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48 IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS, VOL. 5,
NO. 1, FEBRUARY 2011
Design and Optimization of Resonance-BasedEfficient Wireless
Power Delivery Systems for
Biomedical ImplantsAnil Kumar RamRakhyani, Student Member, IEEE,
Shahriar Mirabbasi, Member, IEEE, and
Mu Chiao, Member, IEEE
AbstractResonance-based wireless power delivery is an effi-cient
technique to transfer power over a relatively long distance.This
technique typically uses four coils as opposed to two coilsused in
conventional inductive links. In the four-coil system, theadverse
effects of a low coupling coefficient between primary andsecondary
coils are compensated by using high-quality ( ) factorcoils, and
the efficiency of the system is improved. Unlike its two-coil
counterpart, the efficiency profile of the power transfer is nota
monotonically decreasing function of the operating distance andis
less sensitive to changes in the distance between the primary
andsecondary coils. A four-coil energy transfer system can be
opti-mized to provide maximum efficiency at a given operating
distance.We have analyzed the four-coil energy transfer systems and
out-lined the effect of design parameters on power-transfer
efficiency.Design steps to obtain the efficient power-transfer
system are pre-sented and a design example is provided. A
proof-of-concept pro-totype system is implemented and confirms the
validity of the pro-posed analysis and design techniques. In the
prototype system, fora power-link frequency of 700 kHz and a coil
distance range of 10 to20 mm, using a 22-mm diameter implantable
coil resonance-basedsystem shows a power-transfer efficiency of
more than 80% with anenhanced operating range compared to
efficiency achievedby a conventional two-coil system.
Index TermsBiomedical implants, coupling coefficient, induc-tive
wireless power links, power transmission efficiency,
resonance-based power delivery, telemetry, wireless power
transfer.
I. INTRODUCTION
I MPLANTABLE devices are becoming more and more pop-ular in
health and medical applications due to their abilityto locally
stimulate internal organs and/or monitor and com-municate the
internal vital signs to the outer world. The powerrequirement of
biomedical implants depends on their specific
Manuscript received April 30, 2010; revised July 25, 2010;
accepted August11, 2010. Date of publication October 07, 2010; date
of current version January26, 2011. This work was supported in part
by a research fund from the NaturalSciences and Engineering Council
of Canada (NSERC), in part by the CanadaResearch Chair (CRC)
Program, and in part by infrastructure funding from theCanada
Foundation of Innovation (CFI) and British Columbia Knowledge
De-velopment Fund (BCKDF). This paper was recommended by Associate
EditorB.-D. Liu.
A. K. RamRakhyani and S. Mirabbasi are with the Department of
Electricaland Computer Engineering, University of British Columbia,
Vancouver V6T1Z4, BC Canada.
M. Chiao is with the Department of Mechanical Engineering,
University ofBritish Columbia, Vancouver, BC V6T 1Z4, Canada.
Color versions of one or more of the figures in this paper are
available onlineat http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TBCAS.2010.2072782
application and typically ranges from a few microwatts [1][4]to
a few tens of milliwatts [5][8]. Providing required powerto
implanted devices in a reliable manner is of paramount im-portance.
Some implants use (rechargeable) batteries; however,their
applications are limited due to the size and/or longevityof the
batteries. Wireless power-transfer schemes are often usedin
implantable devices not only to avoid transcutaneous wiring,but
also to either recharge or replace the device battery. Wire-less
power transfer is also used in other application domainswhere
remote powering is required, for example, contactlessbattery
charging [9] and radio-frequency identification (RFID)tags
[10].
A popular technique for wireless power transfer, particularlyin
biomedical implants, is inductive coupling, which was firstused to
power an artificial heart [11], [12] and since then hascommonly
been used in implantable devices [1][8], [13], [14].An inductively
coupled power-transfer system consists of twocoils that are
generally referred to as primary and secondarycoils. In these
systems, power-transfer efficiency is a strongfunction of the
quality factor ( ) of the coils as well as the cou-pling between
the two coils. Hence, the efficiency depends onthe size, structure,
physical spacing, relative location, and theproperties of the
environment surrounding the coils. The cou-pling between the coils
decreases sharply as the distance be-tween the coils increases and
causes the overall power-transferefficiency to decrease
monotonically. Inductive power transferin a (co-centric) 2-coil
system is extensively analyzed in the lit-erature [5], [8], [10],
[15].
The power-transfer efficiency, , versus normalized
distance(i.e., the ratio of the separation between the coils) ( )
and
the geometric mean of the primary and the secondary coil radii(
) is a commonly used performance metric forcomparing different
designs. Due to the low -factor (due tothe source and load
resistances) and low coupling of the coilsin the two-coil system,
two-coil-based power-transfer systemssuffer from relatively
low-power-transfer efficiency, typically,
40% for [5], [6], [16], and generally drops ex-ponentially with
distance ( ) for . In implantabledevices, the size of the implanted
coil is constrained by the im-plant site. Typically, an external
coil can be made big enough toimprove the power-transfer range.
As coupling between coils depends on amount of magneticflux
linkage between primary and secondary coils, for a givenoperating
range and small size of the implanted (secondary) coil,coupling
reduces as difference between external(primary) coil
1932-4545/$26.00 2010 IEEE
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RAMRAKHYANI et al.: DESIGN AND OPTIMIZATION OF RESONANCE-BASED
EFFICIENT WIRELESS POWER DELIVERY SYSTEMS 49
radii and secondary coil radii increases. Increasing external
coildimension, however, increases the inductance of the coil
and,hence, improves its -factor. Thus, an optimum dimension of
anexternal coil exists for which the effect of coupling and
-factor( ) is maximum.
For implants with a high-power requirement, a more
efficientpower-transfer mechanism (e.g., with of 60 to 90% for a
dis-tance of 20 mm or more) is desired. To provide high power atlow
efficiency, a strong alternating magnetic field is requiredwhich
could result in excessive heat in the tissues and, in turn,violates
the safety requirements of the federal regulations. Forexample,
sonodynamic therapy (SDT), a drug delivery approachthat uses
ultrasonic cavitation to enhance the cytotoxicity of
thechemotherapeutic drugs requires comparatively large power
forstimulation and, hence, high-link efficiency is desired.
