`
`DESIGN CONSIDERATIONS FOR
`
`
`
`INDUCTIVELY COUPLED POWER
`
`TRANSFER SYSTEMS
`
`By
`
`
`
`Chwei-Sen Wang
`
`"
`
`A thesis submitted in partial fulfillment of the requirements for the
`degree of Doctor of Philosophy in Electrical and Computer
`Engineering, The University of Auckland, 2004
`
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`Page 001
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`� t, t, ::· I
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`ABSTRACT
`
`Inductively coupled power transfer (ICPT) systems use electromagnetic fields to transfer electric
`power from a primary source (power supply) to one or more secondary loads (pickups). Because there
`is no physical contact between the primary and secondary, ICPT systems are intrinsically safe and
`reliable. This technology has been significantly commercialised for around a decade. Present
`applications include material handling, public transport, and battery charging.
`This thesis focuses on the design of ICPT systems for high power applications where both the
`primary and secondary coils are compensated by capacitors. The main aim is to develop systems with
`smaller size, less weight, lower cost, greater power and better efficiency. Previous work in this field
`has concentrated on either the power supply or the pickup. This thesis instead focuses on the
`interactions between the power supply and the pickup. When power is transferred from the primary to
`the secondary, the primary is affected by the secondary loading. This can result in poor displacement
`power factor (DPF), reduced power transfer capability, and a loss of controllability.
`First, steady state linear mathematical models are developed to represent the load seen by the power
`supply that includes the primary compensation capacitor, the electromagnetic structure, the secondary
`compensation capacitor, and the pickup load. These models quantify the system behaviour in terms of
`the fundamental design parameters, and are used to evaluate a design procedure for ICPT systems.
`This evaluation provides an insight into the system, enabling suitable design decisions as well as
`quantification of frequency bifurcation boundaries in variable-frequency systems.
`Several new primary tuning schemes are also proposed, taking into account the secondary loading
`effects. In loosely coupled systems, the primary and secondary resonant circuits can be tuned
`independently as the secondary loading effect on the primary are negligible. In well-coupled systems,
`the secondary loading affects the primary resonance significantly, and the proposed new tuning
`schemes greatly improve the DPF and power transfer capability. Various sensitivity analyses to
`variations in the primary and secondary compensation capacitances as well as misalignment of the
`electromagnetic structure show that systems designed using the proposed new tuning schemes have
`similar sensitivities compared with the original tuning.
`Throughout the thesis work, an LCL resonant inverter driving a contact-less electric vehicle battery
`charger was used to verify the proposed theory. The operation of this inverter under discontinuous
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`current mode is also investigated. A novel design procedure is detailed and verified that enables this
`inverter to deliver maximum power to the load.
`
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`ACKNOWLEDGEMENTS
`
`The author sincerely appreciates the supervision of Dr. Grant A. Covic and Dr. Oskar H. Stielau.
`Because of their wisdom and patience, the research work is always in a natural process going in the
`right direction. Particular thanks go to Prof. John T. Boys. His experience and leadership enabled this
`work to be carried out smoothly within the research group of inductive power transfer technology. The
`author is grateful for the wise advice and encouragement from EmPr. Ray Meyer. Additional thanks go
`to the power electronic research group, in particular Dr. Patrick A. Hu, Mr. Howard Lu and Mr.
`Edward Xu. Finally, it is an honour to have financial support, as a Doctoral Fellow (Top Achiever
`Doctoral Scholarship), from the Foundation of Research, Science and Technology (FRST), New
`Zealand.
`In memory of my father, Lien-Jiin.
`To my loving, Yu (mother), Annie (wife), Ya-Ting and Ya-Wei (daughters).
