This report will look at optimization under parameters of uncertainties. It will describe the subject in its wider form, then two model examples will be studied, followed by an application to an ABB product. The Monte Carlo method will be described and scrutinised, with the quasi-Monte Carlo method being favoured for large problems. An example will illustrate how the choice of Monte Carlo method will affect the efficiency of the simulation when evaluating  functions of different dimensions. Then an overview of mathematical optimization is given, from its simplest form to nonlinear, nonconvex  optimization problems containing uncertainties.A Monte Carlo simulation is applied to the design process and cost function for a custom made ABB transformer, where the production process is assumed to contain some uncertainties.The result from optimizing an ABB cost formula, where the in-parameters contains some uncertainties, shows how the price can vary and is not fixed as often assumed, and how this could influence an accept/reject decision.

abstract: This dissertation covers three primary topics and relates them in context. High frequency transformer design, microgrid modeling and control, and converter design as it pertains to the other topics are each investigated, establishing a summary of the state-of-the-art at the intersection of the three as a baseline. The culminating work produced by the confluence of these topics is a novel modular solid-state transformer (SST) design, featuring an array of dual active bridge (DAB) converters, each of which contains an optimized high-frequency transformer, and an array of grid-forming inverters (GFI) suitable for centralized control in a microgrid environment. While no hardware was produced for this design, detailed modeling and simulation has been completed, and results are contextualized by rigorous analysis and comparison with results from published literature. The main contributions to each topic are best presented by topic area. For transformers, contributions include collation and presentation of the best-known methods of minimum loss high-frequency transformer design and analysis, descriptions of the implementation of these methods into a unified design script as well as access to an example of such a script, and the derivation and presentation of novel tools for analysis of multi-winding and multi-frequency transformers. For microgrid modeling and control, contributions include the modeling and simulation validation of the GFI and SST designs via state space modeling in a multi-scale simulation framework, as well as demonstration of stable and effective participation of these models in a centralized control scheme under phase imbalance. For converters, the SST design, analysis, and simulation are the primary contributions, though several novel derivations and analysis tools are also presented for the asymmetric half bridge and DAB. / Dissertation/Thesis / Doctoral Dissertation Electrical Engineering 2019

In today's industrial power converters, converter reliability is essential, and converter topologies are well-established. Without a doubt, the power electronic industry continues to seek efficient power delivery and high power density. Resonant converters, especially LLC converters, have been intensively studied and applied in DC-DC converters. One of the most demanding applications for LLC converters is data centers. To date, LLC Resonant converters, are deployed in many applications for improved efficiency, density, and reliability. With the introduction of WBG devices coupled with the soft switching feature, the switching frequency can be extended beyond Mega-Hertz. With the significant increase in operating frequency, complicated magnetic components can be broken down into a cellular structure, each with a few number of turns. They can be easily implemented using 4-6 layers of PCB windings. Moreover, integrating the cellular cores using flux cancellation can further improve the power density. The proposed integrated magnetics can be automated in the manufacturing process. The magnetic size is reduced at this frequency, and planar magnetics using PCB winding become more relevant. PCB magnetics feature multiple advantages over Litz wire. The benefits are summarized as follows: The labor-intensive manufacturing process can be automated, thus reduction of cost. There is much reduced CM noise by using the shield layer. They have parasitics with much-improved reproducibility in large quantities. PCB windings feature less leakage between transformer windings because of the flexibility of the winding interleaving and the reduced number of turns. There is better thermal management due to the increased surface-to-body ratio. The design has a low profile and high-power density. However, it is not without its own limitations. There are challenges for high frequency PCB-magnetic magnetic design for the LLC converter. Firstly, With the recently developed high frequency core material, a phenomenon referred to as the dimensional resonant is observed. The effects of dimensional resonance were discussed in the literature when using an unusually large core structure; however, it