Magnetic Field Generation in an Inductively Coupled Radio-Frequency Power
`Transmission System
`Kathleen O'Brien, Ralph Teichmann*, Henry Gueldner
`
`Dresden University of Technology
`Department of Electrical Engineering
`01062 Dresden
`Germany
`
`General Electric Global Research
`K1-3C34
`Niskayuna, NY 12309
`U.S.A.
`
`Abstract-This paper discusses
`various methods for
`the
`generation of an omni-directional magnetic field suitable for use
`in an inductively coupled power transmission system. The field
`characteristics are evaluated with a focus on minimizing
`shielding
`undesired
`remaining
`effects
`while
`within
`the
`boundaries set by international standards for occupational
`exposure to magnetic fields. The dynamic requirements of load
`resonant converters that allow a minimum disruption in the
`magnetic field are derived. Various topologies are analyzed and
`the theoretical results are verified using a test set-up.
`
`INTRODUCTION
`I.
`This paper describes an inductive power supply system
`which can enable completely wireless applications by
`providing auxiliary energy without wires via magnetic fields
`over distances of up to several meters and covering volumes
`from one to
`several hundred cubic meters.
`Such a
`non-conventional transformer with a large air-gap in the
`magnetic path is preferably supplied by load resonant power
`supplies [1]-[4]. The system consists of one or more source
`coils encompassing an operating volume and one or more
`receiving coils located within that volume.
`Systems using two sets of source coils operating in space
`and phase quadrature are well established [1]-[4].
`These
`systems create a field vector rotating in a single plane.
`Shielding of the source field by objects located within or in
`the vicinity of the operating volume can cause substantial
`reduction in the power available to the receiver coils.
`Several control methods by which the system can be
`expanded to create an "omni-directional" field vector that is
`not restricted to a single plane of rotation are discussed. The
`omni-directional field is to be created such that a maximum
`operating volume is achieved while assuring that a minimum
`field can be provided to a uni-directional receiving receiver
`coil arbitrarily placed inside the operating space. Standards
`for magnetic field exposure will
`limit the maximum
`allowable field strength.
`The choice ofthe source converter topology and its control
`will determine the quality of the omni-directional field.
`Source converters generate the current that controls the i
`magnetic field and are designed to dynamically adjust thel
`load current to create a specific field vector rotation pattern
`with minimal disruption in
`field
`strength.
`Analytical
`description of response times and control limits as a functionx
`of load parameters and converter structure will be provided.
`Finally, results from laboratory experiments are presented
`and compared with theoretical results.
`
`II.
`MAGNETIC FIELD CHARACTERISTICS
`Producing field vectors that rotate outside of the plane to
`whichthey arerestricted in abi-directional system iS clearly
`desirable for the purpose ofmitigating the effects of shielding
`within the operating volume [3]. Several methods to achieve
`field generation in more than one plane are discussed in the
`following sections.
`A.
`Periodic Switching ofthe Plane ofRotation
`Sequential application of a field rotating in a single plane
`to the xy-, yz-, and zx-planes is a logical extension of the
`single-plane solution.
`This can be achieved by applying
`currents in phase quadrature to the x- and y- coils and then to
`the y- and z- coils, and finally to the z- and x- coils (Fig. 1).
`The rate at which switching occurs between the coil pairs
`must be high enough to maintain adequate power at a
`receiving coil when it is shielded in two directions. This rate
`is then directly related to the size of the energy storage
`component on the receiving coil and to the size of the load.
`The period ofone rotation cycle must be determined such that
`a receiving coil shielded in two directions will be able to
`maintain sufficient charge in its energy storage capacitor
`during the 1/3 of the rotation cycle when it receives no
`power.
`This system has the advantage of being relatively
`uncomplicated and easy to implement.
`Field vectors are
`identical to those created in a bi-directional system except
`that they rotate in three planes rather than in a single plane.
`Constant power is maintained at the receiving coils in the
`unshielded case, and no additional frequencies must be
`introduced into the system. However, this method is not truly
`omni-directional because field vectors are created only in
`three planes. Additional methods must be used to obtain a
`system in which field vectors in the center of the system
`rotate outside of these three planes.
