Design And Analysis Of Wireless Power Transfer Using High Frequency Resonant Inductive Coupling By Changing The Coil Geometry A Study On Improving Wireless Power Coil Magnetics Master of Science Thesis Adarsh Bandi Nagendra Gouthamas Chalmers University Of Technology Gothenburg, Sweden 2024 Master Of Science Thesis 2024 Design And Analysis Of Wireless Power Transfer Using High Frequency Resonant Inductive Coupling By Changing The Coil Geometry A Study On Improving Wireless Power Coil Magnetics Adarsh Bandi Nagendra Gouthamas Department of Electrical Engineering Division of Electric Power Engineering Chalmers University of Technology Gothenburg, Sweden 2024 Design And Analysis Of Wireless Power Transfer Using High Frequency Resonant Inductive Coupling By Changing The Coil Geometry A Study On Improving Wireless Power Coil Magnetics Adarsh Bandi Nagendra Gouthamas © Adarsh Bandi, 2024. © Nagendra Gouthamas, 2024. Supervisor: Prof.Torbjörn Thiringer and Res.Fredrik Larsson Examiner: Prof.Torbjörn Thiringer, Chalmers University of Technology Master Of Science Thesis 2024 Department of Electrical Engineering Division of Electric Power Engineering Chalmers University of Technology SE-412 96 Gothenburg Sweden Assisted by Power Board Design Department Division of Power Solutions Ericsson AB SE-417 56 Gothenburg Sweden Typeset in LATEX, template by Kyriaki Antoniadou-Plytaria iv Design And Analysis Of Wireless Power Transfer Using High Frequency Reso- nant Inductive Coupling By Changing The Coil Geometry A Study On Improving Wireless Power Coil Magnetics Adarsh Bandi Nagendra Gouthamas Division of Electric Power Engineering Chalmers University of Technology SE-412 96 Gothenburg Sweden Abstract In this thesis, we have developed a wireless power transfer system for a space of dimensions (15cm x 15cm x 15cm), utilizing a series-connected transmitter (Tx) coil to generate an equally distributed electromagnetic field inside the space. This field can be picked up by a solenoid receiver (Rx) coil placed anywhere within the space to power a DC load. To develop the proposed system, we have studied a conventional wireless power transfer system from Wurth Electronics and investi- gated various coil geometries for both Tx and Rx. The conventional wireless power system has been examined regarding the influ- ence of coil geometry, alignment between the transmitter (Tx) and receiver (Rx), as well as the coil parameters on efficiency. The wireless power system from Wurth Electronics is tested with different Rx coil geometries to evaluate inter- operability between various Tx and Rx coil geometries, as well as to compare the coupling coefficient and magnetic field density of different Rx coil geome- tries with misalignment in order to evaluate most suitable Rx coil geometry for the proposed wireless power system. The different Rx coil geometries investi- gated are: concentric, solenoid, and center-tapped circular coil. The comparison is based on different alignment conditions between the transmitter and receiver coils. We find, from the results obtained by investigating different Rx coil geome- tries with the conventional system, that the solenoid coil geometry with a core provides a stable coupling coefficient under various misalignment conditions. Thus, the solenoid Rx geometry can be optimized to enhance coupling between the transmitter and receiver coils. Additionally, test results show that the use of center-tapped circular coils in wireless power power system helps in improving range from 30mm to 180mm compared to conventional wireless power system with concentric coils. However, the improved range is only achievable with sig- nificantly higher number of coil turns compared to concentric coils which reduces efficiency. Also, a unique BJT based automatically switching transmitter circuit is required for the center-tapped circular coils which makes it a non-viable solution due to inefficiency of the BJTs. Further a suitable transmitter coil geometry is investigated for use in combination v with the solenoid receiver to demonstrate the proposed wireless power system within a space of dimensions (15 cm x 15 cm x 15 cm). Three different transmitter coils are investigated: the concentric coil, 2-series connected concentric coil, and 8-series connected concentric coil. A half-bridge transmitter circuit is designed to drive the various transmitter coils. The experimental and simulation results indi- cate that the concentric transmitter coil with a large diameter enhances high power transfer and better range due to a more effective distribution of the magnetic field. However, when using a solenoid receiver coil, the power transfer efficiency drops by 28% compared to the efficiency of 75% under aligned operation. Conse- quently, the concentric transmitter coil is designed with the coil turns distributed into smaller areas, forming a 2-series connected coil. Test results reveal that it was possible to transfer 10W of power at an efficiency of 75% when the coils were perfectly aligned. In contrast, when the coils were misaligned, power transfer efficiency of up to 48% was achieved. This is in contrast to the power transfer efficiency of 6% under misaligned conditions in the conventional wireless power system. The 2-series connected concentric Tx coil is then extended to an 8-series con- nected concentric Tx coil to form a space of dimensions (15 cm x 15 cm x 15 cm) in combination with a solenoid Rx coil. Simulation results indicate that the coupling coefficient between Tx & Rx improved by approximately 11% and mea- surement results show that power transfer efficiency improved by 4% compared to the 2-series connected concentric Tx coil. Similarly, when the solenoid Rx coil was rotated or misaligned with the Tx coil, the efficiency improved by approxi- mately 33% compared to the 2-series connected concentric Tx coil. The increase in efficiency and coupling with Tx and Rx is mainly due to distribution of coil turns into smaller areas and then connecting them in series which improved the magnetic field distribution compared to other coil geometries. Hence, the 8-series connected concentric coil as Tx and solenoid as Rx are selected as the suitable Tx and Rx coils, respectively, for the proposed wireless power system. In comparison to the conventional wireless power system, the efficiency remains approximately the same at 80% when the coils were perfectly aligned and efficiency improved by more than 60% when the coils were misaligned. Keywords: Wireless power transfer, coil geometry, coil parameter, alignment, coupling coefficient, series connected concentric coil. vi Acknowledgements We extend our heartfelt gratitude to our supervisor and examiner, Prof. Torbjörn Thiringer, for your support, guidance, and expertise. This project was conducted at Chalmers and in Ericsson facilities under the supervision of researcher Fredrik Larsson. We sincerely thank Fredrik for the tremendous support and trust ex- tended throughout the project, as well as for the invaluable opportunity to work at Ericsson Labs. We are equally grateful to our colleagues at Ericsson for their continuous help and support. Our appreciation extends to Wurth Electronics and Infineon for their support in providing coil samples and a half-bridge evaluation board. The simulations un- dertaken would not have been possible without the support of Ansys. We also take this moment to express our gratitude to all who contributed to this project and enriched our learning experience during this time. Finally, we extend our heartfelt thanks to our family and friends for their unwavering interest in our work and their continuous, unconditional love and support. Adarsh Bandi Nagendra Gouthamas Gothenburg, Sweden 2024. viii x List of Acronyms Below is the list of acronyms that have been used throughout this thesis: WPT Wireless power transfer WE Wurth electronik Tx Transmitter Rx Receiver EMF Electromotive force MOSFET Metal oxide semiconductor field effect transistor BJT Bi-polar juntion transistor SS Series-series SP Series-parallel PS Parallel-series PP Parallel-parallel NFT Near field technology FFT Far field technology VMA Vertical misalignment LMA Lateral misalignment AMA Angular misalignment DC Direct current AC Alternating current FEM Finite element method LED Light emitting diode fr Resonant frequency BW Bandwidth PWM Pulse width modulation GaN Gallium Nitride IC Integrated circuit mm millimetre cm Centimetre 3D Three dimension NA Not applicable SWG Standard wire gauge PCB Printed circuit board VR Vertical Rotation HR Horizontal Rotation xi Contents List of Acronyms x 1 Introduction 1 1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 Theory 3 2.1 Wireless power transfer . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1.1 Maxwell’s equations . . . . . . . . . . . . . . . . . . . . . . . 4 2.1.2 Magnetic flux density and induced voltage . . . . . . . . . . 4 2.1.3 Types of wireless power transfer systems . . . . . . . . . . . 7 2.1.3.1 Near field technology(NFT) . . . . . . . . . . . . . 8 2.1.3.2 Far field technology(FFT) . . . . . . . . . . . . . . . 8 2.1.4 Resonant inductive coupling . . . . . . . . . . . . . . . . . . 9 2.2 Resonant circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2.1 Parallel resonant circuit . . . . . . . . . . . . . . . . . . . . . 10 2.2.1.1 Frequency response of parallel resonant circuit . . 12 2.2.1.2 Q-factor and bandwidth . . . . . . . . . . . . . . . 13 2.3 Analytical model of WPT . . . . . . . . . . . . . . . . . . . . . . . . 15 2.4 Compensation of leakage inductance . . . . . . . . . . . . . . . . . . 17 2.4.1 Compensation topologies . . . . . . . . . . . . . . . . . . . . 17 2.4.1.1 Series-series compensation topology . . . . . . . . 18 2.4.1.2 Analytical model of PP compensation topology . . 19 2.5 Coil geometries for wireless power technology . . . . . . . . . . . . 21 2.5.1 Circular coils . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.5.1.1 Inductance of a circular coil . . . . . . . . . . . . . 23 2.5.2 Concentric coils . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.5.2.1 Inductance of a concentric coil . . . . . . . . . . . . 25 2.5.3 Solenoid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.5.3.1 Inductance of a solenoid . . . . . . . . . . . . . . . 28 2.6 Material selection for coils . . . . . . . . . . . . . . . . . . . . . . . . 30 2.6.1 Litz wire . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.6.2 Magnetic wire . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.6.3 Hallow copper tube . . . . . . . . . . . . . . . . . . . . . . . 34 2.7 Current challenges in wireless power system . . . . . . . . . . . . . 34 2.7.1 Alignment between transmitter and receiver coils . . . . . . 35 xiii Contents 2.7.1.1 Vertical misalignment . . . . . . . . . . . . . . . . . 36 2.7.1.2 Lateral misalignment . . . . . . . . . . . . . . . . . 38 2.7.1.3 Angular misalignment . . . . . . . . . . . . . . . . 38 3 Case Setup 41 3.1 Investigation of suitable receiver coil geometry . . . . . . . . . . . . 41 3.1.1 Measurement of suitable receiver coil geometry . . . . . . . 41 3.1.2 WE Development kit . . . . . . . . . . . . . . . . . . . . . . . 43 3.1.2.1 Test case . . . . . . . . . . . . . . . . . . . . . . . . . 44 3.1.3 Automatically switching transmitter circuit . . . . . . . . . . 45 3.1.3.1 Test case . . . . . . . . . . . . . . . . . . . . . . . . . 49 3.1.3.2 Point to multi-point power transfer . . . . . . . . . 50 3.2 Proposed wireless power system . . . . . . . . . . . . . . . . . . . . 51 3.2.1 Investigation of suitable transmitter coil geometry . . . . . . 51 3.2.2 800kHz Half bridge converter . . . . . . . . . . . . . . . . . . 54 3.2.2.1 Concentric coils . . . . . . . . . . . . . . . . . . . . 57 3.2.2.2 2 Series-connected concentric coils . . . . . . . . . 59 3.2.3 1MHz half-bridge converter . . . . . . . . . . . . . . . . . . . 60 3.2.3.1 8 Series-connected concentric coils . . . . . . . . . 63 4 Simulation Setup 65 4.1 Modelling of different coil geometries in Ansys . . . . . . . . . . . . 65 4.2 Modelling of point to multi-point power transfer using circular coils in Ansys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 4.3 Modelling of proposed wireless power system in Ansys . . . . . . . 