Design and Optimization of Resonance-Based Efﬁcient Wireless Power Delivery Systems for Biomedical...

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

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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


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)


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


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


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


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.


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)


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


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




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


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


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


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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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.


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.

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