`
`y coils
`
`I
`
`o
`
`L
`
`X
`
`\|\
`
`Q ol
`
`Fig. 1. Omni-directional source coil system
`
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`
`Momentum Dynamics Corporation
`Exhibit 1014
`Page 001
`
`

`

`B.
`
`(2)
`
`directly proportional to the coil current in an omni-directional
`Frequency Shift
`system with currents described by (1).
`Applying current simultaneously to all three of the source
`Hs X Vx(t)2 + y(t)2 + z(t)2
`coils can create a field vector that rotates through all possible
`Substituting (1) into (2) and reducing,
`angles with respect to each ofthe three axes. However, ifthe
`frequency of the current in all three coils is the same
`H x JK2 + K2 sin2 (n2t)
`(fx=fy=fz), the field will rotate in only one plane (the angle of
`Therefore, HSmax o fK, Hsmfl < K
`the plane of vector rotation relative to the xy-plane being
`(3)
`determined by the relative phase difference between the
`The magnitude of the field vector iS changing according to
`a curentof analtenate
`applid curents. Aplyin
`a sine function at twice the frequency off, with a minimum
`frequency (12) to one or more of the source coils will provide
`at the peak value of the source field (Hs
`')
`aiu
`n
`a field vector that rotates in more than one plane.
`a field vectorthatrotatesimorethanoneplane.atV_JH
`The rms field strength available to the receiving
`The currents applied to the coils are described using the
`s
`following parametric equations:
`coils is then 3/2 times that available to the receiving coils in
`x(t) = K sin(w1t)
`a bi-directional system.
`y(t) = K sin(wlt + T/2)
`z(t) = K sin(o2t)
`Where K is the amplitude of the current. This results in a
`magnetic field at the center of the system with a vector
`rotating in space such that its endpoints trace the lateral
`surface of a cylinder.
`The rotation of the field vector shown is not truly
`omni-directional as directions remain in which there is no
`field vector. To alleviate this problem, and to create a truly
`omni-directional
`carrying the second
`the
`coil
`system,
`frequency is changed periodically. Fig. 2 shows simulation
`results of such a system. The field vectors are effectivelyI_6
`created at all possible angles with respect to the x-, y-, and
`z-axes of the system.
`
`(1)
`
`C.
`
`Double-Axis Amplitude Modulation
`Amplitude modulation can be applied simultaneously to
`two axes to produce an omni-directional field. This solution
`forms an omni-directional field with constant magnitude
`throughout its rotation. A spherical shape is formed by the
`outline of the endpoint of the vector as it rotates through all
`possible angles with the three axes, as is shown in Fig. 3.
`
`0-1
`
`0.6
`
`-1
`
`-05
`
`05
`
`double axis amlplitude
`~~~~~~~Fig.
`3. Outline of vctor roatofo,r a csyse
`X
`usin
`~~~~~~modulation.
`Magnitudes are set to 1, and all three coil sets are in space
`X
`055 < gX
`~~~~~~~~~~~quadlrature. Vliews shodwn arle (clockwise from upper left) three-dimensional,
`
`=;.1E; ~~~~~~~The currents applied to each of the source coil sets are
`
`x(t) =K cos(wt) cos(wmt)
`y(t) - K cos(wt) sin(wmt)
`
`(4)
`
`Fig. 2. Outline of vector rotation for an omni-directional system. Magnitude
`of source currents are set to 1, and source coil sets x and y are in phase
`quadrature and all three coil sets are in space quadrature. Views shown are
`(clockwise from upper left) three-dimensional, xz-plane, xy-plane, and
`fy =120 kH7z, fX
`yz-plane. fX= fy =120 kHUz, f. =124kHtz followed by fz
`=124kHz
`
`z(t) KKsin(ot)
`Where the azimuthal angle of the vector is determined by
`oit and the polar angle by Oimt and a is the carrier frequency
`while 0)m iS the modulation frequency.
`The addition of a second frequency to the system means
`Substituting (4) into (2) shows that the magnitude of the
`that power will be delivered to the receivers
`at two
`source field at the center of the system is constant.
`In order to avoid multi-tuned system and
`frequencies.