68 4.3.1 Custom built concentric coils . . . . . . . . . . . . . . . . . . 69 4.3.2 Series connected concentric coils . . . . . . . . . . . . . . . . 69 5 Analysis 71 5.1 Investigation of suitable receiver coil geometry . . . . . . . . . . . . 71 5.1.1 Solenoid Rx coil . . . . . . . . . . . . . . . . . . . . . . . . . . 72 5.1.2 Circular Rx coil . . . . . . . . . . . . . . . . . . . . . . . . . . 74 5.1.3 Comparison of Rx coil geometries . . . . . . . . . . . . . . . 76 5.2 Proposed wireless power system . . . . . . . . . . . . . . . . . . . . 79 5.2.1 Concentric coils . . . . . . . . . . . . . . . . . . . . . . . . . . 79 5.2.2 Series connected coils . . . . . . . . . . . . . . . . . . . . . . 81 5.3 Comparison & results . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 5.3.1 Power transfer . . . . . . . . . . . . . . . . . . . . . . . . . . 87 5.3.2 Point to multi-point power transfer . . . . . . . . . . . . . . 89 6 Conclusion 91 6.1 Investigation of suitable Tx and Rx coil . . . . . . . . . . . . . . . . 91 6.2 Proposed wireless power system . . . . . . . . . . . . . . . . . . . . 92 7 Future Scope 95 8 Environmental & Ethical Aspects 97 xiv Contents Bibliography 99 A Appendix 1 I A.1 Conventional Wireless Power System . . . . . . . . . . . . . . . . . I xv Contents xvi 1 Introduction 1.1 Background The Wireless power transfer(WPT) is the transfer of electrical energy from a power source to a distant electrical load without using discrete conductors. The wire- less power system was first demonstrated in the 1890’s by Nikola Tesla who laid down the basic principles for the wireless power technology[1]. Tesla’s idea of wireless power transfer using high frequency magnetic coupling at resonance was groundbreaking and was ahead of his time. However, due to fewer applications of the wireless power technology and an underdeveloped power electronics sec- tor became a restriction and set limitations in implementing the wireless power technology[3]. The wireless power system is the transfer of electrical energy based on the funda- mentals of time-varying electric, magnetic, or electromagnetic fields. Today the wireless power technology can be classified into two major categories; near field wireless power technology and far field wireless power technology. The wireless power technology based on the resonant inductive coupling is the most popular and has been used for mid and high power applications across different indus- tries. The resonant inductive coupling outperforms the other WPT techniques in terms of power transfer efficiency and capability, ease of control, and safety. Therefore, the WPT finds its application in electric vehicle charging solutions and changing of portable electronics. The conventional wireless power technologies based on the resonant inductive coupling for charging the portable electronic devices and the electric vehicles use identical coil geometries on the transmitter and the receiver side. In such wireless power systems, it is required to align the receiver coil with the transmitter coil perfectly in order to achieve better power transfer efficiency and capability. The low degree of freedom on the receiver side is inconvenient and does not make the system true wireless since the receiver is bound to be placed at a certain location in the vicinity of the transmitter. The other major challenges in the wireless power are the efficiency and range. The efficiency drop in wireless power is due to a number of reasons, like range, flux leakage, losses in the power converter, and coupling. The main challenge in achieving a greater range between the transmit- ter and the receiver is due to the limited ability of the transmitter to distribute its magnetic fields over a long distance. 1 1. Introduction A method to improve the coupling between the transmitter and the receiver coil is to utilize multiple coils on the transmitter to generate equally distributed electromagnetic field which will enable power delivery to the receiver contained anywhere in the vicinity of the transmitter. The equally distributed magnetic field will improve the coupling between the transmitter and the receiver in all alignment conditions and thereby improving the overall efficiency of the wireless power system. In this thesis, the main objective of the thesis is to implement the wireless power transfer in a room of dimension (3m X 3m X 2.5m), however the idea is demon- strated in a test space of (15cm X 15cm X 15cm) which can be extended to a bigger test space. We study a conventional wireless power system from Wurth Elec- tronics to understand the working and challenges in the wireless power system. The conventional wireless power system is then utilized to investigate suitable Rx coil geometry. Further, a half-bridge Tx converter is designed to investigate suitable Tx coil geometry. All the different coil geometries investigated are tested under aligned and misaligned condition. From the investigation of different coil geometries for Tx and Rx, a suitable Tx coil and a receiver coil are selected to demonstrate the equal distribution of electromagnetic field in an enclosed space which will enable better coupling with the receiver and improve the efficiency of power transfer. 1.2 Objective The objective of the thesis is to determine the feasibility of using a wireless power system to supply power to a DC electrical load in a space with dimensions of (15cm x 15cm x 15cm) by generating an electromagnetic field in the space. In or- der to achieve this objective, different coil geometries will be tested to investigate suitable transmitter and receiver coil geometries. Power transfer of up to 10W will be demonstrated in the given space. A half-bridge transmitter circuit will be developed to reduce losses in the power electronics that will drive the transmitter coils to generate an electromagnetic field in the given space. Additionally, the thesis will focus on improving the coupling factor between the transmitter and the receiver coil and the efficiency of power transfer. In summary, the thesis will address the following research questions: • What is the best coil geometry for the transmitter and receiver to construct the proposed wireless power transfer setup? • Is the center-tapped circular coil geometry suitable for wireless power trans- fer? • Is it beneficial to distribute Tx coil turns into smaller areas to improve cou- pling with Rx? 2 2 Theory 2.1 Wireless power transfer Wireless power transfer (WPT) is the transfer of electrical power from a power source to a load without wires and is based on technologies using time-varying electric, magnetic, or electromagnetic fields. The wireless power transfer works based on the principle of electromagnetic induction. Faraday’s laws of electro- magnetic induction explains the relationship between the electric field and the magnetic field. This law is the basic working principle of most of the electrical motors, generators, transformers, inductors, etc. Faraday’s law of electromagnetic induction states that, "Whenever a conductor is placed in a varying magnetic field, an electromotive force is induced". The induced voltage(EMF) is proportional to the rate of change of magnetic flux with the time and can be expressed as ε = −N ∆ϕ ∆t (2.1) where ε is the induced voltage, N is the number of turns, ∆ϕ is the change in magnetic flux, and ∆t is the change in time. Faraday’s first law: Whenever a conductor is placed in a varying magnetic field an EMF gets induced across the conductor (called as induced emf), and if the conductor is a closed circuit then induced current flows through it. Faraday’s second law: Faraday’s second law of electromagnetic induction states that, "the magnitude of induced emf is equal to the rate of change of flux linkages with the coil". The flux linkages is the product of number of turns and the flux associated with the coil. The minus sign in Faraday’s law of induction is very important. The minus means that the emf creates a current (I) and magnetic field (B) that oppose the change in flux (∆ϕ) which is known as Lenz’s law. Lenz’s law states that, "an induced electric current flows in a direction such that the current opposes the change that induced it". Thus, Faraday’s law of electromagnetic induction and Ampere’s circuit law is used to mathematically describe power transfer using resonant in- ductive coupling. 3 2. Theory 2.1.1 Maxwell’s equations The time varying magnetic field in the inductive power transfer plays an impor- tant role. In time varying fields, the electric field(E) and the magnetic field(H) are closely related and mutually coupled. The electric field and magnetic field together form an electromagnetic wave. Maxwell’s equations provide a uni- fied mathematical relationship between the electrical and the magnetic fields. Maxwell’s equations in integral form can be expressed as[1], ∂ v D.da = Qv (2.2) ∂ v B.da = 0 (2.3)∮ ∂A E.ds = − " A ∂B ∂t .da (2.4)∮ ∂A H.ds = " A (J + ∂D ∂t ).da (2.5) where, E is electrical field intensity vector in (V/m), D is electrical flux density vector in (As/m2), H is magnetic field intensity vector in (A/m), B is magnetic flux density vector in (Wb/m2), and J is current density in (A/m2). Maxwell’s equation expressed in (2.2) is also called as Gauss’s law which describes that the electrical flux density(D) in an enclosed area(da) will have the same total charge(Qv) which is withing the enclosed area. Gauss’s law for magnetism is ex- pressed in (2.3) and it describes that the enclosed area(da) has the same amount of magnetic flux lines(B) coming in and going out forming a closed loop and hence no magnetic charge is built up at any point in space. In general, the net magnetic flux out of any closed surface is zero. Faraday’s law of magnetic induction is expressed in (2.4) and describes that the time changing magnetic field(B) generates an electrical field(E) or it can be de- scribed as the line integral of the electric field around a closed loop is equal to the negative of the rate of change of the magnetic flux through the area enclosed by the loop. Eq(2.5) is also called Ampere’s law which describes that the magnetic field intensity(H) integrated along a closed area is equal to the current flowing through the surface enclosed by the area. 2.1.2 Magnetic flux density and induced voltage The electric field is produced by the static charges while the magnetic field is produced by the moving electric charges. The generation of the magnetic field around a current carrying conductor can be explained by Ampere’s law. The direction of the magnetic field around a conductor can be identified using the 4 2. Theory right hand rule. If the thumb is pointed towards the direction of the current then the fingers curl in the direction of the magnetic field. The magnetic field produced by a current carrying circular coil is shown in figure 2.1. Figure 2.1: Magnetic flux generated by a current carrying circular coil The magnetic field produced by the current carrying conductor can be described using Biot-Savart law. The magnetic field at any point in space produced by a current carrying conductor can be calculated using Biot-Savart equation, B = − µ 4Π ∮ l Idlr̂ r2 (2.6) where I is the current flowing in the circuilar coil, dl is current element, r is referred to the displacement vector from the current element to a point where the magnetic field is calculated, r̂ is the unit vector of r, µ is the permeability, and a is the radius of the circular coil. Biot-Savart law states that a segement of the current carrying conductor produces a magnetic field and this segment is called the current element which is a vector quantity. From (2.6) it is also evident that the magnetic field(db) is proportional to the current flowing in the coil segment(dl). Biot-Savart equation can also be used to calculate the magnetic field at any point p on the axis of the circular coil of radius a and current I at a distance of x as shown in figure 2.1 which can be expressed as B = 2ΠµNIa2 4Π(x2 + a2) 3 2 (2.7) where N is the number of turns, I is the current in each turn, and x is the distance 5 2. Theory from the center of the coil to the point p where the magnetic field B is calculated. The magnetic flux density