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. / Ph. D. / Compact power supplies requires low profile, high quality magnetic components such as inductors and two-winding inductors in order to achieve high efficiency and high density. The plate-core inductors comprise multilayer windings sandwiched by two core plates on the top and bottom, and the total thickness of the inductor is significantly smaller than the conventional surface-mount inductors. A model based on physical examination of the flux pattern is developed to calculate the magnetic field distribution of the plate-core inductor. The other performance factors such as inductance, winding loss, and core loss can also be calculated from the field distribution. An improved equivalent circuit is developed in order to simulate the voltage and current of the inductor in an arbitrary circuit. Compared to conventional equivalent circuit, the improved model includes the winding-loss variation with asymmetric current excitations. A core-loss sub-circuit is developed in SPICE simulation tools so that no finite-element simulations (FES) are required to obtain the core loss in the time domain, and the cost of time is reduced by more than 80%. A prototype is fabricated with inductors of different geometrical dimensions to verify the equivalent circuit under small signal condition. Good correlations among calculation, FES, and measurement are obtained with less than 13% error.

Increasing the power density of power electronic converters while reducing or maintaining the same cost, offers a higher potential to meet the current trend inrelation to various power electronic applications. High power density converters can be achieved by increasing the switching frequency, due to which the bulkiest parts, such as transformer, inductors and the capacitor's size in the convertercircuit can be drastically reduced. In this regard, highly integrated planar magnetics are considered as an effective approach compared to the conventional wire wound transformers in modern switch mode power supplies (SMPS). However, as the operating frequency of the transformers increase from several hundred kHz to MHz, numerous problems arise such as skin and proximity effects due to the induced eddy currents in the windings, leakage inductance and unbalanced magnetic flux distribution. In addition to this, the core losses whichare functional dependent on frequency gets elevated as the operating frequency increases. Therefore, this thesis provides an insight towards the problems related to the high frequency magnetics and proposes a solution with regards to different aspects in relation to designing high power density, energy efficient transformers.The first part of the thesis concentrates on the investigation of high power density and highly energy efficient coreless printed circuit board (PCB) step-down transformers useful for stringent height DC-DC converter applications, where the core losses are being completely eliminated. These transformers also maintain the advantages offered by existing core based transformers such as, high coupling coefficient, sufficient input impedance, high energy efficiency and wide frequencyband width with the assistance of a resonant technique. In this regard, several coreless PCB step down transformers of different turn’s ratio for power transfer applications have been designed and evaluated. The designed multilayered coreless PCB transformers for telecom and PoE applications of 8,15 and 30W show that the volume reduction of approximately 40 - 90% is possible when compared to its existing core based counterparts while maintaining the energy efficiency of the transformers in the range of 90 - 97%. The estimation of EMI emissions from the designed transformers for the given power transfer application proves that the amount of radiated EMI from a multilayered transformer is lessthan that of the two layered transformer because of the decreased radius for thesame amount of inductance.The design guidelines for the multilayered coreless PCB step-down transformer for the given power transfer application has been proposed. The designed transformer of 10mm radius has been characterized up to the power level of 50Wand possesses a record power density of 107W/cm3 with a peak energy efficiency of 96%. In addition to this, the design guidelines of the signal transformer fordriving the high side MOSFET in double ended converter topologies have been proposed. The measured power consumption of the high side gate drive circuitvitogether with the designed signal transformer is 0.37W. Both these signal andpower transformers have been successfully implemented in a resonant converter topology in the switching frequency range of 2.4 – 2.75MHz for the maximum load power of 34.5W resulting in the peak energy efficiency of converter as 86.5%.This thesis also investigates the indirect effect of the dielectric laminate on the magnetic field intensity and current density distribution in the planar power transformers with the assistance of finite element analysis (FEA). The significanceof the high frequency dielectric laminate compared to FR-4 laminate in terms of energy efficiency of planar power transformers in MHz frequency region is also explored.The investigations were also conducted on different winding strategies such as conventional solid