Modelling and Design of Advanced High Frequency Transformers

Transcription

1 Modelling and Design of Advanced High Frequency Transformers Wayne Water Griffith School of Engineering Science, Environment, Engineering and Technology Griffith University Submitted in fulfillment of the requirements of the degree of Doctor of Philosophy December 2013

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3 Abstract Carbon dioxide emission reduction has been a popular topic in recent years because it alleviates the current global warming crisis. Hence, there is an urgent need to adapt current technologies to help reduce carbon dioxide emissions before the global warming situation worsens. Amongst carbon dioxide reduction technologies, Electric Vehicle (EV) and renewable energy technologies are most likely to assist in improving this current status of the environmental issue in coming years. Due to increased interest in energy storage systems, such as EV and renewable energy, there is a pending need to improve the existing DC-DC converters used. The DC-DC converter systems used at present are usually bulky, costly and inefficient due to their low operating frequency. Hence, by increasing the operating frequency of the DC-DC converter, the size of the passive elements can be greatly reduced. Among these passive elements, the transformer occupies the most important role indisputably. A High Frequency Coaxial Transformer (HFCT), with a range of 1 kw to 20 kw was designed and introduced in this dissertation. The operating frequency was raised to between 100 khz and 300 khz in order to achieve high power densities and high performance efficiency. However, the coupling capacitance accompanied by an increased operating frequency (which couples high frequency noise between the primary and secondary windings) can cause serious common mode problems. Hence, the Faraday shield was placed between the windings of introduced transformers. This reduces the coupling capacitance and consequently the electromagnetic interference. The shielding effect analysis has been conducted to verify the HFCT performance with the insertion of the Faraday shield. On the other hand, since the early 1980 s, resonant converters have attracted a great deal of interest for switching power supplies because of their high power efficiencies. Due to the trend for high efficiency and high power density of converter applications, the operating frequency needs to be further increased. However, greater switching losses accompanied by the increased operating frequency, results in reduced power efficiency of the application. Thus, the resonant topology was introduced for this issue, which has the ability to adopt voltage levels within a specific range. There are three types of resonant converters; series, parallel and the combined series-parallel topology. Due to design difficulties in the high frequency control circuit design and the extreme complexity of the magnetic integration, the i

4 series-parallel type resonant converter has only recently been seen on the market. This type of resonant converter is known as Line Level Control (LLC) Converter, which means the leakage inductance (L s ) and the magnetizing inductance (L p ) are utilized as part of the resonant tank in conjunction with the use of the resonant capacitance (C s ). To achieve Zero Voltage Switching (ZVS) or Zero Current Switching (ZCS) for the LLC converter, the design precision of the L s and the L p are very important, whereas the C s can be pre-selected according to the required resonant frequency. A novel structure High Frequency (HF) planar transformer was proposed in this dissertation for uses in the LLC converter; in which the transformer was designed to magnetically couple with its magnetic components. This design reduces the volume of integrated magnetics compared to the other designs, as there are no protruding magnetic pieces. The novel structure has a number of advantages compared with the conventional stand-alone structures. These advantages include a lower profile, improved controllability of the L s, higher efficiency and reduced cost. In addition, compared with commercial magnetic integration products, the introduced transformer is more cost-effective, where the magnetic integration is achieved by introducing the magnetic insertion outside the transformer between primary and secondary windings. Moreover, multi-strand Litz wires are utilized for introduced transformers. The use of twisted Litz wires significantly reduces the manufacturing cost and increases the utilization of the core winding area. However, the drawback is the difficulty of the design work, especially under high power excitation and HF operation. This dissertation presents a detailed analysis of Litz wires utilized at the system level; while other publications have only presented the analysis in strand and bundle level. Finally, Finite Element Method (FEM) analysis was employed to investigate the eddy current losses, power losses, inductance calculation and power loss depletion of the designed transformers. The modeling techniques, analysis, and methodology used to solve problems, simulation procedures and results could be of interest to other researchers and power converter industries. ii

5 Statement of Originality This is to certify that to the best of my knowledge, this work has not been submitted for any degree or diploma in any university. The content of this thesis is my own work, and the report contains no material previously published or written by another person except where the reference is stated in the report itself. Wayne Water Date iii

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7 Acknowledgements The success of this project could not have been guaranteed without the ongoing support and guidance provided by my principal supervisor Professor Junwei Lu. I am more than grateful to have studied and worked with him for the past 5 years, and finally became one of his research students. With his guidance, encouragement and inspiration, this project is now able to be completed with the presented results. Also, to my Associate Professor Steven O Keefe; I have been entirely beneficial from his knowledge and patience during my research time at Griffith University. I would also like to express a special thank you to the Head of the Research Centre at Griffith University, Professor David Thiel, for his support in attending the 12 th MMM/INTERMAG conference at Chicago; along with the supporting scholarship during the thesis writing up stage. This work was supported in part of ARC Funded Projects under grant DP , project named High Frequency and High Power Density Magnetics and its Integrated Magnetic Circuit for Solar Renewable Energy Conversion Systems. Special thanks to the project leader Professor Francis Dawson, with his kindness support, a close collaboration between the University of Toronto and Griffith University has come true. To the staff of Griffith University Office of Technical Services, particularly Mark Ferguson, thank you for the advice and assistance in component acquisition. Also, to the secretary, Lynda Ashworth, truly appreciate her kindness and help during my time at the University. Of course, not forgetting to mention my most helpful research colleagues, Boyuan Zhu, Domagoj Leskarac, Sascha Stegen, Hengxu Li and Chiraq Panchal; particularly Boyuan Zhu and Domagoj Leskarac, who have been my greatest proof-readers for the dissertation and in the paper publications. Finally, I would like to thank my girlfriend Aileen YC Shih, Brother Sean Kennan, my whole family, and also my best friend, Mei Yee Leong who has accompanied all my sports and non-sporting interests. v

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9 Publications Two journal papers and seven conference papers were published throughout the PhD candidature period; publications are listed as below. One poster presentation and two oral presentations have been conducted in person at the conference. Refereed Journal Articles 1. Title Shielding Analysis of Coaxial High Frequency Transformers used for Electric Vehicle On-Board Charging Systems Wayne Water & Junwei Lu IEEE Transactions on Magnetics, Vol. 49, No. 7, July 2013, pp Title Improved High-Frequency Planar Transformer for Line Level Control (LLC) Resonant Converters Wayne Water & Junwei Lu IEEE Magnetics Letters, Vol. 4, Nov 2013 Refereed Conference Articles 3. Title High Frequency and High Power Density Transformers for the On-Board Charging System of the Electric Vehicle Wayne Water,Junwei Lu & Francis Dawson IEEE International Magnetics Conference, INTERMAG April 25-29, 2011 Taipei, Taiwan, INTERMAG 4. Title A Parameters Optimization Method of High Frequency Transformers Used in the On-Board Charging System of Electric Vehicle Wayne Water & Junwei Lu The 18 th Conference on the Computation of Electromagnetic Fields July 12-15, 2011 Sydney, Australia, COMPUMAG vii

10 5. Title Shielding Effect of High Frequency Coaxial Transformers Used in Bi-Directional DC-DC Converter for Energy Storage Systems Wayne Water & Junwei Lu IEEE International Magnetics Conference May 7-11, 2012 Vancouver, Canada, INTERMAG 6. Title Eddy Current and Structure Optimization of High Frequency Coaxial Transformers Using the Numerical Computation Method Wayne Water & Junwei Lu The 6 th International Conf. on Electromagnetic Field Problems and Applications June 19-21, 2012 Dalian, China, ICEF 7. Title Shielding Analysis of Coaxial High Frequency Transformers used for Electric Vehicle On-Board Charging Systems Wayne Water & Junwei Lu IEEE 12 th Joint MMM/Intermag Conference Jan 14-18, 2013 Chicago, Illinois, MMM/Intermag 8. Title 3D Modeling of Integrated Magnetics in High Frequency LLC Resonant Converters Wayne Water & Junwei Lu The 19 th Conference on the Computation of Electromagnetic Fields June 30-July 4, 2013 Budapest, Hungary, COMPUMAG 9. Title Numerical Computation and Design Verification of Integrated Magnetics Used in Liner Level Control (LLC) Resonant Converters Wayne Water & Junwei Lu IEEE Conference on Electromagnetic Field Computation May 25-28, 2014 Annecy, France, CEFC viii

11 List of Abbreviations 2-D - Two Dimension 3-D - Three Dimension AC - Alternative Current APDL - Ansys Parametric Design Language CAD - Computer Aided Design CEFC - International Conference on Electromagnetic Field Computation CO 2e - Carbon Dioxide Emission COMPUMAG - International Conference on the Computation of Electromagnetic Fields DC - Direct Current EMF - Electromotive Force EMI - Electromagnetic Interference EV - Electric Vehicle FEM - Finite Element Method GHG - Greenhouse Gas HF - High Frequency HFCT - High Frequency Coaxial Transformer ICEF - International Conference on Electromagnetic Field Problems and Applications IEC - International Electrotechnical Commission IEEE - Institute of Electrical and Electronic Engineers INTERMAG - International Magnetics Conference ISO - International Organization for Standardization LF - Low Frequency LLC - Linear Level Control MIO - Magnetic Insertion placed Orthogonally MIP - Magnetic Insertion in Parallel OC - Open Circuit PCB - Printed Circuit Board RMS - Root Mean Square SAE - Society of Automotive Engineers SC - Short Circuit VA - Volt-Amps ZCS - Zero Current Switching ZVS - Zero Voltage Switching ix

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13 Contents Abstract... i Statement of Originality... iii Acknowledgements...v Publications... vii List of Abbreviations... ix Contents... xi List of Figures... xiv List of Tables... xix 1 Introduction Motivation Applications and Considerations Aims and Contributions Chapter Summary...6 Chapter Chapter Chapter Chapter Theory and Methodology Introduction Power Electronics Bi-Directional DC-DC Converters Operation Principles of LLC Resonant Circuit Transformer Theory Magnetic Circuit Material Selection Transformer Design Equivalent Circuitry Transformer Losses Core Losses DC Winding Losses Skin Effect Proximity Effect Eddy Current Effect Parasitic Effect Consideration Leakage Inductance Intra-winding Capacitance...30 xi

14 3 Numerical Modelling Introduction Computational Electromagnetic Method Electromagnetic Solvers Electrostatic Solver Magnetostatic Solver Electromagnetic Solver Finite Element Method Modelling Technique Simplification Sectorization Investigation of Eddy Currents Capacitance Verification in FEM Design and Analysis of Coaxial Transformers Introduction Operating Requirement Geometry Specification Magnetic Core Electric Calculation Magnetic Calculation Power Losses Impedance Measurements Operational Frequency Measurements Low Frequency Measurements Simulation Results D Modeling Techniques Flux Distribution Eddy Current Distribution Impedance Optimization Leakage Inductance Intra-Winding Capacitance Discussion Faraday Shield Analysis Shielding Losses Leakage Inductance Intra-winding Capacitance A Novel Integrated Planar Transformer Introduction xii

15 5.1.1 Operating Requirement Consideration of Integrated Structures Geometry Specification Core Selection and Wiring Configurations Magnetic Calculation Power Losses Measurements Simulation Results Flux Distribution Eddy Current Distribution Winding Configurations Analysis Without the Magnetic Insertion With the Magnetic Insertion Winding Resistance Normalization Inductance Analysis Discussion Winding Thickness Evaluation Transformer Losses Prototypes Comparison Conclusions and Future works Dissertation Conclusions Future Work Reference Appendix A. 8 kw HFCT Measurements B. Investigation of Winding Configurations C. The 1.08 kw top-up transformer D. MIO - Prototype I Raw Data E. MIO - Prototype II Raw Data F. Example APDL Codes HFCT - Eddy Current at Coaxial Region HFCT Capacitance at End Region Section HFCT Inductance at Coaxial Section MIO Structure Prototype I xiii

16 List of Figures Figure 1.1. Transportation GHG emissions by mode [3]... 2 Figure 1.2. Energy storage and conversion flow chart... 2 Figure 1.3. EV battery charging process... 3 Figure 2.1. DC/AC conversion process diagram Figure 2.2. Conventional Full-Bridge Bidirectional DC-DC converter [32] Figure 2.3. Simplified LLC resonant circuit Figure 2.4. DC characteristic of LLC resonant converter [39] Figure 2.5. Equivalent resonant circuit Figure 2.6. A simple transformer model [44] Figure 2.7. Equivalent magnetic model in comparison with electric model Figure 2.8. The simplified magnetic circuit in consideration of the air-gap Figure 2.9. Ferrite ring configuration of the HFCT Figure Transformer equivalent circuit Figure Simplified transformer equivalent circuit of the integrated transformer with magnetic insertion (introduced in Chapter 5) Figure Transformer losses Figure Example current distribution of skin effect Figure The proximity effect example, the current flowing in two conductors in same or opposite direction Figure Simple transformer equivalent circuit with perfect short circuit condition [63] Figure Simplified HF transformer equivalent circuit [62] Figure Illustration of the charge distribution in grounded and floating cases 32 Figure 3.1. Procedures of transformer design and simulation Figure 3.2. Electromagnetic problems classification Figure 3.3. Geometry discretization with triangulation Figure 3.4. An example approach by means of 2-D simulations [87] Figure 3.5. Electric potential density simulations (unit: ): (a) Single conductor to single conductor; (b) single conductor to multi-strands wire; and (c) multi-strands wire to multi-strands wire Figure D full model of Electric potential density simulations (V/m). (a) Single conductor and (b) 7-strands Litz wire Figure 3.7. The illustration of sectorization technique Figure 3.8. Example of the single conductor current distribution. The diameter of conductor varies from 0.5 skin depth to 4 skin depth Figure 3.9. The proximity effect simulation example. Conductor diameter is one

17 skin depth, varied the distance of conductors by the ratio of skin depth...53 Figure The proximity effect simulation example. The condutor distance as one skin depth and varied the diameter of condutors from 0.5 to 4 skin depth Figure The proximity effect simulation example with different numbers of windings; conductor diameter: 1, distance between conductors: 0.01 mm...54 Figure Power losses comparison of multi-strand Litz wires (normalized with equivalent solid conductor)...55 Figure Power losses comparison of multi-strand Litz wires (normalized with DC losses)...56 Figure A 3D proximity effect simulation result. Conductor diameter: 1 skin depth, distance between conductors: 0.01 mm...57 Figure D simulation of 7-strands Litz wire. Conductor diameter: 1 skin depth, distance between conductors: 0.3 skin depth Figure D simulation of 6-strands Litz wire example Figure The simulation result of electric field of the parallel-plate capacitor in air...59 Figure The capacitance value comparison between the Ansys computation result and the theoretical result...60 Figure A simple capacitor system of parallel plates with the insertion of Faraday shield...60 Figure The capacitance network of the HFCT [93]...62 Figure 4.1. The completed 3D assembly model of the HFCT...64 Figure 4.2. The 3D assembly model of the HFCT without PCB layers...65 Figure 4.3. Core size and wire configuration of the 8 kw HFCT...65 Figure 4.4. Top view of HFCT configuration...66 Figure 4.5. The cross-section schematic of the 8 kw HFCT...66 Figure 4.6. The magnetizing inductance of the 8 kw HFCT...73 Figure 4.7. The equivalent core resistance of the 8 kw HFCT...73 Figure 4.8. The leakage inductance of the 8 kw HFCT...74 Figure 4.9. The winding resistance of the 8 kw HFCT...75 Figure The intra-winding capacitance of the 8 kw HFCT...75 Figure The isolation resistance of the 8 kw HFCT...76 Figure The square wave test of prototype HFCTs at 75 khz...77 Figure The square wave test of prototype HFCTs at 400 khz...77 Figure D simulation model of the prototype HFCT with the Faraday shield

18 Figure Region definition of the 3D simulation model of the HFCT Figure The flux distribution of the HFCT when the outer winding is used as the primary winding: (a) and (b), under short circuit condition; (c) and (d), under open circuit condition Figure The flux distribution of the HFCT when the inner winding is used as the primary winding: (a) and (b), under short circuit condition; (c) and (d), under open circuit condition Figure The flux density of the HFCT when the outer winding is used as the primary winding: (a) and (b), under short circuit condition; (c) and (d), under open circuit condition Figure The flux density of the HFCT when the inner winding is used as the primary winding: (a) and (b), under short circuit condition; (c) and (d), under open circuit condition Figure The 3-D flux density distribution when the outer winding is used as the primary: (a) and (b), under short circuit condition; (c) and (d), under open circuit condition Figure The flux density distribution when the outer winding is used as the primary under short circuit condition Figure The current density of the HFCT when the outer winding is used as the primary winding: (a) and (b), under short circuit condition; (c) and (d), under open circuit condition Figure The current density of the HFCT when the inner winding is used as the primary winding: (a) and (b), under short circuit condition; (c) and (d), under open circuit condition Figure Current distribution of 3D model in bird view and left side view (Short Circuit Condition) Figure Current distribution of the outer winding under the short circuit condition Figure Current distribution of the inner winding under the short circuit condition Figure Simulation results of the HFCT without the Faraday shield under open circuit condition Figure Current distribution of the HFCT with the Faraday shield (Short circuit condition) Figure Current distribution of the HFCT with the Faraday shield (Open circuit condition) Figure (a) The HFCT equivalent circuit; and (b) relationship of impedance

19 versus the distance between windings...92 Figure The leakage inductance versus the winding distance of the 8 kw HFCT...95 Figure The winding configuration in end region section...95 Figure Coupling capacitance versus winding distance of the 8 kw HFCT...97 Figure The trade-off of calculated coupling capacitance and leakage inductance...97 Figure Power loss versus the thickness of the Faraday shield under short circuit condition; the outer winding is used as the primary winding...98 Figure Power loss versus the thickness of the Faraday shield under open circuit condition; the outer winding is used as the primary winding...99 Figure Power loss versus the thickness of the Faraday shield under short circuit condition; the inner winding is used as the primary winding Figure Power loss versus the thickness of the Faraday shield under open circuit condition; the inner winding is used as the primary winding Figure D simplified model of the HFCT Figure D precise model of the HFCT Figure 5.1. Half bridge LLC resonant circuit Figure 5.2. Investigated transformer structures: (a) top-up structure, and (b) MIP structure Figure 5.3. The explored view of the MIO structure (proposed structure) Figure 5.4. The dimensioned cross-section view of prototype I (unit: mm) Figure 5.5. The dimensioned cross-section view of prototype II (unit: mm) Figure 5.6. Two prototype Transformers Figure 5.7. Winding configuration in single window (Unit : mm) Figure 5.8. The leakage inductance of the 1.08 kw transformer prototypes Figure 5.9. The winding resistance of the 1.08 kw transformer prototypes Figure The magnetizing inductance of the 1.08 kw transformer prototypes Figure The core resistance of the 1.08 kw transformer prototypes Figure Square wave test of prototypes at 90 khz Figure Ringing effect on prototypes at 500 khz Figure Setup for transformer resonant frequency measurement Figure Voltage/turn ratio of HF planar transformers xvii

20 Figure Magnetic flux density of prototype transformers in 2-D Figure Magnetic flux density of prototype transformers in 3-D Figure The 2-D current distribution result under short circuit condition at 110 khz Figure The 2-D current distribution result under open circuit condition at 110 khz Figure The 3-D current distribution result under short circuit condition at 110 khz Figure Different types of winding configurations for planar transformer Figure The comparison result - without insertion and enclosed with magnetic core Figure The comparison result - without insertion and enclosed with magnetic air Figure The comparison result - with insertion and enclosed with magnetic core Figure The comparison result - with insertion and enclosed with air Figure Primary AC resistance ratio under open circuit condition Figure Primary AC resistance ratio under short circuit condition Figure Secondary AC resistance ratio under open circuit condition Figure Secondary AC resistance ratio under short circuit condition Figure Winding resistance - simulation results versus measurements Figure Illustration of flux direction Figure Prototype transformers; prototype I: MIO structure; prototype II: MIO structure, prototype III: top-up structure Figure Normalization factor of primary windings Figure Open circuit losses Figure Short circuit losses Figure The square wave test at 90 khz Figure Efficiency comparison at full-load condition Figure. C.1 The structure and specification of the 1.08 kw top-up transformer prototypes Figure. C.2 The flux illustration of the top-up transformer under open-circuit condition Figure. C.3 The square wave test of prototype III at 50 khz; with and without the top-up inductor Figure. C.4 The square wave test of prototype III at 50 khz; with and without the top-up inductor xviii

21 List of Tables Table 1.1. Charging options developed for the EV...3 Table 2.1. Material characteristics at 20 [55]...24 Table 3.1. Applied elements for FEM simulation...34 Table 3.2. Maxwell s equations...37 Table 3.3. Results comparison of simulation and theory on two simple systems...59 Table 3.4. Comparison of simulation result and theory on a simple system...61 Table 4.1. The specification of 8 kw HFCT prototype...64 Table 4.2. Ring core specifications [51]...67 Table 4.3. Dynamic Magnetisation...68 Table 4.4. Impedance testing results of the 8 kw HFCT with and without the Faraday shield...78 Table 4.5. Capacitance measurements of the 8 kw HFCT with or without the Faraday shield...79 Table 4.6. The intra-winding capacitance comparison of HFCT...80 Table 4.7. Meshing information of the HFCT...82 Table D Calculated inductance results of the 8 kw HFCT...93 Table D Calculated Inductance Results of the 8 kw HFCT under Different Excitation Windings Table Example of inductance distribution in the coaxial section of the 8 kw HFCT...94 Table The 2-D capacitance computation result of the HFCT; the winding configuration of the end region section at aligned and unaligned position...96 Table Intra-winding capacitance distribution of the 8 kw HFCT...96 Table Power Losses of the HFCT 3D Simulation Table The comparison of 2-D and 3D simulation results Table D capacitance simulation result of 8 kw HFCT Table D Capacitance simulation result of the HFCT Table 5.1. The requirement of the LLC transformer Table 5.2. The magnetic characteristic and gapping information Table 5.3. The specification of the sectorized model Table 5.4. Inductance comparison between different magnetic insertion arrangements Table 5.5. The Measurement Results at 40 khz xix

22 Table. A.1 The comparison testing result of 8 kw HFCTs Table. B.1 The comparison results without the magnetic insertion between different winding configurations Table. B.2 The comparison results with the magnetic insertion between different winding configurations Table. C.1 The measurements of 1.08 kw top-up prototype transformer Table. D.1 Prototype I Simulation losses Table. E.1 Prototype II Simulation losses xx

23 INTRODUCTION 1 Introduction In this dissertation, two different types of transformers have been proposed and fabricated. The performance of the proposed prototype transformers was evaluated and verified by Finite Element Method (FEM) simulations and experimental measurements. The first type of transformer developed in this dissertation is the High Frequency Coaxial Transformer (HFCT), which ranges from 1 kw to 20 kw with the operating frequency of 100 khz to 300 khz. The structure of the transformer is very simple and can be easily scaled to suit different power requirements. The second transformer developed is in planar structure, which can be used for the Line Linear Control (LLC) resonant converter. The advantages of this transformer, as well as a detailed structure will be discussed in the corresponding chapter. 1.1 Motivation Carbon Dioxide Emission (CO 2e ) is one of the major causes of global warming, and the mitigation in Greenhouse Gas (GHG) emissions is a topic of concern. Approximately 37% of CO 2e come from daily transportation. In this 37%, passenger vehicles are responsible for the majority of GHG emissions [1], [2]. Figure 1.1 shows transportation GHG emissions by the use of different consumption modes. From the figure, light duty vehicles contribute to a growing portion of overall emissions. It also shows that passenger and freight truck operations represent about 61% and 21% of transportation energy and GHG emissions. This is expecting to be the case for at least one more decade. In 1998, energy consumption in the transport sector was only responsible for 28% of CO 2e ; however, current CO 2e from transport are expected to increase by around 50% [3]. Hence, there is an urgent need to adapt current technologies to help reduce GHG emissions before the global warming situation worsens. 1

24 INTRODUCTION Figure 1.1. Transportation GHG emissions by mode [3] 1.2 Applications and Considerations Electric vehicle (EV) and renewable energy technologies are two of the most important drivers towards a reduction in green-house gas emissions. They occupy important roles in smart grid infrastructure (the integration of renewable energies, such as household and power grids), and capture interest because of their potential usage in the near future [4]. Figure 1.2 shows the concept of the EV technology and renewable energy systems integrated into both the household and the power grid. The variability of the renewable energy sources requires the use of energy storage; and the interconnection of various renewable sources of energy and energy storage requires Direct Current (DC) voltage level translation and galvanic isolation. This implies the need for transformers and DC-DC converters [5], [6]. Figure 1.2. Energy storage and conversion flow chart The future trends and requirements of the EV have been discussed in [7], [8]. By summarizing this information, it can be inferred that the time takes to charge the 2

25 INTRODUCTION vehicle is a very important factor in how well the public accepts and adapts to EV technology. Several charging standards were developed such as the Society of Automotive Engineers (SAE), the International Electrotechnical Commission (IEC) and the International Organization for Standardization (ISO). They all have varied definitions on port communication and power rating [9]. To make it simple, the charging standards can be classified into three categories according to power rating. These include normal charging, fast charging and super charging, with power ratings of 1-2 kw, 2-20 kw and over 20 kw respectively (approximation) [8], [9], [10]. The information based on a 100 km driving range has been tabulated in Table 1.1 for reference. Table 1.1. Charging options developed for the EV Level AC Voltage (V) Power (kw) Time to Charge (14kWh) hours hours minutes Much research has been undertaken on normal charging levels at both low frequency (60 to 100 Hz) and high frequency (1 to 10 khz and above) [8]. However, very little research has focused for power conversion applications in the EV above an operating frequency of 100 khz while the power rating is greater than 2 kw. The power converter commonly seen in the EV market operates at 60 Hz to 200 Hz, in which the converter is bulky and inefficient due to the transformer and its passive elements. Therefore, this dissertation introduces an isolated HFCT with a range of 1 kw to 20 kw. This is well suited for EV charging systems at the fast charging level, as well as for energy storage applications. An example block diagram of the EV charging process is shown in Figure 1.3. This figure illustrates where the isolated HFCT should be implemented. Figure 1.3. EV battery charging process 3