can be observed more frequently under high excitation frequency, particularly with integrated magnetics. This dissertation discusses the dimensional effects of core loss on a PCB-based magnetics structure. A case study is presented on a 3-kW 400-to-48-V LLC prototype running at 1 MHz. The converter utilizes a low-profile matrix of two integrated transformers with a rectangular and thin cross-section area for reduced core loss. Specific solutions are presented. % Secondly, The matrix transformer is suitable for an LLC converter with high output current. However, the matrix transformer also increases the core size and core losses. The core loss degrades the LLC converter's light load and peak efficiency. In this dissertation, We discuss the design process and implementation of the DC-DC stage of the power supply unit for narrow range 48 V data center bus architecture. The optimization takes into account the number of elemental transformers, number of transformer turns, switching frequency, and transformer dimensions, namely winding width and core cross-section area. The optimization process results in a nearly 99% efficient 400-to-48-V LLC with a very high-power density and low profile fully integrated on PCB. A matrix of four transformers is used to reduce the termination loss of the secondary synchronous rectifier and achieve better thermal management. The number of secondary turns is optimized to achieve the best trade-off between winding loss, core loss, and power density. Another challenge arises for magnetic integration when multiple magnetic components with different characteristics come together. For instance, in the case of a transformer and an inductor on the same PCB. The PCB transformer is designed with perfectly interleaved primary and secondary layers to utilize the full PCB layer thickness. As a rule of thumb, the transformer winding layer is designed within 1 to 2 times the skin depth. On the other hand, the inductor's winding lacks interleaving and suffers from high MMF stress on layers. This makes the inductor prone to high eddy currents and eddy loss. Furthermore, this dissertation addresses the challenges associated with the high winding and core loss in the Integrated Transformer-Inductor (ITL). To overcome these challenges, we propose an improved winding design of the ITL by utilizing idle shielding layers for inductor integration within the matrix transformer. This method offers full printed circuit board (PCB) utilization, where all layers are consumed as winding, resulting in a significant reduction in the winding loss of the ITL. Moreover, we propose an improved core structure of the ITL that offers better flux distribution of the leakage flux within the magnetic core. This method reduces the core loss by more than 50% compared to the conventional core structure. We demonstrate the effectiveness of our proposed concepts by presenting the design of the ITL used in a high-efficiency, high-power-density 3-kW 400-to-48-V LLC module. The proposed converter achieves a peak efficiency of 98.7% and a power density of 1500 W/in3. This dissertation presents the concept of matrix inductors to solve such problems. A matrix of four resonant inductors is also designed to reduce the proximity effect between inductor windings and reduce inductor PCB winding loss. The matrix inductor provides a solution for high thermal stress in PCB-based inductors and reduces the inter-winding capacitance between inductor layers. This dissertation solves the challenges in magnetic design in high-frequency DC-DC converters in offline power supplies and data centers. This includes the transformer and inductor of the LLC converter. With the academic contribution in this dissertation, Wide-bandgap devices WBG can be successfully utilized in high-frequency DC-DC converters with Mega-Hertz switching frequency to achieve high efficiency, high power density, and automated manufacturing. The cost will be reduced, and the performance will be improved significantly. / Doctor of Philosophy / Industrial power converters need to be reliable and efficient to meet the power industry's demand for efficient power delivery and high power density. Research should focus on improving existing converter designs to improve fabrication, efficiency, and reliability. Resonant converters have been found to be effective in power conversion, especially in data centers where energy consumption is high. Three-element Resonant converters (LLC) are already used to improve efficiency, density, and reliability. By using Wide Bandgap devices and soft switching, the switching frequency can be extended beyond MHz, simplifying magnetic components and improving power density. The proposed integrated magnetics can be automated during the manufacturing process, further improving power density. At higher frequencies, planar magnetic components made with PCB winding are more effective than Litz wire. They are cheaper to make because of automation, have less common-mode noise, and are more reproducible in large quantities. PCB winding also has a low profile, high-power density, and better thermal management. However, it is not without its own limitations. There