at the center of the coil can be expressed using (2.7) by substituting x=0 and we get, B = µ0NI 2a (2.8) In conclusion, the relationship between the magnetic field db generated by the current element dl with current I can be expressed as dB ∝ Idl sinθ r2 (2.9) where θ is the angle between the displacement vector r and direction of current in the current element dl. Faraday’s law of electromagnetic induction states that the changing magnetic field produces an electric field E. Consider another circular coil is introduced in figure 2.1 as shown in figure 2.2. Figure 2.2: Magnetic flux between two circular coils In figure 2.2, current I1 flows in the Tx coil and generates a magnetic flux. Ac- cording to the law of electromagnetic induction, the generated flux linking with the Rx coil induces voltage in it. The Tx and the Rx coil are separated by an air gap and hence only a part of the magnetic flux generated by the Tx links with the Rx coil which is referred to as Φm. The total magnetic flux linked with the Rx coil can be expressed as Φm = ∫ a Bda (2.10) 6 2. Theory where B is the total magnetic flux density generated by the Tx coil and a is the total surface area of the Rx coil. The induced voltage in the Rx coil can be expressed as E(t) = − dΦm dt (2.11) If the Rx coil consists of N turns and Φm is the flux through one turn, an emf is produced in all the turns and can be expressed as E(t) = −N dΦm dt (2.12) In conclusion, the induced voltage depends on the following factors: • Increasing the number of turns on the receiver coil induces higher voltage as the area of the conductor linking with the flux lines increases[6]. • Increasing the strength of the magnetic field generated by the Tx coil induces more voltage in the Rx coil. • Increasing the radius of the coil induces higher voltage because area is directly proportional to the induced voltage[6]. • The induced voltage can be improved by using stranded wires for operation at high frequency to reduce AC resistance thereby reducing the voltage drop in the coil. 2.1.3 Types of wireless power transfer systems There are different technologies for transmitting the electrical energy by means of electro-magnetic waves. The wireless power system can be divided based on the electromagnetic principle used as shown in figure 2.3. Figure 2.3: Different types of wireless power systems 7 2. Theory The wireless power technology is mainly classified based on the distance of power transmission, maximum power, and method used to achieve the wireless power transfer. The first classification is based on how far the electrical power can be transferred from the source to the load without any physical contact. There are methods capable of transferring power to loads at large distance away from the source while the other methods could only transfer power to the load at a distance of few centimeters from the source. Hence, the first division is based on whether the power transfer is of near field or far field. 2.1.3.1 Near field technology(NFT) The near field power transfer is a non-radiative power transfer technology where the phenomenon used is the electromagnetic induction. The near field technology is subdivided as • Electromagnetic induction • Electromagnetic resonance • Electrostatic induction In electromagnetic induction, the power transfer takes place through mutual cou- pling with the coils tightly coupled. The WPT with the electromagnetic induction works up to a distance of 1/6 of the wavelength of the transmission frequency[1]. The WPT using electromagnetic resonance has largely extended the potential of NFT. In this method, a capacitor is either connected in series or in parallel com- bination to the coils to form a resonant LC tank. The transmitter and the receiver are made to resonate at the same frequency, maximizing the power transfer to the load. The electrostatic induction is a method where the electric field acts as the energy carrier medium. The electrostatic induction is also called as capaci- tive coupling since the power is transferred between two electrodes that forms a capacitance[1]. 2.1.3.2 Far field technology(FFT) The far field power transfer is a radiative power transfer technology where the phenomenon used is the electromagnetic radiation and the power can be delivered to a load far away from the source. The electromagnetic radiation can be concen- trated to a focal point enabling wireless power transfer over longer distance. The two most popular methods of far field technology are • Micro wave power transmission • Laser power transmission The microwave power transfer involves conversion of electrical power into mi- crowaves and transfer of the microwaves using an antenna. The transferred microwaves are then converted into electrical power at the receiver. The wireless power technology using laser radiation is the transfer of photonic energy using a laser in a form either as heat or electricity. The method used in the WPT using laser radiation is same as the method used in the production of solar energy. 8 2. Theory 2.1.4 Resonant inductive coupling The basic building block of the wireless power system using the resonant induc- tive coupling is the resonant circuit. A simple resonant circuit with an AC source, transmitter coil, receiver coil, capacitor C1 and C2 connected in parallel to the Tx and the Rx coil respectively, and a load R is shown in figure 2.4. The resonant inductive coupling is the transfer of electrical energy between two coils that are tuned to resonant at the same frequency while the coils are coupled together by a magnetic field. In the resonant inductive coupling, the energy in the resonant circuit oscillates between electric energy stored in the capacitor and magnetic energy stored in the inductor. The transmitter and the receiver coil are connected with a capacitor either in series or in parallel combination to compen- sate for the inductive reactance of the transmitter coil and the receiver coil. The compensation of the inductive reactance in both the transmitter and the receiver circuit forms the basic operating principle for the WPT using the resonant induc- tive coupling and enables resonance in both the Tx and the Rx circuit. The coils in the resonant inductive coupling can be loosely coupled and can trans- fer power over a range of few times the coil diameters with high Q-factor of the coils to maintain good efficiency. The WPT using the resonant inductive cou- pling improves the efficiency of the power transfer drastically and improves the power transfer range when compared to the WPT using non-resonant inductive coupling. Figure 2.4: Wireless power system using resonant inductive coupling 2.2 Resonant circuits A simple resonating circuit consists of a resistor R, an inductor L and a capacitor C, connected either in series or in parallel to an AC source with variable frequency. The circuit is said to be at resonance when the frequecy of the power supply exactly matches the natural frequency of the circuit’s LC combination. The resonant circuits are used in the power supply circuits to obtain high frequency output voltage or current, low switching loss, and low switching noise. The resonant circuits can be mainly classified based on circuit topology as shown in figure 2.5. 9 2. Theory Figure 2.5: Types of resonant circuits In the series resonant circuit, the inductor and the capacitor are connected in se- ries with the AC source where the inductive and capacitive reactances are equal in magnitude (XL = XC) and cancel each other as they are 180◦ apart in phase. When the circuit is at resonance, it acts as a purely resistive circuit due to low or zero impedance of the circuit and the value of the impedance therefore becomes Z = R. The series resonant circuit is also called as an acceptor circuit because the current flowing in the circuit is at its highest possible point and is in phase with the applied voltage. Unlike series resonant circuit, the parallel resonant circuit offers maximum impedance at resonance and limits the circuit current. The par- allel resonant circuit is also called as the rejecter circuit because it suppresses the circuit current whose frequency is equal to the resonant value. The series and parallel resonant circuits with very low resistance will have sig- nificant affect on the impedance at resonance and the resonant condition can be easily calculated using the expression, fr = 1 2Π √ LC (2.13) However, when a significant value of resistance is added to an LC circuit, (2.13) becomes invalid. The resistor can be added in a number of combination to the se- ries or parallel resonant circuit. The series-parallel resonant circuit can be mainly classified as, • Series LC circuit with R in parallel • Parallel LC circuit with R in series The added resistance in the LC circuit lead to an anti-resonance condition. At anti-resonance, the affects of peak or low impedance occurs at frequencies other than the frequency that gives equal inductive and capacitive reactances. 2.2.1 Parallel resonant circuit In the parallel resonant circuit, the RLC components are connected in parallel to the AC source and parallel resonance occurs when the supply frequency pro- duces zero phase difference between the supply voltage and the current. Figure 2.6 shows the parallel resonant RLC circuit with a current source and figure 2.7 shows the phasor diagram for the parallel resonance. 10 2. Theory Figure 2.6: Parallel resonant circuit Figure 2.7: Phasor diagram The parallel resonant circuit is similar to the series resonant circuit as the reactive components in both the circuits are influenced by the supply frequency. However, the parallel resonant circuit is influenced by the current flowing in each branch of the parallel LC tank. At resonant frequency, the impedance of the parallel resonant circuit is maximised as the circuit acts like an open circuit with the total current being determined only by resistor R. Thus at resonance, the impedance of the parallel circuit is maximum and is equal to the resistance of the circuit. Keeping L and C constant, the amount of current flowing in the circuit can be controlled by varying the value of resistance R. The total impedance in the parallel resonant circuit can be expressed as Ztotal = R ||ZL ||ZC = R 1 − jR( 1 XC + 1 XL ) = R 1 + jR(ωC − 1 ωL ) (2.14) If the resonance occurs atωr and XL = XC then the imaginary part of Ztotal becomes zero and hence the resonant frequency can be expressed as ωrC = 1 ωrL ωr = 1 √ LC fr = 1 2Π √ LC (2.15) The parallel resonant circuit and series resonant circuit produces the same equa- tion for the resonant frequency as expressed in (2.15). Hence, it makes no differ- ence to the resonance if the inductor or the capacitor is connected in series or in parallel. 11 2. Theory 2.2.1.1 Frequency response of parallel resonant circuit The frequency response of the parallel resonant circuit with change in the impedance of the circuit is shown in figure 2.8. As the frequency of the applied voltage is increased beyond the resonant value fr of the circuit, the inductive reactance in- creases and the capacitive reactance decreases. As a result of this, the current in the inductive branch decreases and the current in the capacitive branch increases. Since the inductive and the capacitive reactance are not equal beyond the reso- nant value, the total current in the circuit increases and leads the voltage applied. Similarly, when the frequency of the applied voltage is less than the resonant value, the total impedance of the circuit decreases and the total current increases which is lagging the applied voltage. The parallel resonant circuit offers max- imum impedance at the resonant frequency, and offers less impedance to other frequencies. Hence, the impedance of the circuit at resonance is called dynamic impedance (Zd). The maximum dynamic impedance of the parallel resonant circuit is given by Zd = L RC (2.16) Figure 2.8: Plot of impedance vs frequency in parallel resonant circuit Figure 2.9 shows the circuit current as a function of frequency. The plot shows that if the frequency of the applied voltage is varied from the low value to the maximum value through the resonant frequency, the current magnitude decreases from its maximum value at low frequency to a minimum value at the resonant frequency. The total current is minimum when the circuit is at resonance as the total impedance of the circuit is at its maximum value (Z=R). The impedance reduces as the frequency is varied on either side of the resonant value. The parallel resonant circuit is also called as a rejecter circuit because it rejects or suppresses the current whose frequency is equal to the resonant value. 