26 INTRODUCTION The benefits of using an isolated transformer in the converter system have been discussed widely in the literatures [11],[12],[13]. These benefits include: Prevention of Direct Current (DC) pulse to the Alternative Current (AC) side; prevention of high fault currents flowing through the system; Extended battery life from the elimination of electrical shocks and current leakage; and Easy adaptation of voltage level between the battery and vehicle applications. In order to achieve high power densities and high performance efficiency, the operating frequency of the designed transformer has been increased from a traditional frequency range (10 khz- 50 khz) to between 100 khz and 300 khz. Therefore, coupling capacitance accompanied by an increased operating frequency (which couples HF noise between the primary and secondary windings) can cause serious common mode problems [11], [14], [15]. Hence, a Faraday shield was placed between the windings of the HFCT. This reduces the coupling capacitance and consequently the Electromagnetic Interference (EMI). The analysis of the shielding effect of the HFCT is presented in this dissertation and might be of interest to other researchers and automobile manufacturers. Furthermore, LLC resonant converters have attracted great interests in past decades due to the developments in the power industry. However, these converters have only come onto market more frequently in recent years due to the difficulties of the controlling circuit design [16]. To achieve Zero Voltage Switching (ZVS) or Zero Current Switching (ZCS), a resonant tank is the most attractive and efficient topology in the front end of the converter [17]. The resonant tank in the LLC converter is composed of the resonant inductor, the magnetizing inductor and the resonant capacitor. In order to reduce the converter volume, the best solution is to integrate the resonant tank with the transformer [18], [19]. Therefore, a novel structure of the magnetic integrated transformer is introduced in this dissertation. It has a number of advantages including the low profile, flexible controllability of the, high efficiency and low costs in comparison with other planar structures [20],[21],[22],[23],[24]. The magnetic integration research work presented in this dissertation focuses on the magnetic components integration, which is specifically for the integration of inductors and transformers. Through the magnetic integration, the total number of components is reduced and the converter system benefits from a reduction in both the overall volume and manufacturing costs. 4

27 INTRODUCTION 1.3 Aims and Contributions Transformer design in HF has always been a difficult subject, especially if the transformer structure is very complicated or asymmetric. Based on the 1-D analysis of manual calculation [25], [26], the transformer design achieves an acceptable level of accuracy with simple structures. A modelling technique needs to be used in order to predict the transformer behaviour more precisely. With improvements in computation power and the introduction of the 2-D FEM technique [27], the design precision was further increased. However, once the transformer structure becomes more complicated, the above methods are no longer effective and might give inaccurate results; thus, a 3-D analysis is required especially for the introduced structures in this dissertation [28]. The utilization of the modelling technique is the most essential aspect of this dissertation. It results in a more advanced design methodology compared to the traditional manual calculations with the transformer design. The research work presented in this dissertation aims to provide a transformer design pathway not only for industry engineers, but also for other researchers in the same area. The content focuses on practical applications for transformer design. The contributions of this research are summarised as follows: Development of HFCT, which can be scaled to any required power ratings. It is particularly suitable for energy storage devices. Shielding analysis of the HFCT. The investigation covers various electric and magnetic discussions such as the leakage inductance, the intra-winding capacitance and power losses of the shield. An 80.6% of intra-winding capacitance reduction has been achieved as a result of adding the Faraday shield. Development of a novel structure of magnetic integration planar transformer. The efficiency is above 97% under full-load conditions, which is rarely seen in integrated transformers currently on the market. In addition, the volume of the developed structure is the smallest among all magnetic integration structures that could be found in other research works. Investigation of leakage inductance adjustment and winding configurations of the planar transformer. The presented discussion will be very useful for researchers and industry engineers who work in the same area. Both detailed 2-D and 3-D analysis, which will be valuable to researchers in the magnetic FEM field. In addition, the 3-D sectorization technique and power generalization technique presented are beneficial in reducing the redundant simulation time while maintaining the high accuracy of the simulation results. 5

28 INTRODUCTION 1.4 Chapter Summary Chapter 2 A brief overview of the LLC circuit design is presented for the developed planar transformer. Before the LLC transformer can be designed, parameters such as magnetizing inductance, resonant inductance and resonant capacitance must be obtained. In addition, in order to evaluate the transformer performance, it is essential to understand some theories underpinning the transformer design. This chapter explains the essential magnetic circuit design theory, which is useful for most transformer designs at the initial design phase. An overview of AC losses is also presented, which is especially important to HF operations. Furthermore, the parasitic effect is discussed due to its importance in high frequency transformer design. Chapter 3 The mathematical solutions to practical magnetic and electric problems are always complicated. Not every phenomenon can be explained easily from the measurement results. Traditionally, transformer designers have replied on their experience to solve electromagnetic problems, and it is sometimes very effective. However, this requires a long-term learning curve and their knowledge cannot easily be passed on to young engineers. By employing the FEM technique, magnetic and electric field simulation results can be visualized for the designed applications, and the difficult physics phenomenon is analysed more easily via observation. A software package Ansys Workbech 14.0 was utilized for analysing the electromagnetic problem and the visualization of AC phenomenon. The FEM theory behind this software has proved useful in the analysis of complex transformer structure. Furthermore, 3-D modelling simplification and sectorization techniques are also presented in this chapter. Such techniques are very helpful in reducing the redundant computation time required for precise simulation results in 3-D. 6

29 INTRODUCTION Chapter 4 Detailed discussions regarding the development of the HFCT are presented in this chapter. Two prototypes were built in the power rating of 8 kw and utilized as examples throughout the chapter. One prototype utilized the Faraday shield insertion for the intra-winding capacitance reduction while the other did not. For the transformer performance in HF, an impedance analyser HP 4285A (75 khz to 30 MHz) was utilized for measurements, while a Precision TH2816A (20 Hz to 200 khz) was employed to analyse the static simulated results for leakage inductance and intra-winding capacitance. This chapter also discusses the leakage energy distribution, Faraday shield losses in regards to its thickness and locations, and the difference between 2D and 3D simulation results. In addition, the phenomenon of the intra-winding capacitance, where the HFCT is with or without the Faraday shield, is demonstrated by simulations and experiments. Chapter 5 This chapter presents an investigation and discussion of the magnetic integration planar transformer. The transformer is designed for use in LLC converters. The discussion and analysis focus on the magnetic components design, specifically for the magnetizing inductor and leakage inductor. Three prototype transformers were built and evaluated, which include two prototype transformers in the proposed structure and one in the commercial top-up structure (the latter was used as a benchmark). In order to optimize the proposed structure, winding configurations were investigated, with the manufactured prototypes proving that the optimized outcome is practical. Furthermore, most of the parameters in these two prototypes of the proposed structure are different (e.g. core size, conductor size, core gap and air gap). Power loss curves and power efficiency depletions were also drawn for all three transformer prototypes. The proposed structure performs better within the desired operating frequency range compared with the commercial prototype. 7

30 INTRODUCTION 8

31 THEORY AND METHODOLOGY 2 Theory and Methodology 2.1 Introduction In order to reduce the converter size, the switching frequency of the converter must be increased; the passive elements such as inductance, transformers and capacitance will be reduced in volumes [28]. However, the switching losses become a major concern when the operating frequency reaches a specific level. Therefore, the LLC topology was introduced to overcome this issue [16]. The resonant LLC topology has several advantages such as high efficiency, low EMI and high power density [29]. This chapter presents the method which is used to obtain parameters of the LLC circuitry. Also, the magnetic circuit calculation method has been shown and discussed in this section. The magnetic circuit calculation method is very useful and effective at the beginning phase of the transformer design [30]. On the other hand, the winding loss is one of the major concerns due to AC effects in HF operations. AC effects include the skin effect, proximity effect, eddy current effect and fringing effect [31]. This chapter delivers a brief introduction of the AC effect phenomenon; detailed discussion with examples will be presented in the following chapters. Lastly, the parasitic effects introduction regards to the leakage inductance and intra-winding capacitance will be presented. The knowledge of parasitic effects is very important to be read prior to into the shielding analysis of HFCTs presented in Chapter Power Electronics This disseration introduces two types of transofrmers, they are HFCTs and magnetic integrated transformers. The HFCT can be used (but not limited) in the high power galvanically isolated DC-DC converter system, and the mangetic integrated 9

32 THEORY AND METHODOLOGY transformer targets the utilization in LLC converters less than 2 kw. An example of DC/AC conversion process is shown in Figure 2.1; in which the energy storage system is a DC source and the bi-directional DC-DC converter adapts the voltage level to the requriement. Once a purified DC power output is obainted, the power will be modulated by the inverter to the proper frequencies which can be utilized for home applications. Figure 2.1. DC/AC conversion process diagram Bi-Directional DC-DC Converters Figure 2.2. Conventional Full-Bridge Bidirectional DC-DC converter [32] Figure 2.2 shows a conventional bidirectional DC-DC converter which can be used for the introduced HFCT in the research work. According to the power flow directions, the circuit operates in boost mode to draw energy from the battery or operates in buck mode to recharge the battery [32]. Also, the conventional DC-DC converter topology can be adapted with adding extra switchable capacitors next to the power switches [33]; the capacitor switches are periodically turned on and off so that the converter cycles through a number of states and consequently reduces the switching losses. More examples have been discussed in the application of isolated transformer in area such as photovoltaic system, automobile, energy storage system [34], [35]. Detailed discussions regard to the galvanic isolation have been presented in [36], [37]; in which the HF transformer was utilized to implement the required function. 10

33 THEORY AND METHODOLOGY Operation Principles of LLC Resonant Circuit There are mainly two switching techniques for the switch mode power supply; the hard switching and soft switching techniques. Hard switching means the voltage and current waveform overlaps on each other when there is a status change on switching on or off; the more the overlap area is, the more energy losses are [32]. At high power applications, the switching losses on hard switching do not seem to be obvious; however, for low power applications (< 2 kw), these switching losses occupy the system efficiency by about 5~10 %. For this reason, the LLC resonant circuitry becomes a great topology on overcoming this particular problem [16]. Also, the LLC topology gives the possibility on reducing the required input switch number from 4 to 2 (full bridge circuit to half bridge circuit) while maintaining the output waveform smooths [38]. Figure 2.3. Simplified LLC resonant circuit Figure 2.4. DC characteristic of LLC resonant converter [39] Since this research work focuses on the transformer design, only the relative information corresponding to the LLC resonance parameters will be presented in this 11

34 THEORY AND METHODOLOGY dissertation. Parameters of LLC circuitry include, and as shown in Figure 2.3, the resonant frequency and as shown in Figure 2.4 (where 300m in the figure represents the minimum possible sampling time point). If further details and discussions of the LLC resonant converter are of interests, [29], [39], [40], [41], [42] will be good references. Firstly, to ensure the LLC converter operates at ZCS and ZVS condition, the switching frequency must be operated between resonant frequencies (the resonant frequency under load condition) and (the resonant frequency under bo-load condition); it is preferable to operate above the, so the converter is guaranteed to operate at ZCS condition under all load conditions [41], [42]. The resonant frequencies are defined as: ( 1 ) ( 2 ) The quality factor is in a relationship of the resonant frequency and the load equivalent resistance : ( 3 ) Figure 2.5. Equivalent resonant circuit To simply the calculation and analysis process, the simplified resonant circuit shown in Figure 2.3 can be transformed into a DC equivalent resonant circuit as shown in Figure 2.5 via the Fourier transformation; thus, the AC analysis has been converted into a DC analysis for the ease of calculation. The relationship of the load resistance and the load equivalent resistance (coupled resistance to the transformer primary) is: 12

35 THEORY AND METHODOLOGY ( 4 ) Assuming the transformer turn ratio is N, the output voltage and the input voltage are given, and then the maximum voltage gain and the minimum voltage gain can be obtained as: ( 5 ) ( 6 ) Please note ( 5 ), ( 6 ) are applied if the input switching topology is in full bridge; for half bridge input switching topology, the input voltage must divided by the factor of 2. The maximum in ( 3 ) can also be derived since is known; ( 7 ) where is the ratio of over. Normally, is chosen between 5 to 8 for the better efficiency and broader voltage regulation range [41], [42]. Since the resonant frequency is pre-selected, and and are known, the maximum and the minimum operating frequency can now be obtained; ( 8 ) ( 9 ) Finally, based on ( 4 ) to ( 7 ), the required impedance parameters can be calculated as; ( 10 ) ( 11 ) 13

36 THEORY AND METHODOLOGY ( 12 ) 2.3 Transformer Theory This section gathers the required information for transformer designers. Transformer occupies a very important role in the power electronic applications. A transformer is defined as a bi-directional energy transferring device and rated in power units of Volt-Amps (VA). The most basic function of the transformer is to adapt the input voltage to a desired output level according to the requirement. Transformer design requires the knowledge of electrical principles, material selection and electromagnetics theories. Basically, the transformer operation is based on Faraday s Law of induction; the current drawn from mains creates not only a voltage on the input winding, but also the induced current and the magnetic field on the secondary. The transformer can be treated as two perfectly coupled inductors, and the current flowing through an inductor lags the voltage by 90 degrees for a sinusoidal waveform input Magnetic Circuit Most of the analytical solution of field distribution can be solved by Maxwell s equation. However, the calculation and analysis can be very difficult, especially if the targeted device is in a complex structure. Thus, a simple method of magnetic circuit analysis based on analogy to direct-current mode has been introduced [30], [43], [44]. Magnetic circuit theory has been proven as a useful technique on transformer design [45]. A simple transformer model without the secondary is shown in Figure 2.6 for illustration of magnetic circuit method. Figure 2.6. A simple transformer model [44] Considering a simple magnetic circuit structure has a magnetic mean length, cross sectional area, the permeability of the core as μ, and a magnetizing current 14

37 THEORY AND METHODOLOGY ; where generates flux λ in a N turns wounded coil. Assume results of the magneto-quasistatic in the Maxwell s equation are negligible. The relationship between the magnetic fields and current can be observed via the Amphere s Law: ( 13 ) where is the magnetic field intensity and is the current density. ( 13 ) states the integration of the around a closed contour which is tangential on a length of is equal to the integration of the current density in the closed surface. Thus, it can be re-written in a straight form as: ( 14 ) the magnetomotive force in the unit of A-t is represented as F; where and represents the integration of and over a contour. A definition of the to the F per unit length is shown in ( 15 ); the unit of is A-t/m ( 15 ) Another important parameter in the electromagnetic phenomenon is the flux density. is a concentration measurement of flux flowing through a sectional area in a magnetic circuit. ( 16 ) where is the flux density in core, is the number of flux which is equal to λ. The relationship of the and is commonly assumed as a liner relationship: ( 17 ) where is the magnetic permeability. Therefore, the constitutive equation of the core material is written as: ( 18 ) From ( 14 ), ( 15 ), and ( 18 ), below equation is obtained: ( 19 ) where is the reluctance of magnetic circuit at unit of A-t/Wb. For magnetic materials, if we take the as the current, the as the electromagnetic field (the voltage source) and as the resistance, the magnetic equivalent circuit obtained is quite similar to the electrical circuit. Therefore, Ohm s law is able to be applied on magnetic circuit calculation because of the similarity behavior of both circuitries. The illustration of equivalent electric circuit and magnetic circuit are shown in Figure

38 THEORY AND METHODOLOGY Figure 2.7. Equivalent magnetic model in comparison with electric model Transformer model shown in Figure 2.6 can be simplified as shown in Figure 2.8; in which an air gap is placed in the middle of the magnetic core. ( 14 ) is re-written as: ( 20 ) where ( 21 ) and ( 22 ) Figure 2.8. The simplified magnetic circuit in consideration of the air-gap According to Gauss s law of magnetism, in each volume element of the space, there is the same amount of flux for existing and entering. Thus, the total flux in the magnetic circuit is equivalent to the flux in the magnetic core as well as the flux in the air gap. So, ( 23 ) 16

39 THEORY AND METHODOLOGY Consequently, ( 24 ) In practical systems, the magnetic field lines outward is fringed around the air gap; this phenomenon is named as fringing effect which increases the effective cross-sectional area [46] Material Selection Various materials can be found in the market for transformer production; these are classified as below [30], [43], [47], [48], [49], [51], [52]: Air The least conductivity material; air provides the least magnetic coupling for transformer windings. Iron A most common and cheap material used for the low frequency transformer. Iron-core is made mainly from steel; additives are required for the steel to improve the magnetic performance of the core. Compressed Iron powder The iron magnetic particles are formed to a bit under processes of very high compressed pressure and temperature. This material targets at medium to high frequency application range. The permeability of compressed iron powder which can be achieved is lower than ferrite material. Ferrite Ferrite is a light and highly permeable magnetic ceramic material; Ferrite has an excellent magnetic performance at high frequency ranges. For the example of 8 kw prototype HFCTs presented under this research work, F44 was selected as the core material. F44 is a high saturated Manganes-Zinc ferrite which is specially formulated for low losses, and suitable for applications up to 500 khz. Core losses are minimized at above 80 degree working temperature with higher saturation flux density and amplitude permeability compared to similar product lines. Also, F44 has been manufactured in many shapes with a variety of dimensions. Part No was chosen based on the magnetic circuit calculation with regards to its power requirement is a ring core of magnetic ferrite ring with an outer diameter of 63mm; more details of F44 please refer to [49]. On the other hand, two magnetic materials were chosen for the LLC transformer designs. They are NiZn TN12B [47] and MnZn TP4A [48] with saturated flux densities of 430 mt and 510 mt at room temperature respectively. The purpose of choosing different materials for the prototype transformers is because of the interest of air-gap investigation. With the selection of NiZn material, the air-gap of the 17

40 THEORY AND METHODOLOGY manufactured prototype can be minimized due to the low relative permeability of NiZn as =120; in comparison, the prototype with MnZn material has a greater air-gap as the material is with the =2400. In addition, the core losses are varied among magnetic materials. An investigation of core losses between these two material was conducted, and the analysis is shown to discuss the core characteristic futher. The core resistivity of the NiZn and MnZn are and 6.5 respectively; in which a higher equivalent core resistance should be expected to observe for NiZn prototype transformer in the measurement results Transformer Design To deal with the magnetic behaviour of the transformer design, the Faraday s law is a very good tool. Faraday s law stated [53]: The induced electromotive force in any closed circuit is equal to the negative of the time rate of change of the magnetic flux through the circuit This induction Electromotive Force (EMF) can be produced in many ways. For example, a conductor moving in a closed loop magnetic field; or an alternating current flows in the conductor to generate an alternated magnetic field. Faraday s law can also be named as the law of electromagnetism, which can be described in a set of four Maxwell s equations. The EMF induced in a circuit is directly proportional to the time rate changed of the magnetic flux through the circuit; it can be described as in a simple form: ( 25 ) and ( 26 ) In a coil consisted with N windings, the total induced EMF in the coil becomes: ( 27 ) The minus sign shown in ( 25 ) and ( 27 ) represents a physical phenomenon that the induced EMF against the direction of the power supply EMF ; therefore, sometimes an induced EMF is named as the back-emf. By taking account with factor of frequency and transformer core area, ( 27 ) can be re-written in a different format which is known as transformer universal voltage equation [30] as: 18

41 THEORY AND METHODOLOGY ( 28 ) ( 28 ) describes the relationship of Root Mean Square (RMS) voltage with supplied frequency, winding turns, cross-sectional area of the transformer core and constant ; where for square wave supply,, sine wave supply,. Using the introduced HFCT structure as an example; in Figure 2.9 (c), it shows the HFCT is composed of four ferrite rings. Thus, the area of total cross-section is obtained as: ( 29 ) where A, B and C are denoted as in Figure 2.9. (b) Side view (a) Top view (c) Ferrite ring arrangement Figure 2.9. Ferrite ring configuration of the HFCT The magnetic flux path of the core is written as in: ( 30 ) Based on the magnetic circuit theory introduced in Chapter 2.3.1, the magnetic force of the core can be easily obtained: ( 31 ) The power loss density of the magnetic material is usually provided by core manufacturers. Thus, the core loss of each core can be easily approximated as: ( 32 ) where is the power loss density of the material in the unit of W/kg. The winding loss is calculated with Ohm s law: ( 33 ) 19

42 THEORY AND METHODOLOGY R w is the resistance of the wire. AC resistance calculation is discussed in Chapter 2.4 ; in which only DC analysis will be conducted at the draft phase of the transformer design. Once the core area is given, the estimated power rating P can be calculated. Re-write ( 28 ) and ( 31 ) with the electrical law: ( 34 ) is the current density, and is the cross-section area of the coil per turn. Since ( 35 ) ( 34 ) can also be represented as: ( 36 ) Then, the conductor dimension can be selected based on: ( 37 ) Based on the Faraday s law, the Area Product Method is introduced and being very effective on obtaining the core size parameters by a given power requirement; please refer to [30], [43] for the detail of Area Product Method. In this dissertation, transformer design will be more focused on the structure optimization, AC losses analysis and impedance investigation rather than the basic relationship of the transformer core size versus power rating Equivalent Circuitry Figure Transformer equivalent circuit The transformer equivalent circuit is shown in Figure The equivalent circuit 20

43 THEORY AND METHODOLOGY represents a single phase transformer with turns winding in the primary and in the secondary. Parameters are denoted bellow Primary winding resistance Primary leakage reactance Secondary winding resistance, in reference to the primary circuit by the turns ratio squared Secondary leakage reactance, in reference to the primary circuit by the turns ratio squared Equivalent core loss resistance and core loss current Magnetising reactance and magnetising current No-load current Primary and secondary EMF and, developed over an ideal transformer Primary and secondary terminal voltages and currents,, and By simplifying the transformer structure to an equivalent circuit, the relationship between each parameter can be easily observed. For example, increasing winding turns results in a reduction of the (due to the increase of the magnetizing inductance), but this also increases the winding resistance. On the other hand, the and the are magnetic material dependent. If a higher permeability material is used, the can be reduced with the same transformer specification. In short, if all parameters of the equivalent circuit can be obtained, the evaluation of the targeted transformer is quite straight forward. In transformer evaluations, Open Circuit (OC) and Short Circuit (SC) tests are two main methods to obtain these basic transformer parameters [30]. SC test is conducted by connecting two nodes of the secondary winding together with a low impedance connector, which is usually a piece of copper wire. Under the SC condition, parameters of copper losses and leakage inductance can be obtained from the measurement. On the other hand, OC test represents that the secondary winding of the transformer has the same voltage as the primary windings (say the turn ratio is 1:1). The primary is measured with leaving the secondary connection unconnected. Since the winding resistance is very small compared to the magnetizing branch, all of the voltage drops occurs across the paralleled and. Thus, and can be obtained under OC test. In general, most of transformers can be equivalent to the transformer equivalent circuit shown in Figure 2.10; however, it is not applicable for magnetic integration transformer with the insertion layer which will be introduced and discussed in Chapter 21

44 THEORY AND METHODOLOGY 5. An adapted equivalent circuit is needed for the introduced magnetic integration transformer. The equivalent circuit is shown in Figure The secondary has been coupled to the primary side for convenience; the notation * means the impedance has been coupled according to the winding turn ratio of the transformer. Under SC conditions, because the is very large, compared to the total winding resistance, and. The represents the leakage inductance of the magnetic insertion; it only occurs if the transformer is attached with a load. Figure Simplified transformer equivalent circuit of the integrated transformer with magnetic insertion (introduced in Chapter 5) 2.4 Transformer Losses In a practical transformer system, the energy dissipated during the energy transforming process can be classified as follows: Winding losses: The winding resistance obtained from the impedance test is a good index of winding losses. An ideal transformer would have zero winding resistance; however, this does not exist in practice due to the inherent conductor resistance and losses caused by the AC effects. For the designed transformer, the multi-strand Liz wire is utilized to alleviate the AC effect. Hysteresis: A small amount of energy was consumed when the polarity of the magnetic field changes. This loss is proportional to the frequency and varies between magnetic core materials. Eddy current: Eddy current is a complex function of the square of the supply frequency and inverse-square of the material thickness. For transformer operating at low frequencies, laminated cores are normally utilized to deal with the eddy current effect. In high frequency ranges, ferromagnetic material is a better candidate. Eddy current losses can be reduced by having the core stack electrically insulated from each other. An alternative technology is compressed iron powders magnetic core which has been proven for its HF magnetic performance. Magnetostriction: The ferromagnetic material expands and contacts slightly on 22

45 THEORY AND METHODOLOGY each flux cycle. When this happens, a noise can be observed with the transformer operation and it also causes the frictional heating problem. Mechanical loss: The alternating magnetic field also generates fluctuating forces between windings and transformer physical structure. The fluctuating force brings an additional noise and consumes a small amount of energy. Stray losses: This is also known as leakage inductance losses. The magnetised energy will be stored and sent back to the power supply on every flux cycle. Generally, the leakage inductance should be designed as small as possible for power transformers. Figure Transformer losses The size of the magnetic components can be reduced with the increased operating frequency; however, a number of problems rise while the application operates at a higher frequency. These problems include skin effect, proximity effect and eddy current effect. More considerations have to be taken into account in order to ensure the transformer is designed adequately. This section has briefly introduced transformer losses (Figure 2.12) in five categories. They are core losses, DC winding losses, skin effect, proximity effect and eddy current effect. In fact, the transformer losses are generally classified into two categories, which are core losses and winding losses. After that, the winding losses are further classified as DC loss and AC loss, in which the AC loss includes the skin effect, proximity effect and eddy current effect. This dissertation introduces these power loss effects into individual section to avoid confusion. Therefore, every phenomenon is treated and discussed in a direct manner. In addition, the harmonic loss is another concern of power losses at various HF, in which the harmonic loss is caused by the non-linear loads [54]. This phenomenon can be attributed to the non-linear property of magnetic materials. The non-linear property results in an extra loss to the transformer due to the distorted voltage or current waveforms. The harmonic loss is not analyzed in this dissertation as the discussion will be too complicated. However, further investigations will be 23

