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`Technische Universität Dresden
`
`INDUCTIVELY COUPLED RADIO FREQUENCY POWER
`
`TRANSMISSION SYSTEM FOR WIRELESS SYSTEMS
`
`AND DEVICES
`
`Kathleen O’Brien
`
`von der Fakultät Elektrotechnik und Informationstechnik
`
`der Technischen Universität Dresden
`
`zur Erlangung des akademischen Grades eines
`
`Doktoringenieurs
`
`(Dr.-Ing.)
`
`genehmigte Dissertation
`
`Vorsitzender: Prof. Dr. rer. nat. Bartha
`
`
`1. Gutachter:
`
`Prof. Dr.-Ing. habil. H. Güldner
`
`2. Gutachter:
`
`Prof. Dr.-Ing. N. Mohan
`
`3. Gutachter:
`
`
`Tag der Einreichung:
`
`Dr.-Ing. G. Scheible
`
`05.12.2005
`
`Tag der Verteidigung:
`
`03.11.2006
`
`1
`
`Momentum Dynamics Corporation
`Exhibit 1007
`Page 001
`
`

`

`Momentum Dynamics Corporation
`Exhibit 1007
`Page 002
`
`
`
`2
`
`Momentum Dynamics Corporation
`Exhibit 1007
`Page 002
`
`

`

`Berichte aus der Elektrotechnik
`
`Kathleen O'Brien
`
`Inductively Coupled Radio Frequency Power
`Transmission System for Wireless Systems
`and Devices
`
`Shaker Verlag
`Aachen 2007
`
`Momentum Dynamics Corporation
`Exhibit 1007
`Page 003
`
`

`

`Bibliographic information published by the Deutsche Nationalbibliothek
`The Deutsche Nationalbibliothek lists this publication in the Deutsche
`Nationalbibliografie; detailed bibliographic data are available in the Internet at
`http://dnb.d-nb.de.
`
`Zugl.: Dresden, Techn. Univ., Diss., 2006
`
`Copyright Shaker Verlag 2007
`All rights reserved. No part of this publication may be reproduced, stored in a
`retrieval system, or transmitted, in any form or by any means, electronic,
`mechanical, photocopying, recording or otherwise, without the prior permission
`of the publishers.
`
`Printed in Germany.
`
`ISBN 978-3-8322-5775-0
`ISSN 0945-0718
`
`Shaker Verlag GmbH • P.O. BOX 101818 (cid:129) D-52018 Aachen
`Phone: 0049/2407/9596-0 (cid:129) Telefax: 0049/2407/9596-9
`Internet: www.shaker.de (cid:129) e-mail: info@shaker.de
`
`Momentum Dynamics Corporation
`Exhibit 1007
`Page 004
`
`

`

`Acknowledgements
`
`I would like to thank my advisors Professor Dr.-Ing. habil Henry Gueldner of Dresden
`University of Technology, Dr.-Ing. Guntram Scheible of ABB Corporate Research,
`Ladenburg, Germany, and Professor Ned Mohan of The University of Minnesota,
`USA.
`
`Thanks also to all of my friends and colleagues at Dresden University of Technology
`and at ABB Corporate Research. Your support was always appreciated.
`
`I am also very grateful to Dr.-Ing. Ralph Teichmann, to my parents Michael and Carol
`O’Brien, and to my sister Elisabeth, without whom this work would not have been
`possible.
`
`
`
`3
`
`Momentum Dynamics Corporation
`Exhibit 1007
`Page 005
`
`

`

`Momentum Dynamics Corporation
`Exhibit 1007
`Page 006
`
`
`
`4
`
`Momentum Dynamics Corporation
`Exhibit 1007
`Page 006
`
`