`Chwei-Sen Wang
`Auckland, New Zealand
`Oct. 21, 2004
`
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`CONTENTS
`
`Abstract
`Acknowledgements
`Contents
`Nomenclature
`xv
`List of Figures
`List of Tables •••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••
`
`XXV
`
`Chapter 1 Introduction
`
`Chapter 2 Overview of ICPT Systems
`
`1-1 Background ofICPT Systems
`1-2 Fundamental Structure ofICPT Systems
`1-3 Motivations of the Research
`1-4 Contributions of the Thesis
`1-5 Scope of the Thesis
`References
`2-1 2-2 Introduction
`Electromagnetic Structures
`2-2.1 Material
`2-2.1.1 Magnetic Cores
`2-2.1.2
`Conductor Windings
`2-2.2
`Geometry
`2-2.2.1 Primary Electromagnetic Structures
`2-2.2.2
`Secondary Electromagnetic Structures
`Electromagnetic Coupling Model
`2-2.3
`
`i iii V xi
`1 1 4 4 6 8 9
`11 11 11 12 12 13 13 13 14
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`-v-
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`15
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`2-3
`
`•••••••••••• i ••••••••••••••••••••••••••••••••••••••
`
`....•..•..............•....................•....
`
`2-2.4 Capability of the Electromagnetic Structure
`2-2.4.1 Load Voltage and Current
`2-2.4.2 Power Transfer Capability
`Compensation
`2-3.1 Secondary Compensation
`2-3.2 Secondary Resonance
`2-3.3 Primary Compensation
`2-3.4 Primary Resonance
`2-3.5 Basic Compensation Topologies
`2-4
`Power Converters
`2-4.1
`2-4.3 Overview of Power Converters .....•.........•.........•........•................. � .
`2-4.2
`Voltage-Sourced Power Converters
`Current-Sourced Power Converters
`2-4.4 Impedance Matching
`2-5
`Controllers
`Power Flow Regulation
`2-5.1
`2-5.2
`Frequency Control
`2-5.3
`2-5.5 Switching Control in Voltage-Sourced Full-Bridge Inverters
`2-5.4
`Switching Control in Current-Sourced Full-Bridge Inverters
`Bifurcation Phenomenon
`2-6 2-7
`Future Trends
`Conclusions
`References
`Chapter 3 Development of a General Load Model
`Introduction
`Overview of the Load Model
`The Pickup Load
`3-3 3-4 3-5 3-6 3-7
`The Secondary Resonant Circuit
`The Secondary Quality Factor
`The Reflected Impedance
`Pickup Behaviour and Influences on the Primary
`3-7.1 Operation at the Secondary Resonant Frequency
`
`3-1
`
`3-2
`
`-VI -
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`17 17
`
`18 20 20 21 22 23 24 25 25 27
`28 30 31 31 32 32 33 34 36 38 38
`47 49 50 51 52 54 54
`
`47
`47
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`3-9 The Primary Quality Factor
`3-10 The Power Supply Load Model
`
`4-2
`
`4-3
`4-4
`4-5
`
`65
`67
`67
`
`76
`
`86
`88
`92
`92
`
`Normalization of the Impedance Model
`3-7.2
`56 56 59 61
`Influence of Frequency on the Pickup Behaviour
`3-7.3
`3-7.4
`Influence of Frequency on the Reflected Impedance
`3-7.5
`Operating Conditions for Maximum Power Transfer
`3-8 The Primary Coil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
`3-10.1 Modelling of the Power Supply Load Impedance
`3-10.2 The Normalized Load Impedance
`69 71 75
`3-11 Verification of the Load Model
`3-12 Conclusions
`References
`Chapter 4 Evaluation of a Design Methodology for ICPT Systems
`77
`77 77 78 79
`4-1
`Introduction
`4-2.1 Design of Ordinary Transformers
`A Design Procedure
`4-2.2 Design of ICPT Systems
`4-5.1 Sensitivity of the Displacement Power Factor
`4-5.2 System Behaviour using a Fixed-Frequency Controller ....................... .