46 THEORY AND METHODOLOGY conducted in the future work, because of its significance in the distribution of transformer power losses Core Losses The Core loss of the transformer includes the eddy current loss and the hysteresis loss. Their relationships to are given in the following equations: and ( 38 ) ( 39 ) where and are loss coefficients corresponding to eddy current and hysteresis respectively. To be emphasized, FEM technique is very effective with the calculation of the if the core structure is complicated. Alternatively, the can be obtained from the core manufacturer s datasheets. On the other hand, the estimation of is obtained from the datasheets provided by the core manufacturers. Alternatively, core losses calculation can be conducted with the use of a modified Steinmetz equation [49], [50]. However, this equation is only useful if the manufacturer has published all parameters required, which makes it not compatible in the research work presented in this dissertation DC Winding Losses The DC winding resistance can be represented by: ( 40 ) where is the resistivity, is the length of the conductor and A is the cross sectional area. Also, except from super conductors, the resistance of all materials is temperature dependent which can be written as: ( 41 ) where is the temperature coefficient of resistance. Examples of material characteristics are shown in Table 2.1; in which silver outperforms copper if the cost is not the main concern of transformer fabrication. Table 2.1. Material characteristics at 20 [55] 24

47 THEORY AND METHODOLOGY Material (ohm /m) at 20 / Conductivity ( /Ωm) Silver Copper Aluminium Skin Effect Skin effect is that an AC current tends to distribute itself within a conductor, with the current density being the largest near the conductor surface. Figure 2.13 shows the phenomenon of the current distribution due to the skin effect; where the small black dots represent electrons. Figure Example current distribution of skin effect The skin effect is due to the opposing eddy current induced by the changing magnetic field resulting from the AC current. At higher operating frequencies, the skin depth becomes smaller and consequently results in a higher resistance of the conductor. The skin depth of a conductor is inversely proportional to the square root of the operating frequency; the skin depth δ can be obtained as follows: ( 42 ) where is the resistivity (Ω-m), is the frequency (Hz), is the relevant magnetic permeability of the conductor, and is the magnetic permeability (Henry/meter) of the air. Furthermore, it is suggested that the diameter of each single wire utilized for transformer windings is smaller than double of the skin depth [56]; the diameter of the sufficient wire D is written as: δ ( 43 ) Furthermore, the skin effect losses can be described in terms of AC resistance. Based on Dowell s equations, ( 44 ) was written to describe the AC resistance of an 25

48 THEORY AND METHODOLOGY infinite foil in 1-D analysis [57]. ( 44 ) where is defined as: ( 45 ) ( : thickness of the foil conductor, : conductor diameter) Proximity Effect (a) Same direction (b) Opposite direction Figure The proximity effect example, the current flowing in two conductors in same or opposite direction The proximity effect can be explained as, if there is current flowing in one conductor, the current flowing on the adjacent conductor will be affected on its current distribution. If the current of two conductors flow in opposite directions, the area in close proximity carries higher density of current. In Figure 2.14, where (a) the current flowing in two conductors are in the same direction and (b) is in opposite direction.the AC resistance to the DC resistance ratio of the multi-layer winding in 1-D analysis using orthogonally approach can then be re-written as [26]: ( 46 ) where m means the m th conductor. Although ( 46 ) was originally written for the AC resistance of square foil wires, it is still valid and gives acceptable accuracy for the round wire calculation. For a more detailed Litz wire analysis in bundle level, Sullivan s works are good references [58], [59]. 26

49 THEORY AND METHODOLOGY Eddy Current Effect In many transformer publications, eddy current is normally treated as the phenomenon which includes skin effect, proximity effect and eddy current effect itself. In this dissertation, the author would like to emphasise that the eddy current effect should not be considered as the integration of AC effects. Although theses AC effects (skin effect, proximity effect and eddy current effect) have close relationships with each other, it would be easier if they are treated as individual phenomenon during the electromagnetic analysis process. Nevertheless, for the current distribution results presented in the simulation and the measurement section, eddy current will still be treated as the sum of the AC effects. Hence, readers in the same field shall find it easier to comprehend the content discussed. Eddy current is defined as electric currents induced within conductors by a changing magnetic field in the conductor [60]. Thus, the losses caused by the magnetic field generated from the source winding or induced current are recognized as eddy current losses. For this reason, it is often that the transformer windings designed to be placed away from the transformer air-gap. The closer the windings are to the air-gap, the higher eddy current losses are expected for the designed transformer. The eddy current losses per unit mass (W/kg) can be described as [61]: ( 47 ) where is the peak flux density, =1 for thin sheets and =2 for thin wires, is the density of the material in kg/m Parasitic Effect Consideration Leakage Inductance Inductance is a very important index of the transformer performance. Mainly two inductances are concerned for the transformer design; they are magnetizing inductance and leakage inductance. As the introduction of the equivalent circuitry introduced earlier in Chapter 2.3.4, the inductance characteristic of the 27

50 THEORY AND METHODOLOGY transformer can be analysed with the simplified equivalent circuit shown in Figure A magnetic material with higher permeability has better performance on transforming the electric energy into the magnetic energy. In other words, if the magnetic flux circulates in a higher permeability material, the magnetic field generated will be greater than fluxes flows in a low permeability material (ex. Air, plastic, rubber and etc). Therefore, with a greater, the exciting current required to maintain the magnetic field will be smaller. Alternatively, if the excitation current is the same, then winding turns of the transformer can be reduced. Normally in the practical measurement, the can be measured through the OC test. The OC test is simply carried out by leaving the output winding unconnected, and then the impedance characteristics is to be measured by using the impedance analyser. However, when the is the measured object, the result it obtained would include the. The definition of the leakage inductance ( ) can be explained as the energy generated from one winding is not perfectly transmitting to the other. For example, the primary magnetizes 100% of magnetic energy, if only 97% of energy is received by the secondary, the 3% loss of the magnetic energy can be asserted as leakage energy. In other words, leakage energy is the energy which stores in the air core inductance. This energy is partially fed back to the power supply on the next half excitation cycle, and partially results in an inducing eddy current in surrounding metal materials. To obtain the, the SC test must be conducted by connecting two secondary connection ends. The illustration of the SC connection configuration is shown in Figure With this testing configuration, the magnetizing branch is neglected due to the relatively large impedance. Therefore, the approximated can now be obtained. However, it is impossible to achieve a perfect SC condition. Thus, the measured should be written as [64]: ( 48 ) where is the self-inductance of the secondary winding (please refer to Figure 2.10 for notations of the inductance). Assuming the turn ratio of the transformer is 1, then the below equation is valid: ( 49 ) where is in parallel with and being coupled to the primary side, the value is quite close to because the is relatively smaller than the. Thus, can 28

51 THEORY AND METHODOLOGY be simplified as: ( 50 ) Figure Simple transformer equivalent circuit with perfect short circuit condition [63] The mutual inductance is another index to evaluate the performance of the transformer. M is defined as how two windings are coupled between each other. With a given, the relationship of and the coupling coefficient of the transformer is described as: ( 51 ) The can also be obtained by connecting the primary winding and the secondary winding. If two windings are connected with the same polarity, the measured total inductance is: ( 52 ) If the polarity of two windings is connected reversely, the measure total inductance becomes: ( 53 ) On the other hand, the mutual inductance of two coils can be obtained from ( 54 ) based on the numbers of magnetic flux linkage flowing through [57]. ( 54 ) where λ is the quantity of magnetic flux through the coil, and I is the current. Also, the behavior of the leakage inductance of the transformer can be summarized as in ( 55 ) and ( 56 ), where and represent the leakage inductance on two coils, and are the self-inductance, and = is the mutual inductance. 29

52 THEORY AND METHODOLOGY ( 55 ) ( 56 ) Based on winding structures, the leakage energy can be calculated as [58], [59]: ( 57 ) where is the leakage energy (the energy stored in the air), is the thickness of conductors, is the winding width, is the winding length and x is the distance between windings. For a more complicated configuration of interleaved windings, the following equation should be applied [65]: ( 58 ) where N is the number of winding turns, M is the number of section interfaces, the sum of all section dimensions perpendicular to the section interfaces and the sum of all inter-section layer thickness. is is Intra-winding Capacitance Figure 2.16 shows the simplified HFCT equivalent circuit which is especially useful for capacitance analysis. Because of the common-mode interferences problem of the designed HFCT, a Faraday shield is placed between the primary and the secondary windings. The represents the intra-winding capacitance, in which the can be reduced with the insertion of the Faraday shield if the shield is grounded properly. The intra-winding capacitance becomes as shown in Figure (b). With the insertion of the Faraday shield, it also establishes two new capacitances which are and between the primary and the secondary windings to the Faraday shield. If the Faraday shield is not connected to the ground, the intra-winding capacitance becomes the sum of and in parallel to the. Therefore, the intra-winding capacitance becomes greater than the HFCT without the insertion of the Faraday shield. In addition, an ungrounded Faraday shield also establishes an additional parasitic capacitance to the ground. If the Faraday shield is well-grounded, both windings have their own electric path to the ground. Thus, the intra-winding capacitance can be reduced between the primary and the 30

53 THEORY AND METHODOLOGY secondary windings, and consequently with the ability to suppress the HF noise. (a) Without shield (b) With shield Figure Simplified HF transformer equivalent circuit [62] In fact, the cannot be measured directly if the Faraday shield is at grounding condition. An alternative measuring method is required. Figure 2.17 shows a further simplified capacitance model of the HFCT with the Faraday shield, which focuses on the electric behavior between the input and the output windings. In Figure 2.17 (a), the figure illustrates if the Faraday shield is under grounding condition. Capacitors from the shield to conductors are in reversed polarities and are connected in series. Ideally, the HF noise is transmitted from the input winding conductor to the ground without propagating to the output end. However, since the primary winding and the secondary winding cannot be perfectly isolated from each other in practice, a small amount of always exists. The floating case of the Faraday shield is shown in Figure 2.17 (b); where and have the same polarity with each other, and the total capacitance becomes the sum of, and. This explains why the HF noise problem becomes more serious if the HFCT is with the Faraday shield, but not grounded properly. From the concept explained in Figure 2.17, the of the HFCT with the Faraday shield under grounding condition can be measured indirectly as in following processes: Firstly, and are measured individually with the Faraday shield connects floated. Secondly, measure the intra-winding capacitance of the HFCT while the shield is still at floating condition. Since the total intra-winding capacitance, and become known, the new is now ready to be derived. Note the takes the effect as the actual intra-winding capacitance for the HFCT with the Faraday shield under grounding condition. This means, the intra-winding capacitance cannot be perfectly eliminated in practice even with the utilization of the Faraday shield. 31

54 THEORY AND METHODOLOGY (a) Grounded (b) Floating Figure Illustration of the charge distribution in grounded and floating cases Based on the above discussions, the relationship of HF voltage noise that propagates from the input of the HFCT without the shield to the output can be written as: ( 59 ) If the HFCT is with the Faraday shield inserted and at floating condition, the HF voltage noise propagates to the output becomes: ( 60 ) Once the Faraday shield is connected to the ground properly, the impedance of should become very small due to its almost infinite value. Thus, the HF voltage noise output is then written as: ( 61 ) 32

55 NUMERICAL MODELLING 3 Numerical Modelling 3.1 Introduction To evaluate the performance of designed transformers, 1-D analytical method is no longer appropriate due to the level of accuracy required. Especially, for complex geometrical structures, the accuracy of 1-D approach further decreases. In fact, most of the existing engineering problems are very complicated, and to solve these problems requires simplification and approximation. This means, solutions to these problems will not be exact solutions. This kind of methods has been utilized for years due to the limitation of computational technology in past decades, where most of transformer designs were relied on the manual calculation. However, with the improved computational technology, repeated calculations and complicated calculating processes can now be programmed, and solutions are obtained within a short time. There are various numerical methods which can be found in different areas and applications; in which the Finite Element Method (FEM) is one of the most popular numerical techniques incorporated with the advanced computational technology [66]. The FEM is a numerical method utilized for solving partial differential equations and integral equations [67]. Also, it is an effective tool on solving problems with multiple variables when boundary conditions are appropriately defined The principle of FEM is by discretising the analysed object into a finite number of elements. Each element can be various in shapes, such as dot, line, triangle, circular, rectangle, polygon, block, cylinder and etc. Also, each element will be assigned with a corresponding mathematical equation and boundary conditions prior to the solving stage. The final results are obtained by summing solutions of these global elements together. More FEM introduction can be found in [68], [69]. 33

56 NUMERICAL MODELLING In this research, Ansys Multiphsis 14.5 was employed to deal with problems of electrostatic, magnetostatic and eddy current. This commercial software package offers comprehensive numerical solutions for both single-physics and multi-physics problems, in which it covers areas of structural, thermal, fluid, electromagnetic and etc. The accuracy of the software has been verified by many publications [28], [46], [56], [70], and theories supporting this is the FEM and the famous Maxwell equations, which is mentioned briefly above and will be further discussed in the following sections. For 2D analysis regards to the capacitance calculation, inductance calculation and eddy current simulation, the Ansys Parametric Design Language (APDL) was used; the example APDL coding is presented in Appendix F. The elements applied in the simulations are dependent on the required solvers and analysis types. The elements applied in the simulations were tabulated in Table 3.1. Table 3.1. Applied elements for FEM simulation Solution 2-D Analysis 3-D Analysis Electrostatic PLANE121 SOLID122 Magnetostatic PLANE53 SOLID97 Electromagnetic PLANE53 SOLID236 For 3-D simulations, the geometrical models of prototype transformers were built in the Ansys Workbench. After that, use the geometry information as the input for the Ansys APDL and computes the required solutions. In 3-D modeling, it is a good idea to use the Computer Aided Design (CAD) software such as ProEnginner and AutoCad rather than coding directly with the complex 3-D model. The CAD software saves a lot of time for construction of numerical models. The transformer design with corresponding simulation procedures is shown in Figure 3.1; where capacitance calculation, inductance and eddy current distribution were conducted with different analysis of electrostatic, magnetostatic and electromagnetic. 34

57 NUMERICAL MODELLING Design of Transformer Basic Parameter Definition and Calculation Solution Type Capacitance Calculation Inductance Calculation Current Distribution PLANE121 SOLID122 PLANCE53 SOLID97 PLANCE53 SOLID236 Modelling 2-D Analysis Material Assignment 3-D Analysis Algorithms and Boundaries Meshing Solving Solutions Post-Processing Figure 3.1. Procedures of transformer design and simulation 35

58 NUMERICAL MODELLING 3.2 Computational Electromagnetic Method The transformer is a static electrical device that transfers energy between the primary and secondary winding circuits [71]; the AC current of the primary creates a magnetic flux in the transformer core, and this varying flux induces a corresponding AC current on the secondary winding. To investigate this kind of physical phenomenon, computational electromagnetic modeling technique is a very useful tool [72]. The real-life electromagnetic problems can be classified according to the time variation as shown in Figure 3.2; different mathematical equations are required to the corresponding time varying conditions. Since the operating frequency of the introduced transformers ranges from 40 khz to 300 khz, the analysis can be conducted with uses of static field technique and quasi-static technique. Thus, the full-wave technique is not considered and will not be included in this dissertation. The difference of the static field and the quasi-static field is whether the time varies or in constant. The computation process normally becomes very redundant if the time factor varies; therefore, engineers tend to simplify the quasi-static problems into static problems where possible. Figure 3.2. Electromagnetic problems classification Before taking any further discussion into the FEM, the theory must be understood. The modem electromagnetics are based on a set of Maxwell s equations; which are in a differential form as shown in Table 3.2 (for the convenience of solver basics illustration, equations in integral form has also been included). In fact, Maxwell finished his electromagnetic theory with 20 equations, and only became well-known after the simplification of these equations into four equations by English mathematician and physicist Oliver Heaviside and German physicist Heinrich Hertz 36

59 NUMERICAL MODELLING [73]. These four equations describe how electric field and magnetic field are generated and altered by each other; it also illustrates how the charges and currents are related to electric and magnetic field alternations. Please note that these four equations are all consistent, but not independent from each other. For example, the two divergence equations can be derived from the two curl equations; the relationship between two vector curl equations and two vector constitutive relations are and which can be referred to ( 17 ) and ( 72 ). More details of electromagnetic theory can be referred to [73], [75], [76]. In this dissertation, only discussions related to the transformer design will be presented. Table 3.2. Maxwell s equations Name Differential Form Integral Form Gauss s Law for electric field Gauss s Law for magnetic field Faraday s Law Ampere s circuital law Definition : electric displacement field; : magnetic field density; : electric field; : magnetic field; : charge density; : current density; : surface; : path; : length; : fluxes In the case of static field situations, Coulomb s law and Biot-Savart s law are utilized which are based on experiments and observations. For example, the capacitance calculation can be dealt with Coulomb s law by solving the electric field phenomenon. The magnitude of the electric field created by a single source charge point with the distance can be presented as: ( 62 ) The forces between two charges: ( 63 ) 37

60 NUMERICAL MODELLING Thus, between two charges are obtained by: ( 64 ) Consequently, the capacitance between two conductors can be calculated by volume integral of charge distribution in the whole region. On the other hand, the inductance calculation requires the understanding of the relationship of at position r generated by a steady current, that is: ( 65 ) Since is obtained, the inductance can be easily derived based on its basic definition from Faraday s Law. The inductance is the ratio of the magnetic flux linkage per unit current in the loop. Furthermore, the time-varying problems can be approximated by applying the Galilean limits [77]. Thus, the time-varying problems are transformed into quasi-static problems. The benefits from doing this are [78], [79]: Better understanding of the transition from statics to dynamics. The elimination of particular couplings of electric and magnetic field quantities reduces the required computation power. Not necessary to apply the full set of Maxwell s equations while still obtaining the acceptable accurate results. Quasi-Static analysis has much in common with static analysis; in which simple theories and laws can be utilized for further simplification. According to the conditions of applications, appropriate Galilean limits should be applied to the Maxwell s equations. For the transformer design introduced in this dissertation, magneto quasi-static technique needs to be implemented due to the inductive effects of the transformer (for high-voltage or microelectronic applications, electro quasi-static technique needs to be employed). Define as the velocity of charge in the medium, as the velocity of light in vacume, as the velocity of light in the medium, as the reference quantity of and ; assuming below: and, the Maxwell s equations in differential form is re-written as 38

61 NUMERICAL MODELLING ( 66 ) ( 67 ) ( 68 ) ( 69 ) Since is small with respect to, ( 68 ) can be written as ( 70 ) with the elimination of time derivatives [77]. ( 70 ) 3.3 Electromagnetic Solvers Electrostatic Solver Capacitance computation is one of the primary goals of the electrostatic analysis, and the computation is based on the Energy Method [83], [84], [85]. The electrostatic energy of a single conductor system is written as: ( 71 ) where is the self-ground capacitance, is the potential. For the electrostatic analysis, a specific electric field intensity normally being pre-assigned to the conductor. Thus, the electric flux density can be obtained: ( 72 ) where is the relative permittivity and is the permittivity of free space. Since and are known, the electrostatic energy in ( 71 ) can also be written in an integration form on a total volume : ( 73 ) 39

62 NUMERICAL MODELLING Comparing ( 71 ) and ( 73 ), the capacitance can be obtained as: ( 74 ) Alternatively, the relationship between potential and charge in a multi-conductor system can be described by the following equation, which satisfies Poisson s equation: ( 75 ) where is the space charge density. Integrate on a conductor for a total volume of ; thus, charges is obtained. The coefficients of the capacitance matrix can be calculated as: ( 76 ) ( 77 ) Magnetostatic Solver In ( 54 ), the inductance calculation is based on the numbers of magnetic fluxes flowing in the element and the computed results are not precise enough for complex structures. For this reason, the energy method has been adopted to obtain more accurate results [84], [86]. The inductance computation utilized by the program is revised from Smythe s procedure [86]. With the use of the Energy Method, the inductance is defined as in ( 78 ): ( 78 ) where is the stored energy in the media; which can be obtained from the integration of a specific area as in ( 79 ): ( 79 ) 40

63 NUMERICAL MODELLING Electromagnetic Solver To investigate the eddy current distribution, ( 80 ) was applied to the FEM program to obtain desired solutions. This equation is derived from Maxwell s equation and has transformed the alternating field problem to a sinusoidal quasi-static eddy current problem. The equations are described in terms of the complex magnetic vector potential and an electrical complex scalar potential, where is the permeability, is the conductivity, is the angular frequency and is the excitation current density. ( 80 ) It is possible to investigate the eddy current distribution in alternating field (in time-domain); however, the computation process is too time-consuming. With Maxwell s fourth equation in differential form: ( 81 ) the time-domain description can be transformed into frequency-domain; in which ( 81 ) becomes: ( 82 ) where is the charge density, is the radial frequency, and is the dielectric constant. Also, ( 83 ) To calculate the ohmic losses in the winding, the energy method is still applicable when H is known; where H can be obtained by assuming the magnetic field and time varied quantities are stored as phasors. ( 84 ) is the magnetic permeability. From ( 84 ), the ohmic losses of conductors is obtained as: 41

64 NUMERICAL MODELLING ( 85 ) where is the complex conjugate of H. Furthermore, there are often different medium being used for the designed magnetics in practical problems. Thus, the following boundary conditions have to be specified between media in order to obtain accurate results. For a perfect conductor: ( 86 ) where represents the tangential component to the magnetic field. For a perfect magnetic conductor: ( 87 ) However, if the problems cannot be assumed with the use of perfect conductors, then the integral form of Maxwell s equations should be employed at the places where the medium are discontinuous. 3.4 Finite Element Method In order to solve Maxwell s equation efficiently (particularly for the partial differential equations), FEM is the most effective numerical methods [80], [81]. Normally, the electromagnetic problem of an engineering system needs to be described as a mathematical system as the first step. After that, the governing mathematical expressions is developed and applied to describe the behavior of the solving targeted system. For problems with simple structures, most of the numerical methods can obtain accurate results. However, once the structure of computational model gets too complicated, the accuracy of these normal numerical methods drops to an unacceptable level. Thus, the FEM was developed to find the most accurate results for the engineering problems [82]. The FEM requires the solving mathematical model to be discrete into a finite element of simple shapes, and then obtain the approximations by summing up all results computed for each element. A. Approximation Techniques There are several approaches which can be used to obtain approximations of discrete finite elements. For example, Weighted Residual Method which includes the 42

65 NUMERICAL MODELLING test function is decided by Collocation Method, Least Squares Method or Galerkin s Method [82]. Among these approximation techniques, Galerkin s Method is the most precise and popular if the formulation of the physical problem is known. Also, if the physical problem is intractable (ex. harmonic analysis), then Rayleigh- Ritz Method is often the option. To explain these two methods in brief, a simple one-dimensional example with its differential equation is used as below: ( 88 ) boundary conditions ( 89 ) where is the unknown solution,,,, L are constants and is a variation. Galerkin s Method In order to obtain the solution, the trial function of approximated solution needs to be selected, which can be assumed by an unknown coefficient array. In deep, the accuracy level of the approximated result is very dependent on the proper selection of the trial function: ( 90 ) Thus, the residual R is obtained by substituting the trial function ( 90 ) into differential equation ( 88 ); becomes: ( 91 ) Based on Galerkin s Method, the test function derives from the chosen trial function. That is, ( 92 ) The weighted average of the residual over the problem domain is set to zero, ( 93 ) 43

66 NUMERICAL MODELLING Applying ( 92 ) to ( 93 ) to obtain ; and consequently, is solved with the known by ( 90 ). Rayleigh-Ritz Method The physical problem needs to be transformed into the variational expression in order to derive the approximate solution (the functional, represents energy in many engineering applications) at the stationary point. Thus, the problem described in ( 88 ) is transformed as: ( 94 ) In ( 90 ), the approximated solution has been defined. Assuming: ( 95 ) The unknown coefficient will be obtained from the above operation. For elements more than two nodes, the linear shape function matrix can be used to express the solution for the element. The solution is obtained as: ( 96 ) where shape functions describe the coordinate value at each individual node, and ( 97 ) ( 94 ) can then be re-written as: ( 98 ) Solving the vector and matrix expression of ( 98 ) and ( 95 ), the approximated solution for each nodal can now be obtained. 44

67 NUMERICAL MODELLING B. Finite Elements Figure 3.3. Geometry discretization with triangulation There are many different types of elements from 1-D, 2-D to 3-D; in which triangular finite element was the first finite element proposed for continuous problem [80]. The example problem in 2-D domain Ω with the discretion of triangular elements is shown in Figure 3.3. Using Possion s equation to describe the various physical natures, the common field governing equation can be written as: ( 99 ) where and are real or complex value on a manifold. For example, in electrostatics, the Possion s equation can be used directly to solve the electric potential and the charge density distribution; where is substituted with scalar electric potential and is substituted by ( :charge density, : frequency, : permittivity). In terms of the 2-D Cartesian coordinate system, ( 99 ) becomes ( 100 ) for a 2-D domain Ω. The boundary conditions as shown in Figure 3.3 are and on ( 101 ) ( 102 ) where and denote known variables and flux boundary conditions and is the outward unit vector at the boundary. 45

68 NUMERICAL MODELLING On the other hand, a triangular element in the 2-D Cartesian coordinate system can be represented as: ( 103 ) where is the constant to be determined. Let ( 104 ) and shape functions for the linear triangular element can then be written as: ( 105 ) Thus, ( 106 ) Since shape functions are defined, the element matrix triangular is now obtained within a 2-D domain as: for the example ( 107 ) Please note that the in ( 107 ) was derived with the use of Galerkin s Method, in conjunction with the Possion s equation shown in ( 99 ) as the governing equation. The matrix varies if the approximated technique and the governing equation are different. Furthermore, ( 99 ) can be re-written to a matrix form for computation: ( 108 ) 46

