U.S. patent application number 12/544974 was filed with the patent office on 2010-02-25 for adaptive wireless power transfer apparatus and method thereof.
Invention is credited to Alanson P. Sample, Joshua R. Smith.
Application Number | 20100045114 12/544974 |
Document ID | / |
Family ID | 41695687 |
Filed Date | 2010-02-25 |
United States Patent
Application |
20100045114 |
Kind Code |
A1 |
Sample; Alanson P. ; et
al. |
February 25, 2010 |
ADAPTIVE WIRELESS POWER TRANSFER APPARATUS AND METHOD THEREOF
Abstract
In accordance with various aspects of the disclosure, a method
and apparatus is disclosed that includes feature of coupling a
resonator of a transmitter and a resonator of a receiver together
by a common inductance of the transmitter and the receiver; and
adjusting environmental parameters or system parameters or both of
the transmitter, the receiver, or both, to control power
transmitted wirelessly between the transmitter and the
receiver.
Inventors: |
Sample; Alanson P.;
(Seattle, WA) ; Smith; Joshua R.; (Seattle,
WA) |
Correspondence
Address: |
Pillsbury Winthrop Shaw Pittman LLP;(INTEL)
P.O. Box 10500
McLean
VA
22102
US
|
Family ID: |
41695687 |
Appl. No.: |
12/544974 |
Filed: |
August 20, 2009 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
61189502 |
Aug 20, 2008 |
|
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Current U.S.
Class: |
307/104 |
Current CPC
Class: |
H01F 38/14 20130101;
H02J 5/005 20130101; H02J 50/12 20160201 |
Class at
Publication: |
307/104 |
International
Class: |
H01F 38/00 20060101
H01F038/00 |
Claims
1. A method comprising: coupling a resonator of a transmitter and a
resonator of a receiver together by a common inductance of the
transmitter and the receiver; and adjusting environmental
parameters or system parameters or both of the transmitter, the
receiver, or both, to control power transmitted wirelessly between
the transmitter and the receiver.
2. The method according to claim 1, further comprising: producing a
first and a second resonant mode of different frequencies for some
common inductance value.
3. The method according to claim 1, wherein the environmental
parameters are selected from the group consisting of: a range
between the transmitter and the receiver, a relative orientation
between the transmitter and the receiver, and a variable load on
the receiver.
4. The method according to claim 1, wherein the system parameters
are selected from the group consisting of: a frequency at which
power is transmitted, an impendence between a loop and a coil of
the transmitter, an impendence between a loop and a coil of the
receiver, and an impedance-matching component of the transmitter
and an impedance-matching component of the receiver.
5. The method according to claim 1, wherein at least one of the
transmitter or the receiver includes a loop and a coil.
6. The method according to claim 1, wherein at least one of the
transmitter or the receiver includes an impedance matching network
and a coil.
7. The method according to claim 1, wherein at least one of the
transmitter or the receiver includes a transformer and a coil.
8. The method according to claim 1, wherein one of the transmitter
or the receiver includes an impedance-matching network that
includes inductors and capacitors configured to connect a signal
source to the resonator structure.
9. The method according to claim 1, further comprising: fixing a
value of a loop-to-coil coupling coefficient of the transmitter;
and tuning a frequency adaptively to choose a desired frequency for
a particular value of a coupling coefficient of a transmitter
resonator coil to a receiver resonator coil.
10. The method according to claim 1, further comprising: monitoring
a reflected power; and adjusting a frequency of the transmitter to
minimize the reflected power.
11. The method according to claim 1, further comprising: sweeping
through a range of frequencies while the transmitter receives a
feedback signal from the receiver.
12. The method according to claim 11, further comprising:
determining a desired frequency for a distance between the
transmitter and the receiver based on the received feedback
signal.
13. The method according to claim 11, wherein the feedback signal
includes a radio signal, WiFi, Bluetooth, Zigbee, RFID-like
backscatter, or a load-modulated signal that is modulated on a
carrier signal of the transmitter.
14. The method according to claim 1, wherein the environmental
parameters, system parameters, or both are adjusted to maximize
power transmitted wirelessly.
15. The method according to claim 1, further comprising:
determining a desired frequency for a distance between the
transmitter and the receiver based on an impedance matching value
between a signal source and a coil of the transmitter.
16. The method according to claim 1, further comprising: monitoring
a received power; and adjusting a frequency of the transmitter to
maximize the received power.
17. A transmitter comprising: a resonator configured to couple with
a resonator of a receiver by a common inductance; and a controller
configured to optimize transmitted power based on environmental
parameters or system parameters or both of the transmitter, the
receiver, or both, the transmitter configured to transmit power
wirelessly to the receiver.
18. The transmitter according to claim 17, wherein the resonator
includes one or more of the following: a loop, a coil, a
transformer, and an impedance-matching network.
19. A receiver comprising: a resonator configured to couple with a
resonator of a transmitter by a common inductance; and optimally
receive power wirelessly from the transmitter based on
environmental parameters or system parameters or both of the
transmitter, the receiver, or both.
20. The receiver according to claim 19, wherein the resonator
includes one or more of the following: a loop, a coil, a
transformer, and an impedance-matching network.
Description
CROSS REFERENCE TO RELATED APPLICATIONS
[0001] This application claims benefit under 35 U.S.C. .sctn.119(e)
from U.S. Provisional Application No. 61/189,502 filed on Aug. 20,
2008, incorporated herein by reference in its entirety.
BACKGROUND
[0002] This disclosure relates generally to the field of power
transmission, and in particular, to a method and apparatus for
transmitting and receiving power wirelessly.
[0003] Wireless power transfer has the potential to transform
electronics by "cutting the last cord," freeing users from the need
to plug in to recharge devices, and changing the design space, for
example by enabling devices with no connectors.
[0004] Coupled resonator wireless power transfer is capable of
delivering power with more efficiency than far field approaches and
at longer range than traditional inductive schemes. However,
conventional coupled resonator systems have been limited to
operation at a particular fixed distance and orientation, with
efficiency falling rapidly as the receiver moves away from the
optimal operating point. Moreover, conventional coupled resonator
systems use bulky, non-flat resonator structures.
BRIEF DESCRIPTION OF THE DRAWINGS
[0005] FIG. 1a shows an exemplary system diagram of an auto-tuning
wireless power transfer system in accordance with various aspects
of the present disclosure.
[0006] FIG. 1b shows an equivalent circuit diagram for the
exemplary system of FIG. 1a in accordance with various aspects of
the present disclosure.
[0007] FIG. 1c shows a photograph of an experimental set-up of a Tx
Loop and Tx Coil (left), and Rx Coil and Rx Loop (right) in
accordance with various aspects of the present disclosure.
[0008] FIG. 2a shows a plot of |S.sub.21| as a function of
frequency and Tx-Rx coupling (k.sub.23) in accordance with various
aspects of the present disclosure.
[0009] FIG. 2b shows a plot of |S.sub.21| as a function of k.sub.23
and k.sub.12 in accordance with various aspects of the present
disclosure.
[0010] FIG. 3a shows a locally fit model comparing experimental
data (black dots) to the elementary transfer function (dotted
line), and to the complete transfer function (line), for the best
fit value of k.sub.23 in accordance with various aspects of the
present disclosure.