12 2. Theory Figure 2.9: Plot of current vs frequency in parallel resonant circuit 2.2.1.2 Q-factor and bandwidth The quality factor or Q-factor is a dimensionless quantity and is used to define how well the system can oscillate or gives a measure for the quality of a resonant circuit. A high Q-factor corresponds to the oscillations going further and a low Q-factor corresponds to the oscillations that attenuate faster. The Q-factor of the parallel resonant circuit with the resonant frequency fr can be expressed as Q = 2π Maximum energy stored Energy dissipated f or a period Q = 2Π 1 2CV2 1 2 V2 R T Q = 2Π frCR (2.17) At resonant condition, 2Π frC = 1 2Π frL Q = R 2Π frL (2.18) From (2.18) it can be implied that the circuit with a high Q-factor can store more energy compared to the energy dissipated. The reponse of the parallel resonant circuit is shown in figure 2.10. A high Q-factor is due to low resistance in series with the inductor which produces a high peak with a narrow response curve. While a low Q-factor is due to high resistance in series with inductor that produces a lower peak with a wide response curve. 13 2. Theory Figure 2.10: Response of parallel resonant circuit with change in Q-factor The impedance curve is used to define the bandwidth of the parallel resonant circuit. The bandwidth of the parallel resonant circuit is shown in figure 2.11. The bandwidth of the resonant circuit is measured between the half-power frequencies where the power dissipated in the circuit is half of the power dissipated at the resonant frequency. The upper and lower cutoff frequencies are denoted as fH and fL respectively. The 100% impedance point is when Z=R where the power dissipated is I2R and at 0.707*Z the power dissipated is 0.5*I2R. The bandwidth of the circuit can be expressed as BW = fH − fL = ∆ f (2.19) The Q-factor of the parallel resonant circuit can also be defined as ratio between the resonant frequency and the bandwidth which implies that a high Q-factor has a narrow bandwidth. Also, the bandwidth and the frequency response for a system with fixed resonant frequency can be altered by changing the ratio between the inductor and the capacitor or by changing the value of resistance R. Q = fr BW (2.20) 14 2. Theory Figure 2.11: Bandwidth of parallel resonant circuit 2.3 Analytical model of WPT The transmitter and receiver coils together form a transformer. Therefore, the equivalent circuit of transformer can be used to analyse the wireless power transfer circuit. The circuit diagram of inductive power transfer is shown in figure 2.12. Figure 2.12: Circuit diagram of inductive power transfer In this model, there is no core and the air gap between the Tx and Rx coil is large which results in increased leakage inductance. The equivalent model of inductive power transfer considering leakage inductance is shown in figure 2.13. 15 2. Theory Figure 2.13: Equivalent circuit diagram of inductive power transfer From figure 2.13 VAC = V1 = ( R1 + jωL12 + jωLM ) IP + jωLMIS (2.21) 0 = ( RL + R2 + jωL21 + jωLM ) IS + jωLMIP (2.22) Input impedance of the network as seen by the source is expressed as Zin = V1 IP = ( R1 + jωL12 + jωLM ) IP + jωLMIS IP (2.23) From 2.22 IS = − jωLMIP RL + R2 + jωL21 + jωLM (2.24) Substituting 2.24 in 2.23, we get Zin = ( R1 + jωL12 + jωLM ) ( RL + R2 + jωL21 + jωLM ) + ω2M2 RL + R2 + jωLb + jωLM (2.25) The efficiency of power transfer from source V1 to load RL can be expressed as η = RL |I2| 2 RL |I2| 2 + R2 |IS| 2 + R1 |IP| 2 (2.26) η = RL RL + R2 + R1 [ |IP| |I2| ]2 (2.27) From 2.22 IP I2 = RL + R2 + jωL21 + jωLM − jωLM[ |IP| |I2| ]2 = [RL + R2 ωLM ]2 + [L21 + LM LM ]2 (2.28) substituting 2.28 in 2.27, we get η = RL (RL + R2) [ 1 + R1(R2+RL) ω2L2 M ] + R1 [ L21+LM LM ]2 (2.29) 16 2. Theory From 2.29, the condition for maximum efficiency can be derived. Therefore, maximum efficiency is achieved when 2.30 is fulfilled. The condition for 2.30 is satisfied when R1(R2+RL) ω2L2 M tends to zero. ω≫ √ R1 (R2 + RL) LM (2.30) Hence, the maximum theoretical efficiency for power transfer is given by ηmax = RL RL + R2 + R1 [ L21+LM LM ]2 (2.31) 2.4 Compensation of leakage inductance In a transformer model, the flux generated by the primary circuit links with the secondary circuit, but not all the flux generated is mutual flux. There are magnetic field lines which do not follow the magnetic circuit resulting in leakage flux. The distance between the Tx and the Rx coils in the wireless power system affects the coupling of the system and generates leakage inductance. The leakage inductance increases the reactive power and reduces the efficiency of the system. Hence, there is a requirement for compensation of the reactive power using capacitors on both the transmitter and the receiver side to ensure that the system operates at a power factor close to unity. 2.4.1 Compensation topologies The capacitive compensation is formed by two capacitances, C1 at the transmitter side and C2 at the reciever side. Depending on the capacitor connection, there are four basic compensation topologies available, • Series - Series(SS) compensation • Series - Parallel(SP) compensation • Parallel - Series(PS) compensation • Parallel - Parallel(PP) compensation The four different compensation topologies are represented as shown in figure 2.14. The selection of the topologies is made according to the application since each topology behaves differently for variation in the parameters. 17 2. Theory Figure 2.14: Capacitive compensation topologies The secondary compensation capacitance C2 is chosen such that it compensates the secondary leakage inductance and the mutual inductance. The secondary compensation capacitor C2 is independent of type of topology and it is expressed as sum of the secondary leakage inductance and the mutual inductance as XC2 = XL21 + XM C2 = 1 (2Π fr)2(L21 + LM) C2 = 1 ω2 r (L21 + LM) (2.32) The expression for the primary compensation capacitor C1 is dependent on the type of topology and it differs for each topology. The capacitor C1 is chosen such that the total impedance seen by the supply is purely resistive. This will ensure that the high frequency inverter will have minimum VA rating. Similar to the secondary compensation capacitance, the capacitive reactance XC1 should also be equal to the inductive reactance of the transmitter coil. 2.4.1.1 Series-series compensation topology The equivalent circuit of series-series topology is shown in figure 2.15. The SS topology helps in constant current operation with zero phase shift and hence it is suitable for battery charging and low power applications. The main advantage of the SS topology is that the compensation capacitances are independent of the coupling coefficient k and load. However, the power transfer efficiency for large distance between the coils in relatively low[5]. The expression for the capacitor C1 in SS topology is given as[1] 18 2. Theory C1 = 1 ω2 r .(L12 + LM) (2.33) Figure 2.15: Equivalent circuit diagram of SS compensation topology 2.4.1.2 Analytical model of PP compensation topology The PP topology requires a relatively large primary capacitance for loosely cou- pled coils and it is most commonly used for industrial applications. The power transfer efficiency in the PP topology for a large distance between the transmit- ter and receiver coil is better compared to the rest of the topologies. The main advantage of the PP topology is the high power factor and high efficiency at low mutual inductance and a large distance between the Tx and Rx coils[5]. The network diagram for the Parallel-Parallel compensation topology is shown in figure 2.16. In figure 2.16, R1 and R2 refers to the Tx and Rx coil resistance, L12 and L21 refers to the Tx and Rx coil leakage inductance, LM refers to the mutual inductance between the Tx and Rx coil, and IP and IS refers to the current flowing through the Tx and Rx coils respectively. Figure 2.16: Equivalent circuit diagram of PP compensation topology The input impedance as seen by the voltage source is expressed as Zin = 1 jωC1 + 1 R1+ jω(La+M)+ ω2M2(1+RLC2ω) (RL+R2+ jω(Lb+M))(1+RLC2ω) (2.34) 19 2. Theory The input impedance can also be expressed in terms of admittance as Yin = jωC1 + 1 R1 + jω (La +M) + ω2M2(1+RLC2ω) (RL+R2+ jω(Lb+M))(1+RLC2ω) (2.35) The primary capacitance is chosen such that the imaginary part of the impedance as seen by the source is zero, Im(Yin) = 0 (2.36) WKT C2 = 1 ω2 r (L21 + LM) (2.37) substituting 2.37 in 2.36 we get C1 = (L21 + LM)2 [ (L12 + LM) (L21 + LM) − L2 M ] C2[ (L12 + LM) (L21 + LM) − L2 M ]2 + L4 MR2 L (L21 + LM) C2 (2.38) The effect of primary and secondary resistance are neglected in calculating the compensation capacitor C1. The efficiency of power transfer from source VAC to load RL is given by 2.26. From figure 2.16 IS = IC2 + I2 IS = jωC2VL + VL RL IS = VL [ 1 + jωC2RL RL ] |IS| |I2| = √ 1 + R2 LC2 2ω 2 r (2.39) similarly |IP| |I2| = √ R2 2 + [(L21 + LM)ω0 + R2RLC2ωr] 2 ωrLM (2.40) substituting 2.39 and 2.40 in 2.26, we get η = RL RL + R2 + R2R2 L ω2(L21+LM) + R1R2 2 ω2L2 M + R1 [ (L21+LM)ω2+ R2RL ω2(L21+LM) ]2 ω2L2 M (2.41) rearranging 2.41 20 2. Theory η = RL RL + R2 + R1(L21+LM)2 L2 M [ 1 + R2R2 LL2 M+R1R2 2(L21+LM)2 ω2 r (L21+LM)2L2 M ] (2.42) From 2.42, the condition for maximum efficiency can be derived. If [ R2R2 LL2 M+R1R2 2(L21+LM)2 ω2 r (L21+LM)2L2 M ] tends to zero, maximum efficiency can be achieved. Therefore, ωr ≫  √ R2R2 LL2 M + R1R2 2 (L21 + LM)2 (L21 + LM) LM  (2.43) Hence, the maximum theoretical efficiency can be achieved when condition given by 2.43 is fulfilled. The maximum theoretical efficiency can be expressed as ηmax,PP = RL RL + R2 + R1(L21+LM)2 L2 M (2.44) 2.5 Coil geometries for wireless power technology The efficiency of the wireless power technology using time-varying resonant mag- netic coupling largely depends on the Tx and Rx coil geometries, Q-factor of the coils, coupling coefficient, and air-gap between the coils. An alternating current applied to the Tx coil generates electromagnetic waves which is dependent on the coil geometry besides applied current and frequency. An electromagnetic coil is designed by winding isolated conductors in the shape of a coil, spiral, or helix. The electromagnetic coil parameters such as inductance, resistance, and magni- tude of the desired magnetic field influence the design of the coil. The coils used in the wireless power technology can be divided based on the geometry and core type as shown in figure 2.17. Figure 2.17: Types of coil geometries 21 2. Theory In this thesis, planar circular coils, concentric coils, and solenoids are used both as Tx and Rx coils. The different types of coil geometries used in this thesis are discussed below. 2.5.1 Circular coils If the current carrying conductor is wound to be a loop, the resulting geometry will be a circular coil. The electric current applied to the circular loop generates a magnetic field that is concentrated at the center of the loop. The strength of the magnetic field at the center of the circular coil can be improved by increasing the number of loops on the coil. A single layer circular coil with N turns is shown in figure 2.18. Figure 2.18: Magnetic field lines of single layer circular coil The magnetic field produced by a current carrying circular loop can be described using Biot-Savart law. The magnetic field produced by the circular loop at any point in space as explained in section (2.1.2) can be calculated as B = − µ 4Π ∮ l Idlr̂ r2 Biot-Savart law can also be used to calculate the magnetic field at any point on the axis of the circular loop as explained in section (2.1.2) using the equation B = 2ΠµNIa2 4Π(x2 + a2) 3 2 The magnetic flux density is maximum at the center of the circular loop as all the field lines are concentrated at the center which can be determined by 22 2. Theory B = µ0NI 2a The following factors affect the magnetic field in the circular coil: • The magnitude of the magnetic field in a circular coil is directly proportional to the magnitude of current through the loop i.e., B ∝ I. • The magnitude of the magnetic field is inversely proportional to the radius of the circular coil i.e., B ∝ 1 r . • The magnitude of the magnetic field in the circular coil also depends on the number of loops in the coil. The more the number of loops, higher the magnitude of the magnetic field. • The self-inductance of the circular coil is influenced by the coil geometric parameters such as the inner and outer radius of the wire, inner and outer radius of the coil, and number of turns. 