`4-5.3 System Behaviour using a Variable-Frequency Controller
`98 101
`4-5.4 Design Considerations
`104 105 109 110
`Chapter 5 Tuning to Improve Power Transfer for Variable-Frequency Systems 113
`113
`114
`
`Design Options for the Pickup Regulator
`Design Options for the Power Supply
`Design Evaluations
`
`, r·
`
`, .. ..
`r,
`
`4-6
`A Practical Design Example
`4-7
`Conclusions
`References
`
`5-1 Introduction
`5-2 Primary Tuning for Unity DPF at Rated Load
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`5-3 rower Transfer Capability and Bifurcation Phenomenon ........................ 117
`5-4 Bifurcation Criteria
`........................................................................ 130
`5-5 Discussion ....................................................................................... 139
`5-6 Verification
`.................................................................................... 143
`5-7 Conclusions
`.................................................................................... 145
`References ............................................................................................. 146
`Chapter 6 Tuning to Improve DPF for Fixed-Frequency Systems .................. 149
`6-1 Introduction .................................................................................... 149
`6-2 System Behaviour with Primary Tuning for Unity DPF at Rated Load ...... 149
`6-3 Primary Tuning for Load Independent Unity DPF ............................... .'. 154
`6-3.1 Primary Capacitance and Operating Frequency
`......................•.....•. 155
`6-3.2 Power Transfer Capability and Secondary VA Rating ........................ 156
`6-4 Discussion ....................................................................................... 163
`6-5 Design Examples .............................................................................. 164
`6-6 Verification
`.................................................................................... 167
`6-7 Conclusions
`.................................................................................... 170
`Chapter 7 A Sensitivity Analysis of Systems Using the Proposed Primary
`Tuning Schemes ........................................................................ 171
`7-1 Introduction .................................................................................... 171
`7-2 Fundamentals of the Sensitivity Analysis ............................................. 172
`7-3 Compensation Capacitor Selection ...................................................... 173
`7-4 The Influence of Variations in Primary Capacitance .............................. 177
`7-4.1 Fixed-Frequency Systems ............................................................ 177
`7-4.2 Variable-Frequency Systems ......................................................... 182
`7-5 The Influence of Variations in Secondary Capacitance ........................... 184
`7-5.1 Fixed-Frequency Systems ............................................................ 184
`7-5.2 Variable-Frequency Systems .................................................•....... 188
`7-6 The Influence of Misalignment in the Electromagnetic Structure
`............ 190
`7-6.1 Coupling Parameter Variations in an Electric Vehicle Battery Charger ... 191
`7-6.2 Fixed-Frequency Systems ...........................•................................ 192
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`Chapter 8 Investigating an LCL Resonant Inverter for ICPT Applications
`
`7-6.3 Variable-Frequency Systems
`199
`7-7 7-8
`Discussion
`206
`Conclusions
`209
`209
`References
`211 211
`8-1 8-2
`Introduction
`Overview of the System
`······························ 212 212
`8-2.1 Operating Modes of the LCL Resonant Inverter
`8-2.2 An Analytical Procedure for System Design
`214 214
`8-3
`Capability of the Inverter
`8-3.1 The Inverter Model
`214
`8-3.2 Waveform of the Inverter Current
`215
`8-3.3 Inverter Power Delivery Capability
`218
`8-3.4 Fundamental Component of the Inverter Current
`219
`8-4
`Capability of the Resonant Tank
`221
`8-4.1 The Resonant Tank Model
`221
`8-4.2 Operating Frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
`8-4.3 Power Absorption Capability
`223
`8-5
`Steady State Power Flow Analysis
`225
`8-5.1 An Analytical Procedure for Steady State Analysis
`225 225 228
`8-5.2 The Switching Instants and the Series Inductance
`8-5.3 Behaviour at Light Load
`8-6
`Verification
`229
`....•.......................•......•........•......•........................•.......
`, 8-7
`Conclusions
`230
`.•..................................................................................