are challenges for high frequency PCB-magnetic magnetic design for the LLC converter. Firstly, With the recently developed high frequency core material, a phenomenon referred to as the dimensional resonant is observed. The effects of dimensional resonance were discussed in the literature when using an unusually large core structure; however, it can be observed more frequently under high excitation frequency, particularly with integrated magnetics. This dissertation discusses the effects of core loss on a PCB-based magnetics structure and presents solutions, including a case study on a 3-kW 400-to-48 V LLC prototype running at 1 MHz. Another challenge arises for magnetic integration when multiple magnetic components with different characteristics come together. For instance, in the case of a transformer and an inductor on the same PCB. The PCB transformer is designed with perfectly interleaved winding and low Ohmic loss. On the other hand, the inductor's winding lacks interleaving and suffers from a high proximity field. This makes the inductor prone to high eddy currents and eddy loss. This dissertation presents the concept of matrix inductors to solve such problems. A matrix of four resonant inductors is also designed to reduce the proximity effect between inductor windings and reduce inductor PCB winding loss. The matrix inductor provides a solution for high thermal stress in PCB-based inductors and reduces the inter-winding capacitance between inductor layers. Furthermore, this dissertation addresses the challenges associated with the high winding and core loss in the Integrated Transformer-Inductor (ITL). To overcome these challenges, we propose an improved winding design of the ITL by utilizing idle shielding layers for inductor integration within the matrix transformer. This method offers full printed circuit board (PCB) utilization, where all layers are consumed as winding, resulting in a significant reduction in the winding loss of the ITL. Moreover, we propose an improved core structure of the ITL that reduces the core loss by more than 50% compared to the conventional core structure. We demonstrate the effectiveness of our proposed concepts on a high-efficiency, high-power-density 3-kW 400-to-48-V LLC module. The proposed converter achieves a peak efficiency of 98.7% and a power density of 1500 W/in3. This dissertation solves the challenges in magnetic design in high-frequency DC-DC converters in offline power supplies and data centers. This includes the transformer and inductor of the LLC converter. With the academic contribution in this dissertation, Wide-bandgap devices WBG can be successfully utilized in high-frequency DC-DC converters with Mega-Hertz switching frequency to achieve high efficiency, high power density, and automated manufacturing. The cost will be reduced, and the performance will be improved significantly.

The move toward electric vehicles (EVs) has a significant impact to reduce greenhouse gas (GHG) emissions and make transportation more eco-friendly. Fast-charging stations play a crucial role in this transition, making EVs more convenient for adoption specifically when driving in long distance. However, the challenge is to create a fast-charging system that can work with the different types of EVs and their varying power needs while still being efficient and effective. In this context, this thesis embarks on this journey by introducing an innovative solution for efficient universal fast charging, spanning both low voltage and high voltage battery systems. A novel, configurable dual secondary resonant converter is proposed, which empowers the charging module to extend its output range without imposing additional demands on the resonant tank components. This solution addresses the pressing need for a wide output voltage range in fast-charging standard in the growing EV landscape. To ensure optimal performance across a broad voltage and power range, the thesis employs an analytical model for LLC resonant converters to optimize the resonant components. This strategic component selection aims to achieve the desired output voltage and power range while minimizing conduction losses. The proposed topology and design methodology are rigorously validated through the development of a 10 kW prototype. Furthermore, the study introduces a two degrees of freedom (2DoF) control scheme for the proposed LLC resonant converter with the configurable dual secondary LLC converter topology. An analytical model is formulated to guide the selection of control parameters, ensuring coverage of the desired output voltage and power range without compromising system efficiency. The steady-state analytical model is utilized for determining optimized control parameters at each operating point within the converter's output range. To enhance the charging module's power density and efficiency, a high-frequency litz-wire transformer design methodology is introduced. The transformer's core size is optimized to achieve high power density and efficiency, while the winding configuration is chosen to minimize conduction losses. Finite Element Analysis (FEA) simulations validate transformer losses and operating