2.5.1.1 Inductance of a circular coil The self-inductance of a single turn circular coil as shown in figure 2.19(i) can be analytically expressed as[7] L = µ0x ( ln (8x a ) − 2 ) (2.45) where µ0 ( = 4π ∗ 10−7) is the permeability of free space, x is radius of coil, and a is radius of wire. Using Maxwell’s expression in elliptic integrals, the mutual inductance between two single turn circular coils as shown in figure 2.19(ii) can be analytically expressed as[7] M = µ0 √ xyk 3 2 C (k) = µ0 √ xy [( 2 √ k − √ k ) F(k) − 2 √ k E(k) ] (2.46) where x and y are the radii of two circular coils, functions C(k), F(k) and E(k) are the complete elliptic integrals of the first and second order, and k = 4xy( x + y )2 + h2 (2.47) where h is the distance between the circular coil centers. Similarly, the analytical expression for the self-inductances and the mutual induc- tance for the circular coils with N turns can be expressed as L1 = µ0N2 1x ( ln (8x a1 ) − 2 ) L2 = µ0N2 2 y ( ln ( 8y a2 ) − 2 ) M = µ0N1N2 √ xyk 3 2 C (k) (2.48) 23 2. Theory where x and y are the coil radius of coil 1 and coil 2 respectively, a1 and a2 are the wire radius of coil 1 and coil 2 respectively, and N1 and N2 are the number of turns in coil 1 and coil 2 respectively. (i) (ii) Figure 2.19: (i) Single turn circular coil with coil radius x and wire radius a. (ii) Two single turn circular coil with coil radius x and y respectively with a distance of h between them 2.5.2 Concentric coils The concentric coils are generally flat spirals of isolated conductors mounted on a substrate or a magnetic shielding as shown in figure 2.20. Each turn in the concentric coil has a different radius which is a function of the pitch factor. The pitch factor determines the distance between each turn of the coil. The electromagnetic behaviour of the concentric coil is similar to the circular coil with the maximum flux density at the center of the coil and the strength of the magnetic field depends on number of turns N, magnitude of current, and inner and outer radius of the coil. The magnetic flux density B at any point in space and on the axis of the concentric coil can be calculated similar to the circular coil as explained in section (2.1.2) using Biot-Savart equations. 24 2. Theory Figure 2.20: Single layer concentric coil The following factors affect the magnetic field in the concentric coil: • The magnitude of the magnetic field in a circular coil is directly proportional to the magnitude of current through the loop i.e., B ∝ I. • The magnitude of the magnetic field in the circular coil also depends on the number of loops in the coil. The more the number of loops, higher the magnitude of the magnetic field. • The insertion of a material with high permeability as a substrate or magnetic shielding increases the magnitude of the magnetic field in the concentric coil. • The self-inductance of the concentric coil is influenced by the geometric parameters such as the inner and outer radius of the coil, pitch factor, and number of turns. 2.5.2.1 Inductance of a concentric coil The self-inductance of the concentric coil with N turn as shown in figure 2.21(i) can be approximated by using the concept of average of diameter of the concentric coil[8]. The geometrical parameters of the concentric coil is shown in figure 2.21(ii). In figure 2.21(ii), w is the wire diameter, s is the distance between the turn, dinner and douter are the inner and outer diameter of the coil, respectively. The analytical expression for the self-inductance of the concentric coil can be expressed as[8] L = µ0N2davg 2 [ ln ( 2.46 γ ) + 0.20γ2 ] (2.49) γ = douter − dinner douter + dinner (2.50) davg = douter + dinner 2 (2.51) The mutual inductance between two concentric coils C1 and C2 as shown in figure 2.22 can be expressed using Neumann’s equation as[8] 25 2. Theory M = µ0 4Π ∮ C1 ∮ C2 dl1dl2 R (2.52) where µ0 is the permeability of free space, dl1 and dl2 are line elements, R is the separation distance between the two line elements, andθ is the angle of revolution relative to x-axis. The outer radius R of the coil is determined using the equation R = Ri + aθ (2.53) where Ri is the initial radius of the coil and a is the pitch factor given by, a = s 2π (2.54) θ = 2πN (2.55) Using (2.53), the equation for coil 1 and coil 2 can be expressed as RA = Ri1 + a1θ1 (2.56) RB = Ri2 + a2θ2 (2.57) The tangential line elements dl1 and dl2 can be expressed as dl1 = (Ri1 + a1θ1)dθ1 (2.58) dl2 = (Ri2 + a2θ2)dθ2 (2.59) The dot product of dl1 and dl2 is given by dl1.dl2 = (Ri1 + a1θ1)(Ri2 + a2θ2)cos(θ2 − θ1)dθ1dθ2 (2.60) The distance R between the line elements dl1 and dl2 can be expressed using the cosine law as R2 = (Ri1+a1θ1)2+(Ri2+a2θ2)2 −2(Ri1+a1θ1)(Ri2+a2θ2)cos(θ2−θ1)dθ1dθ2+h2 (2.61) Substituting (2.60) and (2.61) in (2.52), the mutual inductance between perfectly aligned concentric coils can be expressed as M = µ0 4Π ∫ 2Π ∫ N jdθ1dθ2√ (Ri1 + a1θ1)2 + (Ri2 + a2θ2)2 − 2 j + h2 (2.62) where j = (Ri1 + a1θ1)(Ri2 + a2θ2) cos (θ2 − θ1) 26 2. Theory (i) (ii) Figure 2.21: (i) Concentric coil with N turns. (ii) Cross-section of concentric coil Figure 2.22: Two perfectly aligned concentric coils 2.5.3 Solenoid A solenoid is a coil of wire wound in the axial direction with electric current flowing through it. The current flowing in the solenoid generates a magnetic field that starts from the north pole and ends at the south pole similar to a bar magnet. The magnetic field produced by the solenoid is stronger along the axis of the solenoid since the magnetic flux generated by each turn of the coil is concentrated at the center. Whereas the magnetic flux outside the solenoid is considerably low. 27 2. Theory The magnetic field due to current flowing in the solenoid can be expressed using Ampere’s law as ∮ B.dl = µ0Ienc (2.63) The line integral of B around the coil of length l with current enclosed in the coil to be product of number of turns N and current I in each turn will give us B = µ0NI l (2.64) where µ0 is the permeability of free space, N is the number of turns, I is the current. The equation described in (2.64) gives an expression for the magnetic field generated by the solenoid with air core. However, with the introduction of a ferromagnetic core increases the magnitude of the magnetic field in the solenoid due to high permeability of the core. The expression for the magnetic field within a core can be expressed as B = µ0µrNI l (2.65) where µr is relative permeability of the core. From (2.64) and (2.65), it is clear that the magnitude of the magnetic field in a solenoid with core will be higher than the solenoid with air core. Also, the magnetic field in the solenoid with hollow core will be less than the magnetic field of the solenoid with solid core. The following factors affect the magnetic field in the solenoid: • The magnitude of the magnetic field in the solenoid is directly proportional to the magnitude of current through it i.e., B ∝ I. • The magnitude of the magnetic field in the solenoid also depends on the number of loops in the coil. The more the number of loops, higher the magnitude of the magnetic field. • The insertion of a core material with high permeability increases the mag- nitude of the magnetic field in a solenoid. • The self-inductance of the concentric coil is influenced by the geometric parameters such as the cross-sectional area of the wire,length of the coil, and number of turns. 2.5.3.1 Inductance of a solenoid The self-inductance of a coil with N turns is expressed as L1 = L11 = N1 ϕ11 I1 (2.66) The self-inductance for a solenoid as shown in figure 2.23 can be determined using (2.66). The magnetic flux density due to current in the solenoid can be expressed as 28 2. Theory B = µNI l (2.67) where N is the number of turns, and l is the length of the solenoid. The magnetic flux flowing through the solenoid is the product of magnetic field and cross-sectional area of the solenoid. Therefore, the magnetic flux per turn is given by ϕ = B.A (2.68) where A is the cross-sectional area of the solenoid. Substituting (2.67) and (2.68) in (2.66), we get self-inductance of the solenoid as L = µN2A l (2.69) From (2.69), the self-inductance of the solenoid depends on the coil parameters such number of turns on the coil, cross-sectional area of the coil, and length of the coil. The self-inductance of a solenoid can also be increased by selecting a core with high permeability. The mutual inductance between two coaxial solenoids with N1 and N2 turns with currents I1 and I2 respectively is derived below. The mutual inductance of coil 2 with respect to coil 1 (M21) is given by M21 = N2Φ21 I1 (2.70) Similarly, the mutual inductance of coil 1 with respect to coil 2 (M12) is given by M12 = N1Φ12 I2 (2.71) From (2.70) and (2.71), we can write M = N1Φ12 I2 = N2Φ21 I1 (2.72) The magnetic flux Φ21 can be expressed as, Φ21 = B1.A = ( µN1I1 l1 ) A (2.73) Substituting (2.73) in (2.72), we get the mutual inductance between two coaxial solenoids as M = µN1N2A l1 (2.74) 29 2. Theory Figure 2.23: Solenoid with N turns 2.6 Material selection for coils The selection of material for designing electromagnetic coils for wireless power transfer is critical in order to obtain maximum efficiency. The type of material selected for designing the coils contribute in the resistive losses, and losses due to skin and proximity effect when operating at higher frequency. Also, the Q-factor of the coil material plays a vital role in the material selection. The Q-factor is a measure of the performance of the coil. When operating at higher frequencies, the effective resistance of the coil increases due to the skin and the proximity effect which reduces the quality or the Q-factor of the coil. A simple circuit model for an ideal inductor can be represented by connecting a resistance in series as shown in figure 2.24. Figure 2.24: A simple circuit model of ideal inductor with series resistance In case of direct current, the current density is distributed or homogenous over the entire cross-section of the conductor. The DC resistance of the conductor depends on the cross-sectional area of the wire, length of the wire and electrical conductivity of the material used which is expressed as 30 2. Theory RDC = l σA (2.75) where σ is the electrical conductivity [S/m] of the material used for the wire, l is the length of the wire [m], and A is the cross-sectional area of the wire [m2]. In order to get low resistance in the wire, the electrical conductivity of the material should be high. The electrical conductivity of copper is 5.8 ∗ 107[S/m] which is higher compared to the electrical conductivity of aluminium and iron. In case of alternating current, the current density is not homogenous over the cross-section of the conductor and with increasing frequency, the current density is accumulated at the surface of the conductor and it is reduced at the center of the conductor. This effect is known as the skin-effect which reduces the effective conducting area in the wire as shown in figure 2.25. Figure 2.25: Illustration of skin effect at different frequencies The skin-effect is caused by the magnetic field generated by the current flowing in the circumference of the conductor which opposes the current to flow at the center of the conductor. At higher frequencies using AC, the main resistance comes from the skin-effect. The skin depth is used to describe how a high frequency alternating current penetrates the conductor. The skin depth is defined as the distance from the circumference where the current density is reduced by 63% of the surface current density. The skin depth is expressed as δ = √ 2 µσcuω (2.76) where σcu is the conductivity of copper, µ = µ0µr is the permeability, and ω = 2π f is the frequency of the current. When the frequency increases, the skin depth decreases. The effective current carrying area of a conductor is determined by the skin depth. Thus, a conductor thicker than the skin depth will not be an effective use of the conductor. The skin depth in a conductor is illustrated in figure 2.26. 