1554 IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL, VOL. 63, NO. 10, OCTOBER 2016

Design of Tunable Ultrasonic Receivers for EfficientPowering of Implantable Medical Devices

With Reconfigurable Power LoadsTing Chia Chang, Student Member, IEEE, Marcus J. Weber, Student Member, IEEE,

Max L. Wang, Student Member, IEEE, Jayant Charthad, Student Member, IEEE,Butrus (Pierre) T. Khuri-Yakub, Fellow, IEEE, and Amin Arbabian, Member, IEEE

Abstract— Miniaturized ultrasonic receivers are designed forefficient powering of implantable medical devices with reconfig-urable power loads. Design parameters that affect the efficiencyof these receivers under highly variable load conditions, includingpiezoelectric material, geometry, and operation frequency, areinvestigated. Measurements were performed to characterize elec-trical impedance and acoustic-to-electrical efficiency of ultrasonicreceivers for off-resonance operation. Finally, we propose, ana-lyze, and demonstrate adaptive matching and frequency tuningtechniques using two different reconfigurable matching networksfor typical implant loads from 10 µW to 1 mW. Both simulationsand measurements show a significant increase in total implantefficiency (up to 50 percentage points) over this load powerrange when operating off-resonance with the proposed matchingnetworks.

Index Terms— Adaptive matching, implantable medicaldevices (IMDs), matching network, piezoelectric material,ultrasonic receiver, wireless power transfer.

I. INTRODUCTION

IT HAS been proposed that implantable medicaldevices (IMDs) employing neuromodulation therapies or

“electroceuticals” may supplant drugs as the primary treatmentfor many neurological disorders [1]–[3]. Unlike drugs thatfreely diffuse about the body, neuromodulation therapies aremore targeted, allowing for the mitigation of unwanted sideeffects. There are already many neuromodulation deviceson the market or in development to treat disorders likeParkinson’s and chronic pain [4]–[7]; however, some of themare large, invasive, and prone to causing infection [8], [9].In order to alleviate these issues, researchers are attemptingto shrink the implants down to millimeter or submillimetersizes and replace bulky batteries with reliable and highlyefficient wireless power links [10]–[13]. Most of theseresearchers have focused on RF or inductive powering,

Manuscript received May 17, 2016; accepted September 1, 2016. Date ofpublication September 7, 2016; date of current version October 1, 2016.This work was supported in part by the DARPA Young Faculty Award,in part by the National Science Foundation (NSF) CAREER Award underGrant ECCS-1454107, in part by the NSF Graduate Research FellowshipsProgram under Grant DGE-114747, and in part by the 2012 Yansouni Familyand 2015 Dr. Robert N. Noyce Stanford Graduate Fellowship.

T. C. Chang, M. J. Weber, M. L. Wang, J. Charthad, and A. Arbabian arewith the Department of Electrical Engineering, Stanford University, Stanford,CA 94305 USA (e-mail: tcchang3.@.stanford.edu).

B. T. Khuri-Yakub is with the Edward L. Ginzton Laboratory, Departmentof Electrical Engineering, Stanford University, Stanford, CA 94305 USA.

Digital Object Identifier 10.1109/TUFFC.2016.2606655

but as we have described in [12]–[14], ultrasonic powerdelivery has several key advantages over conventional RF andinductive powering when shrinking down to the millimeterscale. That is to say, ultrasound undergoes relatively smallpropagation losses through tissue (∼1 dB · MHz/cm) and hasa high FDA-allowed time-averaged intensity (7.2 mW/mm2),making it ideal for efficient power transmission at greatdepths (>5 cm) [15]–[17]. Additionally, ultrasound has smallwavelengths in tissue (e.g., 1.5 mm at 1 MHz) allowing forsuperior energy focusing down to millimeter spots [18], [19]as well as more efficient energy recovery from a ultrasonicreceiver.

Current and future IMDs may be equipped with severalfunctionalities, such as electrical or optical stimulation,neural recording, and temperature and pressure sensingwithin one module—these functions require a large rangeof average implant load (Pload) typically ranging from10 μW to 1 mW [20]–[22]. In addition, next-generation IMDswill be programmable with duty-cycled operation and differentfunctional modes, leading to dynamically varying Pload foran individual IMD. Static links can become inefficient withlarge load perturbations primarily due to impedance mismatchbetween the power receiver and the nonlinear power recoverychain. As demonstrated in this paper, an implant optimallymatched for 1 mW achieves less than 5% efficiency whenoperated at 10 μW. Low efficiency is a major reliabilityproblem, leading to significantly reduced battery life of theexternal source and potential loss of function of the IMD ifthe required power cannot be achieved. Therefore, an idealpower receiver should be tunable, along with the source, tomaximize the power matching efficiency (PME) over a widevariety of applications and dynamic loads.

With proper choices of material and dimensions, a piezo-electric ultrasonic receiver can be designed to be millimetersized with an optimal electrical impedance for a highly vari-able load. In addition, using frequency as a degree of freedom,we demonstrate the off-resonance operation to modulatethe receiver impedance for adaptive matching. In contrast,millimeter-sized implantable antennas, which are typicallyoperated in the low-gigahertz range to combat tissueloss [10], [11], offer much smaller radiation resistance andefficiency, due to mismatch in aperture and wavelengths aswell as dielectric loading [23], [24].

0885-3010 © 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See h.tt.p://ww.w.ieee.org/publications_standards/publications/rights/index.html for more information.