[0011] FIG. 3b shows a locally fit model comparing experimental S21
magnitude data (black dots) and analytical model (surface) computed
from the complete transfer function, both plotted versus frequency
and Tx-Rx distance in accordance with various aspects of the
present disclosure.
[0012] FIG. 4a shows a model (lines) compared to experimental data
(black circles), with k.sub.23 values calculated from geometry (not
fit to data) where |S.sub.21| is plotted vs distance in accordance
with various aspects of the present disclosure.
[0013] FIG. 4b shows the model of FIG. 4a where resonant peak
locations are plotted as a function of distance in accordance with
various aspects of the present disclosure.
[0014] FIG. 4c shows the model of FIG. 4a where resonant peak
magnitudes are plotted as a function of distance in accordance with
various aspects of the present invention.
[0015] FIG. 5 shows efficiency--range tradeoff:
|S.sub.21|.sub.Critical vs. k.sub.Critical tradeoff curve as a
function of the tuning parameter k.sub.lc, with our system's
operating point indicated (large dot at k.sub.lc=0.135) in
accordance with various aspects of the present invention.
[0016] FIG. 6a shows an experimental implementation where tuning
frequency compensates for range changes in accordance with various
aspects of the present invention.
[0017] FIG. 6b shows the experimental implementation of FIG. 6a
where tuning frequency compensates for orientation changes in
accordance with various aspects of the present invention.
[0018] FIG. 6c shows the experimental implementation of FIG. 6a
where a laptop computer is powered wirelessly in accordance with
various aspects of the present invention.
[0019] FIG. 7 shows a representative top view of the experimental
implementation of FIG. 6a illustrating the varying orientation of
the receiver (Rx Coil and Rx Loop) in accordance with various
aspects of the present invention.
[0020] FIG. 8 shows a plot of range (critical coupling distance)
vs. Rx radius, for Tx radius=0.15 m.
DETAILED DESCRIPTION
[0021] In the description that follows, like components have been
given the same reference numerals, regardless of whether they are
shown in different embodiments. To illustrate an embodiment(s) of
the present disclosure in a clear and concise manner, the drawings
may not necessarily be to scale and certain features may be shown
in somewhat schematic form. Features that are described and/or
illustrated with respect to one embodiment may be used in the same
way or in a similar way in one or more other embodiments and/or in
combination with or instead of the features of the other
embodiments.
[0022] In accordance with various embodiments of this disclosure, a
method is disclosed that includes coupling a resonator of a
transmitter and a resonator of a receiver together by a common
inductance of the transmitter and the receiver; and adjusting
environmental parameters or system parameters or both of the
transmitter, the receiver, or both, to control power transmitted
wirelessly between the transmitter and the receiver.
[0023] In accordance with various embodiments of this disclosure,
an apparatus is disclosed that includes a transmitter comprising a
resonator configured to couple with a resonator of a receiver by a
common inductance; and a controller configured to optimize the
transmitted power based environmental parameters or system
parameters or both of the transmitter, the receiver, or both, the
transmitter configured to transmit power wirelessly to the
receiver.
[0024] In accordance with various embodiments of this disclosure,
an apparatus is disclosed that includes a receiver comprising a
resonator configured to couple with a resonator of a transmitter by
a common inductance; and optimally receive power wirelessly from
the transmitter based on environmental parameters or system
parameters or both of the transmitter, the receiver resonator, or
both.
[0025] These and other features and characteristics, as well as the
methods of operation and functions of the related elements of
structure and the combination of parts and economies of
manufacture, will become more apparent upon consideration of the
following description and the appended claims with reference to the
accompanying drawings, all of which form a part of this
specification, wherein like reference numerals designate
corresponding parts in the various Figures. It is to be expressly
understood, however, that the drawings are for the purpose of
illustration and description only and are not intended as a
definition of the limits of claims. As used in the specification
and in the claims, the singular form of "a", "an", and "the"
include plural referents unless the context clearly dictates
otherwise.
[0026] Turning now to the various aspects of the disclosure, a
model is disclosed of coupled resonators in terms of passive
circuit elements. The conventional analysis, based on coupled mode
theory, is difficult to apply to practical systems in terms of
quantities such as inductance (L), capacitance (C), and resistance
(R) that are measurable in the laboratory at high frequencies (HF
band) that is herein disclosed. The disclosed model shows that to
maintain efficient power transfer, system parameters must be tuned
to compensate for variations in Transmit-to-Receive ("Tx-Rx") range
and orientation.
[0027] FIG. 1a shows an exemplary system diagram of an auto-tuning
wireless power transfer system in accordance with various aspects
of the present disclosure. FIG. 1b shows an equivalent circuit
diagram including four coupled resonant circuits for the exemplary
system of FIG. 1a. FIG. 1c shows a photograph of an experimental
set-up of a wireless power transfer apparatus including a Tx Loop
and Tx Coil (left), and Rx Coil and Rx Loop (right).
[0028] Turning to FIG. 1a, one aspect of the present disclosure is
shown. A transmitter 105 is configured to supply power wirelessly
to a receiver 200. The transmitter 100 is shown having a
transmitter resonator or resonator of the transmitter 105 as a coil
(Tx Coil). Similarly, the receiver 200 is shown having a receiver
resonator or resonator of the receiver 205 as a coil (Rx Coil). In
some aspects, the transmitter resonator (Tx Coil) and/or the
receiver resonator (Rx Coil) is a substantially two-dimensional
structure. The transmitter resonator (Tx Coil) is coupled to a
transmitter impedance-matching structure 110. Similarly, the
receiver resonator (Rx Coil) is coupled to a receiver
impedance-matching structure 210. As shown in FIG. 1a, the
transmitter impedance-matching structure 110 is a loop (Tx Loop)
and the receiver impedance-matching structure 210 is a loop (Rx
Loop). Other impedance-matching structures may be used for the
transmitter 100, the receiver 200, or both which include a
transformer and/or and an impedance-matching network. The
impedance-matching network may include inductors and capacitors
configured to connect a signal source to the resonator
structure.
[0029] Transmitter 100 includes a controller 115, a directional
coupler 120 and a signal generator and radio frequency (RF)
amplifier 125 which are configured to supply control power to a
drive loop (Tx Loop). Impedance-matching structure 110 of the
transmitter 100 such as drive loop or Tx Loop is configured to be
excited by a source (not shown in FIG. 1a) with finite output
impedance R.sub.source. Signal generator 125 output is amplified
and fed to the Tx Loop. Power is transferred magnetically from Tx
Loop to Tx Coil to Rx Loop to Rx Coil, and delivered by ohmic
connection to the load 215.
[0030] If the system becomes mis-tuned because of a change in Tx-Rx
distance, a reflection may occur on the transmitter side. The
directional coupler 120 separates the reflected power from the
forward power, allowing these quantities to be measured separately.
The controller 115 adjusts transmit frequency to minimize the ratio
of reflected to forward power, thereby retuning the system for the
new working distance.
[0031] Turning to FIG. 1b, a simple one-turn drive loop (Tx Loop)
can be modeled as an inductor L.sub.1 with parasitic resistance
R.sub.p1. For element i, distributed inductance is labeled L.sub.i,
distributed capacitance is C.sub.i, and parasitic resistance is
R.sub.pi. The coupling coefficient for the mutual inductance
linking inductor i to inductor j is labeled k.sub.ij. Capacitor may
be added to make drive loop (Tx Loop) resonant at a frequency of
interest, bringing the net capacitance for the loop to C.sub.1.