31 2. Theory Figure 2.26: Illustration of skin depth in a conductor Another effect that adds to the loss when operating at high frequency is the proximity effect. The external field generated by the high frequency current in the conductor influences the current distribution in the nearby conductors or the conductors located in the proximity. The proximity effect is more in the solid conductors compared to the stranded conductors since the surface area of the stranded conductor is smaller than the solid conductor. The AC resistance for a conductor with circular cross-section can be expressed as R = L σπr2 , r≪ δ (2.77) R = L 2σπrδ , r≫ δ (2.78) where r is the radius of the conductor and L is the length of the conductor. Hence, conductors with r ≫ δ have higher higher resistance compared to conductors with r ≪ δ. In order to reduce the AC resistance at high frequency, different conductors are used to design the coil which are discussed below. 2.6.1 Litz wire The litz wires are used typically in applications operating within the frequency range of 10kHz - 5MHz [11]. The cross-section of a litz wire with n strands is shown in figure 2.27. The litz wire consists of individual insulated magnetic wires that are bunched or braided together. Each strand in the litz wire is smaller that the skin depth to ensure effective use of the conducting area. The multiple strands in the wire allows current to divide uniformly between the strands. Also, the strands are bunched together such that the location of each strand alternate between the center of the wire and the circumference of the wire. The multiple strand construction of the litz wire ensures that the proximity effect is same on each strand at all the points. Thus, the litz wire homogenizes the current density and increases the effective conducting area of the wire, reducing AC losses at high frequency. The other benefits of using litz wire is the lower operating tempera- tures and reduced weight. 32 2. Theory Figure 2.27: Cross-section of a litz wire The number of strands and the thickness of each strand in a litz wire is determined by the current amplitude and the operating frequency. The AC resistance of a litz wire can be approximately expressed as R = l σπr2 [1 4 + r 2δ ] (2.79) 2.6.2 Magnetic wire The magnetic wire is a solid conductor with very thin insulation coated around the conductor. The magnetic wire is also called as an enameled wire typically used in the construction of transformer windings, motor windings, inductors, and electromagnets. The insulation around the magnetic wire is often made of polymer layers rather than a layer of enamel paint. Figure 2.28 shows a solenoid made of magnetic wire. Figure 2.28: Solenoid made of magnetic wire The thickness of the magnetic wire is calculated based on the current amplitude, frequency and the operating temperature. The magnetic wire provides greater mechanical and thermal strength compared to the litz wire. However, the AC resistance offered by the magnetic wire when operating at high frequency is higher due to skin effect and proximity effect. The extent to which the frequency affects the resistance of the magnetic wire depends on the gauge of the wire. Large gauge wires exhibit more losses than small gauge wire when operating at high frequency. Hence, the magnetic wires can be used for low frequency applications upto 100kHz beyond which the gauge of the wire should be made small according to the operating frequency. 33 2. Theory 2.6.3 Hallow copper tube An alternate to the litz wire is the copper hollow tube when operating at high frequency. Although, the litz wire offers less resistance due to skin effect, it is required to reduce the diameter of each strand to operate at much higher frequencies that complicates the packing factor for the litz wire. Also, the strand to strand proximity effect affects the uniformity of current distribution. The hollow conductors have lower skin-effect when compared to other solid conductors with the same cross-sectional area[9]. Figure 2.29 shows an air core solenoid made of copper hollow tube. Figure 2.29: Solenoid made of hollow copper tube The other advantages of using a hollow copper tube is easy manufacturing and simplicity in implementing cooling for the coil. If the proximity effect in the hollow conductors are minimised, the hollow tubes can be a good alternative for litz wire in some WPT applications. However, lack of analytical models for the hollow conductors makes it very difficult to analyse the advantages and its limitations. 2.7 Current challenges in wireless power system The major challenges in the wireless power technology is the efficiency of power transfer, range of power transfer, and alignment between the coils. The efficiency drop in the WPT is due to a number of reasons including distance between the coils, flux leakage, losses in the power converter, and magnetic coupling between the coils and the design form factor of the coils. The form factor is the ratio of the length of the coil to the diameter of the coil and it is one of the parameters that affects the inductance of the coils. However, different coils can have the same form factor. Thus, the combination of different coil geometries can have a coupling factor(k) high enough to transfer power with good efficiency. The wireless power technology is limited by the alignment between the Tx and Rx coils, which can be a major drawback in some applications such as wireless charging of portable electronics where the chances of misalingnment between the coils are more. The following section explains how the misalignment between the coils affect the coupling coefficient and its impact on the power transfer efficiency. 34 2. Theory 2.7.1 Alignment between transmitter and receiver coils The inductive wireless power transfer is a technology where the power is trans- ferred by magnetic fields from the Tx coil to the Rx coil through the air gap. The amount of magnetic flux linked between the Tx and Rx coils depends on the mag- netic coupling between the coils. The strength of the coupling is defined by the coupling factor or coupling coefficient(k), and is expressed as k = M √ LTX × LRX (2.80) where LTX and LRX are self-inductances of the transmitter and receiver coil respec- tively, and M is the mutual inductance induced between the two coils. If current I1 flowing in a coil produces a magnetic flux ϕ1, the self-inductance of the coil can be expressed as the ratio of magnetic flux produced to the current in the coil L1 = ϕ1 I1 (2.81) The mutual inductance with the adjacent coil can be expressed as the magnetic flux generated by coil 1 that passes through the area enclosed by coil 2 divided by the current in coil 1 M = L21 = ϕ21 I1 (2.82) The following are the three types of misalignments that result in poor coupling factor, • Vertical misalignment • Lateral misalignment • Angular misalignment Figure 2.30: Types of misalignment between transmitter and receiver coils Figure 2.31 shows the Rx coil misaligned with the Tx coil. The Rx coil is laterally misaligned by distance d = √ x2 1 + y2 1. The angles (θ1,Φ1) describes the line joining 35 2. Theory the centers of the two coils. The receiver coil area vector V2 is expressed using the angles (θ0,Φ0) to describe the angular misalingnment of the receiver coil. Figure 2.31: Misaligned coils The general equation for the coupling coefficient between the two coils that are misaligned is calculated using 2.80 and is expressed as[10] k = ( √ r1r2 r )3 ( 3 2 sinθ0 cosθ1 sinθ1 cos ( φ0 − ϕ1 ) + cos { cos2 θ1 sin2 θ1 2 }) (2.83) where r1 and r1 are the radius of the Tx and Rx coil respectively, and r can be expressed as r = √ R2 + d2 + r2 1 − 2d √ r2 1 + R2 cos ( 90◦ + tan−1 (r1 R )) , r1 ≥ r2 (2.84) r = √ R2 + d2 + r2 2 − 2d √ r2 2 + R2 cos ( 90◦ + tan−1 (r2 R )) , r2 ≥ r1 (2.85) where R is the vertical distance between the centers of the two coils along same axis. 2.7.1.1 Vertical misalignment The vertical misalignment occurs when the receiver coil is vertically displaced by a distance R in the same plane where the Tx coil is placed as shown in figure 2.32. 36 2. Theory Figure 2.32: Vertical misalignment In case of vertical misalignment, the variables defined in the general expression for the coupling coefficient becomes θ0 = 0◦ ,θ1 = 0◦,d=0. Substituting these values in 2.83, we get the expressions for the coupling coefficient under vertical misalignment condition and they are expressed as k =  √ r1r2√ R2 + r2 1  3 , r1 ≥ r2 (2.86) k =  √ r1r2√ R2 + r2 2  3 , r2 ≥ r1 (2.87) From 2.86 and 2.87, the coupling factor is inversely proportional to the distance between the two coils in the same axis. When the receiver coil is vertically moved away from the transmitter coil, the magnetic field linkage reduces with an increase in distance. At some point, when the receiver coil goes away from the magnetic field range of the transmitter coil, there will be no flux linkage and hence EMF will not be induced in the receiver coil. 37 2. Theory 2.7.1.2 Lateral misalignment The lateral misalignment occurs when the receiver coil is laterally displaced with the Tx coil placed in a plane parallel to it as shown in figure 2.33. Figure 2.33: Lateral Misalignment In case of lateral misalignment, θ0 = 0◦ and 2.83 is simplified as k = ( √ r1r2 r )3 [ cos2 θ1 1 − sin2 θ1 2 ] (2.88) 2.7.1.3 Angular misalignment The angular misalignment occurs when the centers of the two coils are on the same axis and the plane of the receiver coil is tilted to form an angle α as shown in figure 2.34. 38 2. Theory Figure 2.34: Angular misalignment In case of angular misalignment, the variables defined in the general expression for the coupling coefficient becomes θ0 = α◦ ,θ1 = 0◦,d=0. Substituting these values in 2.83, we get expression for the coupling coefficient under angular misalignment condition and is expressed as k =  √ r1r2√ R2 + r2 1  3 cosα, r1 ≥ r2 (2.89) k =  √ r1r2√ R2 + r2 2  3 cosα, r2 ≥ r1 (2.90) when α = 0, [2.89] and [2.90] reduces to [2.86] and [2.87] respectively. For α = 90◦, the coupling coefficient becomes zero and hence there will be no power transfer between the two coils. 