`References
`............................................................................................. 231
`233
`Chapter 9 Conclusions and Future Work
`9-1 Conclusions
`233
`...•.......•.......•.......................•.......•................................
`9-1.1 Variable Frequency Systems ........................................................ .
`233
`9-1.2 Fixed Frequency Systems
`235 235
`9-2
`Future Work ................................................................................... .
`References
`237
`.............................................................................................
`-ix -
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`Appendices
`................................................................................................ 239
`A. Primary Voltage and Current Gains ................................................... 239
`B. Reactive and Real Powers of the Pickup Coil
`....................................... 241
`C. Quantified Secondary Current ............................................................ 242
`D. Normalized Reflected Impedance of Compensated Pickup
`..................... 243
`.......................................... 244
`E. Quantified Impedance of the Primary Coil
`F. Normalized Reactance of the Primary Capacitance for Systems with
`Compensated Pickup ........................................................................ 244
`G. Normalized Impedance Functions for Systems with Uncompensated Pickup 245
`••••••••••••••••••••••••••••••••••••••••••••••••••• 246
`H. Primary Tuning for Unity DPF at co0
`Primary Tuning for Load Independent Unity DPF ................................. 250
`I.
`J. Maximum Allowable Alternating Voltage and Current in Capacitors
`...... 252
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`NOMENCLATURE
`
`• Iac,rated
`
`Id
`
`Cm
`�p·
`
`Description
`Symbol
`Capacitor-capacitor-inductor.
`CCL Ci, C2
`Capacitors of inverters.
`de capacitance.
`Cd
`Matching capacitance in CCL inverter.
`Primary compensation capacitance.
`Normalized primary compensation capacitance.
`Secondary compensation capacitance.
`Cpn Cs
`D, D1, D2, D3, D4 Diodes of inverters.
`Displacement power factor.
`DPF
`Equivalent series resistance of capacitors
`ESR
`Frequency (Hz).
`f, fo, ft, fi
`RMS current.
`I i
`Instant current.
`Rated ac current of capacitors.
`Inductively coupled power transfer.
`ICPT
`Secondary capacitor current.
`lcs
`de source current.
`de load current.
`Primary current gain.
`Ide loAIN
`Inverter output current.
`ii, Ii
`Inverter output current at roo.
`liO ImZ
`Imaginary component of the impedance (Z).
`Primary current.
`ip, Ip
`Pickup load current.
`iR, IR
`Secondary current.
`is, Is
`Rated secondary current defined at ro0•
`
`Iso,rated
`
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`lsc lsn k kn LCL Ld Lm Lp Ls M Mn Np Ns pp PS p Pi
`
`Pn Prated Q Qp Qpo
`
`Qso,rated
`
`Qs Qso
`Q;O,rated
`R �c
`ReZ
`SP
`ss Ss S, S1, S2, S3, S4
`T
`
`Short circuit current of the pickup.
`Normalized secondary current.
`Magnetic coupling coefficient.
`Equivalent coupling coefficient of n pickups.
`Inductor-capacitor-inductor.
`de inductance.
`Matching inductance in LCL inverter.
`Primary self-inductance.
`Secondary self-inductance.
`Mutual inductance.
`Equivalent mutual inductance of n pickups.
`Turn number of the primary coil.
`Turn number of the secondary coil.
`Parallel-compensated primary and secondary.
`Parallel-compensated primary and series-compensated secondary.
`Power.
`Inverter power delivery.
`Normalized power.
`Rated power defined at mo.
`Quality factor.
`Primary quality factor.
`Primary quality factor at m0•
`Secondary quality factor.
`Secondary quality factor at mo.
`Rated secondary quality factor defined at m0 I .J1 -k2
`Rated secondary quality factor defined at mo.
`Pickup ac load (Equivalent ac resistance).
`Pickup de load.
`Real component of the impedance (Z).
`Series-compensated primary and parallel-compensated secondary.
`Series-compensated primary and secondary.