`

`Table of Contents
`
`1
`
`Introduction........................................................................................................... 19
`
`2 Theory of Magnetic Power Transfer................................................................... 21
`
`2.1 Fundamental considerations ....................................................................................... 21
`2.1.1
`Transfer of energy in an electromagnetic field.....................................................................21
`2.1.2 Near-field operation vs. far-field operation..........................................................................22
`
`2.2 Method of inductive power transfer ........................................................................... 24
`2.2.1
`Sources .................................................................................................................................24
`2.2.2
`Receivers ..............................................................................................................................25
`2.2.3
`Frequency range ...................................................................................................................27
`
`2.3 Review and comparison of systems using inductive power transfer ....................... 28
`2.3.1
`Inductively coupled RFID systems ......................................................................................28
`2.3.2 Magnetic search coil (MSC) systems ...................................................................................28
`2.3.3 Other Systems using inductive coupling ..............................................................................29
`
`2.4 Alternative power supplies .......................................................................................... 29
`2.4.1
`Electric vs. magnetic energy transfer ...................................................................................30
`
`3 Characterization of the Source Field .................................................................. 33
`
`3.1 Basic source coil shapes ............................................................................................... 33
`3.1.1 Magnetic fields due to rectangular coils...............................................................................33
`3.1.2 Magnetic field due to circular coils ......................................................................................34
`3.1.3 Magnetic field at source coil system center points...............................................................35
`
`3.2 Effects of shape and distance between source coils ................................................... 36
`3.2.1
`Coils at Helmholtz distance..................................................................................................36
`3.2.2
`Coils at other distances.........................................................................................................39
`3.2.2.1 Uni-directional systems ..................................................................................................................40
`3.2.2.2 Multi-directional systems ...............................................................................................................43
`
`3.3 Field generation ............................................................................................................ 45
`
`3.4 Uni-directional field generation .................................................................................. 45
`
`3.5 Bi-directional field generation..................................................................................... 46
`
`3.6 Omni-directional field generation............................................................................... 47
`3.6.1
`Periodic switching of the plane of rotation...........................................................................47
`3.6.2
`Frequency shift .....................................................................................................................49
`3.6.3
`Single-axis amplitude modulation........................................................................................52
`3.6.4 Double-axis amplitude modulation ......................................................................................55
`3.6.5 Wide-band operation ............................................................................................................58
`3.6.6
`Comparison of methods for omni-directional field generation ............................................60
`
`
`
`5
`
`Momentum Dynamics Corporation
`Exhibit 1007
`Page 007
`
`

`

`4 Shielding of the Source Field ............................................................................... 63
`
`4.1 Shielding of low-impedance electromagnetic waves.................................................. 63
`
`4.2 Shielding by highly conductive materials................................................................... 65
`4.2.1 Highly conductive objects inside the operating volume.......................................................67
`4.2.2 Highly conductive objects outside the operating volume.....................................................73
`
`4.3 Shielding by highly permeable materials ................................................................... 75
`4.3.1 Highly permeable objects inside the operating volume........................................................76
`4.3.2 Highly permeable objects outside the operating volume......................................................79
`
`4.4 Supplemental solutions to shielding problems........................................................... 80
`4.4.1
`Incremental increase of the current applied to source coil(s) ...............................................81
`4.4.2 Additional coils carrying compensating currents .................................................................81
`4.4.3
`Compensation of conductive shielding with permeable materials .......................................82
`4.4.4
`Ferrite rod antenna................................................................................................................83
`
`4.5 Conclusions ................................................................................................................... 84
`
`5 Equivalent Circuit Representation ..................................................................... 85
`
`5.1 System layout ................................................................................................................ 85
`
`5.2 System description........................................................................................................ 85
`
`5.3 Methods of calculation of coil self and mutual inductances ..................................... 87
`5.3.1
`Flux-linkage per Ampere......................................................................................................87
`5.3.2
`The Neumann formula..........................................................................................................88
`
`5.4 Self-inductance formulas ............................................................................................. 88
`
`5.5 Effect of core magnetization on receiving coil inductance ....................................... 89
`
`5.6 Calculation of mutual inductances ............................................................................. 91
`
`5.7 Coupling factors ........................................................................................................... 93
`5.7.1
`Simplifications and approximations of coupling factors......................................................95
`5.7.2
`Coupling factors between like coil types..............................................................................96
`5.7.3
`Coupling factors with circular source coils ..........................................................................98
`
`5.8 Source and receiving coil characteristics ................................................................... 98
`
`5.9 Equivalent circuit model............................................................................................ 102
`5.9.1
`Coupling factors .................................................................................................................105
`5.9.2
`Extension of the model for multiple source coils ...............................................................107
`5.9.2.1 Multiple source coils on the same axis – single receiving coil.....................................................107
`5.9.2.2 Multiple source coils on different axes – single receiving coil ....................................................108
`5.9.2.3 Single source coil/multiple source coils on a single axis and three-coil receiver.........................108
`5.9.2.4 Multiple source coils – multiple receiving coils...........................................................................109
`
`
`
`6
`
`Momentum Dynamics Corporation
`Exhibit 1007
`Page 008
`
`