`K2 cos2(t)_cos2(w)t)
`- K
`maintain the benefits of a sharply tuned narrow-band load
`H
`resonant converter, the frequencyf must be chosen such that
`+ K2 COs2(oft) sin2(wt)t+ K2 sin2(oftt)-()
`S
`it is close enough tofto allow a sufficient amount ofpower to
`The field created by this system is at three frequencies
`~ ±~ Wietefedcetdi h -ieto
`a
`be transferred to the receiving coils even when they are
`receiving power only from the coil set with current atf2.,
`m
`components only at the frequency as of the receiving coils,
`The magnitude of the field at the center of the system is
`the fields created in the x- andy-directions have 5000 of their
`
`(5)
`
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`
`Momentum Dynamics Corporation
`Exhibit 1014
`Page 002
`
`

`

`c + cm and the remaining 50%0 of their
`magnitude at
`The Fourier transform of the
`magnitude at
`co - co
`modulated waves is identical to that of a Double Sideband
`Suppressed Carrier (DSSC) amplitude modulated signal used
`in AM radio transmission.
`
`POWER CONVERTER DESIGN
`III.
`Both the source and receiver sides represent the terminals
`of a loosely coupled n-dimensional transformer.
`As
`narrow-band power transmission is sufficient, in fact, desired
`[13], both source and receiver side coil leakage inductances
`can be compensated by a tuned resonant circuit. This
`substantially improves the device utilization and the overall
`efficiency of the power transmission system.
`SourceSidePowerConversion-PeriodicSwitchingof
`A.
`the Plane ofRotation
`Fig. 4 shows a schematic of a three-channel series resonant
`converter. A common dc bus control can be applied to create
`a field of equal magnitude in each direction.
`
`Channel A
`
`Channel B
`
`Channel C
`
`The envelope functions of the capacitor voltage and
`current can then be described by
`ICe- +A
`VCr Env
`CS(Cldoe+WeA)
`IEnv
`
`(8)
`(9)
`
`The rise and decay times of the circuit will also define an
`upper boundary on the cycling frequency. The decay time is
`minimized by the fact that the inverse diodes impress a
`reverse voltage on the load, the rise time cannot be decreased
`beyond the duration of the natural response of the load
`current. This is the limiting value for sequencing time.
`Using (9), the rise time (and decay time assuming a natural
`response) can be expressed as
`-s
`seq
`-
`AC
`CsCiriedc
`riese
`a
`whereas the decay time if a reverse voltage is applied
`across the load is
`-1
`
`t
`
`a
`
`ln|
`
`- c A
`e
`l decay
`
`d
`
`(11)
`
`4H1+gL
`
`Siosis
`
`s3
`
`S 1 2
`s3
`Si
`
`11
`
`1
`3S
`
`F
`
`where Iss is the amplitude of the steady state current
`H2S
`through the load, Cs is the source side capacitance, and Clrise
`S| koOl
`RC, R
`'Cd_TCR ,
`and Cldecay are defined as in (7) for the rise and decay
`,
`, C
`41
`94041IJsH¢l
`conditions, respectively.
`:lS:;H¢
`1_1q92q
`94 ~2 11The cycling frequency can then be defined as
`9j_S2
`'JS4
`'~ ~2
`s
`Fig. 4. Three-channel series resonant converter for sequential bi-directional
`ct
`fields. Constant power is drawn from the source except during transition
`3(tseq +t55)
`periods.
`Giving a maximum when tss=O of
`fA -1
`-a
`ACs) - ln(CsClrseod)]
`3t
`
`=1
`
`3[ln
`
`-
`
`(12)
`
`(13)
`
`Source Side Power Conversion - Frequency shift
`One out three channels operates with a slight frequency
`offset in this type of operation. For the maintenance of an
`identical coil current magnitude in all three axes using a
`~~~common dc bus, the resonant frequency of the load can be
`adsysembo
`adjusedcto
`frequency usn
`the'
`shifte
`~~~adjusted
`shifted frequency using a system of
`to the
`switchable capacitors and/or saturable inductors (Fig. 5(a))
`or a dc/ac converter topology with pulse width control (e.g.