Drive loop (Tx Loop) is powered by source (V.sub.Source). Transmit
coil (Tx Coil) may be a multi-turn air core spiral inductor
L.sub.2, with parasitic resistance R.sub.p2. Capacitance C.sub.2 of
transmit coil (Tx Coil) is defined by its geometry. Inductors
L.sub.1 and L.sub.2 are connected with coupling coefficient
k.sub.12, where
k ij = M ij L i L j ##EQU00001##
is the coupling coefficient linking inductors i and j, and M.sub.ij
is the mutual inductance between i and j. Note that
0.ltoreq.k.sub.ij.ltoreq.1. Coupling coefficient k.sub.12 is
determined by the geometry of drive loop (Tx Loop) and transmit
coil (Tx Coil). Receiver apparatus is defined similarly to the
transmitter apparatus: L.sub.3 is the inductance of receiver coil
(Rx Coil) and L.sub.4 is the inductance of load loop (Rx Loop).
Transmitter coil (Tx Coil) and receiver coil (Rx Coil) are linked
by coupling coefficient k.sub.23, which depends on both Tx-Rx range
and relative orientation. Drive loop (Tx Loop) and load loop (Rx
Loop) may be configured to impedance match source and load to high
Q resonators (Tx Coil and Rx Coil).
[0032] As discussed above, source and load loops (Tx Loop and Rx
Loop) may be replaced by other impedance matching components. The
Tx loop (or equivalent component) and Tx coil may both be embedded
in the same piece of equipment (and likewise for the Rx coil and Rx
Loop or equivalent component). Thus, coupling constants k.sub.12
and k.sub.34 are variables that the can be, in principle,
controlled, unlike coupling constant k.sub.23, which is an
uncontrolled environmental variable determined by usage
conditions.
[0033] Uncontrolled environmental parameters may include parameters
such as a range between the transmitter resonator (Tx Coil) and the
receiver resonator (Rx Coil), a relative orientation between the
transmitter resonator (Tx Coil) and the receiver resonator (Rx
Coil), and a variable load on the receiver resonator (Rx Coil). By
way of a non-limiting example, a variable load can be a device that
experiences variations in a power state, such as a laptop computer
powering on, down, or entering stand-by or hibernate mode. Other
examples, may include a light bulb having various illumination
states, such a dim or full brightness.
[0034] System parameters, such as the coupling constants k.sub.12
and k.sub.34, are variables that the can be, in principle,
controlled and that we can be adjust to compensate for the changes
in environmental parameters. Other such system parameters may
include a frequency at which power is transmitted, an impedance of
the transmitter resonator and an impedance of the receiver
resonator.
[0035] Writing Kirchhoffs voltage law (KVL) for each of the
sub-circuits in the FIG. 1b allows the current in each to be
determine:
I 1 ( R Source + R p 1 + j .omega. L 1 + 1 j .omega. C 1 ) + j
.omega. I 2 k 12 L 1 L 2 = V S ##EQU00002## I 2 ( R p 2 + j .omega.
L 2 + 1 j .omega. C 2 ) + j .omega. ( I 1 k 12 L 1 L 2 - I 3 k 23 L
2 L 3 ) = 0 ##EQU00002.2## I 3 ( R p 3 + j .omega. L 3 + 1 j
.omega. C 3 ) + j .omega. ( I 4 k 34 L 3 L 4 - L 2 k 23 L 2 L 3 ) =
0 ##EQU00002.3## I 4 ( R Load + R P 4 + j .omega. L 4 + 1 j .omega.
C 4 ) + j .omega. I 3 k 34 L 3 L 4 = 0 ##EQU00002.4##
[0036] Solving these four KVL equations simultaneously for the
voltage across the load resistor yields the transfer function for
this system of coupled resonators:
V Gain .ident. V Load V Source = .omega. 3 k 12 k 23 k 34 L 2 L 3 L
1 L 2 R Load k 12 2 k 34 2 L 1 L 2 L 3 L 4 .omega. 4 + Z 1 Z 2 Z 3
Z 4 + .omega. 2 ( k 12 2 L 1 L 2 Z 3 Z 4 + k 23 2 L 2 L 3 Z 1 Z 4 +
k 34 2 L 3 L 4 Z 1 Z 2 ) ( 1 ) ##EQU00003##
where V.sub.Load is the voltage across the load resistor and
Z.sub.1=(R.sub.p1+R.sub.Source+i.omega.L.sub.1-i/(.omega.C.sub.1)
Z.sub.2=(R.sub.p2+i.omega.L.sub.2-i/(.omega.C.sub.2)
Z.sub.3=(R.sub.p3+i.omega.L.sub.3-i/(.omega.C.sub.3)
Z.sub.4=(R.sub.p4+R.sub.Load+i.omega.L.sub.4-i/(.omega.C.sub.4)
[0037] The analytical transfer function was cross-validated by
comparing its predictions with SPICE (Simulation Program with
Integrated Circuit Emphasis) simulations. As is known, SPICE is a
general-purpose analog electronic circuit simulator that is used in
integrated circuit (IC) and board-level design to check the
integrity of circuit designs and to predict circuit behavior. From
Eq. 1, a scattering parameter S.sub.21 can be calculated and shown
to be:
S 21 = 2 V Load V Source ( R Source R Load ) 1 / 2 ( 2 )
##EQU00004##
which can be important experimentally since it can be measured with
a vector network analyzer, which as known, is an instrument used to
analyze the properties of electrical networks, especially those
properties associated with the reflection and transmission of
electrical signals known as scattering parameters (S-parameters).
The entire wireless power transfer apparatus can be viewed as a
two-port network (one port being the input, fed by source, and the
other the output, feeding the load). In a two-port network,
S.sub.21 is a complex quantity representing the magnitude and phase
of the ratio of the signal at the output port to the signal at the
input port. Power gain, the essential measure of power transfer
efficiency, is given by |S.sub.21|.sup.2, the squared magnitude of
S.sub.21. As presented below, experimental and theoretical results
are presented in terms of |S.sub.21|.
[0038] In FIG. 2a, |S.sub.21| is plotted for a realistic set of
parameters, as shown in Table S1 below, as a function of the Tx-Rx
coupling constant k.sub.23 and the driving angular frequency
.omega.. In this plot, k.sub.12 and k.sub.34 are held constant,
which would typically be the case for a fixed antenna design. This
elementary transfer function neglects parasitic coupling, such as
that from the drive loop (Tx Loop) direct to the receiver coil (Rx
Coil), i.e. the k.sub.13 coupling. A more complete model that
includes parasitic effects will be discussed later. However, the
elementary model captures the essential behavior and is likely to
be useful long term, as future systems may have reduced parasitic
coupling.