39 2. Theory 40 3 Case Setup 3.1 Investigation of suitable receiver coil geometry In this section, an investigation of suitable receiver coil geometry is carried out to study the interoperability of different coil geometries, coupling coefficient & the magnetic field distribution. All the coils are tested for aligned & misaligned operation. For the investigation of suitable receiver coil geometry, we have chosen three main commonly used coil geometries which include, • Concentric coils. • Solenoid coils. • Circular coils. A wireless power system from the Wurth Electronics is used to test the concentric & solenoid coils. We have designed automatically switching transmitter circuits for testing centre-tapped circular coils, as they have three terminals & can’t be driven using the WE development kit. Also, the investigation of suitable receiver coil geometry test is conducted by keeping the same transmitter coil to understand the relation between the coupling coefficient & the coil geometry. Table 3.1 shows different transmitter boards & combinations of coils used in the investigation of suitable receiver coil geometry test. The test involves coils with different inductance values, dimensions & coil material as shown in figure 3.1 & figure 3.2. The corresponding coil parameters are shown in table 3.2 & table 3.3. Table 3.1: Transmitter boards and coil combinations used in the investigation of suitable receiver coil geometry test Transmitter Board Transmitter Coil Receiver Coil WE development kit WE concentric coil Concentric coils Solenoid coils Automatically switching transmitter circuit 1 Circular coil 1 Circular coil 2 Automatically switching transmitter circuit 2 Circular coil 3 Circular coil 4 Circular coil 5 3.1.1 Measurement of suitable receiver coil geometry In this thesis, we have conducted measurements & tests on multiple coil geome- tries with different coil materials. The objective of these measurements is to gain 41 3. Case Setup a comprehensive understanding of the coil geometry & its magnetic properties, as well as to investigate power transfer associated with different coil materials. Among all other coils, we have chosen the WE Tx/Rx coil & solenoid coils to an- alyze the coupling coefficient. The coil parameters are measured using Agilent’s E4980A Precision LCR Meter with a frequency setting of 200KHz which is the closest frequency step available to the operating frequency of 205KHz in the WE development kit. Also, the coils are measured without the resonant capacitors connected. Even though we have tested several receiver coil geometries, we have chosen custom built solenoid coil to analyze based on the factors affecting the power transfer. The solenoid receiver coil has a similar diameter compared to the WE Tx coil which should result in stronger coupling and the solenoid core reduces the reluctance of the flux path. Figure 3.1: Concentric & solenoid coil geometries under test Table 3.2: Measured coil parameters for concentric and solenoid coils with corresponding resonant capacitors at a resonant frequency of 205KHz Coil Inductance Number of Turns Q-factor Resonant Capacitor (µF) WE Tx/Rx coil 5.8µH 20 13 0.1 Solenoid coil 123nH 13 15 5 The center tapped circular coils investigated are shown in figure 3.2. The mea- sured coil parameters for center tapped circular coils are shown in table 3.3. All the coils are wound using magnetic wire. The coils are mainly varied for the diameter and number of layers/turns. The center tapping and the coil layers are done to boost the magnetic field. Circular coil 1 has the largest diameter of 180mm, to investigate the effect of coil diameter on the range of power transfer. A larger coil diameter helps to accommodate more receiver coils to test point to multi-point power transfer. 42 3. Case Setup Figure 3.2: Center tapped circular coils under test Table 3.3: Circular coil parameters and their corresponding resonant capacitors Coil Center Tap Inductance (µH) Number of Turns Q-factor Resonant Capacitor (nF) Circular Coil 1 Yes 555 120 25 71 Circular Coil 2 No 53 30 32 74 Circular Coil 3 Yes 226 60 225 5 Circular Coil 4 No 16 30 46 80 Circular Coil 5 Yes 103 30 28 12 3.1.2 WE Development kit In this project, we are using a wireless power transfer system from Wurth Elec- tronics. The power transfer is possible up to 200W when the distance between the coils are less than or equal to 10mm. The wireless power development kit can be used to demonstrate the current wireless power transfer system and that gives an opportunity to develop the system with different concentric & solenoid receiver coils and also has the possibility to vary the resonant frequency accordingly. Table 3.4 shows the key system specification of the WE development kit. 43 3. Case Setup Table 3.4: Key system specification for WE development kit. Parameters Specification Transmitter Input Voltage 24V DC Receiver Output Voltage 20V DC Tx & Rx Current 10A Maximum Transmitted Power 200W Frequency 205kHz Load Resistance 6.8Ω | 27Ω | 220Ω Optimum Coil Distance 10mm 3.1.2.1 Test case The test set-up for investigation of suitable receiver coil geometry using the Tx and Rx board from the WE development kit is shown in figure 3.3. The test is fo- cused only on studying the magnetic coupling of different concentric and solenoid coils. The test case uses all the components from the WE development kit except the receiver coils and the receiver resonant capacitors, which are changed for different test cases with different coils. A resistive load of 6.8Ω is connected to Rx board. An acrylic sheet of 10mm is used as a spacer between the Tx and Rx coils. Figure 3.3: Test set up of WE development kit with solenoid Rx coil 1 Transmitter Board 2 Receiver Board 3 Transmitter Coil 4 Receiver Coil 5 Load Resistor The test case for aligned operation is as follows, • The Tx and Rx coils are aligned properly with no misalignment. • The WE development kit is tested for different load conditions with different resistive loads of 6.8Ω, 27Ω and 220Ω. • For the investigation of a suitable receiver coil geometry test, the voltage and current are measured with a resistive load of 6.8Ω. 44 3. Case Setup • The distance between the Tx and Rx coils is kept constant at 10mm(specified by WE). The test case for misaligned operation where the receiver coils are misaligned with respect to Tx coil as shown in table 3.5. Table 3.5: Different misalignment between Tx and Rx coils Type of Misalignment Misalignment Value Vertical 30mm from Tx Lateral 50% on Tx Angular 40◦ angle above Tx 3.1.3 Automatically switching transmitter circuit A center tapped coil can be used in a wireless power system, as the voltage is in- jected to the center tapped terminal of the coil, which creates magnetic fields in the 2 sections of the coils and the magnetic fields are in phase with each other which adds to the magnetic field strength. The center tapped coils are built to study the magnetic field strength. Figure 3.4 and figure 3.5 shows the block diagram of the automatically switching transmitter circuit 2 and the receiver respectively. Figure 3.4: Block diagram of automatically switching transmitter circuit 2 Figure 3.5: Block diagram of a rectifier circuit for wireless power transfer We have designed 2 automatically switching transmitter circuits, Figure 3.7 shows the schematic diagram of the automatically switching transmitter circuit 1 figure 45 3. Case Setup 3.8 shows the schematic diagram of the automatically switching transmitter cir- cuit 2 and figure 3.9 shows the schematic diagram of the receiver. To explain the working of the BJT schematic, a single section of the automatically switching transmitter circuit at different working stages is shown in figure 3.6, a) A DC power supply is connected to the center tap of the transmitter coil for which a resonant capacitor (C4) is also connected which makes an LC tank. The current flows through both the sections of the coil (L1) and also charges the capacitor (C4). b) The current flows through the inductor and through the resistor (R2), capac- itor (C2) is charged until it reaches a threshold to trigger the BJT. c) All the capacitors in the circuit gets charged, the energy stored in the capac- itors is discharged through the base and a proper base current is supplied to the base of the transistor. d) The transistor conducts and makes the circuit complete and the Tx coil is fully energized and produces the magnetic field. The charging and discharging action of the capacitor switches the BJT at a fre- quency to produce an alternating magnetic field at the coils. Also, the capacitor (C4) and inductor (L1) act as an oscillator that is tuned to a particular resonant frequency. The current flows in the same direction in each coil stacked together to have a strong magnetic field. Figure 3.9 shows the receiver circuit which has a full bridge rectifier that converts AC to DC, then this is fed to a voltage regulator of 5V and 12V and a load is connected to the output of the voltage regulator. It is required to load the receiver all the time as the no load operations may cause higher voltages and break the junctions of the full bridge rectifier and the voltage regulator. 46 3. Case Setup Figure 3.6: Working of a section of the schematic diagram of automatically switching transmitter circuit (figure 3.8) Figure 3.7: Schematic diagram of wireless power transfer for automatically switching transmitter circuit 1 47 3. Case Setup Figure 3.8: Schematic diagram of wireless power transfer for automatically switching transmitter circuit 2 Figure 3.9: Schematic diagram of the receiver rectifier for wireless power transfer 48 3. Case Setup 3.1.3.1 Test case The test case for automatically switching transmitter circuit 1 under aligned op- erating conditions are as follows, • The test is carried out with the circular Tx and Rx coils (refer figure 3.10). The positive supply is applied to the center tapping of the Tx coil and the Rx coil is not center tapped. • The distance between the transmitter coil and the receiver coil is at 50mm and there is no misalignment between the coils. • The power transmitter board is operating at a switching frequency of 8kHz and supplies 48V to the circular transmitter coil. • An inductive motor load of 24W is connected to the receiver coil. • The LC Tank on both the transmitter and receiver board has a parallel resonance. • The test case for automatically switching transmitter circuit 2 follows the same test case. Figure 3.10: Test set-up of 4 parallel center-tapped circular coils 1 Power Supply - 48V DC 2 Transmitter Board 3 Receiver Board 4 Tx and Rx Coils 5 DC Motor The wireless power system operating under conditions where the circular Tx and Rx coils are tested for the different misalignments. The main objective of this test is to study the induced voltage versus misalignment. The Rx coil of inductance 53µH (circular coil 2) is used to misalign, with the Tx coil. For the 49 3. Case Setup vertical misalignment, the receiver is kept at a 180mm vertical distance from the transmitter, for the lateral misalignment the receiver is 50% (100mm) on the transmitter and for the angular misalignment the receiver is at 40◦ angle above the transmitter. 3.1.3.2 Point to multi-point power transfer The main objective of testing the circular coils is to study the point to multipoint power transfer capability of the circular coils with different form factor. The circular coil design has multiple coils which we have used to analyse point to multipoint power transfer. The combination of coils used for this setup are, • Tx coil - Circular coil 1 • Rx coils - Circular coil 4 & 5 The distance between the transmitter coil and the receiver coil is at 50mm and there is no misalignment between the coils. For driving the centre-tapped Tx circular coil 1, a Tx board with 4 BJTs is used and two 24V DC motors are connected to the Rx circular coil 4 & 5. The LC Tank on both the transmitter and receiver board has a parallel resonance and a corresponding resonant capacitor is used for both the Rx coils. Table 3.6: Resonant capacitors for circular coils used in point to multi-point power transfer Coil Inductance Resonant Capacitor Circular Coil 1 555µH 0.7µF Circular Coil 4 16µH 24µF Circular Coil 5 1035µH 4µF 50 3. Case Setup 3.2 Proposed wireless power system The main objective of the proposed system is to achieve alignment freedom for the Rx coil in a given space of (15cm x 15cm x 15cm) by generating an electromagnetic field in the space. Additionally, the section aims to investigate suitable coil geometry for Tx. In this section, we utilize different coil geometries on the Tx side and investigate their influence on the magnetic field and coupling. There are two major models in this section where we use concentric coils and series-connected concentric coils as Tx, with a solenoid as Rx for both. From the investigation of different coil geometries for Rx, it is found that the use of a solenoid as Rx has better coupling with the concentric Tx coil under misaligned operation. Hence, concentric coils are connected in series to distribute coil turns into smaller areas to increase coupling with the solenoid Rx coil. The section also presents the half-bridge circuit used to drive the transmitter coils. 3.2.1 Investigation of suitable transmitter coil geometry This section introduces all the designed coils used in the proposed system and the corresponding coil parameters. There are 2 types of Tx coil geometries inves- tigated namely concentric and series-connected concentric coils. The transmitter and receiver coil geometry combinations are as follows, • Concentric Tx coil - Concentric Rx coil. • 2 Series connected concentric Tx coil - Solenoid Rx coil. • 8 Series connected concentric Tx coil - Solenoid Rx coil. The coil parameters are measured using Agilent’s E4980A Precision LCR Meter with a frequency setting of 800KHz & 1MHz based on the operating frequency of half-bridge transmitter circuit used to drive the coils. Also, the coils are measured without the resonant capacitors connected. Figure 3.11 and table 3.7 show the concentric coils and their parameters respectively. Concentric coil 1 is used as Tx, and concentric coil 2 & 3 are used as Rx. concentric coil 1 & 2 have equal diameters, while concentric coil 3 is smaller in diameter compared to the other two coils. 