`Fig. 5(b)). The currents of the two channels operating at the
`system's
`nominal
`operating
`frequency
`are
`in
`phase
`quadrature. The current ofthe channel operating at the offset
`frequency can have an arbitrary phase angle with respect to
`the other two channels. The power drawn from the source is
`fluctuating with the magnitude and frequency of the offset
`channel.
`os(-5~)The magnetic field vector at the center of the system will
`~~~~~~~~~rotatethrough all possible angles with respect to the source
`~~~~~~~coilsif at least two of the three channels are sequentially
`operated at the offset frequency. The selection of the offset
`frequency is based on the desired vector rotation period and
`the density of the mesh traced by the field vector [6].
`
`The general solution of the inhomogeneous, second-order
`'
`differential equation for the capacitor voltage vCs is
`VCs 'Cecos(wodt) + C2eCtsin(wdt)
`= Cle'+ C2e-' sin(
`+ A cos(wet - 9e) + B sin(oet - Pe)
`where
`
`(7)
`
`v
`
`12
`
`2
`
`____
`
`s
`
`B
`
`A
`
`s
`
`ic
`0)=- iX(c)
`(1- We LsCs)
`BeRsCs
`1- (e2LsCs
`(1 - e2LC )2 + _e,R Cs
`C1 =vC5 (0) - A cos(-0ze) - B sin(-0ze)
`
`C2 =
`
`°d
`ve is the peak value ofthe excitation voltage, aSe iS the
`frequency ofthe excitation voltage, and 9pe iS the phase angle
`of the excitation voltage
`
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`
`An instantaneous turn-on/turn-off transition is impossible
`due to the rise and decay times of the currents in the series
`resonant circuits.
`A series resonant circuit excited by an ac voltage source Ve
`can be described by
`d'2v
`R dv
`+
`L dt
`s
`
`dt
`
`v
`L C
`
`s
`
`s
`
`c
`1
`L C e COS("et
`
`Pe
`
`s
`
`s
`
`B.
`
`(6
`
`Momentum Dynamics Corporation
`Exhibit 1014
`Page 003
`
`

`

`can therefore be controlled using the dc voltage. This is
`HCs2
`1Xe2 e 2 ;0 shown in Fig. 6 and Fig. 7.
`
`CV
`
`V-
`
`+
`
`1~2
`
`Sd1
`
`,
`
`+
`
`Icoil
`Vdc ' 7i JL'
`Ls
`Rs
`tsat
`C12 ~~S22
`
`Vdc
`
`R
`
`L
`
`i
`is C,
`
`R1
`
`R, L,20
`S4
`
`s
`
`(b)
`(a)
`Fig. 5. (a) Saturable inductance applied to one of three channels. (b) One of
`three converter channels with magnitude control.
`
`°
`
`The frequency shift method is considered only for
`situations in which a fully omni-directional system is not
`required, but a bi-directional system is insufficient [6].
`In
`this case, only one source coil set carries current at the offset
`frequency.
`All three axes can be tuned to its desired
`operating frequency.
`This is a simple solution requiring
`minimal control of the source coil currents during normal
`operation.
`Source Side Power Conversion - Double axis amplitude
`C.
`modulation
`Double axis amplitude modulation requires independent
`control over the current magnitude of at least two converter
`channels. Fig. 4 shows a fully flexible three-channel system
`fed from one common dc bus and capable of independent
`Controlling the
`control of the currents in each channel.
`current magnitude requires pulse-width control [6].
`The
`semiconductors are subject to higher switching losses in
`comparison to those incurred while using block modulation
`at tuned operation.
`Alternatively, double axis modulation can be implemented
`with multiple
`single
`channel power converters
`with
`independent dc voltage control. All channels are tuned to the
`system's operating frequency. A similar functionality can
`also be provided by a three-channel arrangement based on the
`series resonant asymmetric half-bridge converter [13].
`The response of the series resonant circuit was discussed
`above. The minimum rise and decay times of the oscillation
`determine the maximum possible modulation frequencies.
`An upper boundary on the modulation frequency is given by
`the damping characteristic ofthe resonant circuit. The decay
`of the current can be forced to be significantly faster than the
`rise time. For this reason, the rising function of the source
`current determines the upper limit of the modulation
`frequency.