Sono-dynamic enhancement of doxorubicin cytotoxicity was
inves-tigated by using micro ultrasonic transducers (MUTs) in
com-bination with a cancer drug in [17]. Using 60 s of toned
burstultrasound at 40 W/cm , the cytotoxicity of doxorubicin
treat-ment increases from 27% to 91%. Using an ultrasound
trans-ducer of area 1 mm (dimension 1 mm 1 mm 0.5 mm), thesystem
requires 400 mW of power to stimulate the transducer. Itshould be
noted that most of reported biomedical implants con-sume less than
100 mW of power [5][7].
Resonant-based power delivery is an alternative
wirelesspower-transfer technique that typically uses four coils,
namely,driver, primary, secondary, and load coils which will be
dis-cussed later. Coupled-mode theory [18] has been used toexplain
this phenomenon in [19][21]. Initially, this methodwas focused on
high-power transfer and, hence, requires bigcoils. In [22], this
technique is used for implantable and wear-able devices, though a
system with a large transmitter coil(radius of 176 mm) around the
waist and several receivers isadvocated. Similar independent work
was performed in [23]using very big external coils (radius of 150
mm) and small loadcoils (radius 6.5 mm). This system uses inductive
couplingbetween the driver and primary coil as well as between
thesecondary and load coil. We have also analyzed
resonant-basedpower delivery for implantable devices and provided a
simpleelectrical model for it [24]. In this paper, we present a
morecomprehensive circuit-based model for the system and analyzethe
effect of each design parameter. Furthermore, given thesystem
requirements, we propose and analyze a step-by-stepdesign procedure
to optimize the system. A sample applicationof the technique for
biomedical implants, in particular, implantsthat require relatively
large power, such as [17] is provided,and design constraints are
applied to find the optimum designto achieve maximum efficiency.
Our focus is on the efficiencyof the power-transfer link itself,
and peripheral circuits, such asthe power amplifier in the
transmitter and rectifier and/or dc-dcconverter in the receiver,
are outside the scope of this paper.
This paper is organized as follows. Section II formulates
thepower-transfer efficiency of resonant-based systems. Section
IIIdescribes the design steps. The resonance-based
power-transfersystem is described in Section IV. Section V presents
the exper-imental setup. Results and analysis are provided in
Section VI.Comparison with previous work is done in Section VII and
con-cluding remarks are provided in Section VIII.
II. POWER EFFICIENCY IN RESONANCE-BASED SYSTEMSThis section
presents the individual models for inductance,
capacitance, and resistance of coils. Analytical models of
eachcomponents are presented and are followed by a detailed
anal-ysis of the resonance power-transfer system. The models
arebased on a multilayer helical coil that uses Litz wire.
However,the presented design steps are general. In case other types
of coilare used, the respective inductance, capacitance, and
resistancemodel of coil can be adjusted accordingly, and the
remainingdesign steps and guidelines will be the same.
A. Inductor ModelSelf inductance is a measure of magnetic flux
through the area
(cross section) enclosed by a current carrying coil. The self
in-ductance of a coil with loop radius and wire radius (as-suming )
can be approximated as [25] and [26]
(1)
Mutual inductance is a measure of the extent of magneticlinkage
between current-carrying coils. The mutual inductanceof two
parallel single-turn coils with a loop radius of andcan be
approximated by using (2) where and are the relativedistance and
lateral misalignment, respectively, between the twocoils [25],
[26]. The mutual inductance is a strong function ofcoil geometries
and separation between them
(2)
where and are the zeroth- and first-order Bessel functions.For
perfectly aligned loops ( ), the mutual inductance
between the coils can be calculated as
(3)
where
(4)
and and are the complete elliptic integrals of the firstand
second kind, respectively [25][27].
Coils with different geometries have been used and modeledin the
literature. The planar spiral coil is modeled in [13], [25],[26].
For a spiral coil with co-centric circular loops withdifferent
radii and wire radius , the self-inductance can be calculated
as
(5)where for and 0, otherwise.
Printed spiral coils are implemented and optimized in [28].It
provides low self-inductance and constrains the maximumachievable
-factor. To achieve large self-inductance, multi-layer helical
coils can be used. For a helical coil with turns
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50 IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS, VOL. 5,
NO. 1, FEBRUARY 2011
per layer and coaxial layers, the total self-inductance can
bemodeled as
(6)
where for and, otherwise. is minimum distance between two
consecutive
turns.
B. Parasitic Capacitance
In general, inductors suffer from stray capacitance
betweenturns. Stray capacitance causes self-resonance and limits
the op-erating frequency of the inductor. Stray capacitance of a
single-layer air-cored inductors is modeled analytically in [29]
and[30], and using numerical methods in [31]. For a multilayer
so-lenoid with layers and turns per layer, stray capacitanceis
approximated as [32]
(7)where is the total turns, is parasitic capacitance betweentwo
nearby turns in the same layer, and is parasitic capaci-tance
between different layers.
For a tightly wound coil, parasitic capacitance between
twonearby turns is
(8)
(9)
where are the average diameter of coil, wire ra-dius, thickness,
and relative permittivity of strand insulation andseparation
between two layers, respectively [32].
C. AC Resistance
To achieve high quality factors, inductors with low
effectiveseries resistance (ESR) are required. At high
frequencies,skin and proximity effect increases the ESR. To reduce
the acresistance, multistrand Litz wires are commonly used [1],
[32].Finite-difference time-domain (FDTD) techniques are usedto
model ac resistance numerically [33]. Analytical modelsof winding
losses in the Litz wires are presented in [34] and[35].
Semiempirical formulation using finite-element analysis(FEA) is
presented in [36]. The ac resistance of coils made ofmultistrand
Litz wires, including skin and proximity effect, canbe approximated
as [32]
(10)
Fig. 1. versus coil aspect ratio ().
where is the frequency at which power dissipation is twicethe dc
power dissipation and is given by
(11)
where , , , are the dc resistance of the coil, radiusof each
single strand, number of strands per bunch, permeabilityof free
space, and the area efficiency of the bunch, respectively.
is area efficiency of coil with width and thickness and canbe
calculated using [32, Fig. 1].