temperatures. The culmination of this research is the development of a 30 kW charging module prototype. This prototype features an LLC resonant converter with a configurable dual secondary and two degrees of freedom control for output voltage control. The component ratings, estimated losses, and power board design are carefully considered to create a compact and efficient charging module. Experimental testing across a universal output voltage and power range con rms the effectiveness of the proposed solution. In summary, this thesis presents a comprehensive approach to design of a module for EV fast charging application addressing voltage range, efficiency, and component optimization, resulting in the successful development of a high-performance charging module prototype. / Thesis / Doctor of Engineering (DEng)

With the rapid increase of cloud computing and the high demand for digital content, it is estimated that the power consumption of the IT industry will reach 10 % of the total electric power in the USA by 2020. Multi-core processors (CPUs) and graphics processing units (GPUs) are the key elements in fulfilling all of the digital content requirements, but come with a price of more power-hungry processors, driving the power per server rack to 20 KW levels. The need for more efficient power management solutions on the architecture level, down to the converter level, is inevitable. Recently, data centers have replaced the 12V DC server rack distribution with a 48V DC distribution, producing a significant overall system efficiency improvement. However, 48V rack architecture raises significant challenges for the voltage regulator modules (VRMs) required for powering the processor. The 48V VRM in the vicinity of the CPU needs to be designed with very high efficiency, high power density, high light-load efficiency, as well as meet all transient requirements by the CPU and GPU. Transferring the well-developed multi-phase buck converter used in the 12V VRM to the 48V distribution platform is not that simple. The buck converter operating with 48V, stepping down to sub 2V, will be subjected to significant switching related loss, resulting in lower overall system efficiency. These challenges drive the need to look for more efficient architectures for 48V VRM solutions. Two-stage conversions can help solve the design challenges for 48V VRMs. A first-stage unregulated converter is used to step-down the 48V to a specific intermediate bus voltage. This voltage will feed a multi-phase buck converter that powers the CPU. An unregulated LLC converter is used for the first-stage converter, with zero voltage switching (ZVS) operation for the primary side switches, and zero current switching (ZCS) along with ZVS operation, for the secondary side synchronous rectifiers (SRs). The LLC converter can operate at high frequency, in order to reduce the magnetic components size, while achieving high-efficiency. The high-efficiency first-stage, along with the scalability and high bandwidth control of the second-stage, allows this architecture to achieve high-efficiency and power density. This architecture is simpler to adopt by industry, by plugging the unregulated converter before the existing multi-phase buck converters on today's platforms. The first challenge for this architecture is the transformer design of the first-stage LLC converter. It must avoid all of the loss associated with high frequency operations, and still achieve high power density without scarifying efficiency. In this thesis, the integrated matrix transformer structure is optimized by SR integration with windings, interleaved primary side termination, and a better PCB winding arrangement to achieve high-efficiency and power density, and minimize the losses associated with high-frequency operations. The second challenge is the light load efficiency improvement. In this thesis a light load efficiency improvement is proposed by a dynamic change of the intermediate bus voltage, resulting in more than 8 % light load efficiency improvements. The third challenge is the selection of the optimal bus voltage for the two-stage architecture. The impact of different bus voltages was analyzed in order to maximize the overall conversion efficiency. Multiple 48V unregulated converters were designed with maximum efficiency >98 %, and power densities >1000 W/in3, with different output voltages, to select the optimal bus voltage for the two-stage VRM. Although the two-stage VRM is more scalable and simpler to design and adopt by current industry, the efficiency will reduce as full power flows in two cascaded DC/DC converters. Single-stage conversion can achieve higher-efficiency and power-density. In this thesis, a quasi-parallel Sigma converter is proposed for the 48V VRM application. In this structure, the power is shared between two converters, resulting in higher conversion efficiency. With the aid of an optimized integrated magnetic design, a Sigma converter suitable for narrow voltage range applications was designed with 420 W/in3 and a maximum efficiency of 94 %. Later, another Sigma converter suitable for wide voltage range applications was designed with 700W/in3 and a maximum