`Using (9), the envelope function for the rising current can
`be described by
`'Env rise =CsA(wode
`- Coe)
`and the modulation function is
`A si(mt ~m)(5
`'m
`The maximum possible modulation frequency C-9m_max iS the
`greatest 0im at which I <IE _
`for all time t.
`If the
`amplitude of the modulation function (Am) is equal to the
`steady state current in the system (Iss), 69m_max iS at its lowest
`9m max
`possible value. As Am is reduced, 69m max increases.
`
`(14)
`
`is
`
`Vd~Load currc nt
`200 envelope
`nt_-
`(no zero st i1fw
`
`15J
`
`5S
`
`A,, 1f6.H
`~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~103
`
`-100
`-150
`-200
`-250
`
`3 54 6
`2
`1
`Fig. 6. Envelope of uncontrolled ramp-up current and the amplitude and
`possible amplitude modulation current envelopes
`frequency of three
`Lr=2OkH, Cr=126nH, Rr=0.06Q, Vdc=20V.
`
`300
`
`v
`/d0=30
`250(F____
`
`____
`
`_
`
`/
`
`Vd_=__0
`__200(_
`_
`
`150
`
`1l00(~
`
`50
`
`_F____
`
`Vd=V=I0
`Vd5 ;____=5
`
`__ ___'
`
`I010o
`
`500
`
`600
`
`t =
`
`3c
`
`(16)
`
`400
`300
`200
`Amplitude ofmodulation current lIml
`Fig. 7. Maximum possible load current modulation frequency vs. the
`amplitude of the load current modulation function for several source voltage
`conditions. Lr=20kH, Cr=126nH, Rr=0.06Q.
`A reasonable estimate of c9m max can be found by restricting
`the modulation function such that it reaches one-third of its
`period when IEnv rise has reached a value ofAm.
`Solving
`A =C,A(deat - ) for com at
`m
`s
`e
`d
`gives
`gives
`max 1r3[ln(Am + CA) - ln(CSAc)
`+ Coe
`d )
`Fig. 6 shows the envelope of an uncontrolled rise in current
`through an example load as well as several possible
`modulation functions. Fig. 7 shows the relationship between
`the amplitude of the modulation function and its maximum
`possible frequency for the same system.
`Receiver Side Power Conversion
`D.
`Threivrsdpo rcnetrdsgnsatae-f
`between cost, reliability, and packaging density vs. the
`desired
`functionality, which includes maximum power
`extraction, dc bus voltage control and autonomous operation
`and start-up. In contrast to the source side system, operation
`
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`
`Momentum Dynamics Corporation
`Exhibit 1014
`Page 004
`
`

`

`converters were extensively discussed in [8], [9].
`The equivalent ac resistance of the dc load can be
`estimated assuming a lossless system by using the power
`balance constraint and the basic duty cycle definitions for
`buck and boost converters. With
`VdC = VdC_,intDbuck
`1
`VdC l=I_D
`
`dc,k
`
`(18)
`
`(17)
`
`boost,k
`Vdc_it is the intermediate dc voltage, Db,ck isthe duty cycle
`of the buck stage, Dboost,k is the duty cycle for boost stage k
`(k={x,y,z}), and Vdc,k isthe average dc voltage at the rectifiers
`in axis k (k={x,y,z}).
`For the special case when all three axes contribute equally
`to the power flow towards the load the equivalent ac
`resistance Rac for one axis becomes
`/T~~~2
`C~~~~ ~R =3
`buck -R(I9
`8(DbS)2 load
`
`at the maximum power point is the essential design criterion.
`The receiver side efficiency at maximum power is 5000 [7].
`An omni-directional receiver design with three coil axes is
`assumed.
`The parallel
`circuit
`represents
`a
`resonant
`voltage-stiff source for the receiver side power converter [5].
`A passive rectifier is chosen to connect the resonant circuit to
`the dc-link as uni-directional power flow is sufficient.
`and
`Fig. 8 and Fig. 9 depict a fully controllable active system
`with individual power extraction for each receiving coil and a
`completely passive system with a common power extraction,
`Advantages of latter design include high
`respectively.