The dc resistance of the coil with coaxial layers and di-ameter
can be calculated using
(12)
where is the dc resistance of the unit-length Litz wirewith , ,
, , and as the wire cross-section area,maximum dc resistance of
each individual strand, number ofbunching operations, number of
cabling operations [37], andnumber of individual strands,
respectively [38]
(13)
D. Coil Model
Considering the effect of the stray capacitance and the ac
re-sistance of an inductor, the total impedance of a coil can
bewritten as [39]
(14)
The coil can be modeled as an inductor with a self-inductanceand
effective series resistance given by
(15)
(16)
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RAMRAKHYANI et al.: DESIGN AND OPTIMIZATION OF RESONANCE-BASED
EFFICIENT WIRELESS POWER DELIVERY SYSTEMS 51
Fig. 2. Coil lumped model.
As the operating frequency of coil approaches
self-resonancefrequency ( ), ESR increases drastically. From (16),
for afrequency higher than the , the coil behaves as a
capacitorand, hence, it cannot be used as an inductor after its
resonancefrequency.
The -factor of an unloaded inductor can be written as
(17)
E. Power-Transfer Model1) Two-Coil System: Conventionally, two
coils are used in
inductively coupled power-transfer systems and power is
trans-ferred from one coil to another coil. Power-transfer
efficiencyis a strong function of the -factor of primary coil ( )
andsecondary coil ( ). Mutual coupling ( ) between the coils is
afunction of alignment and distance between the coils. Efficiencyof
a two-coil-based power-transfer system is given by [6], [10],and
[24]:
(18)
2) Four-Coil System: Couple-mode theory [18] has beenoriginally
used to describe resonance-based coupling [19], [20].A simple
circuit-based model for these systems is presentedin [24]. The
effect of the low -factor and the low couplingbetween the source
and load coils can be compensated by usingintermediate high-
-factor coils. To realize efficient powertransfer, the system
consists of four coils referred to as driver,primary, secondary,
and load coil (also denoted as coils 1 to 4).Fig. 3 shows the
simplified schematic and electrical model ofthe four-coil
system.
By applying circuit theory to this system, the relationship
be-tween current through each coil and the voltage applied to
thedriver coil can be captured in the following matrix form:
(19)
where
for
for
is the amplitude of voltage source applied to the driver
coil,and , , and are the effective resistance, inductance,
Fig. 3. (a) Simplified schematic of the four-coil system. (b)
Electrical modelof the power-transfer circuit (for design
example).
and capacitance of the coil . is the mutual inductancebetween
coil and .
where is the coupling factor between coil and coil .Tuning all
coils to the same resonance frequency and oper-
ating it at their resonance frequency, (forand ). For small
driver and load coil inductanceand relatively large distances
between coils 1 and 4, coils 1 and3, and coils 2 and 4, coupling
coefficients and wouldbe neglected. From (19), at resonance, the
current in load coilcan be calculated as
(20)where is the loaded quality factor of coil at the
frequencyof operation. The power-transfer efficiency can be
computed as
(21)F. Analysis of Four-Coil Power-Transfer System
To optimize the design to achieve high efficiency, the effectsof
different parameters on the power-transfer efficiency will
beanalyzed here.
1) High- Requirement: From (21), low coupling betweencoils 2 and
3 can be compensated by a high- factor of thesecoils. Efficiency is
computed and plotted in Fig. 4 with a varying
-factor of coil 2 (primary coil), , and the distance
betweencoils 2 and 3(d). Note that respective , the coupling
coef-ficient between primary and secondary coils corresponding
todistance, decays exponentially with increasing distance
betweenthem.
Fig. 4 shows the effect of -factor on power-transfer effi-ciency
((21)). It can be deduced that for given coupling between
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52 IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS, VOL. 5,
NO. 1, FEBRUARY 2011
Fig. 4. Efficiency versus the factor ( 0.58, 0.60, 5, 100, 0.15,
coupling model (44)).
primary and secondary coils, as the -factor of the coils
in-creases, power-transfer efficiency increases. To achieve
high-power-transfer efficiency (e.g., 80% or beyond) for a high
oper-ating range, high -factor coils are required.
Using moderate coupling between driver and primary coils( ) and
secondary and load coils ( ) along with high
-factor primary ( ) and secondary ( ) coils, the
followingapproximation can be derived:
(22)
(23)
(24)
Applying the aforementioned assumptions, the efficiency
ex-pression ((21)) can be simplified to
(25)
This approximate model is similar to the model for
two-coilsystems. Since in the four-coil system, and are
indepen-dent of the source and load resistances, high quality
factors forprimary and secondary coils can be achieved.
Power-transfer ef-ficiency increases monotonically as
increases.
Note that for (25) to be a valid approximation, has to bewithin
a certain range as will be explained.
For approximation in (22) to be reasonable
(26)For (24) to be a reasonable approximation, we should
have
(27)
Fig. 5. Sensitivity of efficiency on , ( 0.58, 0.60, 0.05, 368,
108).
From (26) and (27), the range of can be shown as
(28)
2) Effect of and on Efficiency: The driver coils-factor is
limited by the source series resistance, and the
load coils -factor is limited by the load resistance as well
asimplant-size limitation. Due to high load resistance ( )and small
size of the inner coil, is typically limited to asmall value.
However, the moderate -factor of 5 to 20 canbe achieved for the
driver coil. Fig. 5 plots the efficiency of afour-coil system as a
function of and .
Note that for the four-coil-based power-transfer system,
effi-ciency does not vary much with respect to the driver
coilsfactor and it has a maxima for a low load coils -factor
(referto Fig. 5). As mentioned before, it is common for the load
coilto have a low -factor.
G. Design of High- CoilsTo achieve a high factor for primary and
secondary coils,
the Litz wire, which provides low ac resistance, can be
used.Based on operating frequency, the gauge of the single strand
inthe Litz wire is chosen. The number of strands in one bunch
isused as a design parameter.