69 NUMERICAL MODELLING Similarly, the mathematical problem of the transformer can be formulated as a sinusoidal quasi-static eddy current problem, which was derived from Maxwell equations (refers to Chapter 3.2). The equations are described in terms of the complex magnetic vector potential and an electrical complex scalar potential, ( 109 ) where is the permeability, is the conductivity, is the angular frequency and is the excitation current density. Using Galerkin s method to discretize the governing equation and solve this problem. The system matrix equation can be obtained from equation ( 109 ) and rewritten as shown in equation (2) [54]: ( 110 ) Where the matrix [S] is global coefficient matrix. [M] is the time harmonic matrix and G is the weighted residual. It is difficult to solve the quasi-static eddy current problem mathematically with accurate result. However, the use of Galerkin s method brings the approximated result closer to reality. 47

70 NUMERICAL MODELLING 3.5 Modelling Technique Figure 3.4. An example approach by means of 2-D simulations [87] In order to fully simulate the electromagnetic problems of the transformer, 3-D simulation is selected for best accuracy. However, the modelling and the solving process of 3-D simulations are too time-consuming, and require a lot of computation power. For this reason, modelling techniques such as double -2D methodology, simplification, and sectorization are chosen to overcome these issues. In general, a 3-D problem can be solved with double 2-D FEM technique; the illustration is shown in Figure 3.4. The 3-D models are being cut into horizontal or vertical part of conductors; or, being folded or unfolded before the solving process. This kind of modelling technique has been broadly used and more details can be referred to [87]. On the other hand, this dissertation has also introduced two techniques; they are the simplification technique and the sectorization technique Simplification A demonstration example of the simplification technique was presented by using the HFCT transformer as the example in this section, in which the phenomenon of intra-winding capacitance was utilized for the illustration. The intra-winding capacitance computation results of circular conductors in different winding configurations are shown in Figure 3.5. The boundary is 5mm from conductors; each conductor has a radius of 0.5 mm and length as 1 m; distance from center of the conductor to the other is 10 mm. Compared Figure 3.5 (b), (c) with the calculated single conductor capacitance in (a), the capacitance is and times 48

71 NUMERICAL MODELLING greater than that of a single conductor system. In (c), the conducting surface area has increased 7 times than in (a), but the has only increased less than double. This phenomenon can be explained from the definition of capacitance; the capacitance is defined as the ability of a body to store an electrical charge [88]. Even though the overall conducting surface is increased, the area of the surface which towards each other are not increased that much. A very similar example for the parallel-plate capacitor system, that the thickness of the conductor has no much effect on the. (a) : pf (b) : pf (c) : pf Figure 3.5. Electric potential density simulations (unit: ): (a) Single conductor to single conductor; (b) single conductor to multi-strands wire; and (c) multi-strands wire to multi-strands wire. Furthermore, in consideration of the fringing effect which exists in both magnetic and electric field, a 2-D transformer full model was built to further analyze the characteristic of the multi-conductor system. Comparing the full 2-D model in Figure 3.6 with the simplified model showed in Figure 3.5 (a) and (c), the total are and times greater respectively; which is almost identical. Hence, the simplified model shown in Figure 3.5 (a) can be utilized for analysis instead of using the 2-D full model shown in Figure 3.6 (b) for capacitance optimization work. Thus, the simplification technique can be utilized effectively on reducing the required computation power. For example, this technique can be used to investigate the number of strands, conductor diameter, and conductor distance versus the. The full 3-D simulation or the simulation model shown in Figure 3.6 (b) should still be utilized if precise results are required once the optimization process is completed. In short, the simplification technique is achieved by simplifying the simulation model and investigates the relationship of variable parameters with the targeted parameters. Once this relationship is found or becomes known, the simulation process becomes 49

72 NUMERICAL MODELLING facilitated while having the same level of accuracy. (a) pf (b) pf Figure D full model of Electric potential density simulations (V/m). (a) Single conductor and (b) 7-strands Litz wire Sectorization Another modelling technique which can be utilized for 3-D FEM simulations is the sectorization technique. In this research, the sectorization technique was implemented for the multi-strands Litz wire utilized for the transformer design. The example illustration of the sectorization technique of planar transformer (introduced in Chapter 5) is shown in Figure 3.7. It is impractical to compute wire losses for a full 3-D transformer model. This is due to not only the thirst of large computation power, but also the significant time spent on the construction of computational models. Figure 3.7. The illustration of sectorization technique 50

73 NUMERICAL MODELLING The sectorization technique is especially beneficial with the eddy current investigation (electromagnetic simulation). The level of modelling accuracy has a great effect to the simulation results. In comparison, inductance and capacitance calculations are based on magnetostatic and electrostatic analysis; in which the computation results are not so sensitive to the model details. The sectorization technique was achieved in the following process with the example of winding losses investigation. Firstly, full 3-D transformer model was sectorized according to the core length of the transformer. After that, two simplified models (solid wire model and Litz wire model) were analysed and compared in order to obtain the normalization factor. The mathematical description is shown in ( 111 ), where the is the power loss of the solid conductor model and is the power loss of the Litz wire model. Once the was obtained, the 3-D full model transformer analysis with the use of single conductor will then be conducted, and the obtained 3-D result was then multiplied by the coefficient obtained earlier. Thus, the final simulation result of the full 3-D Litz wire transformer model will be very precise and close to the reality (this has been verified by experiment results). ( 111 ) 51

74 NUMERICAL MODELLING 3.6 Investigation of Eddy Currents The transformer losses information has been discussed in Chapter 2.4. Base on the theoretical calculation, basic information of AC resistance can be obtained easily. However, in order to explain the current distribution characteristic more deeply, the FEM modelling technique is required. The FEM modelling technique is not only advantageous on computing the physical problems with complex equations, but also advantageous on visualizing the complicated physical phenomenon. In this section, the discussion of eddy current phenomenon will be presented with the use of the FEM modelling technique. Firstly, the example starts from the calculation of skin depth of the copper conductor at the frequency of 100 khz; which the skin depth can be calculated by ( 42 ) as: δ = π π = m = mm Considering at 100 khz and assuming the conductor diameter as a ratio of skin depth at 100 khz and. 0.5δ 1δ 2δ 4δ Figure 3.8. Example of the single conductor current distribution. The diameter of conductor varies from 0.5 skin depth to 4 skin depth Figure 3.8 shows the relationship of a single conductor with the diameter varies in proportional to the skin depth at 100 khz. As expected, the current distributes more unevenly if the diameter of conductors becomes greater. At higher frequencies, skin effect becomes a great concern especially if the power rating of the application is high. At 4, the peak current density raises 25.7% to compared to one example ; this bring an increase of current density and results in unwanted hot spots. 52

75 NUMERICAL MODELLING The increase of the peak current density also represents a higher AC resistance of the conductor. 0.05δ 0.5δ 1δ 2δ Figure 3.9. The proximity effect simulation example. Conductor diameter is one skin depth, varied the distance of conductors by the ratio of skin depth Another simulation work was conducted to examine the eddy current phenomenon. The simulation results are shown in Figure 3.9, where two conductors were utilized to investigate the proximity effect. Conductors have the diameter of one, and the distance between two conductors varies from 0.05 to 2. The result shows that the current distributes more evenly when wires are within 2 distances from each other. There is only 1% variation on current density distribution when conductors are close to each other at δ 1δ 2δ 4δ Figure The proximity effect simulation example. The condutor distance as one skin depth and varied the diameter of condutors from 0.5 to 4 skin depth. 1% variation of the current distribution due to the proximity effect is almost negligible. However, if the proximity effect counteracts with the skin effect, the phenomenon of uneven current distribution becomes more obvious. Figure

76 NUMERICAL MODELLING illustrates this uneven phenomenon of current distribution. If the conductor diameter is within one, the current distribution has only minor variations. However, once the conductor diameter is above 2, the peak current density increases by 7.52% and 40.58% at 2δ and 4δ respectively. In comparison of 1δ and 4δ simulation results, if the diameter of conductors increase by 4 times, the peak current density is 40 times greater due to the summation influence of skin effect and proximity effect. 3 strands 7 strands 21 strands 49 strands Figure The proximity effect simulation example with different numbers of windings; conductor diameter: 1, distance between conductors: 0.01 mm If the number of wires increases, then the proximity effect becomes dominant. This means, in the worst case, the wire bundle might have an inversed current at its center wires due to the induction of surrounding wires. Figure 3.11 shows this phenomenon, in which the number of bundle strands varies from 3 to 49 strands. The peak current density of 49-strands is almost double to the 3-strands model (let conductor diameter and distance to other conductors be the same). Therefore, it is beneficial for the center wires to be removed if the numbers of strand are too many at the specific frequency. The removal of the central wires not only reduces the physical cost of wires, but also relieves the proximity effect between each wire conductors. Figure 3.12 shows an interested power loss comparison of Litz wire bundles to explain the eddy current effect further. The comparison was conducted under five different numbers of strands across frequencies; they are 7 strands model, 21 strands mode, 49 strands model, 69 strands model and 105 strands model represent Litz wire bundles with 2δ, 3δ, 4δ, 5δ, and 7δ of the bundle radius respectively. The operating frequency of 100 khz was chosen as the base example for illustration. Each conductor of Litz wire bundles has the diameter of one skin depth which is equal to mm. The power losses comparison is aiming to find the best winding configuration among these five models. The simulation results have been normalized, 54

77 NUMERICAL MODELLING in which the power losses of Litz wire is represented as the percentage of extra power losses over its equivalent solid conductor. For example, the power loss of a 49 strands Litz wire is compared with an equivalent single solid conductor which has the cross-section area of mm 2. At 100 khz, 49-strands Litz wire has a power loss reduction by 11.23% compared to its equivalent single solid wire. The simulation result shows, the Litz wire effectively reduces power losses by relieving eddy current effect. However, numbers of wire does not represent a better reduction of power losses; this is because the proximity effect counteracts with unevenly distributed current while the frequency is high. Normalized Power Losses (%) Strands 105 Strands 7 Strands 69 Strands 21 Strands Frequency (khz) Figure Power losses comparison of multi-strand Litz wires (normalized with equivalent solid conductor) Through the analysis of results shown in Figure 3.11 and Figure 3.12, one short comment can be made that the radius of the Litz wire bundle should be kept within 3~4δ in order to obtain the maximum power losses reduction (assume the individual wire conductor has the diameter of 1δ). Since the power loss is directly proportional to the square of current, a reversed current phenomenon brings an obvious additional loss which increases with the frequency and the layers of Litz wire bundle. For this reason, if the conductor is with the diameter of one skin depth as shown in the example, 49-strands (represents Litz wire bundle with the radius of 3δ) is the most cost-effective wire configuration. To verify this comment, another simulation was conducted by having this five wire models with the same current excitation, and power loss results were normalized with their power loss in DC individually. Results of the power loss rate of change versus the frequency are shown in Figure 3.13; the power losses increases 55

78 NUMERICAL MODELLING dramatically with the frequency for models of 69-strands and 105-strands (steep raising curve). The power loss does decrease with numbers of strands; however, this advantage disappears once the frequency increases to a specific point due to the severe proximity effect as shown in the plot. In addition, the power loss of 105-strands and 69-strands are 35.6% and % lower at 100 khz, while the diameter of bundle models are 75% and 25% greater than 49-strands model. Thus, the Litz wire bundle with the radius within 3~4δ is validated to be the most cost-effictive wire configuration without having a large winding in the transformer. Power Losses Ratio Strands 69 Strands 49 Strands 21 Strands 7 Strands Frequency (khz) Figure Power losses comparison of multi-strand Litz wires (normalized with DC losses) To solve the proximity effect problem, twisted Litz wires were utilized for HF power applications and have been proven for its effectiveness [58], [59]. To simulate the twisted Litz wire behaviour, the 2D simulation is no longer effective; therefore, 3D simulation technique was utilized to deal with the twisted wire structure [89]. The comparison results of solid conductors and twisted wires are shown in Figure Comparing 3D result shown in Figure 3.14 (a) and 2D result shown above, both results have a strong agreement on the current distribution without the wire being twisted. For the twisted wire simulation result shown in Figure 3.14 (b), the peak current increases with the number of twisted turn per length; the more turns wires are being twisted, the higher current density is. This is not the expected result at the beginning of the simulation work, as the twisted Litz wires were expected to have lower peak current density distribution. The increase of the current density is because of the increase of the DC resistance (due to the increase of the wire length) as well as wires have the same face towards each other, in that the proximity effect is not relieved. Therefore, rather than just twisting wires, a woven technique needs to be applied, which effectively utilizes the advantage of the Litz wires on reducing the proximity effect. 56

79 NUMERICAL MODELLING (a) Solid conductors (b) Twisted wires Figure A 3D proximity effect simulation result. Conductor diameter: 1 skin depth, distance between conductors: 0.01 mm The simplified woven example of 7-strands Litz wires are shown in Figure 3.15 for illustration. Figure 3.15 (b) shows the elimination of one wire in a 7-strands Litz wire model; in which the current distribution in (b) was slightly different to (a). Current tends to crowd at where a lower magnetic intensity field exist. Therefore, top two wires have a higher current density distribution over other wires. (a) Typical 7-strands Litz wire (b) Elimination of one conductor Figure D simulation of 7-strands Litz wire. Conductor diameter: 1 skin depth, distance between conductors: 0.3 skin depth. Furthermore, the wire configuration is changed by leaving one end of middle conductor at the same position and sweeps the other end to the top. The result is shown in Figure Comparing Figure 3.16 (b) with Figure 3.15 (b), the current distributes more evenly in Figure 3.16 (b). Therefore, the proximity effect can be reduced via the woven technique of the wire arrangements. 57

80 NUMERICAL MODELLING (a) Bird view (b) Back view Figure D simulation of 6-strands Litz wire example. 3.7 Capacitance Verification in FEM Intra-winding capacitance ( is another index of the transformer performance which works in a close relationship with the transformer leakage inductance. With the design of power electronic applications, the and the of the designed application need to be reversely proportional according to its required operating frequency. This is especially important when the LLC topology is applied. If this resonant frequency is not matched with its operating frequency (or switching frequency), a phase shift on the output voltage or current is expected. This phase shift of input source results in the increase of the reactive power, and consequently, the efficiency of the designed applications decreases. On the other hand, the HF noise caused by the intra-winding capacitance is another concern while designing HF devices. The intra-winding capacitance between the input and the output windings always brings the unwanted signal distortion on the output end. Hence, in order to design the transformer to achieve its best performance, the behavior of the winding capacitance between conductors needs to be carefully treated. To verify the accuracy of the FEM simulation result, a simple 2-D model was built and the simulation result was compared with the theoretical result. The electric simulation result is shown in Figure 3.17; and the capacitance of a parallel-plate capacitor is obtained by [90]: ( 112 ) where is the relative permittivity, is the plate area and is the distance between the conductor surface. Please note the boundary selection in the 3D simulation 58

81 NUMERICAL MODELLING software is very important. While the boundary is really close to the conductor, the capacitance simulation result is almost the same as the theory result. However, if the boundary distance is much greater than the distance between two conductors, the fringing effect needs to be taken into account. (a) Electric potential ( ) (b) Electric field ( ) Figure The simulation result of electric field of the parallel-plate capacitor in air Area: 50 ; distance: 10 and thickness: 1 The fringing effect can be observed from the simulation result shown in Figure The electric potential distribution is higher in the centre region of two conductors and starts to decrease in the region away from conductors. In [91], it demonstrates the fringing effect by summarizing its experiments result into formulas. However, the result was only applicable to the Printed Circuit Board (PCB) device. Therefore, in order to find a relationship of capacitance to the geometrical structure, more benchmarks and simulation works are required. Simple structures can be observed and derived according to the current simulation works and theoretical formulas. The calculation of the capacitance system can be achieved by solving the Laplace equation with the constant potential applied on the surface of the conductors [85]. Table 3.3. Results comparison of simulation and theory on two simple systems System 1 System 2 Types Two square plates Two circular conductors Dimensions Length: 5mm Thickness: 1 mm Distance: 10 mm Radius: 0.5mm Distance: 10mm Theory pf pf Ansys pf pf 59

82 NUMERICAL MODELLING The verification of two simple systems on the simulations and theoretical results is shown in Table 3.3. The capacitance result computed by Ansys APDL (based on the energy method) shows a good accuracy in comparison with theoretical calculation results. To calculate the capacitance of a pair of circular conductors, the formula is: ( 113 ) where is the radius of the conductor. Therefore, the relationship between capacitance versus its radius of conductors and the distance is shown in Figure The result shows that the of the parallel wires has an exponential relationship to its conductor radius. Again, the simulation result is in a good agreement to the theoretical result. The small variation of these two results is mainly caused by the definition of the boundary conditions and meshing sizes. Intra-Winding Capacitance (pf) Theory Ansys Conductor Radius (mm) Figure The capacitance value comparison between the Ansys computation result and the theoretical result (b) without the Faraday shield (a) Structure (c) with the Faraday shield Figure A simple capacitor system of parallel plates with the insertion of Faraday shield 60

83 NUMERICAL MODELLING On the other hand, the reduction of the intra-winding capacitance ( of the introduced HFCT is very important in this research. Thus, this section has presented the basic analysis of a simple capacitor system with or without the Faraday shield. In order to reduce the, a very common method is by placing a conductor between two windings. The method is well-known as the Faraday shield insertion [14]; in which a conductor is placed between the windings and effectively insulates the electric field from each other. Therefore, an input voltage pulse will not be transmitted to the output easily. A simple capacitance system with or without the introduction of the Faraday shield is shown in Figure To simplify the capacitance analysis, the self-capacitance was eliminated in the equivalent circuit, so that the analysis focuses on the investigation of the. The Faraday shield is a conductor placed between windings for electric isolation as shown in Figure 3.19 (a). Refer to Figure 3.19 (c), and are neglected if the Faraday shield is perfectly grounded; if the shield is at floating connection, the total becomes the sum of, and. Table 3.4. Comparison of simulation result and theory on a simple system Without shield With the Faraday shield Capacitance (pf) Grounding Floating N/A N/A Plate area: 5mmx1mm, Shield thickness: 0.1mm, shield length: 5mm, distance between plates: 10 mm. Conductor distance to air region: 5mm. The comparison results of shield and non-shield cases are shown in Table 3.4. As expected, the intra-winding capacitance increases if the Faraday shield is inserted in the system but not grounded properly. Under the grounding condition, and were not taking any effect to the total intra-winding capacitance; there were only a small intra-winding capacitance exists between these two conductors. If the Faraday shield area becomes greater and fully encloses on one of the conductor, the intra-winding capacitance can be further reduced. Furthermore, the HF capacitance network model of the introduced HFCT is shown in Figure Based on Maxwell s theory, the relationship between potential and charge in a multi-conductor system can be described by the electric scalar potential V, which satisfies Poisson s equation: 61

84 NUMERICAL MODELLING ( ε V ) = ρ ( 114 ) where ε is the permittivity, and ρ is the space charge density. The shield or each turn of the winding can be taken as an independent conductor. Furthermore, based on the theory of capacitances in multi-conductor systems [92], [93], [94], one can obtain N equations relating the potentials V 1,V 2,, V N of the N conductors to the charges Q 1, Q 2,, Q N ; and the capacitance coefficients C 11, C i1, C 21,, C ij. Figure 3.20 shows a detailed parasitic capacitance network model of the HFCT. The parasitic capacitance can be obtained by using the FEM matrix equation as in ( 115 ) for the relationship between charge and potential where [S] is the global coefficient matrix and {Q} is the charge matrix. [ S ]{ V} = { Q} ( 115 ) By setting up the boundary condition, V 1 =1, V 2 = V 3 = = V N = 0, one can obtain Q 1 = C 11, Q 2 = C 21,, Q N = C N1, and in the same manner, the coefficients C ii s and C ij s can be calculated. Alternatively, the capacitance computation can also use the energy method. (a) Without the Faraday shield (b) With the Faraday shield Figure The capacitance network of the HFCT [93] 62

85 DESIGN AND ANALYSIS OF COAXIAL TRANSFORMERS 4 Design and Analysis of Coaxial Transformers 4.1 Introduction The isolated HFCT can be utilized in any energy storage system such as EV, energy bank, green energy applications and etc. It would be advantageous to have an isolated transformer in the converter system because of the following benefits: (1) prevention of DC pulse to the AC side; (2) prevention of high fault currents flowing through the system; (3) extended battery life from the elimination of electrical shocks and current leakage; and (4) easy adaptation of voltage level. A Faraday shield was placed between the primary and the secondary windings. With the Faraday shield insertion, the reduction of the intra-winding capacitance is achieved and consequently the alleviation of the EMI problem. In this chapter, a thorough analysis with the example of an 8 kw HFCT is presented, along with the investigation of the Faraday shield effects Operating Requirement The power rating specification of the example HFCT is tabulated in Table 4.1. The prototype transformer was built with the turn ratio of 1:1 for uses as the isolation transformer. The unique coaxial winding structure can easily fulfill the transformer requirements of low eddy current loss, high power density, low leakage inductance and high electromagnetic compatibility. The operating frequency was chosen at the range between 100~300 khz because of concerns on the overall size and Electromagnetic Interference (EMI) issue. Higher operating frequency effectively reduces the magnetizing current and sizes of the designed transformer. However, the increase of the operating frequency results in a higher AC winding loss, 63

86 DESIGN AND ANALYSIS OF COAXIAL TRANSFORMERS as well as the HF noise propagation problem. Furthermore, the prototype HFCT has the power efficiency greater than 99 % which has been experimentally verified under full-load condition. Table 4.1. The specification of 8 kw HFCT prototype Operating frequency f 100 khz-300 khz Input Voltage V 1 400V(dc) Input Current I 1 20A Output Voltages V 2 400V (dc) Power Range P 8k VA Turn Ratio N1/N2 1 Voltage Ratio V1/V2 1 Power Efficiency > 99% Current Density J 1 = J A/mm 2 Magnetic Ferrite Neosid F44 Initial Relative Permeability 1900 ±20% Temperature T max 60 C Geometry Specification Figure 4.1. The completed 3D assembly model of the HFCT The 3D model structure is shown in Figure 4.1 (completed model) and Figure 4.2 (without PCB layers). The proposed HFCT is composed with both the primary and the secondary winding in Liz wires, four identical magnetic core rings, PCB layers for the fixture of transformer windings and the Faraday shield placed equidistantly 64

87 DESIGN AND ANALYSIS OF COAXIAL TRANSFORMERS from the primary to the secondary windings (if there is a Faraday shield insertion). Litz wires utilized in the HFCT are a bunch of insulated wires, which can effectively reduce the proximity effect and eddy current effect for high frequency operations. Figure 4.2. The 3D assembly model of the HFCT without PCB layers The dimensioned 2-D cross-section views of the HFCT are shown from Figure 4.3 to Figure 4.5. Figure 4.3 (a) shows the size of the ferrite ring; there are two stacks of the magnetic cores of the HFCT, with one stack composed by two ferrite cores. The wiring configuration is shown in Figure 4.3 (b), in which the inner and outer windings are located with a 30 degree offset between the inner and outer circumferential layers. This unique wire arrangement results in two advantages of the HFCT. Firstly, the parasitic capacitance is minimized because of the maximized winding distance in a limited space. Secondly, the primary and the secondary couple with each other more efficiently and evenly. (a) Ferrite ring size (b) Wiring configuration Figure 4.3. Core size and wire configuration of the 8 kw HFCT 65

88 DESIGN AND ANALYSIS OF COAXIAL TRANSFORMERS The top view dimensions of the HFCT with and without the heat sink are shown in Figure 4.4; the heat sink only utilized for the HFCT with the Faraday shield to improve the heat dissipation performance. Figure 4.5 (a) is the side view of the HFCT where dimensions four ferrite ring stacks in a pair of two rows. Please note that the notation of End Region and Coaxial Region will be used exclusively in the following discussions of simulation results presented in this chapter. (a) Without heat sink (b) With heat sink Figure 4.4. Top view of HFCT configuration (a) Front view (b) End region cross section (c) Top view of half cross-section on the coaxial part Figure 4.5. The cross-section schematic of the 8 kw HFCT Figure 4.5 (b) shows the schematic dimension of the end region section. The end region section locates at the top and the bottom of the HFCT and next to the stacked magnetic cores; the winding wires distribute evenly from each other as shown in the schematic. The half cross-section of the HFCT is shown in Figure 4.5 (c). Both the inner and outer windings are geometrically identical to each other. Each coil consists of 21-strands of insulated wires (Litz wires) and the diameter of each wire is equal to twice of the skin depth thickness. Faraday shield diameter is 8.5mm with the thickness of 0.35 mm; the thickness is selected to be double of the skin depth at 300 khz. For winding configurations, either the outer winding or the inner winding can be used as the primary since they are symmetrically identical to each other. 66

89 DESIGN AND ANALYSIS OF COAXIAL TRANSFORMERS Please note that fiber glass PCB layers are utilized for winding fixtures. Due to the electric characteristic (higher permittivity) of the fiber glass material, it boosts up the intra-winding capacitance. This issue will be further discussed in the simulation section Magnetic Core Table 4.2. Ring core specifications [51] Table 4.2 shows the specification of the selected ring cores which fulfills the dimension requirement of the designed HFCT. The structure of four stacked cores and two stacked cores can be achieved by the utilization of core part number and respectively. Magnetic core part number of was finally chosen for the fabrication of HFCT prototypes due to lower intra-winding capacitance; by stacking up ferrite rings, the distance between two end region sections are maximized. Consequently, the unwanted intra-winding capacitance is able to be minimized due to the increased end region distance. The magnetic property of utilized magnetic cores is tabulated in Table 4.3, which is calculated based on the B-H curve provided from the material datasheet [51]. The calculated data represents the dynamic magnetization characteristics at the temperature of 25 0 C, in which the magnetic characteristic is useful at the first phase of the transformer design. The magnetic properties shown in Table 4.3 were used in the simulation as exact as possible under different load condition. Thus, a non-linear magnetic behavior of the designed HFCT is better simulated. 67