`Apparent power (complex power) of the secondary coil.
`Switches of inverters.
`Period.
`
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`V
`
`t, t1, t2, h
`tn, tnJ, tn2, tn3
`u
`V
`VAcs
`VAs
`VAsn
`VAso
`VAso,rated
`Vac,rated
`VAR
`VARp
`VARs
`Yes vd
`Vdc
`VaAIN
`Vi, Vi
`viO Voe
`Vp, Vp
`Vpo
`VP
`Vpn
`Vs, Vs
`Vso,rated
`Vsn
`Yt
`Yin Zp
`Zr Zr0
`
`VR, VR
`
`Time.
`Normalized time.
`Normalized operating frequency.
`RMS voltage.
`Instant voltage.
`Required VA rating of the secondary compensation capacitor.
`Required secondary VA rating.
`Normalized required secondary VA rating.
`Required secondary VA rating at roo.
`Rated secondary VA rating defined at roo.
`Rated ac voltage of capacitors.
`Reactive power.
`Primary reactive power.
`Secondary reactive power.
`Secondary capacitor voltage.
`de source voltage.
`de load voltage.
`Primary voltage gain.
`Inverter output voltage.
`Inverter output voltage at roo.
`Open circuit voltage of the pickup.
`Primary voltage (parallel resonant tank voltage).
`Primary voltage at roo.
`Peak primary voltage (parallel resonant tank voltage).
`Normalized primary voltage (parallel resonant tank voltage).
`Secondary pickup load voltage.
`Secondary voltage.
`Rated secondary voltage defined at roo.
`Normalized secondary voltage.
`Load admittance seen by the power supply.
`Normalized load admittance seen by the power supply.
`Impedance of the primary track/coil.
`Reflected impedance.
`Reflected impedance at w0 •
`
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`Zr0,rated
`
`Zm
`
`Zs
`
`Z1 Zm Zin
`
`0) roo 81 <l>1 <I> tan 8
`
`Rated reflected impedance defined at ro0•
`Normalized reflected impedance.
`Secondary load impedance.
`Load impedance seen by the power supply.
`Load impedance seen by the power supply at cv0
`Normalized load impedance seen by the power supply.
`Frequency (rad/s).
`Nominal frequency (Secondary resonant frequency).
`Phase of the load impedance seen by the power supply.
`Phase between the fundamental inverter current and the parallel primary voltage.
`Phase between the primary and secondary currents.
`Dissipation factor of capacitors
`
`•
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`LIST OF FIGURES
`
`2
`Application examples from Daifuku (Japan).
`. • . •• . • . •• . •• .• . . .• . .• ••• . . . . .• • . . . . • . •. • . . . . • . . • . •
`Public transport system (New Zealand).
`2
`3
`Application examples from Wampfler (Germany). .......................................
`. ...............•..........................•....... 4
`The block diagram of an ICPT system.
`................ .......................... 15
`.................................... 15
`•. .•. .. .•••..•.•••••. ....•.•.. .. .•.••..•... •. 14
`Common configurations of the primary coil.
`................................. 16
`Common configurations of the secondary core.
`. • . • . . . . . 17
`Circuit of the mutual inductance transformer model.
`............ 18
`The sinusoidal mutual inductance transformer model.
`Equivalent secondary circuit supplying power to a linear and resistive load.
`The normalized load voltage and current of the uncompensated pickup.
`• . .• . • . • . • . . . . • . • . . • . . . . • • . . . . • . . . • . .• . . . . • • • . • .• • .. . .• . • • • . 20
`Series-compensated secondary-.
`• . • . • . . . • . • . • . . . • . • . . . • . • . . • . • • . . • . . • . • . • . . • . . • . • • . • • . • • . 20
`Parallel-compensated secondary.
`Normalized load voltage and current characteristics of uncompensated as well as
`. • . • • . . • . • . • • • . • • . • . . . . . • . . • . • • • . . • • • • . . • . • . . • • . 22
`series and parallel-compensated pickups.