1) Wire Property: Litz wires are commonly used to reducethe ac
resistance of wire and, hence, improve -factor of coils.To define
the link operating frequency, the following consider-ations are
taken into account. First, for the frequency range ofthe 100-kHz to
4-MHz band, no biological effects have been re-ported, in contrast
to the extreme-low-frequency band and themicrowave band [40].
Second, tissues have lower absorptionfor low-frequency RF signals
compared to high-frequency sig-nals. Third, due to the small size
of the implanted coil, it hassmall inductance and small parasitic
capacitance. For lower fre-quency of operation, the coil needs to
be tuned by using a highvalue external resonating capacitor.
Furthermore, by using largetuning capacitance, parasitic
capacitances due to wire winding
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RAMRAKHYANI et al.: DESIGN AND OPTIMIZATION OF RESONANCE-BASED
EFFICIENT WIRELESS POWER DELIVERY SYSTEMS 53
Fig. 6. variation with a number of strands.
and variation in capacitance due to tissues would be
negligible.Hence, the resonating frequency of implanted coil will
not be af-fected by proximity of tissue. Fourth, if the operating
frequencyis close to the self-resonant frequency of coil, the ESR
of thecoil increases drastically [(15)]; thus, for a moderate
self-res-onant-frequency coil, by operating at a lower frequency,
highquality factor can be achieved [(17)]. Based on the
aforemen-tioned points, Litz wire with single-strand wire gauge of
Amer-ican Wire Gauge (AWG) AWG44 is chosen. AWG44 provides
for a frequency range of 350850 kHz [38]. Forapplications where
the operating frequency is fixed, respectivewire gauge can be
chosen to keep close to . re-duces as increases. Due to the
proximity effect, reducesas increases ( ) and causes high ac
resistance[(11)]. The diameter of the Litz wire increases as the
numberof enclosed strands is increased. For a given thickness of
coils,the optimum number of strands that improves and can
becalculated. Fig. 6 shows the product of and for a given
di-mension of primary and secondary coils with a varying numberof
strands. Fig. 7 shows the operating frequency for which thisproduct
is maximum. Based on Figs. 6 and 7, 40 strands Litzwire of strand
gauge AWG44 is chosen for this work. A similarcalculation can be
performed based on design constraints to cal-culate the number of
strands and single-strand wire gauge.
2) Number of Turns: To analyze the effect of the number ofturns
per layer on the -factor of the coils, using (6), (7), (10),and
(17), one can derive an expression for the -factor and itcan be
maximized with respect to the number of turns per layer( ) for a
given number of layers (for ) as follows:
(29)
where , , and . ,, and are a function of (6), (7), (11).
Typically, the operating frequency is kept limited to 2 asac
resistance increases exponentially with operating frequency
Fig. 7. Optimum frequency of operation.
Fig. 8. Optimum number of turns ( 12, 60 mm, , 700 kHz).
(11). For , . From (29) and
(30)
As number of turns increases, increases and the self-res-onating
frequency ( ) decreases. With for which
, the -factor increases monotonically with an incre-ment of ( ,
(30)). can be defined asfor which .
As an example, Fig. 8 shows the graph of the -factor fora coil
with a fixed number of layers and fixed width. is thedistance
between two layers and OD is the diameter of the wire.As can be
seen from the figure, the -factor of the coil
increasesmonotonically when the number of turns is less than
10.
3) Optimum Operating Distance and Effect of : In a typ-ical
case, the relative position and dimension of the driver coiland
primary coil (and of secondary and load coil) is fixed and,hence,
in normal operating mode , , , , and arefixed. For a given
operating distance (respectively, ), only
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54 IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS, VOL. 5,
NO. 1, FEBRUARY 2011
Fig. 9. Effect of the factor( ) on maximum efficiency distance (
368, 108, 0.15, 0.56, 0.59, coupling model (44)).
can be varied by using changing source resistance and, hence,the
effect of on power-transfer efficiency is shown here.
Thepower-transfer efficiency is a strong function of coupling
be-tween coils 2 and 3 ( ). By maximizing efficiency ( )
withrespect to the coupling coefficient, the optimum distance of
op-eration can be achieved. From the efficiency equation [refer
to(21)], we have
(31)for (32)
An expression for efficiency at is given by
(33)
To achieve maximum efficiency at any given distance (whichis
equivalent to a given ), can be varied by controllingthe source
resistance.
Fig. 9 shows that for given system parameters for each valueof ,
a corresponding distance exists for which efficiencyis maximum.
Equation (31) shows the dependence of the op-timum value of on
design parameter . So by changingthe -factor of the driver coil (
), the optimum operatingdistance changes.
4) Sensitivity of Efficiency ( ) to Source Series Resistance:To
compare the effect of source resistance in two-coil-based sys-tems
and four-coil-based systems, we derive an expression forthe slope
of efficiency with respect to source series resistance( )
(34)
Fig. 10. Two- and four-coil system efficiency with respect to .
For two-coil( 700 kHz, 1.1 mH, 1.6, 0.055, 100). Forfour-coil ( 700
kHz, 29.35 H}, 368, 108, 0.15, 0.56, 0.59, 0.055, 100).
For a two-coil system, the rate of change of efficiency is
from(18) and (34), and
for
(35)
For a four-coil system, (36) gives an (approximate)
analyticalexpression for the change in efficiency with respect
to
(36)
For fixed design parameters, (35) and (36) show that effi-ciency
decreases linearly as source resistance increases. To val-idate the
accuracy of (35), efficiency is calculated by using (18)for
different values of and plotted in Fig. 10. A linear regres-sion
model is used to find the slope of changes in efficiency
withrespect to . From the linear regression model of efficiencyfor
varying source resistance, slope 0.00768 and from (35)slope
0.01069.
Similarly to validate the accuracy of (36), with the samesystem
parameters, efficiency is calculated using (21) withvarying and
plotted in Fig. 10. From the linear re-gression model of efficiency
for varying source resistance,
0.00130 and from (36), slope 0.001431 (ap-proximated model).