[0039] FIG. 2a shows the dependence of system efficiency on
frequency and k.sub.23. On the k.sub.23 axis, smaller values
correspond to larger Tx-Rx distances because the mutual inductance
between the transmitter coil (Tx Coil) and receiver coil (Rx Coil)
decreases with distance. Changing the angle of the receiver coil
(Rx Coil) with respect to the transmitter coil (Tx Coil) can also
change k.sub.23. For example, rotating an on-axis receiver coil (Rx
Coil) from being parallel to the transmitter coil (Tx Coil) to
being perpendicular would decrease their mutual inductance and
therefore k.sub.23. Moving the receiver coil (Rx Coil) in a
direction perpendicular to the transmit axis would also typically
change k.sub.23.
[0040] FIG. 2a shows the plot partitioned into 3 regimes,
corresponding to different values of k.sub.23. In the overcoupled
regime, represented in FIG. 2a as the dotted lines that enclose the
V-shaped ridge, k.sub.23>k.sub.Critical. (The value of the
constant k.sub.Critical will be defined below in terms of the
features of the surface plotted in the figure.) In the critically
coupled regime, which is the plane bounding this volume,
k.sub.23=k.sub.Critical. In the under-coupled regime beyond the
volume outlined by the dotted lines,
k.sub.23<k.sub.Critical.
[0041] High efficiency of power transmission occurs on the top of
the V-shaped ridge. The V-shape is due to resonance splitting: in
the over-coupled regime (i.e. for any choice of
k.sub.23>k.sub.Critical) there are two frequencies at which
maximum power transfer efficiency occurs. These correspond to the
system's two normal modes. The more strongly coupled the resonators
(transmitter coil (Tx Coil) and receiver coil (Rx Coil)) are, the
greater the frequency splitting; the difference between the two
normal mode frequencies increases with k.sub.23. As k.sub.23
decreases, the modes move closer together in frequency until they
merge. The value of k.sub.23 at which they merge (the point denoted
by "I" on the V-shaped ridge) is defined to be the critical
coupling point k.sub.Critical. The frequency at which the modes
merge is the single resonator natural frequency
.omega.=.omega..sub.0 (assuming both coils have the same
.omega..sub.0). Note that the mode amplitude is nearly constant
throughout the over-coupled and critically coupled regime, allowing
high efficiency; as k.sub.23 drops below k.sub.Critical, the single
mode amplitude decreases, lowering the maximum system efficiency
achievable.
[0042] Because of the nearly constant mode amplitude throughout the
overcoupled regime, system efficiency could be kept nearly constant
as k.sub.23 varies (as long as k.sub.23>k.sub.Critical), if the
system transmit frequency could be adjusted to keep the operating
point on top of the ridge. In other words, as the Tx-Rx distance
(and thus k.sub.23) changes due to motion of the receiver, the
system could be re-tuned for maximum efficiency by adjusting the
frequency to keep the operating point on the top of the ridge.
[0043] As disclosed below, tuning transmitter resonator (Tx Coil)
automatically to maximize transmission power can be achieved based
on three results. Because the tuning compensates for changes in
k.sub.23, the same technique can compensate for any geometrical
variation that changes k.sub.23 (by a sufficiently small amount),
including changes in orientation, and non-range changing
translations.
[0044] A correctly functioning control system may allow the system
efficiency to be nearly independent of range, for any range up to
the critical range. It may be counter-intuitive that power transfer
efficiency can be approximately independent of range (even within a
bounded working region), since the power delivered by far-field
propagation depends on range r as 1/r.sup.2, and traditional
non-adaptive inductive schemes have 1/r.sup.3 falloff. Therefore,
the top of the efficiency ridge, along which the efficiency is
approximately constant is referred to as the "magic regime" for
wireless power transfer. The values of k.sub.23 that the magic
regime spans are given by k.sub.Critical.ltoreq.k.sub.23.ltoreq.1.
Thus, the smaller k.sub.Critical, the larger the spatial extent
spanned by the magic regime, and thus the larger the system's
effective working range.
[0045] In FIG. 2b, frequency is held constant while k.sub.12 (and
k.sub.34, constrained for simplicity to equal k.sub.12) is varied.
Adapting k.sub.12 to compensate for detuning caused by changes in
k.sub.23 is another method for adapting to varying range and
orientation.
[0046] Further analysis of the transfer function (Eq. 1) gives
insight into the effect of circuit parameters on the performance of
the wireless power system. As explained above, the effective
operating range is determined by the value of k.sub.Critical: the
smaller k.sub.Critical, the greater the spatial extent of the magic
regime.
[0047] So, to understand system range, it will be useful to solve
for k.sub.Critical in terms of design parameters. First, the
transfer function can be clarified by substituting expressions for
quality factor:
Q i = 1 R 1 L i C i = .omega. 0 i L i R i = 1 .omega. 0 i R i C i ,
where .omega. 0 i = 1 L i C i ##EQU00005##
is the uncoupled resonant frequency of element i.
[0048] For simplicity, consider a symmetrical system, with the
quality factor of the Tx and Rx coils equal,
Q.sub.Coil=Q.sub.2=Q.sub.3, and the quality factors of the Tx and
Rx loops equal, Q.sub.Loop=Q.sub.1=Q.sub.4. The symmetric
loop-to-coil coupling k.sub.12=k.sub.34 will be denoted k.sub.lc.
Also it is assumed that R.sub.Source=R.sub.Load,
R.sub.p1<R.sub.Source, R.sub.p4<R.sub.Load, and that the
uncoupled resonant frequencies are equal:
.omega..sub.0.sup.i=.omega..sub.0 for all i. To find an expression
for the critical coupling value, consider the transfer function
when the system is driven at frequency .omega.=.omega..sub.0. This
corresponds to a 2D slice of FIG. 2a along the center frequency of
10 MHz, whose apex is the critical coupling point of the system.
Using the expressions for .omega. in terms of Q above, this slice
of the transfer function can be written
V Gain | .omega. = .omega. 0 = k 23 k lc 2 Q Coil 2 Q Loop 2 k 23 2
Q Coil 2 + ( 1 + k lc 2 Q Coil Q Loop ) 2 ( 3 ) ##EQU00006##
[0049] To derive an expression for k.sub.Critical, the maximum of
Eq. 3 is found by differentiating with respect to k.sub.23. Then
k.sub.Critical is the point along the k.sub.23 axis of FIG. 2a that
(for positive values of k and Q) sets this derivative to zero:
k Critical = 1 Q Coil + k lc 2 Q Loop ( 4 ) ##EQU00007##
[0050] Finally, k.sub.Critical is substituted for k.sub.23 in Eq. 3
to find the voltage gain at the critical coupling point:
V.sub.GainCritical=ik.sub.lc.sup.2Q.sub.CoilQ.sub.Loop/2(1+k.sub.lc.sup.2-
Q.sub.CoilQ.sub.Loop). Using Eq. 2, and assuming that
R.sub.load=R.sub.source, this voltage gain can be converted into
|S.sub.21|, which will be convenient to abbreviate
G.sub.Critical:
G Critical .ident. S 21 Critical = k lc 2 Q Coil Q Loop 1 + k lc 2
Q Coil Q Loop = k lc 2 Q Loop k Critical ( 5 ) ##EQU00008##
[0051] This equation quantifies the system's efficiency at the
furthest point on the magic regime ridge. Recall that in order to
maximize range, we must minimize k.sub.Critical because this
increases the extent of the magic regime, which spans from
k.sub.Critical to 1.0. Examining Eq. 4, reducing k.sub.lc lowers
k.sub.Critical and therefore increases range. However, according to
Eq. 5, reducing k.sub.lc also reduces efficiency. Indeed, the
choice of k.sub.lc trades off the efficiency level in the magic
regime (height of magic regime ridge) vs. the extent of the magic
regime (spatial extent of magic regime, i.e. maximum range). FIG. 5
is a plot of this tradeoff curve, |S.sub.21|.sub.Critical vs
k.sub.Critical as a function of the common parameter k.sub.lc.