90 DESIGN AND ANALYSIS OF COAXIAL TRANSFORMERS Table 4.3. Dynamic Magnetisation B (mt) u r H (A/m) Electric Calculation Primary and secondary windings are symmetrical and with the use of 3 bundles of 7-strands twisted Litz wire. The full-load current was calculated based on the given HFCT requirement of the power rating and the output voltage as: The magnetizing current is relatively small compared to the full-load current; however, it should still be taken into account with magnetic property of the utilized core. The magnetizing current was calculated in Chapter : Therefore, the total current required at the full-load condition is: The current density: A current density between 4 to 6 previous experiment results. is acceptable based on experience and Magnetic Calculation Neosid F44 was utilized as the magnetic core of the HFCT prototype transformers because of its extraordinary magnetic characteristic at HF operations. Refer to the manufacturer s manual [48], the saturation flux density is obtained as shown in below: At 25 C : 500 mt 100 C : 400 mt (Saturation flux H=796 A/m) 68

91 DESIGN AND ANALYSIS OF COAXIAL TRANSFORMERS The transformer universal EMF equation is employed to obtain basic transformer parameters. The universal EMF equation is shown as [53]: ( 116 ) where is used to evaluate purely sinusoidal excitation; and is used when the excitation does not contains even harmonics. The operation of the transformer should be designed within the linear region. Once the transformer operates at the saturated region, the applications would be damaged as a result due to the large magnetizing current (the permeability of the magnetic material drops). Thus, assume the designed HFCT operates at 80% of its saturation flux density. That is, The magnetic core with the model number of was chosen; the selection process is shown in Chapter The detail of physical dimension was shown in Table 4.2. Once the power rating, operating frequency, magnetic ring cross-section area and flux density of the HFCT are given, the required turns per winding of the HFCT for one core can be calculated as: Thus, for a one single ring core transformer structure, 21 turns of winding are required to ensure the normal magnetic operation of the HFCT. In order to reduce the total number of winding turns, four ring magnetic cores was chosen. Thus, the winding turns should become: Substitute =6 into ( 116 ) to derive the maximum acceptable induced voltage: The mean magnetic path length of the ferrite ring is calculated as: Alternatively, of selected cores can be found on the core datasheet provided by manufacturers as mm. 69

92 DESIGN AND ANALYSIS OF COAXIAL TRANSFORMERS By looking at the datasheet of [51]; the Dynamic Magnetization: Typical B-H loops. The magnetic intensity at is obtained as 60 A/m and 80 A/m for temperature 25 C and 100 C respectively. Considering the transformer operates at the worst case, the maximum magnetic force at open-circuit condition is calculated as: The maximum magnetizing current required: This means at least current input from the mains is required for the transformer to be operated at no-load condition, and any required load current is an addition (assuming the input voltage as at exact 400 V). The final maximum flux density is obtained as: Power Losses The volume of each of the ferrite ring is: Thus, The power loss density increases with frequency and decreases with operating temperature. Refer to the datasheet provided by the magnetic material manufacturer [51], the power loss density P v is 1000mW/cm 3 while at 259mT (At 25 0 C, 100 khz). Thus, the core power loss P c is: Also, conductors with 0.5mm in diameter along with multi-strands twisted Litz wire technique were utilized; in which each winding is composed with 3 bundles of 7-strands Litz wire. The total cross-section area of the utilized Litz wire winding is calculated as: 70

93 DESIGN AND ANALYSIS OF COAXIAL TRANSFORMERS The length of the total wiring is calculated as: Let the total wiring distance 1.5 times of the calculated value; also, the power losses exists on both the primary winding and secondary windings. The DC winding loss of one single conductor in consideration with both the primary and the secondary winding is calculated as: where a factor of 2 is to take both primary and secondary windings into account, and the constant of is the cooper resistance per kilometer of the single solid wire at the radius of 0.25 mm (refers to Chapter for the DC resistance equation). Thus, for the total winding loss: The overall transformer loss is now calculated as: At full load condition At light load condition Main losses are from the iron losses (the core loss). 71

94 DESIGN AND ANALYSIS OF COAXIAL TRANSFORMERS 4.2 Impedance Measurements In this section, measurements were conducted in HF with HP 4285A (75 khz to 30 MHz) and in Low Frequency (LF) with Precision TH2816A (20 Hz to 200 khz) respectively. High frequency measurements show the HFCT performance in the normal operation, while the low frequency measurements were utilized to validate the simulation result. For current distributions in simulations, the analysis has been conducted in quasi-static field; thus, measurements in HF and simulation results are comparable. On the other hand, the capacitance and the inductance simulations were conducted with the static field analysis. It is impossible to measure the inductance and the capacitance in DC mode due to their inherent characteristic; therefore, the low frequency measurements were conducted. For impedance measurements, [88], [61] provide good illustrations and examples. Four 8 kw isolated prototypes HFCT were built; prototypes include three HFCTs without the Faraday shield and one HFCT with the Faraday shield and heat sink. Since three HFCTs without the Faraday shield are almost identical, only testing results of HFCT no.1 were shown. In the measurement results, the total winding resistance is denoted as (the sum of primary winding resistance and coupled secondary winding resistance); total leakage inductance is denoted as (the sum of primary winding resistance and coupled secondary leakage inductance); equivalent core loss is denoted as and the magnetising inductance is denoted as. For transformer isolation test, represents the resistance between two windings, and is the coupling capacitance (intra-winding capacitance) between the primary and the secondary winding. In addition, Ground represents the HFCT with the Faraday shield, and the shield was connected to the ground. Float means the HFCT with the Faraday shield, but the shield was not connected to the ground; this condition also known as floating condition. Unshield represents the prototype HFCT without the Faraday shield Operational Frequency Measurements Completed testing results under operational frequency were tabulated in Table. A.1 (Appendix) and results have shown the comparison between the prototype HFCTs with and without the Faraday shield. A comparison result of magnetizing inductance of prototype HFCT is depicted in Figure 4.6. Observing from the testing result shown in the figure, is almost identical under about frequency of 72

95 DESIGN AND ANALYSIS OF COAXIAL TRANSFORMERS 200 khz. This is because the variation of the is basically dependant on the magnetic material properties; in which all prototypes should performance the same due to the utilization of the same core material. Above 400 khz, the HFCT with the Faraday shield under floating condition has a greater increase of. The increase is about 1.3 times higher compared to the HFCT with the Faraday shield under grounding condition and the HFCT without the Faraday shield. Without connecting the shield to the ground, the Faraday shield becomes a magnetic isolation shield in HF operations; thus, more energy is stored in the magnetic core instead of generating an induced eddy current loss on the secondary conductors. This phenomenon represents a lower magnetizing current for the HFCT with the Faraday shield under floating condition if the operating frequency is above 400 khz. Lc(μH) Ground Float Unshield f (khz) Figure 4.6. The magnetizing inductance of the 8 kw HFCT Rc(kΩ) Ground Float Unshield f (khz) Figure 4.7. The equivalent core resistance of the 8 kw HFCT Figure 4.7 shows the comparison result of the core resistance. is frequency dependant, in which the resistance declines with the increased operating 73

96 DESIGN AND ANALYSIS OF COAXIAL TRANSFORMERS frequency. Similar to the characteristic of, the variation of is subject to the magnetic material. Since represents the ability of the transformer to oppose the magnetizing current to flow in its magnetic core (a lower represents the higher eddy current loss), the designed prototype HFCTs are having the least eddy current losses to its core within the operational frequency. This observation also validates the core characteristic provided in manufacturer s datasheet that the core material is designed for frequency up to 300 khz. The leakage inductance comparison result of prototype HFCTs is shown in Figure 4.8. The leakage inductance of the HFCT with the Faraday shield increases slightly due to the finite amount of space required for the insertion of the Faraday shield. Generally, an increase of 6.3% of due to the insertion of the Faraday shield was found across the frequency ranges. Also, a 4.5% variation of the occurs at frequency of 100 khz and 500 khz respectively due to the resonance of the winding with the surrounding air and conductive materials. The decrease of the at resonant point is a good phenomenon since the HFCT has less leakage energy losses. In short, the of the proposed HFCT is small because of the unique winding structure; this is validated from the measurement result shown in the figure Ls(μH) Ground Float Unshield f (khz) Figure 4.8. The leakage inductance of the 8 kw HFCT Figure 4.9 shows the winding resistance comparison result of the prototype HFCTs. From testing results shown in the figure, it can be observed that the HFCT with the Faraday shield has a better performance than the HFCT without the Faraday shield in performance. With the insertion of the Faraday shield, it was expected that the extra copper shielding will bring an extra losses on top of the original ; however, the measurement result shows differently from the expectation. This is because in lower frequency ranges, the Faraday shield induces a reversed magnetic 74

97 DESIGN AND ANALYSIS OF COAXIAL TRANSFORMERS field. This reversed magnetic field alleviates the magnetic intensity stress between the primary winding and the secondary winding and consequently reduces the winding resistance occurring on the secondary winding. Since the loss occur on the Faraday shield is much smaller than on the secondary winding, the HFCT with the Faraday shield results in a lower. In addition, the induced eddy current losses of the Faraday shield increases exponentially with the frequency; in which the HFCT with the Farday shield has the same level of the with the HFCT without the Faraday shield at 800 khz. If the frequency further increases, the HFCT with the Faraday shield start to suffer from a higher and has a much higher compared to the HFCT without the Faraday shield. Rs(Ω) Ground Float Unshield f (khz) Figure 4.9. The winding resistance of the 8 kw HFCT Cp(pH) Ground Float Unshield f (khz) Figure The intra-winding capacitance of the 8 kw HFCT The intra-winding capacitance comparison result of prototype HFCTs is shown in Figure The measurement result demonstrates that with the use of the Faraday shield, the has been effectively reduced compared to the HFCT without 75

98 DESIGN AND ANALYSIS OF COAXIAL TRANSFORMERS the Faraday shield. However, the Faraday shield should be connected to the ground properly, or it will result in a greater compared to the HFCT without the Faraday. On the other hand, the measurement conducted here is with the use of direct measurement method. For the measurement with the direct method, the result of the HFCT with the Faraday shield is not so accurate if the shield is grounded. The in-direct method should be employed as introduced in Chapter The measurement of with the in-direct method will be presented in the following section, and a more accurate result of the is expected. The intra-winding resistance comparison result is shown in Figure It was expected that the should be decreased due to that the Faraday shield causes a negative effect to the electric isolation. However, a drop of thousand kω is very unusual and inadequate. Further investigation is required to examine the issue of the reduced isolation performance Rp(kΩ) Ground Float Unshield f (khz) Figure The isolation resistance of the 8 kw HFCT Waveform measurements of prototype HFCTs with and without the Faraday shield are shown in Figure 4.12 and Figure These results show good outcomes where the input and output voltage measurement is identical for both shield configurations at the desired operating frequency (1: input voltage, 2: output voltage). Also, the insertion of the Faraday shield does not bring any negative effect to the waveform output according to measurements; in which no output distortion is observed. On the other hand, the waveform does not have an ideal square wave shape at low frequency ranges. This is because the impedance of the transformer is relatively low to the internal resistance of the signal generator and consequently more current was draw from the signal generator. This causes that the signal generator is unable to maintain the output voltage at the same level as it should be. 76

99 DESIGN AND ANALYSIS OF COAXIAL TRANSFORMERS (a) Without shield (b) With shield Figure The square wave test of prototype HFCTs at 75 khz (a) Without shield (b) With shield Figure The square wave test of prototype HFCTs at 400 khz Low Frequency Measurements Measurement results with the use of LCR meter Precision TH2816A are shown in Table 4.4. The measurement calibration of the LCR meter was performed before each measurement when the testing frequency changes. A1A2 and B1B2 represent the outer winding and the inner winding connection pair of the introduced HFCT respectively; A1B1 and A2B2 represent the connection is under intra-winding measurements (one end of the primary and the secondary winding are connected). The was found to be inaccurate at 20 Hz and 100 Hz for all prototype transformers due to the internal impedance of the TH2816A is relatively too large to the tested transformers at low frequency. A small increase of the due to the insertion of the Faraday shield was found due to the finite space between the primary winding and the secondary winding. The leakage inductance is identical for both the Faraday shield at ground or floating condition. On the other hand, the is frequency dependent; it becomes almost double at 20 Hz compared to the at 300 khz. Detailed discussion regards to the of the transformer with the Faraday shield insertion is presented in this section. 77

100 DESIGN AND ANALYSIS OF COAXIAL TRANSFORMERS Table 4.4. Impedance testing results of the 8 kw HFCT with and without the Faraday shield (a) and without the shield HFCT without shield Short Circuit Open Circuit A1A2 B1B2 A1A2 B1B2 f(hz) (uh) (mω) f (Hz) (uh) (mω) f (Hz) (uh) (Ω) f(hz) (uh) (Ω) m m k k k k k k k k 10k k (b) and with the shield HFCT with shield Shield connects to the ground Short Circuit Open Circuit A1A2 B1B2 A1A2 B1B2 f (Hz) (uh) (mω) f (Hz) (uh) (mω) f (Hz) (uh) (Ω) f (Hz) (uh) (Ω) m m k k k k k k k k 10k k Since the turn ratio of the prototype HFCTs is 1:1, it would be interesting to investigate if the excitation winding makes any difference to the transformer performance. Based on results shown in Table 4.4, if the inner winding is used as the primary winding, prototype HFCTs have less losses because of lower and. With the insertion of the Faraday shield, the of the HFCT is still lower at higher frequencies if the inner winding is used as the primary winding; however, the increases slightly by 0.58 %. When the inner winding is used as the primary winding, less leakage energy can be stored in the air-region between both windings; thus, the leakage inductance decreases. Similarly, due to that the smaller magnetic intensity occurs between the primary and the secondary windings, the AC resistance drops. On the other hand, the drops by 0.2 % which is almost ignorable while the does not show much difference if the excitation winding is different. Therefore, the inner winding of the HFCT should be used as the primary for better power performance. To investigate this phenomenon, more discussions will be presented in the simulation section. 78

101 DESIGN AND ANALYSIS OF COAXIAL TRANSFORMERS Table 4.5. Capacitance measurements of the 8 kw HFCT with or without the Faraday shield (a) The and of no-shield case (left) and shielded case without grounded (right) No.1 HFCT w/o shield HFCT w/ shield - S1S2 not connected, not grounded. A1B1 A2B2 A1B1 A2B2 f (Hz) (pf) (MΩ) f (Hz) (pf) (MΩ) k k k k f (Hz) (pf) (MΩ) f (Hz) (pf) (MΩ) k k k k (b) Shielded HFCT under grounding or floating condition HFCT w/ shield - S1S2 connected, floating HFCT w/ shield - S1S2 connected, grounding A1B1 A2B2 A1B1 A2B2 f(hz) (pf) (MΩ) f (Hz) (pf) (MΩ) k k k k f (Hz) (pf) (MΩ) f (Hz) (pf) (MΩ) k k k k (c) Capacitance between the Faraday shield and individual winding HFCT w/ shield - S1S2 connected, Shield to winding capacitance A1S B1S A2S B2S f (Hz) (pf) (MΩ) f (Hz) (pf) (MΩ) f (Hz) (pf) (MΩ) f (Hz) (pf) (MΩ) k k k k k k k k As expected, the isolation resistance decreased with the increased frequency due to the AC characteristic (measurements shown in Table 4.5). It is also observed that the introduced HFCT has better isolation performance if a Faraday is inserted. On the other hand, the polarity of the prototype HFCT can be decided by measuring two windings in series using the impedance measuring technique. Therefore, the polarity pair is known as: A1, B1 in the same polarity and A2, B2 in the same polarity. Thus, the intra-winding capacitance is now able to be derived for the HFCT with the Faraday shield. The exact is obtained in the following sequence. 79

102 DESIGN AND ANALYSIS OF COAXIAL TRANSFORMERS First, measure the capacitance of the HFCT with the Faraday shield in floating condition (Table 4.5 (b)). Secondly, measure the capacitance between the Faraday shield to primary and secondary windings individually (Table 4.5 (c)). Thirdly, calculate the obtained capacitances in series ( ). Lastly, the capacitance obtained in the first step minus the capacitance obtained in the third step. The comparison result is shown in Table 4.6; please refer to Chapter for the definition of capacitors listed in the table. As expected, increases if the Faraday shield is inserted to the prototype HFCT. The insertion of the Faraday shield causes about 10.8% to 17.42% increases on the without having the shield connected to the ground. However, the C ps reduces by 77.2% compared to the HFCT without the Faraday shield if the Faraday shield is well-grounded. This measurement result validates the effectiveness of the Faraday shield insertion; an HF noise suppression of % is achieved at operating frequency of 100 khz. Table 4.6. The intra-winding capacitance comparison of HFCT A1B1 (pf) Frequency (NS (WS) - (WS)-Groundin (Hz) ) Floating g k k k k # no shield case (NS), with shield (WS) 80

103 DESIGN AND ANALYSIS OF COAXIAL TRANSFORMERS 4.3 Simulation Results D Modeling Techniques Since the 3-D model of prototype HFCTs with and without the Faraday shield are almost identical, only the simulation model with the Faraday shield is shown; 3-D simulation models with mesh are shown in Figure (a) front view (b) top view (c) side view (d) bird view Figure D simulation model of the prototype HFCT with the Faraday shield Table 4.7 shows the mesh information of the 3D HFCT model. With the insertion of the Faraday shield, the number of elements increased by 32.9% compared to the 3D model without the Faraday shield; and consequently, the total computation time is increased. The simulation was conducted by a personal desktop, with the specifications of INTEL Q GHz CPU, 8 GB DDRII memory and 64-bits Windows 7 operating system. To reduce the computation time while maintaining the acceptable accuracy, the maximum element size has been limited at 2 mm for its edge length. Also, the simulation model was simplified with the use of solid conductors; in 81

104 DESIGN AND ANALYSIS OF COAXIAL TRANSFORMERS which the Liz wires were utilized for the fabrication of prototype HFCTs. The modeling technique presented in Chapter 3.5 was employed so the computation time can be greatly reduced while having an acceptable level of accuracy. For all 3-D simulation, only the last time point was computed rather than computing the whole series of time points. Based on configurations stated above, simulation time of each analysis can be reduced from four hours to less than 30 minutes. Table 4.7. Meshing information of the HFCT Nodes Elements Maximum edge length Without shield 296, ,032 2 mm With shield 399, ,271 2 mm Furthermore, in most of the simulation works, linear material property has been chosen as the first preference; this also reduces the required computation power especial if only a specific working point is investigated. For example, the introduced HFCT is designed to work at at the linear region; thus, the corresponding permeability can be easily found out from the manufacture s datasheet. Due to that the introduced prototype HFCT is designed to work at linear region, the analysis process becomes easier. However, if the application is designed to work at the region near the saturation, or if the excitation condition becomes unknown, the non-linear simulation analysis must be applied. Figure Region definition of the 3D simulation model of the HFCT The region definition of the simulation model is illustrated in Figure The coaxial region is where the windings are surrounded with the Ferrite magnetic core and end region locates on both end of the HFCT. The magnetizing current applied on 82

105 DESIGN AND ANALYSIS OF COAXIAL TRANSFORMERS the outer winding is 1.64 A; which is obtained from the electric calculation shown in Chapter while 20 A is the full-load current applied in the simulation at short circuit condition Flux Distribution Flux distributions of the HFCT when the outer winding is used as the primary winding and the inner winding is used as the secondary winding are shown in Figure Under open circuit condition, the flux distributes mainly in the magnetic core; thus, no significant leakage flux can be observed. While the HFCT is at short circuit condition, leakage fluxes can be observed at the space between the primary winding and the secondary winding. This leakage energy cannot be coupled from one winding to the other, and therefore causes reactive losses to the power supply. Furthermore, the insertion of the Faraday shield does not bring much negative magnetic effects for the HFCT since the flux distribution in Figure 4.16 (a) and Figure 4.16 (b) are almost identical. A more detailed discussion regards to the thickness effect of the Faraday shield will be presented in Chapter (a) Without shield (b) With shield (c) Without shield (d) With shield Figure The flux distribution of the HFCT when the outer winding is used as the primary winding: (a) and (b), under short circuit condition; (c) and (d), under open circuit condition Figure 4.17 shows the flux distribution of the HFCT in a contrast winding configuration to the results shown in Figure The inner winding is used as the primary winding and the outer winding is used as the secondary winding. The major difference that can be observed between these two winding configurations shown in Figure 4.16 and Figure 4.17, is the flux distribution under short circuit condition. Under short circuit condition, less magnetic flux is observed in the magnetic core if the inner winding is used as the primary winding. This phenomenon indicates that less leakage energy is distributed to the core and the air region; and consequently, the leakage inductance is lower if the inner winding is used as the primary winding. This is in a good agreement to the measurement shown in Table 4.4; the leakage 83

106 DESIGN AND ANALYSIS OF COAXIAL TRANSFORMERS inductance measurement is lower if the inner winding is used as the primary winding. (a) Without shield (b) With shield (c) Without shield (d) With shield Figure The flux distribution of the HFCT when the inner winding is used as the primary winding: (a) and (b), under short circuit condition; (c) and (d), under open circuit condition Figure 4.18 and Figure 4.19 show the flux density under different conditions. A current of 20 A and 1.64 A are applied to the excited winding under short circuit condition and open circuit condition respectively. As shown in simulation results, the insertion of Faraday shield does not affect the magnetic performance of the designed HFCT much. In fact, there is even a tiny decrease on flux density of the main core with the insertion of the Faraday shield. This result can be validated by the measurements shown in Table 4.4, the decreases with the insertion of the Faraday shield. Similarly, the maximum flux density is lower if the inner winding of the HFCT is used as the primary; in which the simulation result is in a good agreement to measurements. (a) Without shield (b) With shield (c) Without shield (d) With shield Figure The flux density of the HFCT when the outer winding is used as the primary winding: (a) and (b), under short circuit condition; (c) and (d), under open circuit condition In addition, the flux density results also validate that the designed HFCT works in the linear region since the maximum flux density is only T; where the saturated flux density of the utilized F44 material is 450 mt at room temperature. On 84

107 DESIGN AND ANALYSIS OF COAXIAL TRANSFORMERS the other hand, from the simulation result under the short circuit condition, it can be observed that the winding structure of the HFCT is well-balanced; thus, the flux density exists for a very small amount. (a) Without shield (b) With shield (c) Without shield (d) With shield Figure The flux density of the HFCT when the inner winding is used as the primary winding: (a) and (b), under short circuit condition; (c) and (d), under open circuit condition Even though the introduced transformer works in a non-linear behaviour, a linear analysis can still be conducted via some tricks. For example, the relative permeability was selected based on the required flux density at a specific working point. According to the core manufacturer s datasheet, the relative permeability has been chosen as under open-circuit simulation. For the magnetic property definition under the short circuit condition, same setting was applied due to its coherence under the open circuit condition. The 3-D flux distribution result is shown in Figure 4.20; the simulation shown is when the outer winding is used as the primary under short circuit condition and open circuit condition respectively, for both configurations with and without the Faraday insertion. As expected, the 3-D simulation result shows a similar flux pattern to the 2-D simulation result. The consistence also validates the effectiveness of the 2-D simulation in flux distribution. Therefore, if the computation time is the concern, then 2-D simulation has the acceptable accuracy avoiding the redundant 3-D computation process. On the other hand, the flux distribution result of the 3-D simulation result demonstrates that the magnetic field is cancelling each other at some regions because of the turning winding structure. Under open circuit condition, the magnetic core stores the majority of the magnetic energy; also, the flux density is at its highest level and contributes the maximum iron losses. In comparison, the majority of the magnetic energy distributes at the air region section between the primary windings and the secondary windings under short circuit condition. Only the simulation result of the outer winding used as 85

108 DESIGN AND ANALYSIS OF COAXIAL TRANSFORMERS the primary is shown; simulations of the inner winding used as the primary displayed a similar flux distribution. (a) Without shield (b) With shield (c) Without shield (d) With shield Figure The 3-D flux density distribution when the outer winding is used as the primary: (a) and (b), under short circuit condition; (c) and (d), under open circuit condition Figure The flux density distribution when the outer winding is used as the primary under short circuit condition Furthermore, an example of the completed 3-D magnetic flux distribution under short circuit condition is shown in Figure The magnetic flux is mainly distributed at the air region between the primary and the secondary windings; where the flux density is small due to the magnetic field cancellation between both windings. From the simulation result shown in Figure 4.21, it was observed that the magnetic energy tends to store at the region near the turning angles of windings. Also, more magnetic energy was stored in the end region section than in the coaxial section due to the short distance between the primary windings and the secondary windings. Please 86

109 DESIGN AND ANALYSIS OF COAXIAL TRANSFORMERS note that those energy stored under the short circuit condition is recognized as the leakage energy as discussed in Chapter Eddy Current Distribution Some short comments can be made from simulation results shown in Figure 4.22 and Figure 4.23 regards to the winding resistance and power losses. Firstly, using the outer winding as the primary winding is more beneficial for both shield and no-shield HFCT structures. Secondly, the increase of the peak current density due to the insertion of the Faraday shield is negligible. Thirdly, the power losses caused by the Faraday shield are small because of its thin thickness. (a) Without shield (b) With shield (c) Without shield (d) With shield Figure The current density of the HFCT when the outer winding is used as the primary winding: (a) and (b), under short circuit condition; (c) and (d), under open circuit condition Figure 4.22 shows the eddy current distribution when the outer winding is used as the primary winding under open circuit condition and short circuit condition. Compare results shown in Figure 4.22 (a) and (b), the peak current density only increases by 1.15% due to the insertion of the Faraday shield. The increase is due to the eddy current induced on the inserted shield counteracts with the primary proximity effect of the winding; thus, the current distribution of the primary winding becomes more uneven. Also, one phenomenon can be observed; the eddy current induced on the secondary winding due to the excitation of the primary winding is reduced with the Faraday shield insertion. The eddy current induced on the Faraday shield generates a reversed magnetic field which is against the primary flux on reaching to the secondary winding. Based on the simulation result, there is a % reduction for current induced on the secondary winding if the HFCT is with the Faraday insertion. Figure 4.23 shows the current distribution if the inner winding is used as the 87