efficiency of 95 %. Both designs can achieve higher efficiency than the two-stage VRM and all other state-of-art solutions. The challenges associated with the Sigma converter, such as startup and closed loop control were addressed, in order to make it a viable solution for the VRM application. The 48V rack architecture requires regulated 12V output converters for various loads. In this thesis, a regulated LLC is used to design a high-efficiency and power-density 48V bus converter. A novel integration method of the inductor and transformer helps the LLC achieve the required regulation capability with minimum losses, resulting in a converter that can provide 1KW of continuous power with efficiency of 97.8 % and 700 W/in3 power density. This dissertation discusses new power architectures with an optimized design for the 48V rack architectures. With the academic contributions in this dissertation, different conversion architectures can be utilized for 48V VRM solutions that solve all of the challenges associated with it, such as scalability, high-efficiency, high density, and high BW control. / Doctor of Philosophy / With the rapid increase of cloud computing and the high demand for digital content, it is estimated that the power consumption of the IT industry will reach 10 % of the total electric power in the USA by 2020. Multi-core processors (CPUs) and graphics processing units (GPUs) are the key elements in fulfilling all of the digital content requirements but come with a price of more power-hungry processors, driving the power per server rack to 20 KW levels. The need for more efficient power management solutions on the architecture level, down to the converter level, is inevitable. The data center manufacturers have recently adopted a more efficient architecture that supplies a 48V DC server rack distribution instead of a 12V DC distribution to the server motherboard. This helped reduce costs and losses, but as a consequence, raised a challenge in the design of the DC/DC voltage regulator modules (VRM) supplied by the 48V, in order to power the CPU and GPU. In this work, different architectures will be explored for the 48V VRM, and the trade-off between them will be evaluated. The main target is to design the VRM with very high-efficiency and high-power density to reduce the cost and size of the CPU/GPU motherboards. First, a two-stage power conversion structure will be used. The benefit of this structure is that it relies on existing technology using the 12V VRM for powering the CPU. The only modification required is the addition of another converter to step the 48V to the 12V level. This architecture can be easily adopted by industry, with only small modifications required on the system design level. Secondly, a single-stage power conversion structure is proposed that achieves higher efficiency and power density compared to the two-stage approach; however, the structure is very challenging to design and to meet all requirements by the CPU/GPU applications. All of these challenges will be addressed and solved in this work. The proposed architectures will be designed using an optimized magnetic structure. These structures achieve very high efficiency and power density in their designed architectures, compared to state-of-art solutions. In addition, they can be easily manufactured using automated manufacturing processes.

Modern data center power architecture developing trend is analyzed, efficiency improvement method is also discussed. Literature survey of high frequency isolated power conversion system which is also called solid state transformer is given including application, topology, device and magnetic transformer. Then developing trend of this research area is clearly shown following by research target. State of art wide band gap device including silicon carbide (SiC) and gallium nitride (GaN) devices are characterized and compared, final selection is made based on comparison result. Mostly used high frequency high power DC/DC converter topology dual active bridge (DAB) is introduced and compared with novel CLLC resonant converter in terms of switching loss and conduction loss point of view. CLLC holds ZVS capability over all load range and smaller turn off current value. This is beneficial for high frequency operation and taken as our candidate. Device loss breakdown of CLLC converter is also given in the end. Medium voltage high frequency transformer is the key element in terms of insulation safety, power density and efficiency. Firstly, two mostly used transformer structures are compared. Then transformer insulation requirement is referred for 4160 V application according to IEEE standard. Solid insulation material are also compared and selected. Material thickness and insulation distance are also determined. Insulation capability is preliminary verified in FEA electric field simulation. Thirdly two transformer magnetic loss model are introduced including core loss model and litz wire winding loss model. Transformer turn number is determined based on core loss and winding loss trade-off. Different core loss density and working frequency impact is carefully analyzed. Different materials show