[0052] The area under this tradeoff curve serves as a useful figure
of merit (FOM) for system performance:
FOM=.intg..sub.0.sup.1G.sub.Criticaldk.sub.critical. An optimal
wireless power system, which could losslessly deliver power at
infinite range (0 coupling), would have an FOM of unity. For the
symmetrical case (in which corresponding parameters on the transmit
and receive sides are equal), the FOM integral can be evaluated
analytically. Assuming that Q.sub.Coil>1, the area under the
tradeoff curve turns out to be
F O M = 1 - 1 Q Coil - ln Q Coil Q Coil . ( 6 ) ##EQU00009##
[0053] The FOM turns out to depend only Q.sub.coil, and is
independent of Q.sub.Loop. The quality factor of the resonators
(coils) entirely determines this measure of system performance,
which approaches to unity in the limit of infinite Q.sub.coil. The
measured Q.sub.Coil values for the experimental system, which is
discussed further below, are around 300 and 400, corresponding to
FOM=0.978 and FOM=0.982 (plugging each Q.sub.coil value into the
symmetric FOM formula).
[0054] Choosing a feasible value of Q.sub.Loop is the next
important design question. To derive a guideline, an expression is
found for the "knee" of the range-efficiency tradeoff curve, which
we will define to be the point at which the slope
G Critical k Critical ##EQU00010##
equals unity. The value of k.sub.Critical at which this occurs
turns out to be
k.sub.CriticalKnee=Q.sub.Coil.sup.-1/2 (7)
[0055] If Q.sub.Loop is too small, then even setting k.sub.lc to
its maximum value of 1.0, k.sub.Critical will not be able to reach
k.sub.CiticalKnee. To find the minimum necessary Q.sub.Loop value,
Eq. 4 can be solved for Q.sub.Loop with
k.sub.Critical=k.sub.CriticalKnee and k.sub.lc=1, which yields
Q.sub.Loop=(Q.sub.Coil.sup.1/2-1)Q.sub.Coil.sup.-1.apprxeq.Q.sub.Coil.sup-
.-1/2 for large Q.sub.Coil. Specifically, a good operating point on
the tradeoff curve should be achievable as long as
Q.sub.Loop>Q.sub.Coil.sup.-1/2. For Q.sub.Coil=300, this
condition becomes Q.sub.Loop>0.06.
[0056] A conclusion is that Q.sub.Coil determines system
performance (as measured by our FOM), as long as a minimum
threshold value of Q.sub.Loop is exceeded. The actual value of
Q.sub.Loop is dominated by the source and load impedances. The
larger Q.sub.Coil is, the smaller the required minimum Q.sub.Loop.
Conversely, moving to a more demanding load (with Q.sub.Loop below
the current threshold value) could be accomplished by sufficiently
increasing Q.sub.Coil.
[0057] Turning now to FIG. 1c which shows an experimental
validation of the model. FIG. 1c shows transmitter coils (Tx Coil)
and receiver coils (Rx Coil) that was used to validate the
theoretical model, and to implement automatic range and orientation
tuning. The transmitter on the left includes a small drive loop (Tx
Loop) centered within a flat spiral transmit resonator (Tx Coil);
the receiver side loop (Rx Loop) and coil (Rx Coil) are visible on
the right. The system was characterized with a vector network
analyzer in addition to the circuit values shown in Table S1 and
S2, below. The first group of measurements consisted of S.sub.11
measurements; the S.sub.11 scattering parameter is the ratio of
complex reflected voltage to complex transmitted voltage at the
input port. The ratio of reflected to transmitted power is given by
|S.sub.11|.sup.2. L, C, and R values were extracted for each loop
by fitting a model with these parameters to the S.sub.11 data. The
second group of measurements were S.sub.11 measurements of the Tx
Loop coupled to the Tx Coil, and corresponding measurements on the
receiver side. Values were extracted for coil resonant frequency
f.sub.0 and Q, as well as loop-coil coupling coefficients k.sub.12
and k.sub.34, again by fitting a model to data from both groups of
measurements. It is not likely to extract L, C, and R values for
the coils from these measurements because more than one parameter
set is consistent with the data. So, an inductance value was
calculated numerically for the coils based on their geometry, which
then allowed C and R values to be calculate given the Q and f
values.
[0058] The distance-dependent coupling coefficients are k.sub.23
(the main coil to coil coupling constant), and the parasitic
coupling terms k.sub.13, k.sub.24, and k.sub.14. To measure these,
vector S.sub.21 data (not just |S.sub.21|) was collected at a
variety of Tx-Rx ranges for the complete 4 element system. Then at
each distance, a non-linear fit was performed to extract the
coupling coefficients. As an alternative method for finding the
coupling coefficients, Neumann's formula was used to calculate the
coupling coefficients directly from geometry.
[0059] Table S1 shows circuit values used to evaluate the
elementary model.
TABLE-US-00001 TABLE S1 PARAMETER Value R.sub.source, R.sub.Load 50
.OMEGA. L.sub.1, L.sub.4 1.0 uH C.sub.1, C.sub.4 235 pF R.sub.p1,
R.sub.p4 0.25 .OMEGA. K.sub.12, K.sub.34 0.10 L.sub.2, L.sub.3 20.0
uH C.sub.2, C.sub.3 12.6 pF R.sub.p2, R.sub.p3 1.0 .OMEGA. K.sub.23
0.0001 to 0.30 f.sub.0 10 MHz Frequency 8 MHz to 12 MHz
[0060] It is to be noted that the expression for k.sub.Critical
(Eq. 4) specifies the value of k.sub.23 that would be required to
achieve critical coupling; it is not the case that the required
coupling is achievable for all choices of Q, since only values
corresponding to k.sub.23.ltoreq.1 are realizable. Since all
quantities in Eq. 4 are positive, it is clearly necessary (though
not sufficient) that 1/Q.sub.Coil.ltoreq.1 and that
k.sub.lc.sup.2Q.sub.Loop.ltoreq.1 for a realizable k.sub.Critical
to exist. If a realizable k.sub.Critical does not exist, then there
is no tuning that will allow the system to achieve the full
efficiency of the magic regime; even when the system is maximally
coupled, so that k.sub.23=1, the system would operate in the
sub-optimal under-coupled regime. It is to be noted that in
practice it may not be possible to achieve k.sub.lc=1, which would
then require a larger minimum value of Q.sub.Loop. Also, it is
merely a coincidence that the minimum value of Q.sub.Loop happens
to be numerically so close to the value of k.sub.CriticalKnee,
since these are logically distinct.