This example provides the validity of (35) and (36). Fora given
example, by comparing the slope of efficiency for atwo-coil-based
and four-coil-based system, the efficiency ofthe latter decreases
times slower compared to that ofthe former. The slope for a
two-coil-based system is inverselyproportional to (equivalent to )
and, hence, have a highvalue compared to a four-coil-based system
in which the slopeis proportional to (note that ). In the
typicalcase, an increase in value of has a more severe effect
intwo-coil-based systems compared to four-coil-based systems.
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RAMRAKHYANI et al.: DESIGN AND OPTIMIZATION OF RESONANCE-BASED
EFFICIENT WIRELESS POWER DELIVERY SYSTEMS 55
Fig. 11. Sensitivity of with frequency ( 60 mm, 11, ).
5) Sensitivity of to Frequency: The factor of an inductoris a
function of frequency
(37)
At low frequencies, increases with frequency and for, due to the
dominance of proximity effect on ac resistance
[32], the -factor decreases. To utilize the coil for a
differentoperating frequency, it is desirable to have a -factor
that isnot too sensitive to frequency. The bandwidth of is
mainlydefined by . To reduce sensitivity to the operating
frequency,
should be kept sufficiently high so that the ac resistance
stayssmall (10).
Fig. 11 shows the -factor variation with respect to
operatingfrequency for coils with a different number of layers. As
thenumber of layer increases, decreases (11) and the
self-res-onating frequency ( ) decreases due to the increase in
straycapacitance and inductance.
H. Effect of Operating Frequency VariationA four-coil-based
system provides better immunity to oper-
ating frequency variation compared to its corresponding
two-coil-based system. For a four-coil system, by itself. the
drivercoil has a low -factor due to low inductance and, hence, hasa
high bandwidth of operation. The driver coil and high- pri-mary
coil are closely coupled and mutual inductance seen bythe driver
coil due to the primary coil is high. This increases theinfluence
of frequency variation on the driver coil. When the dis-tance
between the secondary coil and the primary coil decreases,the
current in the secondary coil opposes the current in the pri-mary
coil which, in turn, reduces the effect of the primary coilon the
driver coil (reduced ). Hence, the closer the secondarycoil is to
the primary coil, the lower the effective factor ofthe driver coil.
For the two-coil-based system, with comparableprimary coil size and
same source resistance as of the four-coilsystem, the -factor of
the primary coil is higher than that of
Fig. 12. Effect of operating frequency variation on
power-transfer ef-ficiency. (a) Sensitivity of efficiency with
frequency, coil separation(four-coil-based system). (b) Sensitivity
of efficiency with frequency, coilseparation (two-coil-based
system).
the driver coil in the four-coil system. Therefore, the
two-coilsystem is a narrower band and is thus more sensitive to
oper-ating frequency.
Fig. 12(a) and (b) shows that for a
four-coil-basedpower-transfer system as the coil separation between
pri-mary and secondary coils decreases, the frequency rangeover
which the four-coil system has a higher efficiency iswider compared
to the corresponding two-coil-based system.Note that for comparison
in these two figures, practically thesame-size external and
implantable coils are used for two-coil-and four-coil-based
systems.
I. Series Versus Parallel Connection of Load ResistanceTo
improve the -factor of the load coil, the load resistance
can be either attached in series or parallel to a resonating
capac-itor ( , refer to Fig. 13). For parallel connection of the
loadresistance as shown in Fig. 13(a), we have
(38)
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56 IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS, VOL. 5,
NO. 1, FEBRUARY 2011
Fig. 13. Series versus parallel connection of load resistance.
(a) Resonant coil:Parallel connection of load resistance. (b)
Resonant coil: Series connection ofload resistance.
(39)
For series connection of the load resistance as shown in
Fig.13(b), we have
for (40)
(41)
The difference between the parallel- and series-connectedfactors
can be calculated as
(42)
Note that for , the parallel connection of loadresistance will
improve the factor.
As a side note, it should be mentioned that in a practical
im-plantable device with a four-coil-based wireless
power-transfersystem, typically a rectifier block will be the load
of the loadcoil. In general, the rectifier exhibits an impedance
with a re-sistive and reactive part (where the reactive part is
typically ca-pacitive). The reactive part (capacitive component )
of this loadimpedance can be considered as part of the tuning
capacitor, .In case the load reactance cannot be completely
compensatedwith the tuning capacitor, the frequency of the
operation of theload coil would be detuned from its resonance
frequency. How-ever, since the quality factor of the load coil is
small (e.g.,0.15), it has a relatively large bandwidth of operation
and, there-fore, even if this detuning occurs, it will not have a
significanteffect on the overall efficiency and performance of the
system.
J. Tissue EffectsSince the implantable coils are surrounded by
tissue, in this
subsection, an overview of the effects of tissue on the
perfor-mance of the four-coil-based power-transfer system is
provided.Let us first consider the effects of tissue on the
implanted coilparameters (i.e., self inductance) ( ), parasitic
capacitance( ), ac resistance ( ), self-resonance frequency ( ),and
the -factor. Since the tissue is typically free of
magneticmaterials, the permeability of tissue is close to
permeability offree space [41]. The inductance of any coil depends
on coilstructure, dimensions, and the permeability of its
surroundingsand, hence, in the proximity of the tissue, the
implantable coilinductance will be very close to that of the coil
in the free space.However, the tissue has a high dielectric
constant [1], [42] and,hence, the parasitic capacitance of the
implantable coil increasescompared to the case when the coil is not
implanted. The acresistance of the coil depends on the surrounding
permeabilityand is independent of the dielectric property of tissue
(10) and,therefore, when surrounded by the tissue, the ac
resistance of theimplanted coil will remain practically the same.
Due to the in-crease in the parasitic capacitance of the implanted
coil (becauseof tissue effects), the self-resonance frequency of
the im-planted coil decreases. Thus, due to tissue effects, the
-factorof the implanted coil will also decrease [refer to (17)].