`

`6 Power Converter Design .................................................................................... 111
`
`6.1 General system design considerations ...................................................................... 111
`
`6.2 Semiconductor technology......................................................................................... 113
`
`6.3 Tuning circuit characteristics.................................................................................... 114
`6.3.1 Generic single tuned circuits ..............................................................................................114
`6.3.2 Generic double-tuned circuit ..............................................................................................115
`6.3.3 Multiply tuned circuits .......................................................................................................118
`
`6.4 Single channel source side power converter ............................................................ 118
`6.4.1
`Source side load characteristic ...........................................................................................118
`6.4.2
`Source side resonant circuit................................................................................................119
`6.4.3
`Source side power conversion output stage........................................................................119
`6.4.3.1 Tuned operation............................................................................................................................123
`6.4.3.2 De-tuned operation .......................................................................................................................124
`6.4.4
`Source side power conversion input stage..........................................................................125
`
`6.5 Multi-channel source side power converter............................................................. 126
`6.5.1
`Bi-directional field .............................................................................................................126
`6.5.2 Omni-directional field ........................................................................................................127
`6.5.2.1 Periodic switching of the plane of rotation...................................................................................127
`6.5.2.2 Frequency shift .............................................................................................................................130
`6.5.2.3 Double axis amplitude modulation...............................................................................................131
`
`6.6 Receiver side power converter .................................................................................. 132
`6.6.1
`Receiver side winding connection......................................................................................132
`6.6.2
`Receiver side resonant circuit.............................................................................................133
`6.6.3
`Receiver side impedance characteristics ............................................................................134
`6.6.4
`Receiver side converter stage .............................................................................................136
`
`7 Experimental Validation .................................................................................... 139
`
`7.1 Source side systems .................................................................................................... 139
`
`7.2 Receiver side systems ................................................................................................. 141
`
`7.3 Test equipment ........................................................................................................... 142
`
`7.4 Magnetic field validation ........................................................................................... 143
`7.4.1
`Bi-directional field generation............................................................................................143
`7.4.2 Omni-directional field generation ......................................................................................143
`7.4.3 Validation of shielding effects ...........................................................................................145
`
`7.5 Validation of electrical system characteristic .......................................................... 147
`7.5.1 Uni-directional transfer characteristics for axis alignment.................................................147
`7.5.2 Uni and bi-directional transfer characteristics for axis misalignment ................................149
`7.5.3
`Transfer characteristic of aligned omni-directional systems ..............................................151
`
`7.6 Conclusions ................................................................................................................. 152
`
`8 Conclusions.......................................................................................................... 153
`
`
`
`
`7
`
`Momentum Dynamics Corporation
`Exhibit 1007
`Page 009
`
`

`

`Momentum Dynamics Corporation
`Exhibit 1007
`Page 010
`
`
`
`
`
`8
`
`Momentum Dynamics Corporation
`Exhibit 1007
`Page 010
`
`

`

`List of variables, abbreviations, and indices
`
`
`Ds,rms
`
`Dcenter
`
`D*
`
`D
`
`DA
`
`DB
`
`DC
`
`Ds
`
`İ
`
`İ0
`
`ȁsr
`
`G
`
`I
`
`Im
`
`rms shielding factor
`
`Shielding factor at the center of a system
`
`Shielding factor at point *
`
`Angle between the axis of the source and receiving coils
`
`Shielding factor at point A
`
`Shielding factor at point B
`
`Shielding factor at point C
`
`Shielding factor
`
`Permittivity
`
`Permittivity of free space
`
`Flux linkage between a source and receiving coil
`
`Skin depth
`
`Angle between two elements
`
`Modulation angle
`
`Ireceiver
`
`Flux crossing the receiving coil
`
`Ireceivingcoil, max Maximum flux crossing a single receiving coil
`
`Isource
`
`Isr
`
`Istray
`
`ITotal
`
`Ix
`
`Iy
`
`Iz
`
`Irs,max
`
`MH
`
`ȡ
`
`ȡ
`
`Total flux produced by one source coil
`
`Flux linking source and receiving coils
`
`Stray flux
`
`Total flux
`
`Flux crossing the x-coil
`
`Flux crossing the y-coil
`
`Flux crossing the z-coil
`
`Maximum flux crossing a single receiving coil winding
`
`Phase of exciting voltage
`
`Radial distance from the origin of the coil
`
`Radius of a conductor
`
`9
`
`Momentum Dynamics Corporation
`Exhibit 1007
`Page 011
`
`