110 DESIGN AND ANALYSIS OF COAXIAL TRANSFORMERS primary winding and the outer winding is used as the secondary winding. For the HFCT without the Faraday shield insertion, the peak current under the short circuit condition is 10.1 A/mm 2. In comparison, for the HFCT with the Faraday shield, the peak current density of the inner winding under short circuit condition only increases by 0.1 %. Same observation was made under the open circuit condition; the peak current density has an identical value for both the HFCT with or without the Faraday shield. For this reason, it is again concluded that the insertion of the Faraday shield has a very minor effect on the current distribution of windings as only 1 percent of peak current increment was found. (a) Without shield (b) With shield (c) Without shield (d) With shield Figure The current density of the HFCT when the inner winding is used as the primary winding: (a) and (b), under short circuit condition; (c) and (d), under open circuit condition The 3-D current distribution of the HFCT without the Faraday shield in bird view is shown in Figure The higher current density distribution occurs at end region and outer windings in the coaxial region. (a) Bird view (b) Side view Figure Current distribution of 3D model in bird view and left side view (Short Circuit Condition) 88

111 DESIGN AND ANALYSIS OF COAXIAL TRANSFORMERS Figure 4.25 and Figure 4.26 show a close look of the inner winding and the outer winding with the focus on the distribution of the end region section. The peak current densities are A/m 2 and A/m 2 for the outer winding and the inner winding respectively, which is equivalent to a difference of 15.88%. In comparison, the peak current density in coaxial region is % lower than in the end region. This also validates that the phenomenon of greater leakage inductance is contributed from the end region section compared to the leakage inductance distribution from the coaxial region. (a) Front view (b) Back view Figure Current distribution of the outer winding under the short circuit condition (a) Front view (b) Back view Figure Current distribution of the inner winding under the short circuit condition The open circuit simulation result is shown in Figure 4.27; where (a) shows the 3-D flux density simulation result, and (b) shows the current distribution under open circuit condition. The flux simulation result shown in Figure 4.27 (a) validates that the HFCT operates within the saturation region; where the maximum flux density of the utilized magnetic material is 450 mt. There is a finite amount of induced current occurring on the inner winding as shown in Figure 4.27 (b); hence, there will still be a small voltage drop due to the winding losses because of the non-perfect characteristics of the conductor. 89

112 DESIGN AND ANALYSIS OF COAXIAL TRANSFORMERS (a) Flux Distribution (b) Current Distribution Figure Simulation results of the HFCT without the Faraday shield under open circuit condition (a) Windings (b) Faraday shield Figure Current distribution of the HFCT with the Faraday shield (Short circuit condition) The Faraday shield was placed between the primary winding and the secondary winding in order to reduce the intra-winding capacitance. A lower coupling capacitance is very effective on reducing the HF noise as well as EMC issues. The simulation result of the current density distribution with the insertion of the Faraday shield is shown in Figure With the insertion of the Faraday shield, the peak current density under short circuit condition reduces 72.57% (the result shows differently from the 2-D simulation since the 3-D simulation has taken into account of the end region section). This is because of that the induced current occurs on the Faraday shield, which generates a magnetic field against the excitation source, and therefore current distributes more evenly. Figure 4.28 (b) shows the current density distribution of the Faraday shield under short circuit condition. In general, higher 90

113 DESIGN AND ANALYSIS OF COAXIAL TRANSFORMERS current distribution occurs on the end region section of the HFCT; therefore, higher winding losses are expected compared to windings in coaxial section. The higher peak current density occurs on the end region because of the shorter distance between the primary winding and the secondary winding; in which a severe proximity effect causes the current distribution more imbalanced. Figure 4.29 is the simulation result of the HFCT with the insertion of the Faraday shield under open circuit condition. Higher current density occurs on the Faraday shield in the end region section; especially, at the edges of the shield. Also, the induced current on the shield of the coaxial section is very minor; the leakage flux is generated by the magnetic interaction of the primary winding and the secondary winding, which especially becomes obvious under short circuit condition. Three hot spots (color in red) are observed in the result; the higher current density occurs at the region of edges on the Faraday shield, as well as the turning corner of the windings. (a) Winding (b) Faraday shield Figure Current distribution of the HFCT with the Faraday shield (Open circuit condition) There are three methods to reduce the winding losses for the introduced HFCT; firstly, increase the winding distance to reduce the proximity effect; secondly, the utilization of multi-strands Litz wires; and thirdly, reducing thickness of winding conductors for lower eddy current effects. According to these comments, the thickness of the shield copper should be minimized as well. A further reduction of the shielding thickness can effectively reduce the power losses of the shield caused by the eddy current effect; but, this also makes it difficult to fabricate if the shield is too thin. An optimization work of the Faraday shield thickness and location has been presented in chapter

114 DESIGN AND ANALYSIS OF COAXIAL TRANSFORMERS 4.4 Impedance Optimization To meet the requirements of switching mode power systems and EMC standards, the trade-off of and can be determined by using a multi-objective optimization method. The approximated optimization value of leakage inductance and coupling capacitance is calculated using a magnetic energy technique [91], [92]. The FEM simulation technique was then be utilized to obtain a more accurate result. Figure 4.30 shows the HFCT equivalent circuit and the variation of impedances against the distance (D) between the primary and secondary windings. (a) (b) Figure (a) The HFCT equivalent circuit; and (b) relationship of impedance versus the distance between windings Leakage Inductance The detailed simulation result of leakage inductance distribution in the prototype HFCT has been tabulated in Table 4.8. In 2D analysis, the HFCT was spited into the coaxial region section and the end region section (double 2-D technique was presented in Chapter 3.5 ). The 8 kw prototype HFCT has the core height of 38.2 mm and the end region length of 120 mm. For the 2D analysis on wire length of the coaxial section, the length of 38.2 mm according to the core length was assumed. However, for wire length in the end region section, 100 mm was assumed in consideration of the real wire length for fabricated prototype transformers. As expected, end region section distributes 2/3 leakage inductance of the transformer due to the short distance between the primary and the secondary windings. Comparing the simulation result with the measurement result shown in Table 4.4 (a), the leakage inductance at 10 khz is 2.19 uh and 2.25 uh in measurement and simulation results respectively. Thus, a deviation of 2.67 % to the measurement is really small and it shows a very high level of the accuracy of the simulations. Furthermore, the level of accuracy of the 2-D simulation depends on numbers of benchmarks. This means, the accuracy is very much relying on the correct definition of the wire length of the 92

115 DESIGN AND ANALYSIS OF COAXIAL TRANSFORMERS coaxial section as well as the end region section. For this reason, 3-D simulation is still preferable for a higher level of accuracy if multiple benchmarks are not applicable. Table D Calculated inductance results of the 8 kw HFCT Coaxial Section (Length 38.2mm) Air Core Outer Winding Inner Winding Stored Energy (J/m) 1.10E E E E-05 Equivalent Inductance (H) 5.51E E E E-08 Leq ( H) Half model End Region Section (Length 100 mm) Stored Energy (J/m) 7.43E E E E-05 Equivalent Inductance (H) 3.71E E E E-08 Leq ( H) Half model Leq (uh) Primary + Secondary at full model On the other hand, since the winding configuration is the main factor of the leakage inductance distribution, it is of particular interest to investigate the leakage inductance if the outer winding or the inner winding is used as the excitation source. The simulation result is shown in Table 4.9, a small difference of leakage inductance was found between two excitation configurations. The leakage inductance is slightly greater if the outer winding is used as the primary winding. Table D Calculated Inductance Results of the 8 kw HFCT under Different Excitation Windings. Inner winding is used as the Primary Air Core Outer Winding Inner Winding Stored Energy (J/m) 1.10E E E E-05 Equivalent Inductance (H) 5.52E E E E-08 Coaxial Leq (μh) Outer winding is used as the Primary Stored Energy (J/m) 1.10E E E E-05 Equivalent Inductance (H) 5.51E E E E-08 Coaxial Leq (μh) The inductance optimization result regards to the winding distance by using the 8 kw HFCT as an example is shown in Table The distance between the primary and the secondary winding was divided into 10 segments, and the energy stored in 93

116 DESIGN AND ANALYSIS OF COAXIAL TRANSFORMERS each section is tabulated as shown in the table. The inductance is a function of the stored energy in the transformer and which can be classified in three sections: the air region section between the primary winding and the secondary winding, the magnetic core and the winding conductor itself. By applying an appropriate excitation current on the winding, the correspondent inductance can be derived from the stored energy in each section. The calculation work simulates the practical condition of the transformer testing by applying the current on one winding, while setting the other winding at SC condition. Table Example of inductance distribution in the coaxial section of the 8 kw HFCT Winding Distance Stored Energy (J/m) Steps (mm) Air Core Outer Winding Inner Winding E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-08 The inductance behavior regards to the distance between two windings of the 8 kw HFCT is depicted in Figure 4.31 ; where both results of the end region section and the coaxial section are generalized for the convenience of analysis. With the position of the outer winding fixed, the inner winding is moving towards to the outer winding. Distance ratio 1 represents a winding distance of 7.35 mm and 4.2 mm for the coaxial section and the end region section respectively. Distance 0 represents the outer winding and the inner winding are at the same circle line, which the inner and the outer winding are next to each other. Both the coaxial and the end region results show that the have an exponential relationship regards to the winding distance. The contributed from the end region section is almost the double to the contributed from the coaxial region. This is because the winding configuration in the coaxial section is more symmetrical; thus, most of the energy can be coupled from the primary to the secondary or to the magnetic core. In comparison, windings in the end region section were arranged in parallel, the magnetic energy leaks more into the surrounding 94

117 DESIGN AND ANALYSIS OF COAXIAL TRANSFORMERS air. A small increase of the for the end region section at a distance ratio of 0.2 is due to geometrical structure of the transformer; where windings has shortest distance from each other. Leakage Inductance (H) 1.6E E E E E E E-07 End Region (4.2mm) Coaxial (7.35mm) Distance Ratio Figure The leakage inductance versus the winding distance of the 8 kw HFCT Intra-Winding Capacitance There are two possible winding configurations for the end region section of the introduced HFCT as shown in Figure 4.32; where (a) is when the primary and the secondary winding at the aligned position, and (b) shows that the primary and the secondary winding are at the unaligned position. The capacitance computation result is shown in Table F/m is the capacitance of the computation result per unit length, and the represents the actual capacitance distributed in either the coaxial section (56.5 mm in length) or the end region section (52.3 mm in length) in a half crossed-section transformer simulation model. The sum of whole model shows the exact intra-winding capacitance of the completed prototype HFCTs. As expected, the winding configuration of unaligned position has smaller ; the winding distance is shorter at the configuration of aligned position compared to the unaligned position. Therefore, the winding configuration of aligned position was implemented for the fabrication of the prototype HFCTs. (a) Aligned position (b) Unaligned position Figure The winding configuration in end region section 95

118 DESIGN AND ANALYSIS OF COAXIAL TRANSFORMERS Table The 2-D capacitance computation result of the HFCT; the winding configuration of the end region section at aligned and unaligned position F/m ( F) Coaxial 2.91E End Region 5.86E Sum (Whole Model) 83.6 (a) Aligned position F/m ( F) Coaxial 2.91E End Region 4.74E Sum (Whole Model) 71.8 (b) Unaligned position By applying appropriate voltages on windings, the charges on each conductor can be calculated based on a static field computation. Therefore, the coefficients of the capacitance matrix can be derived from the obtained static field energy in this multi-conductor system. The computational results shown in both Figure 4.33 and Table 4.12 have taken into account of practical issues (fiber glass has been used as the intermediate material with a relative permittivity of 4.2, and the conductor insulation shield Teflon has a relative permittivity of 2; these properties were being applied for the analysis). In this simulation, a 21-strands Litz wire was utilized with the diameter of mm in each conductor. The result shown in Figure 4.33 proves the concept introduced in Figure 4.30 (b) and fulfills the basic capacitance theory; that the decreases with the increased winding distance. Furthermore, the end region section again has the greater portion of the distribution compared to the distributed by the coaxial section. Table Intra-winding capacitance distribution of the 8 kw HFCT Winding Distance Coaxial End Region Steps (mm) F/m ( F) F/m ( F) E E E E E E E E E E E E E E E E E E E E E E

119 DESIGN AND ANALYSIS OF COAXIAL TRANSFORMERS Coupling Capacitance (F) 1.1E E E E E E-12 End Region (4.2 mm) Coaxial (7.35mm) Distance Ratio Figure Coupling capacitance versus winding distance of the 8 kw HFCT Discussion Figure The trade-off of calculated coupling capacitance and leakage inductance In Figure 4.34, the broken line represents the computed results of the end region section, and the solid line represents the computed results of the coaxial section. The square dots represent the calculated results and the star dots represent the calculated leakage inductance. By arranging computation results of coupling capacitance and leakage inductance into the same scale, a trade-off point was found at the distance ratio of 0.7 and 0.9 of the coaxial section and the end region section respectively. That is, the best winding distance was found to be mm and 3.78 mm for the coaxial section and end region section respectively based on the geometrical structure of an 8 kw prototype HFCT. On the other hand, in order to reduce the design time of the HFCT for the future prototypes, this chart can also be used to determine the best winding distance if specific C ps or L eq are required (for example, with uses in LLC converter). Furthermore, a 2D FEM simulation is 97

120 DESIGN AND ANALYSIS OF COAXIAL TRANSFORMERS well-suited for the structural optimization work, but a 3D FEM should be employed if a higher precision of the result is required. Currently, the calculation time for each step takes approximately 10 to 15 minutes with 15,218 elements on a 2D HFCT model. This can definitely increase to more than one hour when a 3-D simulation is undertaken. 4.5 Faraday Shield Analysis The coupling capacitance accompanied by an increased operating frequency (which couples HF noise between the primary and secondary windings) can cause serious common mode problems [94], [95], [96]. Hence, a Faraday shield is placed between the windings of the HFCT. This reduces the coupling capacitance and consequently the EMI. The analysis of the shielding effect of the HFCT is presented in this chapter and maybe of interest to other researchers and automobile manufacturers Shielding Losses 2 Power Loss (W/m) Shield Outer winding Inner winding Thickness ratio - Skin depth mm Figure Power loss versus the thickness of the Faraday shield under short circuit condition; the outer winding is used as the primary winding From the previous chapter, the analysis of the current distribution of the HFCT with and without the Faraday shield has been conducted. To investigate the thickness effect of the Faraday shield insertion of the HFCT, a further investigation was undertaken. Figure 4.35 shows the power loss analysis of the 8kW HFCT when the Faraday shield thickness varies under short circuit condition. The ratio on the horizontal axis refers to the skin depth of the copper material at 100 khz; ratio 1 means the thickness of the Faraday shield is at mm; the vertical axis is the power loss in the unit of watts per meter. Based on the simulation result, the power losses of the Faraday shield increases with thickness in an exponential trend. About 98

121 DESIGN AND ANALYSIS OF COAXIAL TRANSFORMERS 1.2 watt/m was consumed due to the insertion of the Faraday shield if the shield thickness is twice of the skin depth. In fact, the insertion of the Faraday shield does not bring much power losses to the primary winding and the secondary winding of the HFCT. In summation, the thickness ratio of 0.3 to 0.7 should be implemented for the HFCT fabrication to obtain the least power losses of the inserted Faraday shield. 1.5 Power Loss (W/m) Shield Outer winding Inner winding Thickness ratio - Skin depth mm 2 Figure Power loss versus the thickness of the Faraday shield under open circuit condition; the outer winding is used as the primary winding The shield losses analysis under open circuit condition is shown in Figure 4.36; the outer winding is used as the primary winding. As discussed in the flux simulation analysis that the HFCT does not have much flux leakage under open circuit condition. Therefore, it shows the same phenomenon in the power losses simulation result; the power loss of the Faraday shield under open circuit condition is almost negligible. The power loss of the inner windings and the Faraday shield are relatively small compared to the primary winding loss at watts and 0.03 watts per meter respectively. If the inner winding is used as the primary winding under short circuit condition, the power losses cuve of the HFCT is quite similar to the configuration of the outer winding is used as the primary winding; the simulation result is shown in Figure However, the power losses behavior shows differently if the inner winding is used as the primary windings under short circuit condition (see Figure 4.38). If the inner winding is used as the excitation winding, power losses of the Faraday shield and the outer winding become much greater. The power loss of the Faraday shield is proportional to the skin depth ratio; if the thickness is within one skin depth, the power loss of the shield does not increase much. A loss variation of 0.1 to 0.2 watt per meter can be observed from the simulation result. The loss increases remarkably larger with the increased thickness of the Faraday shield. 99

122 DESIGN AND ANALYSIS OF COAXIAL TRANSFORMERS 2 Power Loss (W/m) Shield Outer winding Inner winding Thickness ratio - Skin depth mm Figure Power loss versus the thickness of the Faraday shield under short circuit condition; the inner winding is used as the primary winding 2 Power Loss (W/m) Shield Outer winding Inner winding Thickness ratio - Skin depth mm Figure Power loss versus the thickness of the Faraday shield under open circuit condition; the inner winding is used as the primary winding As the inserted Faraday shield is perpendicular to the main magnetic flux of the transformer, it brings minor negative effects on its electric performance. The power losses of the shield were caused due to the eddy current effect; a further investigation on the power loss of copper conductors in 3-D should be conducted. The 3-D simulation result of the copper losses for the proposed HFCT is shown in Table The result shown was computed with 2 mm wires in diameter of the simulation model at the operating frequency of 100 khz; while Litz wire was utilized for prototype fabrication with 21-strands Litz wire bundle with mm in the diameter of each conductor. The DC resistance per kilometer for the simulation model is almost half to the prototype transformer due to greater cross-sectional area of the conductor. However, the equivalent model gives an accurate result based on the use of the simplification technique; the relevant discussion was presented in Chapter The power losses comparison of the HFCT with and without the Faraday shield is tabulated in Table Due to the Faraday shield insertion, the power losses increases by 13.16% and decreases by 11.17% for the HFCT under short circuit and 100

123 DESIGN AND ANALYSIS OF COAXIAL TRANSFORMERS open circuit condition respectively. The majority of power losses occur under short circuit conditions, and which are commonly known as copper losses. The copper loss of the Faraday shield is about 1.03 W under short circuit conditions and winding losses was increased by 3.48% due to the inserted shield. The increased losses are too small to be significant compared to the overall power rating of the HFCT (8 kw). Furthermore, the Faraday shield has a positive impact on the electric field of the HFCT under open circuit conditions. The peak eddy current is reduced at open circuit condition due to the insertion of the Faraday shield. In short, the load efficiency due to the insertion of the Faraday shield is decreased; while the efficiency under light-load condition is increased. Table Power Losses of the HFCT 3D Simulation Power Loss (Watt) Without Shield With Shield SC OC SC OC Inner Winding Outer Winding Top Shield N/A N/A E-3 Bottom Shield N/A N/A E-3 Left Shield N/A N/A E-5 Right Shield N/A N/A E-5 Total Leakage Inductance 3D simulation has the higher level of accuracy especially with complex structures. In addition, the highly visualization ability is beneficial on observing the electric and magnetic distribution, specifically for the end region section of the HFCT. In comparison, the 2-D simulation has the advantages over 3-D simulation such as: faster simulation process, simplified modeling process and acceptable accuracy (with simulated parameters being selected carefully). In order to verify the accuracy of the 2D- simulation, a comparison was conducted and the result shown in Table 4.14; the result shown compares the simulation results of 3-D simplified model over 2-D sectional model. 2-D simulation model was composed by 21-strands Litz wire, and the 3-D simulation model was constructed with equivalent single solid wire. Even though the winding configurations were different between the 2-D model and 3-D model, the accuracy of the computed inductance result should not be affected. This is because the inductance is determined mainly by the winding distance, winding turns and applied 101

124 DESIGN AND ANALYSIS OF COAXIAL TRANSFORMERS excitation current. According to the HFCT testing result at 100 khz, the relative permeability of the magnetic material is obtained by looking up Table 4.3; thus,. Energy method has been applied in conjunction with the FEM technique for the inductance analysis; Energy method is a very effective method for the inductance calculation especially with the complicated models. For 2-D simulation, 38.2mm and 120mm have been used when converting the calculated result to the practical model dimension in coaxial region and end region respectively. From the test results shown in Table 4.14, is consistent between the measurements, 2-D simulations and 3-D simulations; less than 0.5 % variation can be observed. Based on the result, the majority of the is contributed by the end region section; in which the 2-D result and the 3-D result show a good agreement. The simulation result is smaller due to the perfect winding configuration of the simulation model. This can be explained as, during the transformer fabrication process, extra leakage inductance was caused by fabrication defects of soldering, the imperfect winding turns and the connection effect. The difference between the measurements and simulation result is about 0.7 H, in which the accuracy is still at an acceptable level (the low accuracy level in percentage is due to the small leakage inductance, in which any variation in measurements becomes obvious). In order to increase the level of simulation accuracy, more benchmarks are required for both simulation and measurements, and an empirical formula can be consequently written for the correction of the accuracy level. In addition, the error is about % between the 2-D and 3-D simulations; in which the main difference is contributed by the calculation result of the end region section. Table The comparison of 2-D and 3D simulation results Unit: H Without shield With shield Testing result at 100kHz D, coaxial region D, end region N/A N/A D, full model D, coaxial region D, full model

125 DESIGN AND ANALYSIS OF COAXIAL TRANSFORMERS Intra-winding Capacitance The 2-D capacitance simulation result is shown in Table It can be observed that the accuracy of 2-D simulation result is just acceptable; in which the simulation result is about 1.5 times greater than the measurements. The variation can be attributed by two factors: firstly, the definition of the dielectric material between the primary and the secondary windings; and secondly, the winding turning angle in the practice. Even though the result shown is dissatisfied because of the 50 % error to the measurements, 2-D capacitance simulation is very useful if proper compensation parameters can be carefully chosen. For example, if more benchmarks are built and tested, the compensation factor can be selected to increase the level of the simulation accuracy. Again, another benefit of the 2-D simulation is the computation power required for the optimization work; in which less computation power is required over the 3-D simulations. Table D capacitance simulation result of 8 kw HFCT No-Shield Shield-Floating F/m F (Practical) C1F (F/m) C2F (F/m) C12 Cps F (Practical) Coaxial 2.68E E E E E E E1 Coaxial E-11 End Region E E E E E-1 Sum (Whole Model) 67.8 pf End Region E-11 Testing Result - 20 Sum (Whole Model) 93.3 pf Hz 48.9 pf Testing Result - 20 Hz pf In 3-D simulations, since the capacitance is proportional to the area surrounding the corresponding conductors, all conductor surfaces need to be pre-selected and named as a group in the workbench interface; this needs to be done before the the post-processing. Two types of 3-D model were fabricated: they are the simplified model and the precise model. The simplified 3-D model of the HFCT with and without the Faraday shield is shown in Figure 4.39; and the precise 3-D model is shown in Figure The precise model shown in Figure 4.40 provides higher accuracy of simulation results. However, the cost is the increased requirement of the computation power in 103

126 DESIGN AND ANALYSIS OF COAXIAL TRANSFORMERS order to achieve a higher level of accuracy. The precise model requires elements and nodes. The simulation work of it needs to be undertaken under a 64-bit operating system since the requested memory reaches 7~8 GB. A 32-bit operating system can only handle about elements, but only requires the less than 3 GB of the operational memory. The main difference between models of the simplified model and the precise model are the shape of the Faraday shield, and the fiber glass definition in end region section. For precise model, space around wires has been precisely defined as the fiber glass with the relative permittivity of 4.2, and the Faraday shield in the end region is identical to the prototype transformer; while for simplified model, the modelling of the Faraday shield and the fiber glass enclosure have been simplified as shown in Figure 4.39 in order to reduce the required computation time. (a) Without the Faraday shield (b) With the Faraday shield Figure D simplified model of the HFCT (a) Without the Faraday shield (b) With the Faraday shield Figure D precise model of the HFCT 104

127 DESIGN AND ANALYSIS OF COAXIAL TRANSFORMERS The computation results between measurements and simulations of the simplified model and the precise model are shown in Table Please refer to Chapter for the definition of,,, and. As expected, the simulation result of the precise model has a higher accuracy than the simplified model; however, the simplified model is still very useful if a 3-D optimization is required due to the short computation time. The of measurements at no-shield case is lower than the simulation results due to the imperfect fibre glass material in the practice. In practice, the fibre glass has a lot of tiny air bubbles in the material. In comparison, the simulation model has none of these bubbles at all. The computed at no-shield case are 10.5 % and 7.72 % higher than measurements for simulation results in simplified model and precise model respectively. At shielding case, the are % and 3.5 % lower than measurements for simulation results in simplified model and precise model respectively. In addition, an observation was made regards to the area of the Faraday shield. Comparing the of the simplified model and the precise model, if Faraday shield fabricated between the primary winding has a larger surface area, the intra-winding capacitance can be minimized. In short, the result shown in Table 4.16 verifies the advantage of the Faraday shield insertion, in which the insertion of the Faraday shield has effectively reduced the intra-winding capacitance by 80.6 % and % according to the measurements and simulation results respectively. Table D Capacitance simulation result of the HFCT No-Shield (pf) Shield-Floating (pf) Measurement Simplified Precise Measurement Simplified Precise

128 DESIGN AND ANALYSIS OF COAXIAL TRANSFORMERS 106

129 A NOVEL INTEGRATED PLANAR TRANSFORMER 5 A Novel Integrated Planar Transformer 5.1 Introduction From the early 1980 s, resonant converters have attracted a great deal of interest for switching power supplies because of their high power efficiencies [16]. There are three types of resonant converters; series, parallel and the combined series-parallel topology. Due to difficulties in the HF control circuit design and the extreme complexity of the magnetic integration analysis, the series-parallel type resonant converter has only been seen on the market recently. This type of the resonant converter has a well-known name as an LLC Converter (see Figure 5.1) which means the leakage inductance ( ) and the magnetizing inductance ( ) are utilized as part of the resonant tank in conjunction with the use of the resonant capacitance ( ). Figure 5.1. Half bridge LLC resonant circuit To achieve zero voltage switching (ZVS) or zero current switching (ZCS) for the LLC converter, a resonant tank is required in the front end of the converter. In order to reduce the converter volume, the best solution is to integrate the resonant tank with the transformer. The research work presented in this chapter focuses on the 107