`reliability, low cost, and high packaging density. The main
`disadvantage is that the maximum power that can be
`extracted for a given field strength is lower by a factor of
`three than in the solution with individual power extraction.
`Dlx D,x
`
`x-axis
`
`~
`
`Vdc xT,w
`
`Llx
`
`Dx
`
`ac
`
`(9
`
`T<1
`
`s
`
`_ < s1
`
`D; J,
`whIeI I
`T
`1
`
`_ _
`
`- RI
`
`U ing the power balance constraint and the fundamental
`transformation
`frequency
`across
`rectifiers
`resistance
`
`~~~described in [11l], the control circuit can be designed such
`J
`|~~thait maximum power is extracted from each axis by matching
`<
`-
`~~the equivalent impedance of load with that of the receiving
`z-axis F rr " | Vbz 1ZHX l
`~~~~~~~~~oil
`(including the parallel resonant circuit).
`<
`For a completely passive system with the rectifier fed by
`Fig. 8. Independent impedance matching of coil axes and regulation of dc
`thpalelrsntciutaddrclyupyngac
`upygad
`teprle eoatcrutaddrcl
`voltage using a combination of a buck and a boost converter
`capacitor as shown in Fig. 9, the average dc voltage can be
`D1
`determined as a function of the ac voltage, frequency, dc-bus
`-~~~~~ ~ ax|
`capacitor, and load resistance [12].
`Without stabilization
`~~~~~~~~~~circuit(RjoO, CdJC=dC]±CdC2, no Dz) the average dc voltage
`F
`for a single pulse rectifier is determined by
`Vd -vn=co2
`V/§
`~~~~Cdc2where p =arctan(CdCRload)
`and
`sin(8 + p) -sin p exp{- (2gT -8S) cot p} -0O.
`Invoking the power balance criteria, an approximate value
`fo h qiaeta eitneRecnbeieo
`aiu
`cnbdrvdfrvrou
`values of CdC and R/oad. The ac resistance is given by
`(
`2
`20 27COSco
`K (l1-cos8))
`The same principle can be applied ifthe power is extracted
`from each individual coil through a separate single pulse
`rectifier and fed to a common dc bus. A single pulse rectifier
`will introduce orientation dependence for maximum power
`extraction [6]. The introduction of a double pulse rectifier
`connecting the parallel resonant capacitance to the dc
`capacitor will reduce this dependence.
`The completely passive system will not permit an
`extraction of the maximum power unless the load has a
`of the
`constant
`impedance.
`However, determination
`
`(20)
`
`(21)
`
`Ra
`
`Ria
`
`X
`
`~~~
`
`y-axis
`
`H
`
`Rz <
`
`D:)
`
`~~Cdl1
`
`~~~
`
`~
`
`z-axis
`.-
`9
`.
`Fig. 9.Minimum design with no impedance matching and overvoltage
`limitation of the dc voltagefotheqiaetareitneR
`
`8 provides independent
`The circuit shown in
`Fig.
`impedance matching and regulation of the dc bus voltage.
`Maximum power can be extracted from the coils in each axis,
`however, the losses in the power conversion stages will
`reduce the power available
`to
`the
`load.
`The three
`independent boost converters must be designed to operate
`above 1MHz which results in a typical power conversion
`efficiency of 80-90% for this power range. The buck stage
`can be operated with moderate switching
`frequencies
`assuming that the dc capacitor, Cdt, is rated adequately.
`Boost and buck regulation can be started once the dc link
`capacitor is charged sufficiently to allow operation of the
`regulators. Further design aspects of high frequency dc/dc
`
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`
`Momentum Dynamics Corporation
`Exhibit 1014
`Page 005
`
`

`

`equivalent source resistance of the receiving coil with the
`parallel
`circuit
`conjunction
`with
`in
`the
`resonant
`determination of the load impedance range will support
`circuit design for maximum power transfer.
`An energy storage device is required at the receiver side
`converter to balance short-term power imbalances between
`the load requirements and the power obtained from the
`magnetic field. The size of the energy storage device at the
`secondary side is dependent on the operating frequency and
`the anticipated shielding at the receiver.