[0061] To evaluate the integral of the parametric curve
G.sub.Critical vs k.sub.Critical (both of which are parameterized
by k.sub.lc), k.sub.lcMax is solved for in Eq. 4, the value of the
parameter k.sub.lc corresponding to the upper integration limit
k.sub.Critical=1.0, finding
k lcMax = Q Coil - 1 Q Loop Q Coil . ##EQU00011##
The correct lower integration limit is k.sub.lc=0. So,
F O M = .intg. 0 k lcMax G Critical k Critical k lc k lc , with k
Critical k lc = 2 k lc Q Loop . ##EQU00012##
[0062] Note that the power vs. range tradeoff does not indicate
that power deliverable falls as the receiver moves further from the
transmitter; it indicates that choice of k.sub.lc trades off the
extent of the "magic regime" (width of the magic regime plateau)
with the amount of power delivered within the magic regime (height
of the plateau).
[0063] The model was experimental validation using a drive loop
that was 28 cm in diameter, with a series-connected variable
capacitor used to tune the system to about 7.65 MHz. A SubMiniature
version A (SMA) connector was also placed in series so that a RF
amplifier was able to drive the system as described in FIG. 1a. The
large transmitter coil started with an outer diameter of 59 cm and
spiraled inwards with a pitch of 1 cm for approximately 6.1 turns.
It was difficult to accurately predict the self capacitance of the
coils, so the resonant frequency was tuned by manually trimming the
end of the spiral until it resonates at 7.65 MHz. The receiver was
constructed similarly although minor geometrical differences which
resulted in the Rx coils having roughly 6.125 turns after being
tuned to 7.65 MHz. All the elements were made of 2.54 mm diameter
copper wire, supported by Plexiglas armatures.
[0064] A first group of measurements of the experimental set-up
included S.sub.11 measurements (where S.sub.11 is the ratio of
reflected voltage to transmitted voltage at the input port) of the
Tx loop (denoted Measurement 1T in Table S2) and Rx loop
(Measurement 1R), without the coils. From these, L, C, and R values
were extracted for the loops by least squares fitting. The second
group of measurements were S.sub.11 measurements of the Tx loop
coupled to the Tx coil (Measurement 2T), and a corresponding
receiver-side measurement denoted 2R. Using data from the second
group of measurements and the previously extracted loop parameters,
values were extracted for coil resonant frequencyfo and Q, as well
as loop-coil coupling coefficients k.sub.12 and k.sub.34. It was
not possible to extract L, C, and R values from these measurements.
So, an inductance value for the coils based on their geometry was
calculated numerically, which then allowed C and R values to be
calculated.
[0065] Table S2 is shown below.
TABLE-US-00002 TABLE S2 MEASURED AND CALCULATED STATIC
(NON-DISTANCE DEPENDENT) SYSTEM PARAMETERS TRANSMITTER RECEIVER
COMPONENT VALUE SOURCE COMPONENT VALUE SOURCE L.sub.1 0.965 uH
Measurement 1T L.sub.4 0.967 uH Measurement 1R C.sub.1 449.8 pF
Measurement 1T C.sub.4 448.9 pF Measurement 1R R.sub.p1 0.622
.OMEGA. Measurement 1T R.sub.p4 0.163 .OMEGA. Measurement 1R
R.sub.source 50 .OMEGA. Manufacturer R.sub.load 50 .OMEGA.
Manufacturer Spec Spec Q.sub.1 0.91 L.sub.1, C.sub.1, R.sub.p1,
R.sub.source Q.sub.4 0.93 L.sub.4, C.sub.4, R.sub.p4, R.sub.load
F.sub.1 7.64 MHz L.sub.1, C.sub.1 F.sub.4 7.64 MHz L.sub.4, C.sub.4
K.sub.12 0.1376 Measurement 2T; K.sub.34 0.1343 Measurement 2R;
L.sub.1, C.sub.1, R.sub.p1 L.sub.4, C.sub.4, R.sub.p4 Q.sub.2 304.3
Measurement 2T; Q.sub.3 404.4 Measurement 2R; L.sub.1, C.sub.1,
R.sub.p1 L.sub.4, C.sub.4, R.sub.p4 F.sub.o2 7.66 MHz Measurement
2T; F.sub.o3 7.62 MHz Measurement 2R; L.sub.1, C.sub.1, R.sub.p1
L.sub.4, C.sub.4, R.sub.p4 L.sub.2 39.1 uH Calculation 1T L.sub.3
36.1 uH Calculation 1R C.sub.2 11.04 pF L.sub.2, F.sub.o2 C.sub.3
12.10 pF L.sub.3, F.sub.o3 R.sub.p2 6.19 .OMEGA. L.sub.2, F.sub.o2,
Q.sub.2 R.sub.p3 4.27 .OMEGA. L.sub.3, F.sub.o3, Q.sub.3
[0066] The experimental set-up showed that the system was able to
perform adaptive frequency tuning for range-independent maximum
power transfer. The lower frequency mode had a higher amplitude in
the experimental set-up (partly because of the sign of the
parasitic signals), so when splitting occurs, the lower mode was
automatically selected. From this, the benefit of the frequency
tuning is apparent at short range, because the frequency that was
chosen for the non-adaptive case (7.65 MHz) was appropriate for the
long range situation. However, if a different frequency had been
chosen for the fixed case, the benefit could have been apparent at
the longer ranges rather than the shorter range.
[0067] Note that increasing range and increasing angle mismatch
both decrease k.sub.23, and the range and orientation mismatch
together diminish k.sub.23 further; thus if the receiver had been
further away, orientation adaptation would not have succeeded over
such a wide range of angles. For extreme values of receiver angle,
discussed further below, the coupling k.sub.23 drops sufficiently
that the system is no longer in the over-coupled regime, so there
is no splitting and no change in optimal system frequency with
coupling constant; thus the fixed and auto-tuning performance
coincide.
[0068] FIG. 3a compares experimentally measured |S.sub.21| data to
the simple model of Eq. 1, and to a more complete model that
includes parasitic couplings. The Figure shows a comparison of
experimental data (dots) to the elementary transfer function
(dotted line), and to the complete transfer function (line), for
the best fit value of k.sub.23. The simple model neglects parasitic
coupling and does not reproduce the amplitude difference between
the upper and lower modes. The complete model reproduces this
amplitude difference, which is explained by the phase of the
parasitic (e.g. k.sub.13) coupling terms relative to the
non-parasitic terms (e.g. k.sub.23) for the two resonant modes. The
agreement between the complete model and the experimental data is
excellent. The difference in the magnitude of the |S.sub.21| peaks
for the upper and lower modes (in FIG. 3a visible in the
experimental data and in the complete model, and not present in the
elementary model) can be explained by considering the phase of the
two modes.
[0069] Based on the dynamics of coupled resonators, the lower
frequency mode that the current in the transmitter coil is expected
to be approximately in phase with the current in the receiver coil;
in the higher frequency mode, the coil currents are expected to be
approximately anti-phase (180 degrees out of phase).
[0070] In the lower mode, in which the Tx coil and Rx coil are in
phase, the parasitic feed-through from the drive loop to the Rx
coil (associated with coupling constant k.sub.13) contributes
constructively to the magnitude of the current in the receive coil.
In the upper mode, the Rx coil phase is inverted but the parasitic
feed through is not, so the feed through interferes destructively
with the Rx coil current. Similar arguments apply to the other
parasitic couplings. The fact that the mode magnitude differences
are modeled well only when parasitic couplings are included (as
shown in FIG. 3a) supports this conclusion.