`. . . . . . . . . . . . . . . . . . . . . . • . . . . . . . • . . . . . . . . . . . . . . . • . . . . . . . . . . . . . . . . 23
`Series-compensated primacy.
`Fig. 2-10.
`.....•......•............•..................•.........•..... 23
`Fig. 2-11. Parallel-compensated primacy.
`
`Fig. 1-1.
`Fig. 1-2.
`Fig. 1-3.
`Fig.1-4.
`Fig. 2-1.
`Fig. 2-2.
`Fig. 2-3.
`Fig. 2-4.
`Fig. 2-5.
`Fig. 2-6.
`Fig. 2-7.
`Fig. 2-8.
`Fig. 2-9.
`.. .. .. .. .. .. .. .. . .. .. .. .. . .. . .. . .. .. .. . 24
`Fig. 2-12. Basic compensation topologies ofICPT systems.
`Fig. 2-13. The block diagram of a power converter in an ICPT system. .. .. .. .. .. .. .. .. .. .. .. .. .. . 25
`••..•.•..•.•.•.••.•..•.........•....... 27
`Fig. 2-16. The voltage-sourced full-bridge power converter.
`.. . .. .. .. .. .. .. .. . .. .. .. .. . .. .. . .. .. .. . 28
`Fig. 2-17. The voltage-sourced half-bridge power converter.
`Fig. 2-18. Voltage-sourced single-switch power converters.
`.. .. • .. .. .. ... . .. .. .. .. . .. . .. .. .... .. .. 28
`.. .. .. .... . .. .. .. .. .. .. .. .. .. .. .. .. .. .. 29
`Fig. 2-19. The current-sourced full-bridge power converter.
`Fig. 2-20. The current-sourced half-bridge power converter.
`. . . . . • . . . . . . • • • . . . . . . . . . . • . • • . . . . • . . . • . 29
`Fig. 2-21. Current-sourced single-switch power converters.
`.....•.•..•.. .... .....•.•... ... . ... . . .. 29
`-xv-
`
`Fig. 2-14.
`Fig. 2-15.
`
`...•................................................•. 26
`Fundamental types of power source.
`. . . . . . .•................ .. ... . . . . • . . . . . . . .. •..........•. .. .. . . .•. .. . . 27
`Switch configurations.
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`Fig. 2-22. The LCL resonant inverter. . ... .-. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
`Fig. 2-23. The CCL resonant inverter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
`Fig. 2-24. The rectangular inverter voltage being in-phase with the current.
`• . . • • . . • . • . • • • . . . . . . . 33
`Fig. 2-25. The rectangular inverter voltage leading the current.
`.. . .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. 33
`Fig. 2-26. The rectangular inverter voltage lagging the current.
`•... ..•..•..•..•..••....•.•••..•. .. . 33
`Fig. 2-27. Pulse-width of the rectangular inverter voltage is less than a full half cycle.
`......... 33
`Fig. 2-28. The rectangularinverter current being in-phase with the voltage.
`... • .. .. .. .... .. . .. .. 34
`Fig. 2-29. The rectangular inverter current leading the voltage.
`.. .. .. . .. .. .. .. .. • .. .. . .. .. .. .. . .. .. 34
`Fig. 2-30. The rectangular inverter current lagging the voltage. • . . . • . . • . • . . . • . • • . • • . . • . • • • • . . . • . • . • 34
`.. . • . . . • • 34
`Fig. 2-31. Pulse-width of the rectangular inverter current is less than a full half cycle.
`. 37
`Fig. 2-32. Futuristic ICPT applications.
`Fig. 3-1.
`Fig. 3-2.
`.. .. .. ..... • . .. . .. .. .. .. .. .. . .. .. 50
`Fig. �-3.
`.. ...... .. .. .. . • . .. • .. . .. . . ...... 50
`Fig. 3-4.