`
`EXPERIMENTAL VALIDATION
`IV.
`An omni-directional system using the frequency shift
`method was built and tested (Fig. 10). The nominal operating
`frequency of the system was set to 120kHz. The source side
`frequency of the z-axis coil set was varied between ll9kHz
`and 121kHz. The frequency was digitally controlled.
`Each receiving coil comprising the receivers used in the
`experiments is separately compensated and tuned to the
`system's operating frequency of 120kHz. Multiple parallel
`ceramic surface mounted capacitors are used to tune the
`circuits. Three single pulse Schottky rectifiers connect the ac
`voltages of the three axes to a common dc-bus (Fig. 11). A
`dc-link capacitor of lOOnF is chosen.
`
`three receiving coil axes.
`With a bi-directional source coil system carrying currents
`in phase quadrature and with identical magnitude, the dc
`voltage at the receiver side at and around the maximum
`power point is <2 times higher than that of a comparable
`uni-directional system (Fig.
`12).
`The maximum power
`obtained in a bi-directional system is twice that available in a
`uni-directional system. The nonlinear characteristic of the
`single pulse rectifier will not retain this exact ratio over the
`entire load range. Fig. 13 shows that the maximum power for
`the uni-directional and bi-directional system is achieved at
`different load resistances.
`One of the three source coil sets is excited with 119kHz or
`121kHz current for omni-directional field excitation. The
`power available to a load in an omni-directional system is
`predicted to be 1.5 times higher than that of a comparable
`bi-directional system. The peak power values measured for
`the omni-directional system are higher (121kHz) and lower
`(119kHz) than expected with reference to the bi-directional
`excitation.
`The differences are due to the effect of the
`resonant circuit in the receiver being tuned to a frequency
`that is closer to 120.5kHz than to 120 kHz, which leads to a
`higher power at 121 kHz and a lower power at 119kHz.
`
`;;;
`
`Fig. 10. Test set-up for an omni-directional system. Source coils are seen in
`the background with power converters in the foreground.
`
`4 -.
`2 x
`
`x-axis
`
`y - axis
`
`z-axis
`
`D
`
`Cd,
`
`Rd,
`
`VVd,
`
`D|<
`Cy
`
`D,
`
`1
`
`C
`
`Fig. I1. Equivalent circuit of receiver used for tests
`
`The measured output voltages and power and function of
`are shown in Figures
`12 and 13,
`the load resistance
`and5
`Results
`are shown for
`uni-,
`bi-,
`respectively.
`omni-directional systems (uni-directional systems use only
`one set of source coils, and bi-directional systems use only
`two sets of source coils). The source and receiving coils are
`aligned such that each source coil axis is parallel to one of the
`
`3D g 12 IkH
`
`,/~~~~~~~319kHz
`xXjX
`
`0kH
`
`18-
`
`16-
`
`14
`
`10
`
`6
`
`0
`
`0
`
`2
`
`6
`4
`Rload (kOhm)
`Fig. 12. Measured voltage on receiving coils for various loads and operation
`(ID),
`(Uni-directional
`(2D),
`modi
`Bi-directional
`system
`system
`Omni-directional system (3D))
`zu
`
`8
`
`10
`
`1 l
`
`3D @ 121kHz
`3D °119kHz
`
`45
`
`40
`35
`35-
`
`30-
`
`20
`
`I51 |"|"|
`10 AD @ 120kHz
`
`0
`
`0
`
`2
`
`6
`4
`Rload(kOhm)
`Fig. 13. Measured power at load resistance (Uni-directional system (1D),
`Bi-directional system (2D), Omni-directional system (3D))
`
`8
`
`10
`
`Authorized licensed use limited to: Reprints Desk. Downloaded on March 23,2021 at 23:31:30 UTC from IEEE Xplore. Restrictions apply.
`
`Momentum Dynamics Corporation
`Exhibit 1014
`Page 006
`
`

`

`CONCLUSIONS
`V.
`which
`a
`medium-frequency
`by
`methods
`Three
`field can be created were
`omni-directional
`magnetic
`presented.