`

`ı
`
`V rc
`
`'f
`
`O
`
`P0
`
`Prod
`
`Prc
`
`μ
`
`μ’
`
`μi
`
`μr
`
`Z
`
`Zd
`
`Ze
`
`Zm
`
`Zr
`
`Zr0
`
`Zp,res
`
`Zr
`
`Zs,res
`
`T
`
`\
`
`A
`
`a
`
`Conductivity
`
`Conductivity of a shielding material related to copper
`
`Difference between frequencies in a system
`
`Wavelength
`
`Permeability of free space
`
`Effective permeability of a ferrite rod antenna
`
`Permeability of a shielding material related to copper
`
`Permeability
`
`Effective permeability
`
`Initial relative permeability
`
`Relative permeability
`
`Radian operating frequency
`
`Angular frequency of damped resonant circuit
`
`Frequency of the exciting voltage
`
`Modulation radian frequency
`
`Resonant frequency
`
`Ideal Resonant Frequency
`
`Resonant frequency in a parallel resonant circuit
`
`Resonant frequency
`
`Resonant frequency in a series resonant circuit
`
`Angle of rotation relative to the y-axis
`
`Angle of rotation relative to the x-axis
`
`Area enclosed by one receiving coil
`
`Radius of a circular coil
`
`a, b, c
`
`Variables defining position with respect to the x-, y-, and z-axes
`
`ak (k={x,y,z}) Unit vector in the x-, y-, and z-directions
`
`Aloss
`
`Am
`
`Ar
`
`B
`
`
`
`Absorption loss
`
`Amplitude of modulation function
`
`Area encompassed by a receiving coil
`
`Magnetic flux density
`
`10
`
`Momentum Dynamics Corporation
`Exhibit 1007
`Page 012
`
`

`

`Brect
`
`Magnetic flux density created by a rectangular coil
`
`Bs
`
`bw
`
`Bx
`
`By
`
`Bz
`
`C1decay
`
`C1rise
`
`Cdc
`
`Cpr
`
`Cr
`
`Cres
`
`Cs
`
`Cs’
`
`Csr
`
`d
`
`D
`
`Dboost
`
`Dbuck
`
`dcoils
`
`dH
`
`Dm
`
`ds
`
`Magnetic flux density created by a source coil
`
`Bandwidth
`
`Magnetic flux density in the x-direction
`
`Magnetic flux density in the y-direction
`
`Magnetic flux density in the z-direction
`
`Constant in the decaying condition
`
`Constant in the rising condition
`
`dc side capacitor
`
`Capacitance in a parallel resonant circuit
`
`Number of receiving coils in a system
`
`Resonant capacitance
`
`Number of source coils in a system
`
`Source side resonant capacitance referred to the receiving side
`
`Capacitance in a series resonant circuit
`
`Distance
`
`Distance of separation for source coils
`
`Duty cycle of boost stage
`
`Duty cycle of buck stage
`
`Distance between coils
`
`Helmholtz distance
`
`Demagnetization factor
`
`Thickness of a shield
`
`DSSC
`
`Double Sideband Suppressed Carrier
`
`E
`
`EI
`
`emf
`
`f
`
`fbeat
`
`fcarrier
`
`fcycle
`
`
`
`Electric field
`
`Electric field in the I direction
`
`Electromotive force
`
`Frequency
`
`Beat frequency
`
`Carrier frequency
`
`Cycling frequency
`
`11
`
`Momentum Dynamics Corporation
`Exhibit 1007
`Page 013
`
`