130 A NOVEL INTEGRATED PLANAR TRANSFORMER magnetic components integration, which is specifically for the integration of inductors and transformers. Through magnetic integration, the total number of components is reduced and the converter system benefits from a reduction of both the overall volume and in manufacturing costs. The design precision of the and the is very important, whereas the C s can be pre-selected according to the required resonant frequency. The design can be done easily through the use of the magnetic circuit calculation, or with the 2D FEM technique [97]. In contrast, the precise design of the parameter is much more difficult to obtain. Though, for simple winding structures, the Flux Method [98] has been commonly used to do a quick analysis. For more complicated structures, obtaining an accurate analysis through the Flux Method is not possible, thus; the Energy Method [84], [85], [86] was utilized to obtain a more accurate result. To obtain an accurate computation result of the winding losses is another difficult task, especially for Litz wire windings which have been used in the proposed transformer. [59] and [99] have conducted numerous investigations on the Litz wire analysis in stranded level and bundle level, whereas [100] studied a practical case of Litz wire winding level; investigating the relationship between factors of strands, frequency and number of turns per length of the transformer. However, their work cannot be easily adapted to the prototype design due to the complicated impedance behavior of the Litz wire at the prototype winding level. For the above reasons, a full 3-D FEM modeling technique in conjunction with the use of the Energy Method was employed for this work to deal with the above issues. Three prototype transformers were fabricated, which include one transformer in top-up structure and two transformers in proposed structure. Details of these structures are discussed and presented in following sections. The FEM simulation technique was employed to analyze the performance of the introduced structures over other magnetic integration structures; and measurements were conducted for prototype transformers. In this chapter, the discussion is focused on the introduced structure; however, other magnetic integration structure will be briefly introduced. The power efficiency evaluation shown in the last section of this chapter presents a comparison of the introduced structure with the commercial top-up structure. In addition, detail of the top-up structure is presented in Appendix C., the content introduces the specification of the fabricated top-up prototype, flux illustration and measurements. 108

131 A NOVEL INTEGRATED PLANAR TRANSFORMER Operating Requirement The requirement of the integrated transformer for a 1.08 kw LLC converter is tabulated in Table 5.1 Table 5.1. The requirement of the LLC transformer Power Rating P 1.08 kw Resonant frequency f 1 90 khz Operating frequency fs ~ khz LLC Converter Input Voltage V in 385~ 445 V (dc) LLC Converter Topology Half Bridge Input Voltage (Nominal) V V Input Current I A max Output Voltages V 2 36 V(dc) Output Current I 2 30 A Turn ratio N1/N2 18/3=6 Magnetizing Inductance OC 175 uh Leakage Inductance SC 33 uh Based on the converter requirements, assumes the optimal voltage as 216 V, the turns of the designed transformer is: The required maximum and minimum gain can be obtained from the given turn ratio: The equivalent AC resistance: 109

132 A NOVEL INTEGRATED PLANAR TRANSFORMER Let k=5.3, which is the ratio of over ; thus, Since k and G max are known, the minimum operating frequency can be calculated as: The maximum operating frequency: Next step, calculate the required C r and L r according to the obtained Q max and R ac. Thus, all required parameters of the resonant tank are now obtained Consideration of Integrated Structures In the case of the magnetic integration of the LLC transformer, several different magnetically integrated transformers have been designed for LLC converters. However, efforts are still needed to further reduce the transformer volume while maintaining the controllability of the L s. The simplest structure of an LLC transformer is by designing an extra core on top of the transformer [20] as shown in Figure 5.2 (a) and named as top-up structure throughout this dissertation. Discussion of the similar structure has been presented in [21], [22], [23]; in which the L s is designed on the side of the transformer. This kind of structure is very reliable and the design process is relatively simple as the L s and the L p have their own flux path. However, the drawback for this structure is the large volume of the transformer size. Even though this kind of structure was asserted as magnetically integration, but it is 110

133 A NOVEL INTEGRATED PLANAR TRANSFORMER more like fabricating two components in one manufacturing process. A more cost-effective design has been introduced by [24] as shown in Figure 5.2 (b) and is named as MIP structure throughout this chapter; the magnetic integration was achieved by introducing the magnetic insertion inside the transformer between primary and secondary windings. This design reduces the volume of integrated magnetics effectively compared to other designs, as there are no protruding magnetic pieces. However, the disadvantage of this structure is that the adjustment of L s mainly relies on the physical dimensions of the magnetic piece (assuming winding distances and dimensions of magnetic components are fixed). On the other hand, PCB windings utilized by [24] have a higher manufacturing cost and increase the complexity of the transformer fabrication process when compared to utilizing Litz wires. (a) Top-up structure (b) MIP structure Figure 5.2. Investigated transformer structures: (a) top-up structure, and (b) MIP structure Geometry Specification Because of the consideration discussed in Chapter 5.1.2, a novel structure of the magnetic integrated transformer was introduced (see Figure 5.3). The proposed integrated magnetics has advantages over the above structures such as low profile, easy controllability of the L s, higher efficiency and lower costs. The introduced structure of the prototype transformer is named as MIO structure throughout this dissertation; where traditional EE shape cores are used as the transformer core with primary and secondary windings on each end of the window. The magnetic insertion is placed horizontally between the primary and secondary windings and locates outside of the main core, in which the primary winding is fabricated by 14-strands of twisted Litz wire and the secondary winding is fabricated with copper sheets. 111

134 A NOVEL INTEGRATED PLANAR TRANSFORMER Figure 5.3. The explored view of the MIO structure (proposed structure) (a) Side view (b) Front view Figure 5.4. The dimensioned cross-section view of prototype I (unit: mm) (a) Side view (b) Front view Figure 5.5. The dimensioned cross-section view of prototype II (unit: mm) Two prototype transformers in proposed structure were built with the same requirement except from using different size of EE cores and conductors. Both transformers were required to have a power rating of 1.08 kw, output voltage of 36 V, nominal input voltage of 216 V (voltage ratio of 18:3), resonant frequency at 90 khz, and an inductance ratio of 5.3, with the L p at 175 μh and the L s at 33 μh respectively. The operating temperature is between 60 and 80 degrees and the detailed dimensions of prototype I and prototype II are shown in Figure 5.4 and Figure 5.5 respectively. Prototype I utilized the EE core of dimension 38/25/16; respectively in mm; prototype II utilized the EE core of dimensions 43/28/19; respectively in mm. Prototype images are shown in Figure

135 A NOVEL INTEGRATED PLANAR TRANSFORMER (a) Prototype I (b) Prototype II Figure 5.6. Two prototype Transformers Core Selection and Wiring Configurations The magnetic materials chosen for the design are NiZn TN12B [47] and MnZn TP4A [48] for prototype I and prototype II respectively; saturated flux densities are 430 mt and 510 mt respectively for both materials at room temperature. The relative permeability of the magnetic materials as well as the air-gap and insertion gap is tabulated in Table 5.2. Furthermore, the detailed dimension of prototype I and II are shown in Figure 5.7; where the primary windings in both prototypes utilized two bundles of 7-strands Litz wire with 3 insulation layers and the secondary windings are copper plates. For primary windings of prototype I, each strand has the diameter of 0.25 mm; whereas the secondary is with the dimension of 0.5 X 8.8 mm (LxT). In comparison, primary windings on prototype II, each strand has the diameter of mm; whereas the secondary is with the dimension of 0.4 X 10 mm (LxT). (a) Prototype I (b) Prototype II Figure 5.7. Winding configuration in single window (Unit : mm) Table 5.2. The magnetic characteristic and gapping information Core gap Insertion gap Prototype I mm 1 mm Prototype II mm 2 mm 113

136 A NOVEL INTEGRATED PLANAR TRANSFORMER Magnetic Calculation Prototype I The turn ratio characteristic of the proposed transformer is known upon on the requirement of the LLC resonant tank; thus, the maximum operating flux density and consequently the required magnetizing current is now able to obtain. The following calculation has taken into account with a sine wave input and the lowest operating frequency of 60 khz according to the requirement listed in Table 5.1; thus, The required open circuit inductance is 175 H; therefore, the relative permeability of the current magnetic circuit with the use of FEE38/16/25 core is obtained as: The magnetic intensity, The magnetizing current for the primary winding is also obtained as: The maximum primaries current under short-circuit condition becomes: Thus, 8.73 A is the maximum current required on the primary at 60 khz under full load condition. The core gap to achieve L m =175 uh is calculated as: Prototype II 114

137 A NOVEL INTEGRATED PLANAR TRANSFORMER Power Losses Based on the known core size and pre-selected wires, the power losses can be calculated manually; in which the copper losses is calculated under DC condition, and the iron losses is obtained based on manufacturer s datasheet [47][48]. Prototype I Litz wires Resistance Length of Litz wire per turn: Total length of Litz wire (18 turns): Copper resistance in a diameter of 0.25 mm round conductor: At a working temperature of 60, resistance becomes: 115

138 A NOVEL INTEGRATED PLANAR TRANSFORMER Copper Wire Resistance Total length of Copper wire: Copper resistance of the cross-section of 0.5mmX8mm: At a working temperature of 60, resistance becomes: Winding Losses at 60 Primary: I m =3.73 A, I sc =5 A, I total =8.73 A Secondary: Isc=30 A At no-load condition, At load condition, Core Losses at 60 Consider the core losses at 60 khz, and a working temperature of 60 (a 100 kw/m 3 less core losses occurred if the temperature increased from 60 to mt 500 kw/m 3 (The core losses per volume unit of prototype I at open circuit condition) At Full-load condition Prototype II Similarly, the power losses of prototype II in DC mode can be obtained with the same calculation process. Litz wires Resistance 116

139 A NOVEL INTEGRATED PLANAR TRANSFORMER Copper wire Resistance Winding Losses at 60 Primary: I m =3.74 A, I sc =5 A, I total =8.74 A Secondary: Isc=30 A At no-load condition, At load condition, Core Losses at 60 Consider the core losses at 60 khz, and a working temperature of mt 400 kw/m 3 At Full-load condition 117

140 A NOVEL INTEGRATED PLANAR TRANSFORMER 5.2 Measurements The measurement results of 1.08 kw prototype transformers are shown from Figure 5.8 to Figure 5.11; all parameters are frequency dependant. The measurements of the is shown in Figure 5.8; where a result difference of 1 H occurs between prototype I and prototype II. The difference is mainly caused by the level of accuracy due to the manual manufacturing process. The decreases with frequency due to the increased AC winding resistance, in which less energy can be distributed to the air-core inductance and the magnetic insertion. Ls (μh) Frequency (khz) Prototype II Prototype I Figure 5.8. The leakage inductance of the 1.08 kw transformer prototypes The phenomenon of increased AC winding resistance can also be illustrated by the result shown in Figure 5.9. The increases with the frequency due to AC effects introduced in Chapter 2.4. Based on the DC resistance calculated in Chapter 5.1.6, the equivalent resistance can be obtained as Ω and Ω for prototype I and prototype II respectively; where the measured is equal to the sum of the primary resistance and coupled secondary resistance. Compare the measured along with the DC resistance calculation result; it was found that these two results are not identical. The is found to be lower in prototype I than prototype II in HF measurements; but prototype II was designed for a lower winding resistance due to the use of larger conductors. From the measurements, it can be observed that prototype II has a much higher AC effects compared to prototype I. These AC effects include the eddy current effect, proximity effect and fringing effect. A further analysis of this interesting phenomenon will be presented in the simulation section; please refer to Chapter for further discussions. 118

141 A NOVEL INTEGRATED PLANAR TRANSFORMER Rs (Ω) Prototype II Prototype I Frequency (khz) Figure 5.9. The winding resistance of the 1.08 kw transformer prototypes Lp (μh) Prototype II Prototype I Frequency (khz) Figure The magnetizing inductance of the 1.08 kw transformer prototypes The result shown in Figure 5.10 presents that a greater variation of occurs in prototype II compared with prototype I. Geometrically, prototype I does not have the core gap; where prototype II has a core gap of 3 mm. The greater variation of can be attributed to the core gap of prototype II; in which the fringing flux generated around the air-gap consumes more magnetizing energy if the frequency increases. However, exist of air gap is very advantageous for the prototype transformers due to the lesser sensitivity to the working temperature, as well as the prevention from the magnetic saturation due to the harmonic effect (refer to Chapter 2.4 ). On the other hand, the decrease of accords to the increased frequency is because of the magnetic property of the transformer core material; in which the permeability of the core material drops with the increased frequency. Furthermore, the variation of the is about 1 %, which has very minor effect to implemented applications. 119

142 A NOVEL INTEGRATED PLANAR TRANSFORMER According to the manufacturer s datasheet [47], [48], the characteristic is as expected as shown in Figure The resistivity are and 6.5 for core material of prototypes I and prototype II respectively. For this reason, measurements of prototype I show a higher resistance over prototype II. The measurement result verifies this characteristic where the difference between prototypes I and II becomes greater with the increased frequency. Rc (kω) Prototype I Prototype II Frequency (khz) Figure The core resistance of the 1.08 kw transformer prototypes The signal generator and the oscilloscope were used to obtain the waveform measurements of prototype transformers directly. Results are shown in Figure 5.12 and Figure 5.13, where the top waveform (1) is the input voltage and the bottom waveform (2) is the output voltage. Compared to the full LLC bench testing, this testing configuration is more effective on evaluating the transformer performance across operating frequencies (the voltage gain varies with the frequency due to the inherent characteristic of the LLC circuit is ignored). Also, the square wave signal was chosen as the input due to its criticism for the transformer testing; a square wave has the rapid rising and falling edges. In the waveform measurements, the input and output waveforms are almost identical for both prototypes; the resonant frequency of 90 khz has been chosen to show the difference between the prototype I and II. Due to the integration of the leakage inductance, a voltage pulse on the rising edge of the output can be observed. Prototype I has a higher voltage pulse than prototype II, as prototype II has a greater parasitic-capacitance (self-capacitance), in which the capacitance regulates the voltage pulse. If the frequency increases to 500 khz (Figure 5.13) from 90 khz, another phenomenon becomes more obvious; known as the ringing effect. 120

143 A NOVEL INTEGRATED PLANAR TRANSFORMER (a) Prototype I (b) Prototype II Figure Square wave test of prototypes at 90 khz (a) Prototype I (b) Prototype II Figure Ringing effect on prototypes at 500 khz Furthermore, self-resonant frequency was obtained by connecting a 1 kω resistor to the transformer input, and then monitoring the frequency where the resistor has the minimum and maximum voltage distribution (represents in series resonant frequency and parallel frequency respectively). The test bench setup is shown in Figure 5.14; where V1 and V2 are channels of the oscilloscope. Those self-resonant frequencies have an indirect relationship to the ringing effect. The self-frequency test was conducted for two purposes; firstly, to confirm whether the introduced transformer operates normally at operating frequencies; and secondly, to obtain the parasitic capacitance. Series self-resonant frequencies are MHz and 9.44 MHz, and parallel self-resonant frequencies are MHz and MHz respectively for prototype I and prototype II. The parasitic capacitance in prototype II is greater than in prototype I based on the measurement result of frequency at self-resonance. This can be attributed to the larger physical size of prototype II s windings, thus, larger parasitic capacitance. Since the resonant frequency requirement is at 90 khz, the prototype transformers are guaranteed to operate safely, as the requirement frequency is well below the self-resonant frequencies. 121

144 A NOVEL INTEGRATED PLANAR TRANSFORMER Figure Setup for transformer resonant frequency measurement The ideal voltage ratio should be the same as the transformer turn ratio of 6:1. But from the measurement results shown in Figure 5.15, the voltage ratio maintains an average value of between 6.2 and 6.5 thought the frequency range. This increase of the voltage ratio (from 6 to between 6.2 and 6.5) can be attributed to the existence of the air-core section of. Because of the unique structure of the introduced transformer, only air-core leakage inductance in primary is taking the effect if the voltage is measured without the load (open circuit case). This also makes the introduced structure more advantageous (higher efficiency) at no-load condition compared to the top-up or add-on transformer structure introduced by other researches [20], [21], [22], [23]. From Table 5.4 shown in the simulation section, the leakage inductance without the insertion was found to be When the voltage divider principal is applied, the voltage delivered to is reduced by a factor of 0.069, which results in a voltage ratio increase to 6.445:1. This voltage ratio increase obtained from the simulations agrees with the measurement results shown here. In addition, ratio of is obtained from the calculation below: Voltage Ratio Prototype I Prototype II Frequency (khz) Figure Voltage/turn ratio of HF planar transformers 122

145 A NOVEL INTEGRATED PLANAR TRANSFORMER 5.3 Simulation Results Flux Distribution The flux density result of prototype transformers is shown in Figure In 2-D flux density simulations, the result demonstrates that prototype transformers operate under their saturation region. As expected, prototype II has a lower flux density due to the utilization of the larger magnetic core. Same amount of the magnetizing energy was required to store in a larger core (both prototype transformers designed at ) and therefore a lower flux density was achieved in prototype II. In comparison with the manual calculation result presented in Chapter 5.1.5, the 2-D simulation gives acceptable results for both the flux density and the. For the computed results of leakage flux and the, 2-D results can only give a rough index for the proposed MIO structure. This is because of the magnetic insertion placed orthogonally to the main core for the proposed MIO structure; thus, the problem cannot be solved accurately in the 2-D domain. Prototype I - SC Prototype II - SC Prototype I - OC Prototype II - OC Figure Magnetic flux density of prototype transformers in 2-D For this reason, 3-D simulation works were conducted and results are shown in Figure The result demonstrates how leakage inductance is adjusted with the use of the magnetic insertion under the SC condition. The amount of energy stored in the air-core inductor is limited, and cannot be increased easily unless the distance between windings is increased. Therefore, with the use of the magnetic insertion, the leakage inductance can be adjusted freely by controlling the insertion gap without increasing the transformer volume. Under the open circuit condition (light-load condition), the flux density of prototype II is 11.94% lower than of prototype I. This 123

146 A NOVEL INTEGRATED PLANAR TRANSFORMER satisfies the Faraday s law, that the magnetic flux flowing in the core is inversely proportional to the core area. The maximum flux densities for both prototypes I and II at full-load (short circuit) and light-load conditions are in the operation of the linear region. Prototype I - SC Prototype II - SC Prototype I - OC Prototype II - OC Figure Magnetic flux density of prototype transformers in 3-D On the other hand, the insertion layer should be designed as close to the main core body as possible. By observing results on both prototypes under the short circuit condition, the energy stored in the magnetic insertion of the prototype I is greater than in prototype II. This represents that prototype I utilizes the insertion layer more efficiently for the adjustment of the (both prototype are designed to achieve the same leakage inductance). Furthermore, the magnetic intensity has the highest at the insertion layer under short circuit condition; thus, higher current density occurs due to the magnetic field unbalancing, and brings a positive effect to winding heat dissipation. That is, the higher heat generation occurs at the winding near the insertion layer (compared with the MIP structure, the higher current density occurs at the in-core region); in which the space near the insertion layer has a better air circulation. Furthermore, the leakage layer was utilized as part of the magnetizing energy storage as observed from the open circuit results. There are partial magnetizing energy stores in the insertion layer, and the flux density of the transformer main core can be decreased without having the core size increased. This kind of characteristic is not seen in MIP structures and the top-up structures since the main flux only flows in the transformer main core Eddy Current Distribution The analysis of eddy current distribution was conducted at 110 khz since this is the most difficult condition for the prototype transformers to operate. Under the short circuit condition, the current distributes more evenly in prototype II than in 124

147 A NOVEL INTEGRATED PLANAR TRANSFORMER prototype I as shown in Figure The peak current density of prototype II is 11 % lower than in prototype I. The simulation result makes a good agreement to the manual calculation result regards to the primary winding resistance; in which the winding resistance of prototype II should be lower than prototype I. However, refer to the measurement result shown in Figure 5.9; in which prototype II has a higher winding resistance across the frequency ranges than prototype I. This can be explained as that, the AC winding resistance of prototype II is higher than prototype I and this higher AC winding resistance of prototype II is attributed by the fringing effect and the proximity effect. Prototype I - SC Prototype II - SC Figure The 2-D current distribution result under short circuit condition at 110 khz Prototype I - OC Prototype II - OC Figure The 2-D current distribution result under open circuit condition at 110 khz This phenomenon of higher AC winding resistance of prototype II can also be demonstrated by the 3-D result shown in Figure In comparison to prototype I, the peak current density of prototype II is % higher under short circuit condition (3D results shows only the short circuit case as it distributes the most of the winding losses). This is mainly attributed to the fringing effect which is caused by the existence of the core-gap; in which fringing flux cuts conductors around the core-gap and consequently induces the eddy currents on the surface of the conductor. Also, proximity effect is another factor causes the increase of the AC winding resistance; the winding configuration of prototype II is more squeezed than in prototype I (less space from turn to turn). Therefore, it can be concluded that the winding resistance of prototype II is higher than of prototype I based on above analysis; this is also validated by the measurement result shown in Figure 5.9. The 125

148 A NOVEL INTEGRATED PLANAR TRANSFORMER amount of the fringing loss depends on the resistivity and the thickness of the conductor object. Therefore, the winding resistance of prototype II can be decreased if the air-gap is reduced. More discussion about the winding resistance will be presented in Chapter (a) Prototype I (b) Prototype II Figure The 3-D current distribution result under short circuit condition at 110 khz 5.4 Winding Configurations Analysis Figure Different types of winding configurations for planar transformer

149 A NOVEL INTEGRATED PLANAR TRANSFORMER In order to analyze the prototype transformers in regards to the winding arrangement with their magnetic and electric performance, several winding configurations have been studied in both with and without the magnetic insertion. There are nine different types of winding configurations as shown in Figure 5.21; where configurations 7 to 9 were analysed without the magnetic insertion due to the wiring arrangement (no space for magnetic insertion inside the core). Simulations were conducted under short circuit condition with the use of air or magnetic material as the enclosure. The result represents the phenomenon of the in-core section if the magnetic material is used as the enclosure; and the result represents the phenomenon of out-core section if air property was assigned to the enclosure (enclosure means the winding surrounding objects). The FEM technique is employed to investigate the leakage inductance and the winding loss; alternatively, ( 57 ) and ( 58 ) shown in Chapter can be utilized for windings characteristic calculation in regular arrangements Without the Magnetic Insertion AC Resistance Leakage Energy Structure Figure The comparison result - without insertion and enclosed with magnetic core The analysed results without the magnetic insertion are shown in Figure 5.22 (enclosed with the magnetic core) and Figure 5.23 (enclosed with the air). Also, the AC resistance and leakage inductance results have been generalized under the same scale for a better presentation among comparisons. Based on results shown in Figure 5.22 and Figure 5.23, some observations are made. Firstly, the leakage inductance is proportional to the peak current density. Thus, if a higher leakage inductance is 127

150 A NOVEL INTEGRATED PLANAR TRANSFORMER required, a higher AC resistance will be expected as the outcome. Secondly, the material of enclosures is one of causes for the inductance adjustment; the AC resistance and the leakage inductance are both higher if the magnetic material is utilized as the enclosure AC Resistance Leakage Energy Structure Figure The comparison result - without insertion and enclosed with magnetic air On the other hand, inter-leaving winding structure is very effective on minimizing the AC resistance as well as the leakage inductance. As expected, structure 7 has the least peak current density as the winding configuration distributes more evenly; in which the magnetic intensity is not accumulated with the number of winding layers. Structures 5 and 6 have a slightly lower leakage inductance compared to structure 7 while they are all interleaving structure. This is because structure 7 has a greater interleaved space from winding to winding; in which this space is utilized as the air core inductance on storing the leakage energy. Thus, if the winding space of structure 7 is reduced, it is still the most effective structure for lower AC resistance and leakage inductance. In short, if a maximum leakage inductance is required for the transformer, structure 1 is the best candidature due to its characteristics as analysed from the simulations With the Magnetic Insertion For the winding configuration with the magnetic insertion, the comparison results which the winding configurations were enclosed with the magnetic core and air are shown in Figure 5.24 and Figure 5.25 respectively. Because the space limitation in winding structures 7 to 9, only the comparison result of structures 1 to 6 are shown and discussed in this section. As expected, the leakage inductance increases due to the insertion of the magnetic material. However, this does not represent that the leakage 128

151 A NOVEL INTEGRATED PLANAR TRANSFORMER inductance can be increased with any kind of magnetic insertion. The dimension and the magnetic properties of the magnetic insertion as well as the placed location are all essential factors. The magnetic insertion creates a shorter magnetic path for energy to circulate if the transformer is under loaded condition; thus, more energy can be stored while the same amount of the load current is exciting. In the simulation result, the leakage inductance is 3 times higher while the peak current density increases only 175% for structure 1 compared to windings without the magnetic insertion (enclosed with magnetic core). The structure 1 is the most effective structure on obtaining the maximum leakage inductance without having the AC resistance increased too much. This is demonstrated by comparing the result of structures 1 and 2 due to their similarity of winding structures. Compare structure 1 over structure 2, the inductance is 18 times higher while the AC resistance is only double with the enclosure of magnetic core. In addition, the magnetic insertion has little effect if the transformer is with the interleaving winding structure AC Resistance Leakage Energy Structure Figure The comparison result - with insertion and enclosed with magnetic core AC Resistance Leakage Energy Structure Figure The comparison result - with insertion and enclosed with air 129