`Periodic switching of the plane of rotation
`provides power to receiving coils at a single frequency, but
`does not provide a true omni-directional rotation. Operation
`of one of the three source coil sets at a slightly offset
`frequency is relatively simple to implement and is useful in
`cases where a second frequency is required in only one
`source coil pair. Double-axis amplitude modulation provides
`constant power to the receiving coils, but does so at three
`frequencies.
`specifically
`modulation
`the
`dynamics,
`The system
`frequency for the omni-directional fields, is influenced by the
`characteristics of the resonant circuit.
`
`[1]
`
`[2]
`
`[3]
`
`[4]
`
`REFERENCES
`G. Scheible, J.Schutz, and C. Apneseth, "Novel wireless power supply
`system for wireless communication devices in industrial automation
`systems," in IEEE 2002 28th Annual Conference of the Industrial
`Electronics Society (IECON2002), vol. 2, Nov. 2002, pp. 1358 - 1363.
`K. O'Brien, G. Scheible, and H. Gueldner, "Design of large air-gap
`transformers for wireless power supplies," in Records of the Power
`Electronics Specialist Conference 2003 (PESC '03), vol.4, June 2003,
`pp. 1557- 1562.
`K. O'Brien, G. Scheible, and H. Gueldner, "Analysis ofwireless power
`supplies for industrial automation systems," in Records of the 29th
`Annual Conference ofthe IEEE Industrial Electronics Society (IECON
`'03), vol.1, Nov. 2003, pp. 367 - 372.
`J.Schutz, G. Scheible, and C. Willmes, "Load adaptive medium
`frequency resonant power supply," in IEEE 2002 28th Annual
`Conference ofthe Industrial Electronics Society (IECON 2002), vol. 1,
`Nov. 2002, pp.282 - 287.
`M.K. Kazimierczuk, D. Czarkowski, Resonant Power Converters. New
`York: John Wiley & Sons, 1995.
`O'Brien,
`"Inductively
`Coupled
`Radio
`Frequency
`Power
`K.
`Transmission System for Wireless Systems and Devices," Dissertation,
`Dresden, Germany, Jan. 2006.
`H. Elschner, Grundlagen der Elektrotechnik und Elektronik, vol. 2,
`Berlin-Munich: Verlag Technik GmbH, 1992.
`A.S. Kislovski, Introduction to Dynamic Analysis ofSwitching DC-DC
`Converters. Bern: BWV Engineering, 1985.
`K. Liu, F. Lee, "Zero-voltage switching techniques in DC/DC
`converter circuits," in Records of the Power Electronics Specialist
`Conference 1986 (PESC'86), pp. 58-70.
`[10] N. Mohan, T.M. Undeland, and W.P. Robbins, Power Electronics.
`New York: John Wiley & Sons, 1995.
`[11] R. Steigerwald, "A comparison of half-bridge resonant converter
`topologies," IEEE Transactions on Power Electronics, vol. 3, no.
`2,pp. 174-182, April, 2005.
`[12] R. Lappe, H. Conrad, and M. Kronberg, Leistungselektronik. Berlin:
`Verlag Technik, 1991.
`[13] S. Kolnsberg, "Drahtlose Signal- und Energieubertragung mit Hilfe
`von Hochfrequenztechnik
`in
`CMOS-Sensorsystemen,"
`Dr.-Ing.
`Dissertation,
`Gerhard-Mercator-Universitat
`- Gesamthochschule
`Duisberg, Duisberg, Germany, 2001.
`[14] J. M. Burdio Pinilla, F. Canales, P.M. Barbosa, and F.C. Lee. "A
`comparison study of fixed-frequency control
`strategies
`for ZVS
`DC/DC series resonant converters," in IEEE 32nd Power Electronics
`Specialists Conference (PESC '01), June 2001, pp. 427-432.
`
`[8]
`
`[5]
`
`[6]
`
`[7]
`
`[9]
`
`Authorized licensed use limited to: Reprints Desk. Downloaded on March 23,2021 at 23:31:30 UTC from IEEE Xplore. Restrictions apply.
`
`Momentum Dynamics Corporation
`Exhibit 1014
`Page 007
`
`