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
`Fig. 3-5.
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
`Fig. 3-6.
`syste:r:ris.
`Fig. �-7.
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
`systems.
`.. .. .. • . • .. .. .. .. .. • .. .. .. • .. . .. . .. • .. .. .. .. • . . .. .. • 62
`Fig. 3-8.
`Fig. 3-9.
`.................. 64
`Fig. 3-10. . The ratio Zp/GcooLp) with k=0.2.
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
`Fig. 3-11.
`-65
`Fig. 3-12.
`• . • • . . . • . . • • . . . • • • • • • • • • . • . • • . • . . . . • 67
`Fig. 3-13.
`........................ 72
`Fig. 3-14.
`••.•..•..••••.• 73
`............... 74
`Fig. 3-15. Measured and calculated load admittance (Y1) of the battery charger.
`Fig. 4-1.
`. ..................................... : .. . 79
`Fig. 4-2.
`...................... ........ ...•.. .•....... ......... 80
`Fig. 4-3.
`A block diagram of a pickup regulator. . • . . .. • • .. . . .. . . • . . . . • . .. . . . .. . . . . . . . . . . . . . .. .. .. . . . . • 87
`Fig. 4-4.
`. • . . . . . . . • • . . . . . . . • . • • . . . . . 89
`
`. ..............................................................
`Diagram of the load seen by the power supply.
`Full-bridge diode rectifier with inductor output filter.
`_Full-bridge diode rectifier with capacitor output filter.
`. Equivalent circuits of the secondary systems.
`Quantified secondary current.
`Normalized reflected resistance for series and parallel-compensated secondary
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . • . 60
`Normalized reflected reactance for series and parallel-compensated secondary
`Equivalent circuit of the primary coil.
`The ratio Zp/Gro0Lp) at the secondary resonant frequency ro0 (u=l).
`The ratio Zp/GrooLp) with k=0.6.
`Primary resonant circuits with reflected impedance.
`Electromagnetic structure of the contact-less battery charger.
`The measured coupling parameters (Lp, Ls, M) of the battery charger.
`
`AS
`
`A design procedure of the ordinary transformer.
`A design procedure ofICPT systems.
`Examples of current-sourced power supply configurations.
`- xvi -
`
`Momentum Dynamics Corporation
`Exhibit 1025
`Page 018
`
`

`

`Examples of voltage-sourced power supply configurations.
`• • . • . . • . . . . . . . . . . • . . . . . . • . . 90
`Fig. 4-5.
`Sensitivity of DPF to u and kin systems having both the primary and secondary
`Fig. 4-6.
`uncompensated.
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
`Sensitivity of DPF to u and k in systems having a compensated primary and an
`Fig. 4-7.
`uncompensated secondary.
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
`Sensitivity of DPF to u, k and Qso in systems having an uncompensated primary and a
`Fig. 4-8.
`compensated secondary.
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
`Sensitivity ofDPF to u, k and Qso in systems having both the primary and secondary
`Fig. 4-9.
`. ................................ ; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
`compensated.
`Fig. 4-10. DPF operating with fixed frequency at ro0•
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .' . . . . . 99
`Fig. 4-11. Required relationship between k and Qso to achieve unity DPF at ro0 for the PP
`topology.
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
`Selection ofQso to improve DPF when operating at ro0 over a wider range ofk for the
`Fig. 4-12.
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
`PP topology.
`Operating frequency with unity DPF.
`. ..................................................... 102
`Fig. 4-13.
`Frequency shifts for bifurcation-free operations.
`.. ............... � ..................... 104
`Fig. 4-14.
`DPF and power transfer capability of the contact-less electric vehicle battery charger
`Fig. 4-15.
`using a fixed-frequency controller operating at ro0•
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
`Fig. 4.;16. Measured waveforms of the inverter current and the resonant tank voltage for the
`=19.7kHz).