51 3. Case Setup Figure 3.11: Custom-built concentric coils wound using cable magnetic wire Table 3.7: Concentric coil parameters and their corresponding resonant capacitors at a resonant frequency of 800KHz Coil Inductance No. of Turns DC Resistance Inductive Reactance Q Factor Resonant Capacitor Concentric Coil 1 32.29µH 15 1.08Ω 161.73Ω 145.75 1.60nF Concentric Coil 2 27.95µH 15 0.78Ω 140.53Ω 178.56 1.41nF Concentric Coil 3 59.25nH 7 0.37Ω 25.96Ω 105.35 872.48nF Figure 3.12 and table 3.10 show the series-connected concentric Tx and solenoid Rx coils and their respective parameters. The dimensions of the series-connected coils and solenoid coils are shown in tables 3.8 and 3.9, respectively. 2 series- connected coils are used to generate a horizontal magnetic field and investigate the possibility of increasing coupling with the solenoid Rx coil. This system is then expanded to 8 series-connected coils on the Tx side to form a space with dimensions of (15 cm x 15 cm x 15 cm). The electromagnetic field generated by the 8 series-connected coils is picked up by the solenoid Rx coil to power a DC lamp load. 52 3. Case Setup Figure 3.12: Series connected concentric Tx and solenoid Rx coils used in proposed system Table 3.8: Series connected concentric coil dimensions Coil Coil Thickness Coil Inner Diameter Coil Outer Diamter Shielding Thickness 2 Series Connected Coil 1.5mm 45.20mm 105mm 1mm 8 Series Connected Coil 1.5mm 10mm 49.5mm 1mm 53 3. Case Setup Table 3.9: Dimensions of solenoid Rx coils used in proposed system Coil Coil Thickness Coil Inner Diameter Coil Outer Diameter Coil Hieght Solenoid Coil 1 1.5mm 5mm 11.5mm 20mm Solenoid Coil 2 1.5mm 5.45mm 7.8mm 40mm Table 3.10: Series connected concentric and solenoid coil parameters and their corresponding resonant capacitors at a resonant frequency of 1MHz Coil Inductance Number of Turns DC Resistance Inductive Reactance Q Factor Resonant Capacitor 2 Series-connected 81.65µH 46 1.30Ω 0.40Ω 8.32 0.63nF 8 Series-connected 71.90µH 112 0.25Ω 451.75Ω 166.74 0.35nF Solenoid Coil 1 37.25µH 26 2.33Ω 233.52Ω 101.49 0.68nF Solenoid Coil 2 160µH 70 0.021Ω 998.12Ω 37.15 0.15nF 3.2.2 800kHz Half bridge converter The main objective of testing different coils using half-bridge circuit is to increase the operating frequency and voltage of the transmitter circuit. The half-bridge circuit helps in increasing the range and can operate at higher power levels. Go- ing higher in frequency can help to study the effect of frequency on the range, misalignment and power transfer. Figure 3.13 shows the block diagram of the proposed high frequency half bridge Tx circuit and Rx circuit. Figure 3.13: Block diagram of proposed 800KHz half bridge transmitter circuit & receiver circuit Table 3.11 shows the key specification of the proposed half bridge circuit. Table 3.12 and table 3.13 shows the list of components required to build the proposed transmitter and receiver board respectively. 54 3. Case Setup Table 3.11: Key system specification of 800kHz half bridge circuit Parameters Specification Input Voltage 48V DC Maximum Current 10A Rectifier Input Voltage 48V AC Frequency 800kHz Maximum Power 480W Coil Distance 10cm Table 3.12: Components required to build proposed 800kHz half bridge circuit Sl No Component Value 01 Resistors 1kΩ & 1.2kΩ 02 Potentiometer 50kΩ & 1MΩ 03 Inductors 20µH & 100µH 04 Capacitors 100µF, 1000µF, 2200µF & 100nF 05 LED 3mm 06 Zener Diode 1N5822 & MUR460 07 MOSFET IRF540N 08 MOSFET Driver IR2184PBF 09 12V Voltage Regulator LM2576HVT 10 5V Ericsson Flex Converter PKU4717YA 11 µ Controller ATmega328 Arduino Nano 12 Display OLED Display Table 3.13: Components required to build receiver rectifier circuit Sl No Component Value 01 Diode ERC84009 02 Inductor 20µH 03 Capacitor 100µF 04 Resistor 1kΩ 05 LED 3mm Figure 3.15 and 3.16 shows the schematic diagram of the high frequency half bridge Tx and Rx circuits respectively. For explaining the working of the half bridge circuit, 2 MOSFETs with the transmitter tuned inductor and the capacitor section is shown in the figure 3.14, a) DC power supply of 48V is connected to the drain of the MOSFET(Q1). When the PWM is applied to the gate of the MOSFET(Q1) and MOSFET(Q2) 55 3. Case Setup is off. The current flows through the MOSFET(Q1) and charges the LC tank CTx and LTx. b) When the MOSFET(Q1) is off the PWM is applied to the MOSFET(Q2). The energy stored in the CTx and LTx is discharged as the MOSFET(Q2) is closed and completes the circuit. The charging and discharging action of the LC tank creates an alternating mag- netic field. This magnetic field is alternating at high frequency according to the frequency set by the PWM. Figure 3.15 has the power circuit and the half bridge circuit. The 48V DC is converted to 5V DC with Ericsson flex converter (series DC-DC converter) to supply the micro-controller and the OLED display. The 48V is converted to 12V DC with a high voltage version of linear voltage regulator - LM2576HVT. The arduino nano is programmed to generate 800kHz at the digital pin D9 where a smoothing resistor R5 is connected. The IC IR2184PBF takes the high frequency PWM from the arduino and then drives the MOSFETs Q1 and Q2. The Tx coil and a resonant capacitor is connected to the drive point to the ground in the circuit where the high frequency at 48V is generated. Figure 3.14: Working of proposed half bridge transmitter circuit 56 3. Case Setup Figure 3.15: Schematic diagram of proposed 800kHz half bridge transmitter circuit Figure 3.16: Schematic diagram of the receiver rectifier circuit 3.2.2.1 Concentric coils The concentric coil combination is intended to investigate the possibility of in- creasing the range and power transfer by increasing the coil diameter. Figure 3.17 shows the test setup of concentric coils 1 & 2 using 800kHz half-bridge converter. 57 3. Case Setup Figure 3.17: Test set-up of concentric coil 1 as Tx & concentric coil 2 as Rx using 800kHz half-bridge converter 1 Power Supply - 48V DC 2 Power Board 3 Transmitter Board 4 Tx Coil 5 Rx Coil 6 Receiver Board 7 DC Motor The test case for the concentric coils under aligned operating conditions are as follows, • The distance between the concentric Tx coil 1 and concentric Rx coil 2 is at 17.5cm and there is no misalignment between the coils. • After testing the concentric Rx coils 2 & 3 under normal operation for the induced voltage, the best coil is selected for misalignment and in this case concentric coil 2 is misaligned. • The power transmitter board is operating at a switching frequency of 800kHz and supplies 48V to the concentric transmitter coil. • A 50W motor is connected to the receiver coil as load. • The changing coils on the Tx and Rx boards change the resonant frequency of the LC Tank and hence a suitable tuned capacitor is used for each coil to maintain the system resonant frequency at 800KHz. • The LC Tank on both the transmitter and receiver board has a parallel resonance. 58 3. Case Setup The test case for the concentric coils under misaligned operating conditions has a value for the vertical misalignment, the receiver is kept at a 180mm vertical distance from the transmitter, for the lateral misalignment the receiver is 50% (100mm) on the transmitter and for the angular misalignment the receiver is at 40◦ angle above the transmitter. The voltage and current plots of the Tx and Rx coils are measured at the input terminal of the receiver board. 3.2.2.2 2 Series-connected concentric coils Figure 3.18 shows the test set-up of 2 series-connected concentric Tx coil & solenoid Rx coil 1 using 800kHz half-bridge converter. The test case for the 2 series con- nected concentric coils under aligned operating conditions are as follows, • The test is carried out with 2 series-connected concentric coil as Tx coil and solenoid coil 1 as Rx coil. • The distance between 2 series-connected concentric Tx coil and solenoid Rx coil 1 is at 30mm and there is no misalignment between the coils. • The power transmitter board is operating at a switching frequency of 800kHz and supplies 48V to the concentric transmitter coil. • A DC load of 10W is connected to the receiver coil. • The LC Tank on both the transmitter and receiver board has a parallel resonance. 59 3. Case Setup Figure 3.18: Test set-up of 2 series-connected concentric Tx coil & solenoid coil 1 as Rx using 800kHz half-bridge converter 1 Power Supply - 48V DC 2 Power Board 3 Transmitter Board 4 Tx Coil 5 Rx Coil 6 Receiver Board 7 LED 8 DC Motor The test case for 2 series-connected concentric coils under misaligned operating conditions has a value for the horizontal and vertical rotation 180◦ at a distance of 30mm. The voltage and current plots of the Tx and Rx coils are measured at the input terminal of the receiver board. 3.2.3 1MHz half-bridge converter Infineon half-bridge converter board is used to drive 8 series-connected concentric transmitter coil to demonstrate the equal distribution of magnetic field in a given space of (15cm X 15cm X 15cm). The Infineon converter is a GaN based half- bridge circuit with dedicated gate driver ICs and isolated power supplies for the gate drivers. The board consists of a half-bridge of GaN power transistors, GaN gate driver ICs, power supply for gate drivers, and input logic to adjust the deadtime. The converter can be configured to operate in either buck or boost mode by connecting an external inductor. The half-bridge converter board is shown in figure 3.19. The specifications of the Infineon half-bridge converter board is shown in table 3.15. 60 3. Case Setup Figure 3.19: Front & back view of Infineon’s GaN based half-bridge converter The block diagram of half-bridge converter board setup is shown in figure 3.20. Table 3.14 has the list of equipment required for series connected coils using Infineon’s GaN based half-bridge converter test setup. The transmitter block has 48V DC line power supply for the half bridge and 5V DC is supplied as the board power which supplies control and logic circuits. In the board power supply of 5V, the current is limited to 250mA as the high current flow may destroy the control and logic ICs. The parameters in the signal generator are set according to the table 3.16 and then connected to the board by a 50Ω MMCX coaxial connector. The circuit connection and the terminals in the Infineon’s GaN based half-bridge converter is as shown in the figure 3.20. The Tx coil is connected to the Vo and Vsw of the Infineon’s GaN based half-bridge converter which refers to the inverted double-pulse test from the data sheet (Infineon datasheet). The receiver coil is a solenoid and is directly connected to an LED to demonstrate the concept of the equal distribution of electromagnetic field in a space. Table 3.15 lists the specifications for GaN based half-bridge converter. Figure 3.20: Block diagram of proposed wireless power system with 8 series connected concentric transmitter coil 61 https://www.infineon.com/dgdl/Infineon-ApplicationNote_EvaluationBoard_EVAL_1EDF_G1_HB_GAN-ApplicationNotes-v01_02-EN.pdf?fileId=5546d46268554f4a01685ac9e48d0291 3. Case Setup Table 3.14: Equipment required for series connected coils using Infineon’s GaN based half-bridge converter test setup Equipment Required Specification Signal Generator 2MHz Coaxial Connector 50ΩMMCX DC Power Supply 5V, 48V Infineon’s Half Bridge GaN based Table 3.15: Specifications for GaN based half-bridge converter obtained from Infineon datasheet Parameters Specifications Board Input Voltage 5V Board Input Current 50 - 250mA PWM Input Level 5V Half-bridge Input Voltage 0 - 450V Half-bridge Maximum Current 35A Operating Frequency ≤ 3 MHz Deadtime Adjustment Range 0 - 180ns Table 3.16: List of parameters for signal generator in the case setup of series connected concentric Tx and solenoid Rx Param