winding and the parallel winding strategies, which play an important role in the design and development of a high frequency transformer and suggested a better choice in the case of transformers operating in the MHz frequency region.In the second part of the thesis, a novel planar power transformer with hybrid core structure has been designed and evaluated in the MHz frequency region. The design guidelines of the energy efficient high frequency planar power transformerfor the given power transfer application have been proposed. The designed corebased planar transformer has been characterized up to the power level of 50W and possess a power density of 47W/cm3 with maximum energy efficiency of 97%. This transformer has been evaluated successfully in the resonant converter topology within the switching frequency range of 3 – 4.5MHz. The peak energy efficiency ofthe converter is reported to be 92% and the converter has been tested for the maximum power level of 45W, which is suitable for consumer applications such as laptop adapters. In addition to this, a record power density transformer has been designed with a custom made pot core and has been characterized in thefrequency range of 1 - 10MHz. The power density of this custom core transformer operating at 6.78MHz frequency is 67W/cm3 and with the peak energy efficiency of 98%.In conclusion, the research in this dissertation proposed a solution for obtaining high power density converters by designing the highly integrated, high frequency(1 - 10MHz) coreless and core based planar magnetics with energy efficiencies inthe range of 92 - 97%. This solution together with the latest semiconductor GaN/SiC switching devices provides an excellent choice to meet the requirements of the next generation ultra flat low profile switch mode power supplies (SMPS).

The trend in isolated DC/DC bus converters is to increase the output power in the same brick form factors that have been used in the past. Traditional intermediate bus converters (IBCs) use silicon power metal oxide semiconductor field effect transistors (MOSFETs), which recently have reached the limit in terms of turn on resistance (RDSON) and switching frequency. In order to make the IBCs smaller, the switching frequency needs to be pushed higher, which will in turn shrink the magnetics, lowering the converter size, but increase the switching related losses, lowering the overall efficiency of the converter. Wide-bandgap semiconductor devices are becoming more popular in commercial products and gallium nitride (GaN) devices are able to push the switching frequency higher without sacrificing efficiency. GaN devices can shrink the size of the converter and provide better efficiency than its silicon counterpart provides. A survey of current IBCs was conducted in order to find a design point for efficiency and power density. A two-stage converter topology was explored, with a multiphase buck converter as the front end, followed by an LLC resonant converter. The multiphase buck converter provides regulation, while the LLC provides isolation. With the buck converter providing regulation, the switching frequency of the entire converter will be constant. A constant switching frequency allows for better electromagnetic interference (EMI) mitigation. This work includes the details to design and implement a hard-switched multiphase buck converter with planar magnetics using GaN devices. The efficiency includes both the buck efficiency and the overall efficiency of the two-stage converter including the LLC. The buck converter operates with 40V - 60V input, nominally 48V, and outputs 36V at 1 kW, which is the input to the LLC regulating 36V – 12V. Both open and closed loop was measured for the buck and the full converter. EMI performance was not measured or addressed in this work. / Master of Science / Traditional silicon devices are widely used in all power electronics applications today, however they have reached their limit in terms of size and performance. With the introduction of gallium nitride (GaN) field effect transistors (FETs), the limits of silicon can now be passed with GaN providing better performance. GaN devices can be switched at higher switching frequencies than silicon, which allows for the magnetics of power converters to be smaller. GaN devices can also achieve higher efficiency than silicon, so increasing the switching frequency will not hurt the overall efficiency of the power converter. GaN devices can handle higher switching frequencies and larger currents while maintaining the same or better efficiencies over their silicon counterparts. This work illustrates the design and implementation of GaN devices into a multiphase buck converter. This converter is the front end of a two-stage converter, where the buck will provide regulation and the second stage will provide isolation. With the use of higher switching frequencies, the magnetics can be decreased in size, meaning planar magnetics can be used in the power converter. Planar magnetics can be placed directly inside of the printing circuit board (PCB), which allows for higher power densities and easy manufacturing of the magnetics and overall converter. Finally, the open and closed loop were verified and compared to the current converters that are on the market in the 48V – 12V area of intermediate bus converters (IBCs).