`

`fmodulation
`
`Modulation frequency
`
`fx
`
`fy
`
`fz
`
`H
`
`HI
`
`HT
`
`Hcirc
`
`Hmin
`
`HP
`Hr
`
`Hrect
`
`Frequency of current in the x-axis source coil(s)
`
`Frequency of current in the y-axis source coil(s)
`
`Frequency of current in the z-axis source coil(s)
`
`Magnetic field intensity
`
`Magnetic field intensity in the I direction
`
`Magnetic field intensity in the T direction
`
`Magnetic field intensity created by a single circular coil
`
`Minimum field intensity required to power a receiver
`
`Magnetic field intensity at point P
`
`Magnetic field intensity at the location of the receiving coil
`
`Magnetic field intensity created by a rectangular coil
`
`Hrect,axis
`
`Magnetic field intensity on the axis of a rectangular coil
`
`Hres
`
`Hrms
`
`Hs
`
`Hset
`
`HSp
`
`Hsum
`
`Hu
`
`Magnetic field intensity vector resulting when a shield is present
`
`RMS value of magnetic field intensity
`
`Magnetic field intensity at a point P when shielding is present
`
`The intensity of the field created by a set of rectangular coils
`
`Peak value of the source field
`
`Magnetic field intensity vector
`
`Magnetic field intensity at a point P when shielding is not present
`
`Hunshielded
`
`Unshielded magnetic field vector
`
`Hv
`
`Hx
`
`System transfer function
`
`Magnetic field intensity in the x-direction
`
`Hx_eddy
`
`Magnetic field intensity created by eddy currents
`
`Hy
`
`Hz
`
`I
`
`i
`
`ICr_k
`
`IEnv
`
`Ii
`
`
`
`Magnetic field intensity in the y-direction
`
`Magnetic field intensity in the z-direction
`
`rms current
`
`Current
`
`Current in receiving coil k (k={1,2,3})
`
`Envelope function of capacitor current
`
`Image current
`
`12
`
`Momentum Dynamics Corporation
`Exhibit 1007
`Page 014
`
`

`

`Ioff
`
`Ion
`
`Irated
`
`Ires
`
`Is
`
`Isrx
`
`Iss
`
`Iss_fb
`
`Iss_hb
`
`J
`
`k
`
`K
`
`krr
`
`krxry
`
`ksr
`
`kss
`
`ksxry
`
`ksxsy
`
`L
`
`l
`
`"
`m
`
`L’
`s
`
`L12
`
`Lcircle
`
`lcm
`
`Lcoil
`
`Turn off current
`
`Turn on current
`
`Rated current
`
`Resonant current
`
`Current in a source coil
`
`Current in a series resonant circuit (coil x)
`
`Amplitude of the steady state current through a load
`
`Steady state current in a full bridge converter
`
`Steady state current in a half bridge converter
`
`Current density
`
`Coupling factor
`
`Constant
`
`Coupling factor between receiving coils
`
`Coupling factor between the xth and yth receiving coils
`
`Coupling factor between source and receiving coils
`
`Coupling factor between source coils
`
`Coupling factor between the xth source and yth receiving coil
`
`Coupling factor between the xth and yth source coils
`
`Self inductance of a coil
`
`Length of a conductor
`
`Length of a shielding material
`
`Source coil inductance referred to the receiving side
`
`Mutual inductance between circuit elements 1 and 2
`
`Inductance of a circular coil
`
`Least common multiple
`
`Inductance of a coil without its core in place
`
`Lcoil+core
`
`Inductance of a coil with its core in place
`
`Lm
`
`Lpr
`
`Lr
`
`Lrec
`
`
`
`Mutual inductance
`
`Inductance in a parallel resonant circuit
`
`Self inductance of a receiving coil
`
`Self inductance of a rectangular coil
`
`13
`
`Momentum Dynamics Corporation
`Exhibit 1007
`Page 015
`
`

`

`Resonant inductance
`
`Leakage inductance between source and receiving coils
`
`Inductance of a ferrite rod antenna
`
`Self inductance of a source coil
`
`Inductance in a series resonant circuit
`
`Mutual Inductance
`
`Mutual inductance referred to the receiving side of the system
`
`Mutual inductance for a fully aligned system
`
`Mutual inductance between source and receiving coils
`
`Magnetic Search Coil
`
`Mutual inductance between a source and receiving coil
`
`Number of turns
`
`Turns ratio (ns/nr)
`
`Number of coupling factors needed to define a system
`
`Number of turns on a receiving coil
`
`Number of turns on a source coil
`
`Perimeter
`
`Poynting vector
`
`Power
`
`Average power
`
`Point at which H is at its minimum value
`
`Power to the load on the receiving coil
`
`Perimeter of the receiving coil
`
`Power to the load on the source coil
`
`Perimeter of the source coil
`
`Ohmic power density
`
`Quality factor
`
`Quality factor for a parallel resonant circuit
`
`Quality factor of the reciever
`
`Quality factor for a ferrite rod antenna
`
`Quality factor for a series resonant circuit
`
`14
`
`Lres
`
`Lrl
`
`Lrod
`
`Ls
`
`Lsr
`
`M
`
`M’
`
`M”
`
`Mrs
`
`MSC
`
`Msr
`
`n
`
`n
`
`Nk
`
`nr
`
`ns
`
`
`
`p
`
`P*
`
`P
`
`Pave
`
`PHmin
`
`Pr
`
`pr
`
`Ps
`
`ps
`pV
`
`Qinductor
`Qp
`
`Qr
`
`Qrod
`
`Qs
`
`
`
`Momentum Dynamics Corporation
`Exhibit 1007
`Page 016
`
`