However,by keeping the operating frequency of the system
sufficientlylower than of the implanted coil, the adverse effects
oftissue on the implanted coil can be kept low (17). Also,
consid-ering that the inductance of the implanted coil is typically
small(due to its small size), when the operating frequency is
properlychosen (i.e., it is sufficiently low) (lower than 4 MHz),
thetuning capacitance ( in Fig. 13), used in conjunction with
theimplanted coil, is much larger than the parasitic capacitance
ofthe implanted coil and, hence, the change in the parasitic
capac-itance (due to tissue) has minimal effects on the operating
fre-quency of the system. Note that as presented in [42], the
effectsof tissue on the behavior of the implanted coils, in
particular, ontheir parasitic capacitance, can be included in the
design cycle.
It should also be noted that in the proximity of tissue, part
ofthe magnetic field is absorbed by tissue due to the generation
ofeddy currents in the tissue. However, it is known that the
tissuehas a lower absorption for low-frequency RF signals
comparedto high-frequency signals [40] and, thus, another advantage
ofusing a low operating frequency (below 4 MHz) for the powerlink
is that the degradation in link efficiency due to tissue effectscan
be kept low. In this paper, the operating frequency of
thepower-transfer link is chosen to be 700 kHz.
III. DESIGN STEPSIn this section, design steps for
resonance-based (4-coil)
power delivery systems are presented. These steps are
presentedin the context of a design example that requires
relatively highpower to be transferred to the implantable
device.
A. Design ConstraintsThe first step is to identify the design
constraints. The spe-
cific application requirements constrain the design
parameters(particularly in terms of size and source and load
resistances) of
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RAMRAKHYANI et al.: DESIGN AND OPTIMIZATION OF RESONANCE-BASED
EFFICIENT WIRELESS POWER DELIVERY SYSTEMS 57
TABLE IDESIGN CONSTRAINTS
TABLE IILITZ WIRE PROPERTY
the implantable device. For example, Table I shows the
designconstraint dictated by the specific application of [17].
B. Initial Values and Range of ParametersThe initial design
parameters are chosen as follows.1) External Coil Radius: In a
single-turn circular coil with
radius , the magnetic-field strength at distance along theaxis
can be written as [28]
(43)
For , will be maximized and, therefore, a goodchoice of diameter
for an external coil is . For
20 mm, can be chosen as 60 mm.2) Wire Property: Single strand
copper wire has high ac re-
sistance for high-frequency operation. Using multistrand
Litzwire and using them in their operating frequency range, ac
re-sistance can be kept very close to their dc resistance. For
im-plantable coils, Litz wire is commonly used [1], [32]. Based
onanalysis done in Section II-G for properties of the Litz wire
witha different number of strands (Fig. 6), to improve the
-factor,one can choose a specific Litz wire. In our sample
application, a40-strand Litz wire with gauge 44 is chosen. Table II
shows theproperties of this particular Litz wire [38].
3) -Factor: As for the -factor of the four coils that areused in
the system, we have:
: As shown in Fig. 5, for high values of and , theeffect of on
efficiency is not considerable. For constrainedsystem dimensions,
driver coil is made of a single layer (
) to keep enough room for primary coil winding. It is kept inthe
outermost layer to obtain considerable inductance comparedto the
case when driver coil is wrapped in the innermost layerof the
primary coil. The number of turns are maximum permis-sible given
the design constraints so that the overall size of the
Fig. 14. versus the number of layers and operating
frequency.
external coils in the four-coil system (i.e., a combination of
thedriver coil and the primary coil) is almost the same as the size
ofthe external coil in the conventional two-coil system (i.e.,
pri-mary coil). Since the power amplifier has an output impedanceon
the order of 5 to 6 , a source resistance of 5.6 is chosenas sense
resistance to mimic the source impedance.
: For a small number of turns per layer, increasing thenumber of
turns improves the -factor. The number of turns incoil 2 is
constrained by design requirements. In our example,
of 5.5 mm implies 11 with 0.48 mm. Fig. 14shows the variation of
with the changing number of layersand operating frequency.
Increasing the primary coil size in-creases the parasitic
capacitance between its turns. To obtainhigh -factor at low
frequency, the inductance of primary coilshould be a large value.
It results in a significant effect of par-asitic capacitance on its
self-resonating frequency. To reducethe parasitic capacitance
between coil turns, low dielectric in-sulating material is inserted
between layers. As a rule of thumb,the thickness of the dielectric
layer should be varied until theself-resonating frequency (SRF) is
34 times higher than the op-erating frequency of operation so that
the effect of SRF can bereduced in the -factor ((17)). In this
design example, the insu-lating layer of the dielectric constant is
similar to that of strandinsulation ( 5) and a thickness of 0.3 mm
is taken.
: With the constraint of 2.5 mm, five turns perlayer can be
accommodated and Fig. 15 shows the variation of
for different numbers of layers and operating frequencies.
Inthis design, the self-resonating frequency of the secondary
coil,without dielectric between layers is high enough compared
tothe operating frequency range so no dielectric layer is used.
: Given the load resistance (e.g., 100 , and singleturn per
layer, Fig. 16 shows the variation of for a differentnumber of
layers and operating frequencies. To approximatethe four-coil
power-transfer model with a two-coil equivalent,(26) and (27) can
be used to find the desired from thegraph. Additional consideration
is to keep the overall size ofthe implantable coils in the
four-coil system (i.e., combinationof the driver coil and the
primary coil) to almost be the same as
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58 IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS, VOL. 5,
NO. 1, FEBRUARY 2011
Fig. 15. versus the number of layers and operating
frequency.
Fig. 16. versus the number of layers and operating
frequency.
the size of implantable coil in the conventional two-coil
system(i.e., secondary coil).
C. Optimizing Design ParametersTo implement coils, the driver
and primary coils are made
co-centric (and coaxial), and the number of turns per layer
indriver ( ) and primary ( ) coil are equal and kept closeto . Due
to the small size of the secondary coil, theself-resonating
frequency is high compares to the operating fre-quency so the
number of turns are mainly limited by design con-straints. The
number of turns per layer in secondary coil ( )and load coil ( )
are also chosen as equal.
Fig. 17 shows the design steps to obtain system parameters( and
for ) to achieve the optimumefficiency at a given distance. The
range for the number of layersin coil and turns per layer depends
on the design constraints andmay vary per the application
requirement.