their best performance among different frequency range. Transformer prototype is developed following designed parameter. We test the developed 15 kW 500 kHz transformer under 4160 V dry type transformer IEEE Std. C57.12.01 standard, including basic lightning test, applied voltage test, partial discharge test. 500 kHz 15 kW CLLC converter gate drive is our design challenge in terms of symmetry propagation delay, cross talk phenomenon elimination and shoot through protection. Gate drive IC is carefully selected to achieve symmetrical propagation delay and high common mode dv/dt immunity. Zero turn off resistor is achieved with minimized gate loop inductance to prevent cross talk phenomenon. Desaturation protection is also employed to provide shoot through protection. Finally 15 kW 500 kHz CLLC resonant converter is developed based on 4160V 500 kHz transformer and tested up to full power level with 98% peak efficiency. / Master of Science

With the fast development of information technology (IT) industry, the demand and market volume for off-line power supplies keeps increasing, especially those for desktop, flat-panel TV, telecommunication, computer server and datacenter. An off-line power supply normally consists of electromagnetic interference (EMI) filter, power factor correction (PFC) circuit and isolated DC/DC converter. Isolated DC/DC converter occupies more than half of the volume in an off-line power supply and takes the most control responsibilities, so isolated DC/DC converter is the key aspect to improve the overall performance and reduce the total cost for off-line power supply. On the other hand, of all the power supplies for industrial applications, those for the data center servers are the most performance driven, energy and cost conscious due to the large electricity consumption. The total power consumption of today's data centers is becoming noticeable. Moreover, with the increase in cloud computing and big data, energy use of data centers is expected to continue rapidly increasing in the near future. It is very challenging to design isolated DC/DC converters for datacenters since they are required to provide low-voltage high-current output and fast transient response. The LLC resonant converters have been widely used as the DC-DC converter in off-line power supplies and datacenters due to its high efficiency and hold-up capability. Using LLC converters can minimize switching losses and reduce electromagnetic interference. Almost all the high-end offline power supplies employs LLC converters as the DC/DC converter. But there are three major challenges in LLC converters. Firstly, the control characteristics of the LLC resonant converters are very complex due to the dynamics of the resonant tank. This dissertation proposes to implement a special LLC control method, state-trajectory control, with a low-cost microcontroller (MCU). And further efforts have been made to integrate all the state-trajectory control function into one MCU for high-frequency LLC converters, including start-up and short-circuit protection, fast transient response, light load efficiency improvement and SR driving. Secondly, the transformer in power supplies for IT industry is very bulky and it is very challenging to design. By pushing switching frequency up to MHz with gallium nitride (GaN) devices, the magnetics can be integrated into printed circuit board (PCB) windings. This dissertation proposes a novel matrix transformer structure and its design methodology. On the other hand, shielding technique can be employed to suppress the CM noise for PCB winding transformer. This dissertation proposes a novel shielding technique, which not only suppresses CM noise, but also improves the efficiency. The proposed transformer design and shielding technique is applied to an 800W 400V/12V LLC converter design. Thirdly, the LLC converters have sinusoidal current shape due to the nature of resonance, which has larger root mean square (RMS) of current, as well as larger conduction loss, compared to pulse width modulation (PWM) converter. This dissertation employs three-phase interleaved LLC converters to reduce the circulating energy by inter-connecting the three phases in certain way, and proposed a novel magnetic structure to integrated three inductors and three transformers into one magnetic core. By pushing switching frequency up to 1MHz, all the magnetics can be implemented with 4-layer PCB winding. Additional 2-layer shielding can be integrated to reduce CM noise. The proposed magnetic structure is applied to a 3kW 400V/12V LLC converter. This dissertation solves the challenges in analysis, digital control, magnetic design and EMI in high-frequency DC/DC converters in off-line power supplies. With the academic contribution in this dissertation, GaN devices can be successfully applied to high-frequency DC/DC converters with MHz switching frequency to achieve high efficiency, high power density, simplified but high-performance digital control and automatic manufacturing. The cost will be reduced and the performance will be improved significantly. / Ph. D.

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No description available.