152 A NOVEL INTEGRATED PLANAR TRANSFORMER Winding Resistance Normalization To investigate the AC resistance distribution of the introduced structure (MIO structure), 3D modelling technique discussed in Chapter was employed due to the structure complexity of the Litz wire windings. Results are shown from Figure 5.26 to Figure 5.29; solid represents the primary has the equivalent cross-section area in a solid conductor according to the total cross-section area of the Litz wire windings; Litz represents the Litz wire conductor, which is utilized for the manufactured prototype transformers. The wire model specification for both prototypes is tabulated in Table 5.3. Also, the sectorized model is an extruded model in a length of 10 mm; in which extruded models were built and followed the dimensioned cross-sectional figure as shown in Figure 5.7. The simulations were conducted under both open circuit and short circuit condition with the corresponding current excitation (refers to Chapter ). All results have been normalized as the AC resistance ratio versus the frequency; the normalization technique is presented as shown in Chapter Table 5.3. The specification of the sectorized model Diameter (mm) Solid conductor Litz wire (14-strands) Prototype I Prototype II In Figure 5.26 and Figure 5.27, the simulation results are almost identical; except from the primary resistance at resonant frequency (90 khz) under short circuit condition is slightly higher. It was expected that a higher AC resistance under the short circuit condition due to the reversed magnetic field from the secondary winding; in which the current distribution of the primary winding becomes more uneven. However, this kind of uneven current distribution seems not so obvious for the introduced transformer structure due to the greater windings distance between the primary and the secondary. Refers to Figure 5.18 and Figure 5.19 for the current distribution of prototype transformer, the primary current distributes more unevenly under the open circuit condition; in which the results are in a good agreement to the AC resistance simulation result shown here. Furthermore, the utilization of Litz wires increases the DC resistance by about 50% and 70% for prototype I and prototype II respectively (observe the AC resistance under 40 khz). However, once the operating frequency reaches the designated frequency, the Litz wire starts showing its advantages. Within the designated frequency ranges of 60 khz to 110 khz, AC 130

153 A NOVEL INTEGRATED PLANAR TRANSFORMER resistance of the Litz wire model is about half to the solid conductor model. In addition, the AC resistance of prototype II is about 30 % lower than of prototype I below 100 khz. AC resistance ratio Prototyep I - Solid Prototyep I - Litz Prototyep II - Solid Prototyep II - Litz Frequency (khz) Figure Primary AC resistance ratio under open circuit condition AC resistance ratio Prototyep I - Solid Prototyep I - Litz Prototyep II - Solid Prototyep II - Litz Frequency (khz) Figure Primary AC resistance ratio under short circuit condition The secondary AC resistance under open circuit condition was obtained by normalizing the induced eddy current loss of the secondary winding into the equivalent resistance index; this index can then be used to evaluate the power loss performance of the proposed transformer prototypes. Thus, the AC resistance shown in Figure 5.28 has slightly different meaning from other conditions since there is no current flowing in the practice. Using prototype I result at 100 khz as the example, the AC resistance of the secondary under open circuit condition has increased by almost double due to the use of the Litz wire on the primary. The increase of this AC resistance is because of the skin effect; in which the excitation field from the primary winding induces eddy current on the secondary winding. In order to relieve this skin 131

154 A NOVEL INTEGRATED PLANAR TRANSFORMER effect phenomenon, thinner copper plates in parallel should be utilized for the secondary windings (this could be in an interest for the future work). In fact, the Litz wire model has the same cross-section area as the solid conductor model, but the overall diameter of the Litz wire bundle is greater than the solid conductor due to the insulation space between each wire. For this reason, the AC losses of the secondary windings with the Litz wire model is greater than the solid conductor model due to the reduced winding space; more induced eddy current was generated on the secondary winding of the Litz wire model. This phenomenon is especially more obvious under open circuit condition as shown here. AC resistance ratio Prototyep I - Solid Prototyep I - Litz Prototyep II - Solid Prototyep II - Litz Frequency (khz) Figure Secondary AC resistance ratio under open circuit condition Furthermore, the secondary AC resistance comparison under short circuit condition is shown in Figure The AC resistance is almost identical on both prototypes; AC resistance in prototype II is slightly lower compared to prototype I due to the utilization of larger secondary windings. AC resistance ratio Prototyep I - Solid Prototyep I - Litz Prototyep II - Solid Prototyep II - Litz Frequency (khz) Figure Secondary AC resistance ratio under short circuit condition 132

155 A NOVEL INTEGRATED PLANAR TRANSFORMER The winding resistance result shown in Figure 5.30 validates the accuracy of simulation results over measurements. The winding resistance simulation result shown in Figure 5.30 represents the actual resistance for prototype transformers. The simulation results were obtained in the following process: firstly, conduct the power loss simulation of the 3-D full model in solid conductor winding of the primary; secondly, conduct the power loss simulation of sectorized model for solid conductor and Litz wire conductor respectively; thirdly, the generalized factor was obtained from the second step; and lastly, applied the obtained generalized factor to the results obtained on the first step, and couples the secondary winding resistance to the primary side with the corresponding transformer turn ratio. 1.2 Winding Resistance (Ω) Measurement - II Measurement - I Simulation - II Simulation - I Frequency (khz) Figure Winding resistance - simulation results versus measurements The result shows a small variation of Ω between the simulation results and measurements. The difference can mainly be attributed by the wire used to short-circuit the secondary side; in which the wire resistance is being amplified in a step-down transformer when coupled to the primary side. This phenomenon becomes more apparent if the frequency increases. As manufacturing process is always imperfect, an awful soldering connection might diverge the measured results from the simulated model. This consideration of termination effects should be undertaken as further work for simulations. 5.5 Inductance Analysis In this section, the inductance analysis is presented by comparing the introduced structure with the MIP structure (refers to Figure 5.2 (b)). Figure 5.31 shows the 133

156 A NOVEL INTEGRATED PLANAR TRANSFORMER difference between the flux directions of the Magnetic Insertion in Parallel (MIP) structure [24] and the proposed Magnetic Insertion placed Orthogonally (MIO) transformer structure. The major improvement to the structure of MIP is the position of the magnetic insertion, which is placed outside of the transformer. Two major benefits are obtained from doing this; firstly, the current distribution in the windings becomes more evenly distributed, and secondly; there is the flexibility in the adjustment of the L s. (a) MIP (b) MIO Figure Illustration of flux direction For LLC transformer design, the basic and most important requirement is the controllability of and due to the impedance matching requirement of the power supply. With the use of the energy method, is approximated as the energy stored in the magnetic core and is approximated as the energy stored in the space between windings (the energy cannot be coupled from one winding to the other). Once the permeability, physical dimension, excitation current and winding turns of a magnetic core has been specified, the can be obtained easily with the utilization of 2D FEM computation (or it can be obtained with the magnetic circuit calculation). On the other hand, to analyze the is a more complicated task since the leakage flux does not flow in a regular path. Instead, it follows the shortest magnetic path and returns to the excitation coil. Normally, varies with factors such as the physical structure of the transformer, winding distance, wire configuration, and permeability of magnetic material of the core. Despite from this, the easiest and most economical way to adjust is by inserting a piece of magnetic material in the transformer. Figure 5.31 illustrates the flux direction in MIP and MIO, in which the flux circulates in parallel (parallel leakage flux direction to the main flux) and at an orthogonal angle from the core to the magnetic insertion respectively for MIP and MIO. Once the dimension of the magnetic insertion is fixed, MIP cannot easily adjusts the while the of MIO can be adjusted from 1 H to 85 H with the requirement of 33 H. 134

157 A NOVEL INTEGRATED PLANAR TRANSFORMER Table 5.4 shows the inductance requirements and comparisons between the MIP and MIO structure. Both EE cores for MIP and MIO have the same inductance characteristics prior to the addition to an insertion. As can be seen, the values for the MIP structure can be adjusted to fit the requirement with ease, but cannot be varied easily without increasing the physical dimensions of the insertion. The MIO structure on the other hand has the ease of fulfilling the requirement like the IMP structure, but also the requirement by simply adjusting the distance of the air gap between the insertion and the EE structure. Adjusting the distance of the air gap benefits both the variability of and, as the insertion is magnetically coupled to the transformer core. The proposed MIO structure is beneficial from reducing the manufacturing costs as the same transformer can be utilized for different requirements without modifying the dimensions of the magnetic materials. Table 5.4. Inductance comparison between different magnetic insertion arrangements Structure Insertion Configuration: L p (μh) L s (μh) Requirement No insertion Outside the core MIP Inside the core Length increased to 50.4 mm mm insertion gap MIO 0.01 mm insertion gap No insertion gap Discussion Figure Prototype transformers; prototype I: MIO structure; prototype II: MIO structure, prototype III: top-up structure There are three prototypes built, two in the proposed MIO structure and one in the top-up structure; the images of the fabricated prototype transformers are shown in 135

158 A NOVEL INTEGRATED PLANAR TRANSFORMER Figure Prototype I was the first prototype to demonstrate if the introduced structure functions correctly for the designated LLC converter; prototype II was the adapted prototype transformer with larger cores and conductors; and the top-up prototype was built with the same power rating of 1.08 kw as the comparison model of the transformer efficiency evaluation. The physical dimension of the top-up prototype transformer has been stated in detail in Appendix C Winding Thickness Evaluation The winding losses normalization chart is depicted in Figure 5.33, where N is the most efficient operating point for prototype structures in consideration of winding losses. The definition of normalization factor was introduced in ( 111 ); it represents as an index (the lower the better) to evaluate if the thickness of the selected winding conductor is appropriate. Three prototypes have their optimal operation frequency region respectively as: prototype I: 100 ~ 110 khz; prototype II: 40~60 khz; and prototype III: 120 ~ 140 khz). Prototype II has the lowest optimal operating frequency compared to prototype I (same winding structure) due to the greater thickness of winding conductors utilized. Same thickness of winding conductors were utilized for prototypes I and III, in which they are in the winding structure of isolated windings (windings on each end of the transformer window) and sandwich structure (windings interleaved on each other) respectively. It is observed that sandwich structure has the ability to relieve skin effect due to the phenomenon of magnetic field cancellation between the primary windings and the secondary windings. Figure Normalization factor of primary windings 136 Based on results shown in Figure 5.33, some short comments can be made. For

159 A NOVEL INTEGRATED PLANAR TRANSFORMER the proposed structure, the maximum conductor diameter needs to be smaller than one skin depth to avoid unnecessary winding losses regards to the skin effect. In comparison, the sandwich winding structure has the advantage for higher frequency operation with the same winding specification compared to proposed structure. To be more specified, a maximum conductor thickness of one skin depth, and two skin depths should be followed as design principles for the proposed structure and the sandwich winding structure respectively Transformer Losses Total losses comparison results are shown in Figure 5.34 and Figure 5.35 for open circuit condition and short circuit condition respectively. Magnetic loss means the transformer core losses plus the insertion losses for prototype I and prototype II; and represents the transformer core losses plus the top-up core losses for prototype III. Because of the utilization of the high resistive iron-powered material, the appears to very small at the maximum of 0.1 W for the completed prototype transformers across all conditions and frequency ranges. However, the varies with operating conditions, prototype structures and operating frequencies. (the definition of and are eddy current losses and hysteresis losses; please refer to Chapter ). It is observed that the total core loss in prototype II is relatively smaller compared to prototype I due to the utilization of the larger core, along with the less resistivity of the core material. In comparison, the of prototype III is greater than prototype II due to the extra top-up inductor core Magnetic loss (W) Secondary Loss (W) Primary Loss (W) I II III I II III I II III I II III I II III I II III I II III I II III Frequency (khz) Figure Open circuit losses Generally, the reduces as the operating frequency increases due to the 137

160 A NOVEL INTEGRATED PLANAR TRANSFORMER reduced ; also, the is almost negligible under short circuit condition. However, the has a different losses depletion for prototype III because of the utilization of the top-up inductor; the increases gradually as the operating frequency increases. In addition, the sandwich structure is very effective for the minimum winding losses. Under open circuit condition, the total power losses are: Prototype III > Prototype I > Prototype II; under short circuit condition, the total power losses are: Prototype II > Prototype I > Prototype III Magnetic loss (W) Secondary Loss (W) Primary Loss (W) I II III I II III I II III I II III I II III I II III I II III I II III Frequency (khz) Figure Short circuit losses Based on both the eddy current and winding loss simulation results, the following design principles are made and should be followed to minimize the AC losses: (1) the dimension of conductors needs to be no more than double of the skin depth for all structures; (2) the winding layers and transformer winding turns must be minimized; (3) the core gap must be less than 3 mm in order to minimize the fringing effect; and (4) both primary and secondary windings should be placed away from the core gap, as to minimize the induced eddy currents from the core gap Prototypes Comparison The comparison measurement result is shown in Table 5.5; except from L p of the proposed structure, all parameters are dependent on the frequency. The L p of the proposed structure fluctuates with the frequency due to the magnetic integration, in which the magnetic bar stores the magnetizing energy in a unpredictable manner. However, the variation is relatively small to the whole magnetizing inductance. As expected, the R s of the top-up structure is smaller compared to the proposed structure due to the use of sandwich winding configuration. The higher AC resistance of the proposed structure is because of the severe proximity effect on the primary winding. 138

161 A NOVEL INTEGRATED PLANAR TRANSFORMER On the other hand, a badly intra-winding capacitance can be observed in prototype III due to the inter-leaving winding structure. This brings the top-up transformer the disadvantage of electromagnetic interference issue if the required operating frequency is high. A Faraday shield can be utilized to reduce the intra-winding capacitance for the top-up prototype, but this brings an extra loss to the transformer. Table 5.5. The Measurement Results at 40 khz Lp (μh) Rp (kω) Ls (μh) Rs (Ω) Cp (pf) Requirement 175 N/A 33 N/A N/A Prototype I Prototype II Prototype III The waveform test results at 90 khz for prototype I, II and III are shown in Figure 5.36 (1: input voltage; 2: output voltage). The input and output waveform are almost identical in three prototype transformers, except from peak of the ringing effect which can be observed from the rising and falling edge of the waveform. The ringing effect is caused by the counteraction of the L s and the intra-winding capacitance of the transformer (the ringing effect has been discussed in Chapter 5.2 ). Thus, prototype III has the most serious ringing effect among three prototype transformers due to the additional top-up windings. (a) Prototype I (b) Prototype II (c) Prototype III Figure The square wave test at 90 khz 3-D FEM AC resistance simulation results are in a good agreement with measurements. At 1 khz, the simulated R s are Ω, Ω and Ω for prototype I, II and III respectively. Compared to the measurements, a small variation of 0.1~0.2 Ω is observed due to the manufacture tolerance and the termination effect (also the short circuit conductor phenomenon discussed earlier). The full-load efficiency ccomparison of three prototypes based on measurement results is shown in Figure The efficiency measurement was conducted by having a constant 139

162 A NOVEL INTEGRATED PLANAR TRANSFORMER voltage of 216 V applied across the testing frequencies, and measured the input and output power difference. The efficiency curve climbs gradually under light-load condition as the required magnetizing current reduces with frequencies. Also, Prototype I has the best efficiency performance within the operating frequency range due to the sufficient selection of the winding specification. Prototype III performs poorly at low frequency ranges because of the extra magnetic losses caused from the top-up core (add-on inductor). On the other hand, prototype II was designed with a larger core and winding conductors than prototype I; however, the result shows that the efficiency of prototype I is still better than prototype II. Therefore, some conclusions can be made based on the above measurements and simulations. Firstly, the flux density decreases with the utilization of a larger core, but it does not decrease the core loss. Secondly, with a proper selection of conductor size, the winding losses can be minimized. Thirdly, the greater conductor size is very helpful with heat dissertation. Therefore, prototype II has a lower working temperature compared to prototype I while having a higher winding resistance. Lastly, the introduced MIO structure outperforms the top-up structure in the efficiency performance. The proposed MIO structure is proven for its advantages on the inductance controllability, size reduction and higher efficiency η 97.5 (%) 97.0 Prototype I Prototype II Prototype III Frequency (khz) Figure Efficiency comparison at full-load condition 140

163 CONCLUSIONS AND FUTURE WORKS 6 Conclusions and Future works 6.1 Dissertation Conclusions The research for this dissertation involved developing two different structures of HF transformers, which are able to cope with varying power requirements (from a few hundred watts to 20 kw). The first structure is a coaxial transformer. It is suitable for a power rating greater than 2 kw, and it can be easily scaled due to its highly symmetrical structure. The second structure is a planar transformer with magnetic integration. It is suitable for use in LLC type resonant circuitry. The planar structure is very compact and highly efficient for power applications requiring less than 2 kw. The developed transformers can be utilized in energy storage systems, such as EV and renewable energy technologies or switching power supplies. In addition, in order to achieve high power densities and high power efficiency, the operating frequency was increased to between 100 khz to 300 khz with the use of Ferrite magnetic material. The planar transformer prototype example discussed in this dissertation has an operating frequency of 40 khz to 60 khz based on the requirements of the resonant circuit. The operating frequency can be increased to further reduce the transformer volume. One problem raised with the increased operating frequency is the HF noise, in which the unwanted HF signal is propagating from the input side of the transformer to the output end. Therefore, a Faraday shield was inserted for the prototype HFCTs to reduce this common-mode HF noise issue. The insertion of the Faraday shield proved effective in reducing the HF noise issue, and both experimental and simulated results have been presented in this dissertation. The C ps reduces from 48.9 pf to 9.49 pf, which results in an 80.6% reduction in intra-winding capacitance. More importantly, a novel planar structure magnetic integration transformer (with two 141

164 CONCLUSIONS AND FUTURE WORKS built prototypes) was developed for this dissertation. This is the smallest magnetic integration structure on the market since there are no protruding magnetic pieces. The introduced structure has been analysed and compared with the commercial top-up structure and MIO structure. The magnetic and electric performance has been verified through experiments and simulations. The structure s power efficiency is higher than that in commercial structures while the magnetic performance is maintained. In addition, the investigation of nine types of different winding configurations was conducted in regard to the AC winding resistance and leakage inductance. The optimized winding configuration for the introduced integrated magnetic transformer was found and utilized for the prototype transformers. For HF transformer designs, the behaviour of the magnetic and electric components is very dependent on operating frequencies. Since the transformer needs to be operated under the AC source, due to its inherent characteristics, the AC effects become the main concern prior to the fabrication process. Generally, AC effects include skin effect, proximity effect and eddy current effect. In this dissertation, these effects have been thoroughly investigated and analysed by using the introduced transformers as examples. In order to solve design problems more efficiently, the FEM technique was employed in conjunction with theoretical calculations for the transformer analysis. Both 2-D and 3-D FEM simulation works were conducted and the results are highly accurate. In general, 2-D simulation with optimization procedures should be used in the first stage of the design process, while 3-D simulation is used if the final specifications are confirmed. 3-D simulation is more accurate compared to 2-D simulation, especially with complex model structures. However, the computation power required for 3-D simulation is enormous. Therefore, simplification and sectorization techniques were introduced to tackle the disadvantage of the 3-D simulation. Both techniques are very effective in reducing the required simulation time while producing highly accurate results. Furthermore, visualization of the results was an extra benefit with the use of the FEM technique. In comparison with traditional analysis that verifies results with a lot of numbers, it can now be done by observation. 6.2 Future Work A. Thermal Analysis The 3-D coupled analysis has been conducted in this research, which 142

165 CONCLUSIONS AND FUTURE WORKS includes both the electric field and magnetic field. Thermal analysis should be undertaken to improve the transformer evaluation process. Since the eddy current analysis was conducted in a 3-D simulation, the result can be used as the input data for the thermal solver and solve temperature related problems. B. Magnetic Integration of the HFCT The HFCT is designed for high power applications, thus, the switching losses are relatively small and insignificant to the overall power rating at a high power level. However, these losses should not be ignored since they are still part of the energy consumption and become obvious if the operating frequency increases. The converter with the utilization of HFCT has the ability to operate at a broader voltage range and maintain high power efficiency. This occurs via magnetic integrations of the HFCT and the use of LLC topology. C. Simulation of Transformer Core Resistance In this dissertation, some simulation work regarding the core resistance of the transformer was presented. However, the level of accuracy still needs to be improved. More prototype transformers should be fabricated with different core sizes and materials; thus, more benchmarks can be obtained to increase the accuracy of simulations. In addition, an improved transformer equivalent circuit is required to depict the magnetic core characteristic more accurately based on the results of the current simulation work. D. Integrated Capacitor Layer Due to time constraints and the focus on the magnetic components design, the fabricated LLC transformer has not yet included capacitor layer integration. This will be done shortly in the next phase of the research project; thus, the completed resonant tank can be condensed into one piece. The efficiency of the converters with the utilization of the all-in-one transformer will definitely be higher than those with stand-alone transformers (resonant inductor, resonant capacitor and transformer are not integrated), and the volume will also be lower overall. Consequently, the manufacturing costs will be reduced because fewer materials are required for fabrications. The difficulty of capacitor integration is that the capacitor layer becomes a copper shielding within the magnetic field. However, this problem can be overcome by the simulation and design technique presented in this dissertation. 143

166 CONCLUSIONS AND FUTURE WORKS 144

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175 APPENDIX Appendix A. 8 kw HFCT Measurements Table. A.1 The comparison testing result of 8 kw HFCTs W/S: with the Faraday shield, W/O: without the Faraday shield, Ground: Faraday shield connects to the ground, and Floated: Faraday shield is floated (a) (μh) (b) (kω) W/S W/O W/S W/O f (khz) Ground Floated f (khz) Ground Floated (c) (μh) (d) (Ω) W/S W/O W/S W/O f (khz) Ground Floated f (khz) Ground Floated (e) (ph) (f) (kω) W/S W/O W/S W/O f (khz) Ground Floated f (khz) Ground Floated N/A

176 APPENDIX B. Investigation of Winding Configurations Table. B.1 The comparison results without the magnetic insertion between different winding configurations Structure Enclosed Peak J (A/m2) Reversed Peak J (A/m2) Stored Energy (J/m) 1 Core 4.77E E E-04 Air 2.64E E E-04 2 Core 3.45E E E-05 Air 3.18E E E-05 3 Core 1.45E E E-05 Air 1.44E E E-05 4 Core 2.32E E E-05 Air 1.84E E E-05 5 Core 1.15E E E-05 Air 1.09E E E-05 6 Core 1.20E E E-05 Air 1.18E E E-05 7 Core 1.06E E E-05 Air 1.01E E E-05 8 Core 1.30E E E-05 Air 1.30E E E-05 9 Core 1.35E E E-05 Air 1.33E E E-05 Table. B.2 The comparison results with the magnetic insertion between different winding configurations Structure Enclosed Peak J (A/m2) Reversed peak J (A/m2) Stored Energy(J/m) 1 Core 8.71E E E-03 Air 3.41E E E-04 2 Core 4.25E E E-04 Air 3.82E E E-04 3 Core 1.56E E E-05 Air 1.55E E E-05 4 Core 2.32E E E-05 Air 1.84E E E-05 5 Core 1.22E E E

177 APPENDIX Air 1.15E E E-05 6 Core 1.20E E E-05 Air 1.18E E E-05 C. The 1.08 kw top-up transformer The top-up transformer is composed with three EE cores (FEE 43/16/29) [48], while two cores utilized as transformer core and the top-up core utilized as the add-on inductor; the structure and the specification of the 1.08 kw top-up prototype is shown in Figure. C.1. The fascinating characteristic of this structure is the sharing magnetic path between the transformer core and the inductor core; thus, the size of the magnetic component is redued. The adjustment of the and the is controlled by the air-gap distance in the centre leg of the magnetic cores. The primary winding is composed with 2 bundles of 7-strands Litz wires, whereas the secondary is composed by copper sheets. Also, primary windings and secondary windings are interleaving from each other to minimize the L s. Primary@18 Turns Use two 7-strands Litz wire with 3 layers insulation. Each single wire has a diameter of 0.3 mm and distance between Litz wires is 0.4 mm Φ0.3 mmx14 strands X18 turns (Litz wire) Secondary@2 Turns x2 Copper square wire with an area of 0.25 x 8.8 mm 2 ; the spacing between each conductor and the core window is 0.08 mm. 2X 0.25 mmx8.8 mmx3 Turns (Copper plates) Top-up@3 Turns Use three 7-strands Litz wire with 3 layers insulation. Each single wire has a diameter of 0.3 mm and distance between Litz wires is 0.4 mm Φ0.3 mmx21 strands X4 turns (Litz wire) 155

178 APPENDIX (a) The explorer view (b) Half-cross section (unit: mm) Figure. C.1 The structure and specification of the 1.08 kw top-up transformer prototypes There are two ways to wound the top-up windings of the top-up transformer which the top-up winding winds in the same direction to the transformer (Figure. C.2 (a)) or in the reversed direction (Figure. C.2 (b)). Transformer designers should avoid having the top-up windings and transformer windings in reversed winding direction due to the saturation of the sharing core (the total flux is accumulated with the transformer flux and the top-up flux). The winding configuration in (b) brings the benefit of lower on the primary winding, but the increase of the core loss makes it unworthy. Other than that, number of top-up turns needs be carefully selected by taking account with the. The winding turns of the top-up inductor should be designed at least number if possible. Due to the inherent characteristic of the LLC transformer that the L p is small, the top-up cores get saturated more easily (especially for buck converters). (a) Same winding direction (b) different winding direction Figure. C.2 The flux illustration of the top-up transformer under open-circuit condition 156

179 APPENDIX (a) No inductor (b) Inductor integrated Figure. C.3 The square wave test of prototype III at 50 khz; with and without the top-up inductor (a) No inductor (b) Inductor integrated Figure. C.4 The square wave test of prototype III at 50 khz; with and without the top-up inductor Furthermore, the measurement result of the top-up prototype transformer is shown in Table. C.1. Compared with the introduced prototype structure, the top-up transformer has better performance for winding resistance in HF. Table. C.1 The measurements of 1.08 kw top-up prototype transformer Topup prototype FEE 43/19/28 - System f (khz) f (khz) Prototype III L s (uh) Prototype III Rs (Ohm) Prototype III Lp (uh) Prototype III Rc (kohm) Topup prototype FEE 43/19/28 -Top-up Only f (khz) f (khz) Prototype III L s (uh) Prototype III Rs (Ohm) Prototype III Lp (uh) Prototype III Rc (kohm) Topup prototype FEE 43/19/28 - Transformer Only f (khz) f (khz) Prototype III L s (uh) Prototype III Rs (Ohm) Prototype III Lp (uh) Prototype III Rc (kohm)