side. A mutual resistor is added to each side in parallel with one mutual inductor to model the winding loss with open circuit and phase-shift impact. Two time-varying resistors are employed to represent the core loss in the time-domain. The equivalent circuit is verified by both finite-element simulation (FES) and prototypes fabricated with flexible circuit.