[0071] As disclosed above, other impendence-matching components
such as discrete matching network or shielded transformer may be
used to connect the source/load to the coils, eliminating
inductively coupled loops. This would eliminate the cross coupling
term and simplify the model, and possibly also simplify system
construction. On the other hand, the parasitic feedthrough benefits
system performance in the lower mode, and this benefit will be lost
by eliminating the loop.
[0072] FIG. 3b shows experimental data and the theoretical model,
using coupling coefficients extracted separately for each distance.
Experimental S21 magnitude data (dots) and analytical model
(surface) computed from the complete transfer function, both
plotted versus frequency and Tx-Rx distance. Note that each
distance slice in the analytical surface is for an independently
fit value k.sub.23. As discussed above, the dotted box encloses the
over-coupled region. For distances between experimental
measurements (i.e. between the contours), k.sub.23 values were
interpolated linearly from neighboring k.sub.23 values. Results
using k.sub.23 computed directly from geometry are presented in the
FIGS. 4a, 4b and 4c discussed below.
[0073] FIGS. 4a, 4b and 4c compare experimental data to the model,
using only calculated coupling coefficients in the model. The model
(lines) compared to experimental data (circles), with k.sub.23
values calculated from geometry (not fit to data). FIG. 4a shows
|S.sub.21| vs distance. Predicted maximum coupling point is plotted
as a solid dot. FIG. 4b shows resonant peak locations as a function
of distance. Frequency splitting is apparent below a critical
distance. This plot can be thought of as the ridge lines of FIG. 3b
viewed from above. FIG. 4c shows resonant peak magnitudes as a
function of distance. This plot can be thought of as the ridge
lines of FIG. 3b viewed from the side. In the simple model, these
two branches would have the same magnitude; including parasitic
couplings accounts for the magnitude difference between the
modes.
[0074] In FIGS. 4a, 4b and 4c, only the static system parameters
were measured; the dynamic (distance-dependent) parameters were
calculated. The agreement is generally good, although at close
range the numerical calculations become less accurate. This may be
because capacitive coupling effects, which were not modeled, become
more significant at close range.
[0075] Adaptive frequency tuning may be implemented for
range-independent maximum power transfer. When the system is
mis-tuned, for example when a non-optimal frequency is chosen, the
impedance mis-match causes a reflection at the transmitter side;
when the system is optimally tuned, the ratio of reflected to
transmitted power is minimized. Thus if the transmitter is capable
of measuring S.sub.11, and adjusting its frequency, it can choose
the optimal frequency for a particular range or receiver
orientation by minimizing S.sub.11 (that is, minimizing reflected
and maximizing transmitted signals). FIGS. 6a and 6b shows
experimental data for power transfer efficiency from a non-adaptive
(fixed frequency) system compared with efficiency data from a
working frequency auto-tuning system.
[0076] For each distance, the system swept the transmit frequency
from 6 MHz to 8 MHz and then chose the frequency with minimal
|S.sub.11| to maximize efficiency. At the optimal frequency for
each distance, the power delivered into a power meter was measured.
The range of tuned values was 6.67 MHz to 7.66 MHz. Analogous
results are shown in FIG. 6b for receiver orientation adaptation.
The system efficiency is nearly constant over about 70 degrees of
receiver orientation. Only in the range from 70 to 90 degrees does
the power transfer efficiency fall toward zero. In both cases shown
in FIGS. 6a and 6b, the fixed frequency chosen was the single coil
resonant frequency (i.e. the undercoupled system frequency), so as
the system leaves the overcoupled regime, the auto-tuned frequency
coincides with the fixed frequency, and so the efficiencies
coincide as well.
[0077] FIG. 7 shows a representative top view of the experimental
implementation of FIG. 6a illustrating the varying orientation of
the receiver (Rx Coil and Rx Loop) in accordance with various
aspects of the present invention. As seen in the top of FIG. 7, Rx
Coil and Rx Loop are aligned in orientation with Tx Loop and Tx
Coil along a center line. The boom of FIG. 7 shows Rx Coil and Rx
Loop rotated through an angle .theta. with respect to the center
line. When the Rx Coil and Rx Loop are arranged as in the top of
the Figure, .theta.=0.degree.. If Rx Coil and Rx Loop were arranged
parallel to the center line, then .theta.=90.degree..
[0078] A tracking scheme that is able to keep the system in tune if
the receiver is moved sufficiently slowly and an adaptation
techniques for narrowband operation are disclosed. Rather than
considering k.sub.lc to be a static design parameter to be
optimized (as above), k.sub.lc may be consider as a dynamically
variable impedance matching parameter that can enable range
adaptation without frequency tuning. If the system is driven at
.omega..sub.0 (the un-coupled resonant frequency) even though it is
actually over-coupled (k.sub.23>k.sub.Critical), frequency
splitting will result in the system being off resonance, and little
to no power will be transferred. To bring the efficiency of the
system back to a maximum, k.sub.lc can be decreased, causing
k.sub.Critical in Eq. 4 to decrease, until k.sub.23=k.sub.Critical,
at which point maximum power transfer can resume. The inventors has
we have successfully implemented a form of this tuning method in
laboratory demonstration systems that allows tuning for a variety
of Tx-Rx distances (k.sub.23 values) with a hand adjustment of a
loop that can be rotated about its coil, changing k.sub.lc. The
k.sub.lc adaptation method has the advantage of allowing operation
at a single frequency .omega..sub.0, which would be advantageous
for band-limited operation. Thus, it is of practical interest to
develop electronically controllable techniques for k.sub.lc tuning.
As noted earlier, the system's loops could be replaced by discrete
matching networks; making these matching networks electronically
variable could allow automatic k.sub.lc tuning.
[0079] By way of a non-limiting example of the tracking and tuning
scheme, a value of a loop-to-coil coupling coefficient of the
transmitter resonator may be fixed and a frequency may be tune
adaptively to choose a desired frequency for a particular value of
a transmitter resonator coil-to-receiver resonator coil coupling
coefficient. Reflected power may be monitored by the transmitter,
for example, and a frequency of the transmitter resonator can be
adjusted to minimize the reflected power. In some aspects, the
transmitter resonator may sweep through a range of frequencies
until the transmitter resonator receives a feedback signal from the
receiver resonator. A desired frequency may be determined for a
distance between the transmitter resonator and the receiver
resonator based on the received feedback signal. The feedback
signal may include signals such as a radio signal, WiFi, Bluetooth,
Zigbee, RFID-like backscatter, or a load-modulated signal. The
load-modulated signal may be modulated on a carrier signal of the
transmitter resonator. In some aspects, a desired frequency may be
determined for a distance between the transmitter resonator and the
receiver resonator based on an impedance matching value between a
signal source and a coil of the transmitter resonator.
[0080] As discussed above, the coupled resonator wireless power
transfer system is capable of adapting to maintain optimum
efficiency as range and orientation vary. This is practically
important, because in many desirable application scenarios, the
range and orientation of the receiver device with respect to the
transmit device varies with user behavior. For example, a laptop
computer being powered by a coil embedded in the wall of a cubicle
would have a different range and orientation each time the user
repositioned the device. One feature of the disclosed adaptation
scheme is that the error signal for the control system can be
measured from the transmitter side only. A separate communication
channel to provide feedback from the receiver to the transmitter
may not be required.