`

`ƒm
`
`R
`
`r
`
`R’
`s
`
`Rac
`
`Reluctance of a shielding material
`
`Resistance, radius
`
`Distance from an object
`
`Source coil resistance referred to the receiving side
`
`Ac resistance
`
`Rac, input
`
`Input impedance
`
`Rc
`
`rc
`
`Rdc
`
`Requ
`
`RFID
`
`Rloss
`
`Rpr
`
`rr
`
`Rr
`
`rs
`
`Rs
`
`Rsr
`
`Rsrx
`
`Rss
`
`Rt
`
`rw
`
`Rwinding
`Rx,y,z(\,T,I)
`
`S
`
`Sp
`
`Sr
`
`Ss
`
`tp
`
`tr
`
`trise
`
`
`
`Core loss resistance
`
`Radius of a coil
`
`dc resistance
`
`Equivalent source/load impedance
`
`Radio Frequency Identification
`
`Reflection loss
`
`Coil resistance in a parallel resonant circuit
`
`Radius of a receiving coil
`
`Resistance of a receiving coil
`
`Radius of a source coil
`
`Resistance of a source coil
`
`Coil resistance in a series resonant circuit
`
`Parasitic resistance in the series resonant circuit of coil x
`
`Source or sink impedance
`
`Terminal impedance
`
`Radius of a wire
`
`Winding loss resistance
`
`Rotation matrix
`
`Cross sectional area
`
`Peak value of the source field magnitude
`
`Surface of receiving coil
`
`Surface of source coil
`
`Duration that each source coil set is energized
`
`Duration that each source coil set carries a single frequency
`
`Rise time
`
`15
`
`Momentum Dynamics Corporation
`Exhibit 1007
`Page 017
`
`

`

`tseq
`
`tss
`
`v
`
`V
`
`Vcmin
`
`vCr
`
`VCr_0
`
`VCr_Env
`
`VCr_k
`
`VCsrx
`
`Vdc
`
`ve
`
`Vlb
`
`vLr
`
`VLsrx
`
`Vpr
`
`vr
`
`Vr
`
`Vrated
`
`Vrms
`
`vRr
`
`VRsex
`
`vs
`
`Vs
`
`Sequencing time
`
`Steady state time
`
`Detuning factor
`
`Volume
`
`Minimum acceptable receiver capacitor voltage
`
`Voltage of the resonant circuit capacitor
`
`No load voltage of coil
`
`Envelope function of capacitor voltage
`
`Capacitor voltage for receiving coil k
`
`Capacitor voltage in a series resonant circuit of coil x
`
`dc voltage
`
`ac voltage
`
`Lower boundary of receiver capacitor voltage
`
`Voltage of the resonant circuit inductor
`
`Inductor voltage for a series resonant circuit (coil x)
`
`Equivalent source voltage in a parallel resonant circuit
`
`Voltage at the terminals of a receiving coil
`
`rms receiving coil voltage
`
`Rated voltage
`
`rms voltage
`
`Voltage across the resonant circuit resistor
`
`Voltage across the resistor in a series resonant circuit of coil x
`
`Voltage at the terminals of a source coil
`
`rms source coil voltage
`
`Vsdc,avg
`
`Average output voltage for a two-pulse rectifier
`
`Vsr
`
`Vsrx
`
`Vub
`
`w
`
`we
`
`wm
`
`
`
`Equivalent source voltage in a series resonant circuit
`
`Ac rms voltage
`
`Upper boundary of receiver capacitor voltage
`
`Width
`
`Electric energy density
`
`Magnetic energy density
`
`16
`
`Momentum Dynamics Corporation
`Exhibit 1007
`Page 018
`
`