IV. RESONANCE-BASED POWER TRANSFERPrevious sections provide the
models of different design pa-
rameters of the four-coil-based power-transfer system.
Design
Fig. 17. Flowchart for coil dimension optimization.
TABLE IIICOILS PHYSICAL SPECIFICATION
steps help select the design parameters based on design
con-straints (Table I). Based on the design constraints, the
power-transfer efficiency can be maximized for a targeted
operatingdistance (e.g., 20 mm) and operating frequency can be
cal-culated for which the design provides the maximum
efficiency.Table III shows the mechanical specifications of the
optimizeddesign by following the design flowchart (Fig. 17).
Based on simulation by following the design flowchart (Fig.17),
the operating frequency of 700 kHz is chosen. Dependingon the
application and the design constraints, the optimum de-sign
parameters can be calculated based on the design flowchartin Fig.
17. Table IV shows the simulated electric parameters forthe
optimized coil dimensions to obtain high-power-transfer
ef-ficiency. A source series resistance of ( ) is used toemulate
the nominal output impedance of the power amplifier
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RAMRAKHYANI et al.: DESIGN AND OPTIMIZATION OF RESONANCE-BASED
EFFICIENT WIRELESS POWER DELIVERY SYSTEMS 59
TABLE IVCOILS ELECTRICAL SPECIFICATION
Fig. 18. Mutual coupling ( ) versus distance.
for driver coil. A load resistance of ( ) is used whichis a
realistic load for a targeted application.
Coupling between coils 1 and 2 ( ) can be calculated usingthe
coil dimensions and parameters. From simulation0.6335, 0.601 and
0.058 for 20 mm.
For coaxial primary and secondary coil with physical dimen-sions
per Table III, Fig. 18 shows the coupling coefficientalong with the
fitted curve based on regression model (95% con-fidence). The curve
is modeled as
(44)
where and are the edge-to-edgeminimum distance between the
coils. and are the radius ofthe primary (coil 2) and the secondary
coil (coil 3), respectively.For other applications based on design
constrains and dimensionof coils (calculated based on the
flowchart), coefficients of thecoupling model will change.
V. EXPERIMENTAL SETUPTo demonstrate the validity of the
presented modeling tech-
niques and the design flow, a prototype four-coil wireless
power-transfer system is designed and implemented. Table III
showsthe optimized dimension of the coils based on the design
con-straints. Multi-strand Litz wire ( 40) of strand AWG 44is used
to implement the coils. The HP4194A impedance/gain-phase analyzer
is used to measure the electrical parameters ofthe coils which are
reported in Table V. The -factor of eachcoil is limited due to the
high ac resistance for the operating
Fig. 19. Power-transfer system.
frequency above (10) and the increase in effective resistancedue
to low self-resonant frequency (SRF) [32]. and aremeasured to be
0.56 and 0.59, respectively, which are close tosimulated coupling
factors. and do not change duringthe operation of the system (since
coils 1 and 2 and coils 3 and4 do not move with respect to each
other). A 50- sinusoidalsource is used to generate a signal with a
10.2-V amplitude at700 kHz. A resistance of 5.6 is used in series
with the drivercoil to measure the current of this coil. Since most
energy is dis-sipated at an internal source resistance of 50 , a
supply witha lower impedance should be used to improve the
efficiency ofthe system. In this setup, the efficiency is
calculated from theoutput terminal of the signal source and the
effect of the re-alistic power-amplifier source resistance is taken
into accountby using 5.6- sense resistance. When an input voltage
sourcewith a constant amplitude is used as the input source, the
inputpower supplied to the system depends on the load impedanceseen
by the source. Changing the distance between the primaryand
secondary coils will result in the variation of the impedanceseen
by the source and, thus, the input power to the system willchange
accordingly. The plots of the measured and simulatedinput and
output power of the four-coil-based power-transfersystem are
presented later (Figs. 24 and 25). For the conven-tional
two-coil-based system when driven by a fixed-amplitudeinput voltage
source, the input and output powers show similartrends as those of
the four-coil system. The simulated and mea-sured values of the
power-transfer efficiency of the conventionaltwo-coil-based system
are provided in Fig. 22.
For this system, primary coil is wound over plastic tube witha
height of 5.5 mm with side walls. After making the primarycoil, the
driver coil is wrapped over the primary coil to obtainhigh coupling
between these coils ( ). Similarly, secondarycoil is made on a
smaller tube, and the load coil is wrappedover secondary coil (Fig.
19). Fig. 21 shows the structure andcross section of the primary
(or secondary) coil, position of thedriver (or load) coil, and the
order of the turns in each coil. Thestructure of coil Fig. 20 shows
the relative dimensions of thecoils. Since plastic does not affect
the magnetic field, the effectof tube on the operation of the
system can be neglected. In ourexperiment, all coils are centered
around the same axis and the
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60 IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS, VOL. 5,
NO. 1, FEBRUARY 2011
Fig. 20. Coil dimensions.
Fig. 21. Driver (or load) and primary (or secondary) coil
structure.
horizontal distance between the primary and the secondary
coilsvaries to change their coupling factor ( ).
VI. RESULTS AND ANALYSISThe distance between the primary and
secondary coils varies
from 6 mm to 52 mm in steps of 2 mm. Measured efficiencyof the
power-transfer system (Fig. 19) for four-coil-based andthe
conventional two-coil-based power-transfer systems is illus-trated
in Fig. 22 and shows that even with a relatively large dis-tance
between the coils of 20 mm (equivalent 1.07),high power-transfer
efficiency is achieved. The measured resultsmatch very well with
the SPICE simulations and the analyticalequations derived to
calculate power-transfer efficiency. Thefour-coil-based
power-transfer system provides stable power-transfer efficiency
over a long operating range. When the pri-mary coil and the
secondary coils are close ( 5-10 mm), ex-perimental results are
slightly different from the approximatedanalytical model derived
for the power-transfer model (21). This
Fig. 22. Power-transfer efficiency (experiment, SPICE
simulation, efficiency(21), traditional two-coil model).