[0081] In some aspects, it is desirable to optimally power smaller
size devices, such as hand held devices and scale the power
transmitted based on the device size. Powering devices that are
smaller than the transmitter is a case of practical interest:
consider a computer display or laptop that recharges a mobile
phone. The dependence of range on receiver coil size can be
discussed by presenting the asymmetric form of Eq. 4, where the
critical coupling (where asymmetric means that it is possible that
k.sub.12.noteq.k.sub.34, Q.sub.1.noteq.Q.sub.4, and
Q.sub.2.noteq.Q.sub.3):
k Critical = ( 1 + k 12 2 Q 1 Q 2 ) ( 1 + k 34 2 Q 3 Q 4 ) Q 2 Q 3
.ltoreq. 1 ( 8 ) ##EQU00013##
[0082] For completeness an asymmetric form of Eq. 5 can be shown to
be:
S 21 Critical = k 12 k 34 Q 1 Q 4 R Load k Critical L 1 L 4 .omega.
0 ( 9 ) ##EQU00014##
[0083] Insight into the scaling of range with coil sizes can be
gained by starting from an approximate formula for coupling
coefficient linking two single-turn coils. Although the coils as
tested had five turns, the behavior is expected to be qualitatively
similar. The formula assumes that the receive radius is less than
the transmit radius (r.sub.Rx<r.sub.Tx) and that both are
on-axis:
k(x).apprxeq.r.sub.Tx.sup.2r.sub.Rx.sup.2(r.sub.Txr.sub.Rx).sup.-1/2(x.su-
p.2+r.sub.Tx.sup.2).sup.-3/2. The distance of critical coupling
(which measures range) can be solved as:
x Critical = ( ( r Tx k Critical 2 / 3 - r Rx ) r Rx ) 1 / 2 ( 10 )
##EQU00015##
into which the right hand side of Eq. 8 can be substituted.
Substituting the measured values from Table S2 above into the right
hand side of Eq. 8, substituting the resulting k.sub.Critical into
Eq. 10, and assuming r.sub.Tx=30 cm, plot Eq. 10 is plotted in FIG.
8. According to this plot, it may be possible to power a device of
radius 5 cm from a transmitter of radius 15 cm at a range of about
30 cm. This parameter set may support the charging of a cell phone
from a wireless power transmitter in a laptop computer.
[0084] In some aspects, Tx Coil and/or Rx Coil may be arranged as
substantially flat or planar in design. In addition to improving
integration with smaller and more planar-sized structure such as a
laptop, a flat coil structure can also reduce unwanted spurious
radio frequency (RF) emissions, because the substantially flat coil
will have a smaller dipole moment in the direction perpendicular to
the flat coil.
[0085] In some aspects, flat coils may be fabricated by forming a
suitable number of turns of magnet wire, solid core wire, stranded
wire, Litz wire, hollow copper tubing (producing better weight to
conductivity ratio) on a non-conductive substrate or armature that
maintains the appropriate flat geometry. Moreover, other methods of
manufacturing a multi-turn 2D coil may be used including etched or
otherwise patterned conductors and those manufactured by any
methods used in printed circuit board fabrication.
[0086] Dielectric losses due to the armature materials may be
minimized by eliminating all excess material not required for
structural stability. The armature may be laser cut from acrylic or
plastic, or injection molded from plastic. The substrate may also
be glass, plexiglass, Flame Retardant 4 (FR4), silicon, low-loss
printed circuit board material, flexible printed circuit board
material, polyamide, polycarbonate sold by, for example, Honlex
Flexible PCB Industrial Co. Ltd of Taiwan.
[0087] In the embodiments herein, the apparatus could be
manufactured by semiconductor device fabrication methods such as
deposition, removal, patterning, and modification of electrical
properties. Deposition methods, for example, include physical vapor
deposition (PVD), chemical vapor deposition (CVD), electrochemical
deposition (ECD), molecular beam epitaxy (MBE) and, atomic layer
deposition (ALD) among others. Removal methods, for example,
include wet etching, dry etching, chemical-mechanical planarization
(CMP) among others. Patterning methods, for example, include
lithography among others. Modification methods, for example,
include reduction of dielectric constant via exposure to
ultraviolet light in UV processing (UVP) among others.
[0088] Substantially flat coils for wireless power transfer may be
fabricated by standard printed circuit board (PCB) fabrication
methods: traces can be designed in standard CAD programs such as
Altium Designer. Wider traces and thicker copper produce higher
conductivity values, which provides for better resonator quality
factor (Q), which in turn is a determinant of system range and
efficiency. The resonator frequency is given by
f=1/(2.pi.(LC).sup.1/2); the resonator quality factor is given by
(1/R)(L/C).sup.1/2. More turns provides additional inductance,
which improves Q if C can be decreased to keep the desired resonant
frequency f constant. At some point, the capacitance C can be
decreased no further however, limiting the maximum inductance value
that can be used for a particular resonant frequency f. An
additional factor limiting the number of turns is that increased
trace length increases resistance, which decreases Q. The need to
increase L by using more turns limits the width of the traces.
Balancing these factors has led the inventors to a design with
around 6 turns, for operating frequencies in the range 5 MHz to 15
MHz.
[0089] Coils for wireless power transfer may also be fabricated
using flexible printed circuit board (PCB) methods. Because the
flexible PCB substrates are thinner than conventional circuit
boards, they may be expected to cause less dielectric loss. PCB
substrates made from low dielectric loss materials such as that
from Rogers corporation may also be used to reduce dielectric
losses. In a micro-electrical-mechanical systems (MEMS) process
such as lithography, electroforming and molding (LIGA), thick (high
aspect ratio) metal coils (which may be expected to have higher
conductivity) may be fabricated on a silicon substrate.
[0090] The flat coils may also be fabricated by die stamping sheet
metal; cutting metal foil using a vinyl cutter or similar tool;
patterning metal using a waterjet, laser cutter, or saw. Flat coils
may be fabricated from transparent conductors such as Indium Tin
Oxide (ITO) or other Transparent Conductive Material.
[0091] Flat coils on the interior of a laptop lid may be patterned
by screen printing, silk screening, stenciling, inkjet printing, or
other processes capable of printing conductive materials.
[0092] The performance of the coils fabricated by several of the
methods above can be improved by plating the materials with a
higher conductivity, non-oxidizing materials such as silver, gold,
or platinum. The coil performance can also be improved by
increasing the amount or thickness of conductive material by
electroplating or electroless plating (even if the plated material
is not particularly high conductivity). The flat coils may be
designed to receive power from outside the laptop, and shield
emissions from inside. The outline of the 2-D coil is not limited
to a specific shape and can adapt to mobile device design
considerations, such as circular, rectangular, square or any other
arbitrary shape in outline.
[0093] Although the above disclosure discusses what is currently
considered to be a variety of useful embodiments, it is to be
understood that such detail is solely for that purpose, and that
the appended claims are not limited to the disclosed embodiments,
but, on the contrary, is intended to cover modifications and
equivalent arrangements that are within the spirit and scope of the
appended claims.
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