Rapid expansion of the information technology (IT) sector, market size and consumer interest for off-line power supply continue to rise, particularly for computers, flat-panel TVs, servers, telecom, and datacenter applications. Normal components of an off-line power supply include an electromagnetic interference (EMI) filter, a power factor correction (PFC) circuit, and an isolated DC-DC converter. For off-line power supply, an isolated DC-DC converter offers isolation and output voltage adjustment. For an off-line power supply, it takes up significantly more room than the rest; thus, an isolated DC-DC converter is essential for enhancing the overall performance and lowering the total cost of an off-line power supply. In contrast, data center server power supplies are the most performance-driven, energy-efficient, and cost-aware of any industrial application power supply. The full extent of data centers' energy consumption is coming into focus. By 2030, it is anticipated that data centers will require around 30,000 TWh, or 7.6% of world power usage. In addition, with the rise of cloud computing and big data, the energy consumption of data centers is anticipated to continue rising rapidly in the near future. In data centers, isolated DC-DC converters are expected to supply even higher power levels without expanding their size and with much greater efficiency than the present standard, which makes their design even more challenging. LLC resonant converters are frequently utilized as DC-DC converters in off-line power supply and data centers because of their high efficiency and hold-up capabilities. LLC converters may reduce electromagnetic interference because the primary switches and secondary synchronous rectifiers (SRs) both feature zero-voltage-switching (ZVS) and zero-current-switching (ZCS) for the SRs. Almost every state-of-the-art off-line power supply uses LLC converters in their DC-DC transformations. However, LLC converters face three important challenges. First, the excessive core loss caused by the uneven flux distribution in planar magnetics, owing to the huge size and high-frequency operation of the core. These factors led to the observation of dimensional resonance within the core and an excessive amount of eddy current circulating within the core, which resulted in the generation of high eddy loss within the ferrite material. This was normally assumed to be negligible for small core sizes and lower frequencies. This dissertation proposes methods to help redistribute the flux in the core, particularly in the plates where the majority of core losses are concentrated, and to provide more paths for the flux to flow so that the plates' thickness can effectively be reduced by half and core losses, particularly eddy loss, are reduced significantly. Second, the majority of power supplies in the IT sector are needed to deliver high-current output, but the transformer is cumbersome and difficult to build because of its high conduction losses. In addition, establishing a modular solution that can be scaled up to greater power levels while attaining a superior performance relative to best practices is quite difficult. By increasing the switching frequency to several hundred kilohertz using wide-band-gap (WBG) transistors, printed circuit board (PCB) windings may include magnetics. This dissertation offers a modular and scalable matrix transformer structure and its design technique, allowing any number of elemental transformers to be integrated into a single magnetic core with significantly reduced winding loss and core loss. It has been shown that the ideal power limitations per transformer for PCB-based magnetics beat the typical litz wire design in all design areas, in addition to the unique advantages of PCB-magnetics, such as their low profile, high density, simplicity, and automated construction. Alternatively, shielding layers may be automatically put into the PCB windings between the main and secondary windings during the production process to reduce CM noise. A method of shielding is presented to reduce CM noise. The suggested transformer design and shielding method are used in the construction of a 3 kW 400V/48 V LLC converter, with a maximum efficiency of 99.06% and power density of 530W/in3. Thirdly, LLC converters with a matrix transformer encounter a hurdle for extending greater power, including the number of transformers needed and the magnetic size. In addition to the necessity of resonant inductors, which increase the complexity and size of the magnetic structure, there is a need for a resonant inductor. By interconnecting the three-phases in a certain manner, three-phase interleaved LLC converters may lower the circulating energy, but they have large and numerous magnetic components. In this dissertation, a new topology for three-phase LLC resonant converters is proposed. Three-phase systems have the advantage of flux cancellation, which may be used to further simplify the magnetic structure and decrease core loss. In addition, a study of the various three-phase topologies is offered, and a criterion for selecting the best suitable topology is shown. Compared to the single-phase LLC, the suggested topology has less winding loss and core loss. In addition, three-phase transformers have a lower volt-second rating, and smaller core sizes may be used to mitigate the impact of eddy loss in the ferrite material. In contrast, three-phase systems offer superior EMI performance, which is shown in the loss and size of the EMI filter, and much less output voltage ripple, which is reflected in the size of the output filter. Finally, several methods of integrating resonant inductors into transformer magnetics are presented in order to accomplish a simple, compact, and cost-effective magnetic architecture. By