Fig. 23. Efficiency with varied source resistance for two- and
four-coil-basedsystems (simulated and measured results).
slight discrepancy is due to the assumption of low , , andto
derive (21). When coils are close, these parameters cannot
be neglected. For SPICE simulations, the effect of , , andis
taken into account and, hence, closer matches are obtained
with respect to measured data.In the traditional two-coil
inductively coupled power-transfer
system [10], the decrease in with respect to distance is
morepronounced (see Fig. 22). This is because the coupling
coeffi-cient of the two coils drops rapidly with the distance (
)and the coils have a small -factor (in this case, the loaded
-factor for the external coil is and for the implanted
coil,which is loaded by a 100 load is 1.28). Fig. 23 shows the
ef-fect of source resistance on power-transfer efficiency. For a
lowvalue of series resistance, a high efficiency can be obtained.
A
-factor of the driver coil changes the optimum efficiency
pointand shifts with the distance as shown by simulation (Fig. 9).
For
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RAMRAKHYANI et al.: DESIGN AND OPTIMIZATION OF RESONANCE-BASED
EFFICIENT WIRELESS POWER DELIVERY SYSTEMS 61
Fig. 24. Input power of the four-coil-based system (simulated
and measuredresults).
Fig. 25. Output power of the four-coil-based system (simulated
and measuredresults).
TABLE VCOILS ELECTRICAL SPECIFICATION (MEASURED)
the same series resistance, the two-coil power-transfer
systemhas more severe effects as shown in Fig. 23. The results
confirmthat when using the presented four-coil power-transfer
system,high-power-transfer efficiency can be achieved and can be
opti-mized for a relatively longer operating range compared to that
ofconventional two-coil systems. Measured , , , , ,and are used for
simulation. Power-transfer efficiency is ob-tained as 82% for coil
separation of 20 mm (with )
TABLE VICOMPARISON WITH PREVIOUS WORK
between primary and secondary coils. Using a constant-ampli-tude
voltage source (10.2 V), the measured and simulated inputpower of
the four-coil-based prototype power-transfer system isplotted in
Fig. 24. The output power at 100- load resistance ofthe system is
measured and plotted in Fig. 25. As can be seenfrom these figures,
the measured and simulated values closelymatch.
VII. COMPARISON WITH PREVIOUS WORK
The design based on the proposed technique is comparedwith
previously reported power-transfer methods applied forimplanted
devices. Table VI summarizes the results. To makea fair comparison
with different designs, efficiency at a normal-ized distance is
presented. where and are the radius of pri-mary and secondary
coils. is the geometric mean of and
.
VIII. CONCLUDING REMARKS
In this paper, the design and optimization steps for
resonance-based four-coil wireless power delivery systems are
described.The focus of this paper is on power delivery in
implantable de-vices. However, the method is general and can be
applied toother applications that use wireless power transfer [9],
[10]. Ex-perimental results show that significant improvements in
termsof power-transfer efficiency are achieved (compared to
tradi-tional inductively coupled two-coil systems). Measured
resultsare in good agreement with the theoretical models and
matchwell with the simulation results. Efficiency is enhanced by
usinghigh- factor coils ( ) and high coupling between driverand
primary coils ( ) and secondary and load coils( ). The prototype
four-coil system achieves at least2 more efficiency compared to
prior art inductive links oper-ating with comparable size and
operating range. With externaland implanted coils with diameters of
64 mm and 22 mm, re-spectively, and at an operating distance of 20
mm, a power-transfer efficiency of 82% is achieved. For an
operating distanceof 32 mm, efficiency slightly drops to 72%, which
confirms therobustness of the four-coil-based power-transfer system
whenoperating at long range.
ACKNOWLEDGMENT
The authors would like to thank Dr. R. Rosales for his
tech-nical assistance and support for the measurements.
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62 IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS, VOL. 5,
NO. 1, FEBRUARY 2011
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2009.
Anil Kumar RamRakhyani (S09) received theB.Tech. degree in
electrical engineering from theIndian Institute of Technology,
Kanpur, India, andthe M.A.Sc. degree in electrical and computer
en-gineering from the University of British Columbia,Vancouver, BC,
Canada, in 2006 and 2010, respec-tively, and is currently pursuing
the Ph.D. degree atthe University of Utah, Salt Lake City.
In 2006, he joined Sarnoff Corporation as a De-sign Engineer
where he was a Senior Design Engi-neer from 2007 to 2008. He was
involved in soft-
ware and hardware design of health-care and
radio-frequency-based products.His main research interests include
bioelectromagnetics, wireless-implantablebiomedical systems, and
integrated analog circuit design.
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RAMRAKHYANI et al.: DESIGN AND OPTIMIZATION OF RESONANCE-BASED
EFFICIENT WIRELESS POWER DELIVERY SYSTEMS 63
Shahriar Mirabbasi (M02) received the B.Sc. de-gree in
electrical engineering from Sharif Universityof Technology, Sharif,
Iran, in 1990, and the M.A.Scand Ph.D. degrees in electrical and
computer engi-neering from the University of Toronto, Toronto,
ON,Canada, in 1997 and 2002, respectively.
Since 2002, he has been with the Department ofElectrical and
Computer Engineering, University ofBritish Columbia, Vancouver, BC,
Canada, wherehe is currently an Associate Professor. His
currentresearch interests include analog, mixed-signal, and
radio-frequency integrated-circuit and system design for
biomedical applica-tions, wireless and wireline communication
transceivers, data converters, andsensor interfaces.
Mu Chiao (M04) received the B.S. and M.S.degrees from National
Taiwan University, Taipei,Taiwan, in 1996, and the Ph.D. degree in
mechanicalengineering from the University of California,Berkeley,
in 2002.
From 2002 to 2003, he was with the BerkeleySensor and Actuator
Center, University of Cali-fornia, Berkeley, as a Postdoctoral
Research Fellow.Since 2003, he has been with the Department
ofMechanical Engineering, The University of BritishColumbia,
Vancouver, BC, Canada, where he is cur-
rently an Associate Professor. His current research interests
include the designand fabrication of microelectromechanical systems
(MEMS) and nanodevicesfor biomedical applications. He is supported
by the Canada Research Chairs,Tier 2 program.