`• ........... 107
`contact-less electric vehicle battery charger (operating at ro0
`Fig. 4-17. Operating frequency and power transfer capability of the contact-less electric vehicle
`battery charger using a variable-frequency controller operating with unity DPF.
`• .. 108
`Fig. 5-1. Primary tuning for unity DPF at rated load.
`. ............................................ 116
`SS topology - Operating frequency and power transfer capability under variable-
`'i ;�
`Fig. 5-2.
`frequency operation.
`. .......... � ............................................................ 122
`SP topology - Operating frequency and power transfer capability under variable-
`Fig. 5-3.
`frequency operation.
`. ....................................................................... 123
`Fig. 5-4. PP topology with loose coupling (k=0.05) -Operating frequency and power transfer
`capability under variable-frequency operation.
`• •..•..•.•....•.•..•...•.•.....•.....••... 124
`Fig. 5-5. PP topology with middle coupling (k=0.2) -Operating frequency and power transfer
`capability under variable-frequency operation.
`.. ........................................ 125
`Fig. 5-6. PP topology with good coupling (k=0.4) -Operating frequency and power transfer
`capability under variable-frequency operation.
`• ......•..........•.•............•..•..... 126
`
`-xvii -
`
`Momentum Dynamics Corporation
`Exhibit 1025
`Page 019
`
`

`

`PS topology with loose coupling (k=0.05) -Operating frequency and power transfer
`Fig. 5-7.
`capability under variable-frequency operation.
`. ......................................... 127
`PS topology with middle coupling (k=0.2) -Operating frequency and power transfer
`Fig. 5-8.
`capability under variable-frequency operation.
`• ......................................... 128
`PS topology with good coupling (k=0.4) -Operating frequency and power transfer
`Fig. 5-9.
`capability under variable-frequency operation.
`.. ........................................ 129
`Fig. 5-10. Normalized load reactance.
`. .............................................................. 132
`Fig. 5-11. Normalized load susceptance.
`. ........................................................... 133
`• •••••.•••••••.•••••••••••.••.•••••••••••••••••.•••.•.•.• 135
`Fig. 5-12. Normalized function G(u,Qpo,Qso).
`Fig. 5-13. Analytical bifurcation boundary for the SS and SP topologies.
`. •...••.....••....•.•••• 137
`Fig. 5-14. Numerical algorithm for finding bifurcation boundary.
`. •.••.•..•..••..•.••.••.•..•..•.. 13 7
`Fig. 5-15. Numerical bifurcation boundary for the PP and PS topologies.
`.. ...................... 138
`Fig. 5-16. Bifurcation boundary defined by k and Qso for the four basic topologies .
`............... 139
`Fig. 5-17. A contact-less electric vehicle battery charger with PP topology -Operating
`frequency and power transfer capability under variable-frequency operation (a
`comparison of the original and modified tuning schemes).
`.. ............................ 144
`Fig. 6-1. SP topology-DPF under fixed-frequency operation at mo assuming modified primary
`tuning to achieve unity DPF at rated load. . .................................................. 151
`Fig. 6-2. PP topology-DPF under fixed-frequency operation at mo assuming modified primary
`tuning to achieve unity DPF at rated load. . ............................. .-.................... 152
`Fig. 6-3. PS topology-DPF under fixed-frequency operation at mo assuming modified primary
`.. ................................................. 153
`tuning to achieve unity DPF at rated load.
`Influences of k to the required change in Cp to achieve load independent unity DPF .••. 156
`Fig. 6-4.
`Fig. 6-5.
`Influence of k to the required change in m to achieve load independent unity DPF (the · · :
`. ...................................................................... ·. 156
`Fig. 6-6. PP topology-System behaviour under fixed-frequen�y operation (Qso,rated=5).
`• ••••• 159
`Fig. 6-7. PS topology-System behaviour under fixed-frequency operation (Qso,rated=5).
`.. .... 160
`Fig. 6-8. Limit of k and Qso,