increasing the switching frequency to 500 kHz, all six transformers and six inductors may be achieved using four-layer PCB winding. To decrease CM noise, additional 2-layer shielding may be implemented. A 500 kHz, 6-8 kW, 400V/48V, three-phase LLC converter with the suggested magnetic structure achieves 99.1% maximum efficiency and a power density of 1000 W/in3. This dissertation addresses the issues of analysis, magnetic design, expansion to higher power levels, and electromagnetic interference (EMI) in high-frequency DC/DC converters used in off-line power supply and data centers. WBG devices may be effectively used to enable high-frequency DC/DC converters with a hundred kilohertz switching frequency to achieve high efficiency, high power density, simple yet high-performance, and automated manufacture. Costs will be minimized, and performance will be considerably enhanced. / Doctor of Philosophy / The IT industry, market size, and customer interest in off-line power supply continue to grow quickly, especially for computers, flat-panel TVs, servers, telecom, and datacenter applications. Off-line power supplies usually have a DC-DC converter, an EMI filter, and a PFC circuit. A DC-DC converter is needed for an off-line power supply. An isolated DC-DC converter makes an off-line power supply work better and cost less, even though it takes up more space than the rest. But power supplies for data center servers are the most performance-driven, energy-efficient, and cost-conscious industrial applications. It's becoming clear how much energy data centers use. By 2030, data centers will use 7.6% of the world's power, or 30,000 TWh. With the rise of cloud computing and big data, energy use in data centers is likely to go up by a lot. In data centers, isolated DC-DC converters are expected to have much more power without getting bigger and to be much more efficient than the current standard. This makes their design even harder. LLC resonant converters are often used as DC-DC converters in data centers and off-line power supplies because they are very efficient and easy to control. LLC converters may have less electromagnetic interference because both the primary switches and the secondary synchronous rectifiers (SRs) have zero-voltage-switching (ZVS) and zero-current-switching (ZCS). Almost every modern off-line power supply uses LLC converters for DC-DC stage. LLC converters have to deal with three big problems. Due to the large size of the core and the high frequency of operation, the uneven distribution of flux in planar magnetics causes too much core loss. This dissertation suggests ways to redistribute flux in the core, especially in the plates where most core losses are concentrated and provide more flux paths to reduce plate thickness by half and core losses, especially eddy loss. Second, most IT power supplies need to put out a lot of current, but transformers are bulky and hard to build because they lose a lot of current. It is hard to make a modular solution that can scale up to higher levels of power and perform better than best practices. With wide-band-gap (WBG) transistors, the switching frequency can be raised to several hundred kilohertz so that magnetics can be added to PCB windings. This dissertation describes a modular and scalable matrix transformer structure and design method that lets any number of elemental transformers be put into a single magnetic core with much less winding loss and core loss. PCB-based magnetics have a low profile, a high density, are easy to build, and can be built automatically. Their ideal power limits per transformer beat the typical litz wire design in every way. Shielding layers can be added automatically between the main and secondary PCB windings to cut down on CM noise. CM noise is lessened by shielding. The suggested transformer design and shielding method are used to build a 3 kW 400V/48 V LLC converter with a maximum efficiency of 99.06% and a power density of 530W/in3. Third, LLC converters with matrix transformers can't get more power without more transformers and a bigger magnetic size. Resonant inductors, which add to the size and complexity of a magnetic structure, are also needed. By connecting the three phases, three-phase interleaved LLC converters use less energy, but they have a lot of magnetic parts. In this paper, a three-phase LLC resonant converter topology is proposed. In three-phase systems, flux cancellation makes magnetic structures easier to understand and reduces core loss. There is also a study of three-phase topologies and a set of criteria for choosing one. Compared to the single-phase LLC, the topology cuts down on winding and core loss. Three-phase transformers have a lower volt-second rating, and ferrite material eddy loss can be reduced by making the core smaller. The size and loss of the EMI filter show that three-phase systems have less output voltage ripple and better EMI performance. Finally, several ways of putting resonant inductors into the magnetics of a transformer are shown to make a magnetic architecture that is simple, small, and cheap. At 500 kHz, all six transformers and all six inductors can be wound on a four-layer PCB. CM noise can be cut down with 2-layer shielding. With the suggested magnetic structure, a 500 kHz, 6-8 kW, 400V/48V, three-phase LLC converter can reach 99.1% maximum efficiency and 1000 W/in3. This dissertation presents analysis, magnetic design, expanding to higher power levels, and electromagnetic interference (EMI) in high-frequency DC/DC converters used in off-line power supplies and data centers. WBG devices can be used to make high-frequency DC/DC converters with a switching frequency of a few hundred kilohertz that are powerful, easy to use, and can be automated. Both cost and performance will get better.