`

`x
`
`y
`
`z
`
`Zcoil
`
`Zload_opt
`
`Zr0
`
`Distance along the x-axis
`
`Distance along the y-axis
`
`Distance along the z-axis
`
`Coil impedance
`
`Load impedance for maximum power transfer
`
`Resonant impedance of ideal LC circuit
`
`
`
`17
`
`Momentum Dynamics Corporation
`Exhibit 1007
`Page 019
`
`

`

`Momentum Dynamics Corporation
`Exhibit 1007
`Page 020
`
`
`
`
`
`
`
`
`18
`
`Momentum Dynamics Corporation
`Exhibit 1007
`Page 020
`
`

`

`1 Introduction
`
`Wireless communication technologies have advanced substantially in recent years,
`enabling a new level of flexibility and efficiency in electronic systems. Parallel
`advances in the areas of low power electronics and microsystems technology have
`resulted in the development of many new devices requiring low cost power supplies.
`The development of Micro-Electro-Mechanical Systems (MEMS) (the integration of
`mechanical elements, sensors, actuators, and electronics on a common silicon
`substrate) is a rapidly expanding field [1-1]. Many of these devices will be deployed
`in areas where wired energy supply is not possible and regular maintenance is not
`desired or practical. The increasing prevalence of low-cost, low power electronic
`devices in applications where wired energy transfer is not suitable or even possible
`calls for power supply options beyond those which are currently offered. In systems
`involving, for example, robots or robot chains, fully automated production machines,
`inaccessible or hazardous environments, or applications with high insulation
`requirements, wired power supplies are often not a viable option. Wires provide
`opportunities for failure, especially in moving or rotating systems where wire fatigue is
`a problem and in industrial automation systems with sensor and actuator densities high
`enough to significantly complicate maintenance.
`
`There are currently several options available when a wired supply is not feasible.
`Batteries can be an alternative, but require regular recharging and/or replacement at
`high cost if production must be stopped before maintenance work can begin. Micro
`fuel cells are also an option, but the technology remains nascent, the reliability is low,
`and fuel cells also require recharging (albeit less often than batteries). A reliable
`alternative which requires little maintenance, no regular recharging or replacing of
`components, and is available at a reasonable cost, is clearly of interest. This thesis
`presents a novel alternative to the problem of providing power to devices without the
`use of wires or regular maintenance.
`
`A non-conventional transformer with a large air-gap in the magnetic path can be
`operated with resonant switch mode power supplies to supply energy to a load [1-2],
`[1-3], [1-4]. It can enable completely wireless applications by providing auxiliary
`energy without wires via magnetic fields. The fields can cover distances of up to
`several meters and volumes from one to several hundred cubic meters. The system
`consists of one or more source coils encompassing an operating volume and one or
`more receiving coils located within that volume.
`
`For reliable operation the system must be designed and powered in such a way as to
`transfer the energy to receivers that may be shifting in position and may be
`magnetically shielded by metallic objects within the operating volume. The field
`created by the source coils must be at or above a minimum value required to transfer
`power to the receivers while remaining within limits set by international standards for
`magnetic field strength.
`
`
`
`19
`
`Momentum Dynamics Corporation
`Exhibit 1007
`Page 021
`
`

`

`This thesis focuses on the development and analysis of methods by which reliable
`power can be delivered to a load even in highly shielded environments. Systems are
`developed in which the magnetic fields have components in all three vector directions.
`This gives the system a high degree of resiliency to shielding, even in cases when a
`receiver is almost completely encased in a shielding material. Non-field related
`solutions are also introduced, allowing operation of receivers even under the most
`difficult conditions.
`
`This work begins with a general description of the system and its operating principles,
`with reference to existing technologies using similar principles. It continues by
`exploring various design options for the source side of the system with respect to
`optimum coil separation distance, uniformity of power transfer, generation of desired
`magnetic field vectors, and ability to overcome the problems associated with shielding
`of the magnetic field. Uni-directional and bi-directional systems are discussed, and
`omni-directional systems are introduced along with several methods for creating them.
`The effects of shielding by conductive or permeable objects located within the
`operating volume are then investigated and several methods for the mitigation of this
`effect are presented. A coupling model is developed and a circuit model is derived.
`Source and receiver power converter c