CHANG et al.: DESIGN OF TUNABLE ULTRASONIC RECEIVERS FOR EFFICIENT POWERING OF IMDs 1555

Fig. 1. Schematic of an ultrasonic power recovery chain. An effective loadimpedance Rin models the nonlinear power recovery circuits along with theimplant power load Pload.

In this paper, we first introduce the implant power recoverychain for an IMD and describe the impedance match interfacebetween the piezoelectric receiver and implant loads. We con-sider the effect of average Pload on the input impedance ofthe power recovery circuit and demonstrate the concept ofoff-resonance operation for adaptable impedance tuning. Thena design procedure is presented to achieve the impedancespecifications with a piezoelectric receiver. The selectionof material and dimensions for ultrasonic receivers greatlyinfluences frequency of operation and the impedance tuningrange, so several different materials, including biocompatibleoptions, are compared. Finally, we use two adaptive matchingtopology examples to show a significant improvement in thetotal implant efficiency over a nontunable power recoverychain.

II. POWER RECOVERY CHAIN UNDER A VARIABLE LOAD

A schematic of an ultrasonic power recovery chain for anIMD in the steady state is shown in Fig. 1, which includesa piezoelectric receiver, a matching network, power recoverycircuits, and an average application load. The total implant effi-ciency (ηimplant) is determined by three major components: theacoustic-to-electrical power conversion efficiency (PCE) of thereceiver, the efficiency of the power recovery circuit (ηac–dc),and the PME between the first two components. Therefore,ηimplant can be represented as

ηimplant = Pload

Pacou= PCE · PME · ηac–dc (1)

where Pacou is the total incident acoustic power on top of thereceiver. There is extensive literature on designing power elec-tronics for power receivers to achieve high ηac–dc [25]–[28];hence, we focus on optimizing efficiency of the ultrasonicreceiver and impedance matching interface due to the largevariation of Pload in an IMD.

A first-order calculation can be made to model any nonlinearpower recovery circuits along with the implant load as aneffective average load impedance (Rin) annotated in Fig. 1using the following equation [12], [29]:

Rin � V 2in

2Ploadηac–dc (2)

where Vin is the peak input rectified voltage. As a first-order estimation, when assuming a peak input of 2 V and

Fig. 2. Impedance plot of a 1.5 mm × 1.1 mm × 1.1 mm ultrasonic receivermade from PZT5H measured with an impedance analyzer (Agilent 4294A).The shaded region indicates the IB for off-resonance tuning.

ηac–dc of ∼80%, the effective resistance can be com-puted from (2) to be between ∼200 and ∼2 k� for10 μW–1 mW load powers. An input voltage of 2 V isassumed since it is much greater than typical CMOS thresh-olds, allowing for high ηac–dc (>80%) while also remainingbelow typical CMOS technology voltage limits. This calcu-lation and the approximations are sufficient for our purposeof getting a first-order estimate of the effective implant loadsince modest differences do not greatly influence the PME andfurther refinements can be made using circuit simulators.

In order to achieve a high PME over the wide rangeof Rin, a power receiver should exhibit a similar impedancerange as Rin. Fig. 2 shows an example measured impedanceprofile of a millimeter-sized ultrasonic receiver made fromlead zirconate titanate 5H (PZT5H), a piezoelectric material,with dimensions of 1.5 mm × 1.1 mm × 1.1 mm. As seenin Fig. 2, there are nearly two orders of magnitude changein the real part of the impedance (Rpiezo) between the short-circuit ( fsc) and open-circuit ( foc) resonances. The large valueand range of Rpiezo offers a significant advantage for poweringvarious Pload values. With the appropriate design methodologyto choose material and dimensions of the ultrasonic receiver,Rpiezo can be tuned to match the targeted Rin range. Fur-thermore, we can leverage the inherent inductive nature of apiezoelectric receiver operating around mechanical resonance,in a band hereinafter referred to as the inductive band (IB),for impedance matching to obtain high PME. Conventionally,passive reactive components are used in order to performimpedance matching [30]–[32]. Though a large inductancearound megahertz is not practical when the form factor ofimplantable device is limited to millimeter dimensions, capac-itance is easy to obtain in a small volume or even on chip. Thelarge inductive reactance with a reasonable quality factor in theIB allows for impedance transformation with purely capacitivematching networks. Depending on the operating frequencyand the topology of matching network, the required matchingcapacitance ranges only from ∼1 to 40 pF. The details of thematching network design will be described in Section V.

1556 IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL, VOL. 63, NO. 10, OCTOBER 2016

Fig. 3. Schematic of the 1-D series circuit model around fundamentalresonance [33]. The circuit elements are functions of material constants withLE mode and dimensions as shown in the equations.

III. ULTRASONIC RECEIVER DESIGN FOR IMDS

In this section, we focus on how to obtain the impedancebehavior discussed in Section II by introducing a first-ordercircuit model that aids with the design process. The modelprovides sufficient accuracy for capturing the frequency behav-ior of the impedance and the radiation resistance of thepiezoelectric receivers.

A. Ultrasonic Receiver Modeling

We use the 1-D series circuit model shown in Fig. 3 for first-order design of the piezoelectric receivers around fundamentalresonance [33]. The model is composed of a series RLC tankwith the intrinsic capacitance of the device (C0) in shunt. Thecircuit element values are determined by width (w) and thick-ness (t) of the device and the piezoelectric material proper-ties: relative permittivity (εT ), electrical–mechanical couplingconstant (k33), acoustic impedance of the material (ZC ), frontacoustic loading (Z F ), and back acoustic loading (Z B). Themodel is more accurate when Z F , Z B � ZC . This conditionis satisfied in the design as the front of the device is loadedby tissue (Z tissue � 1.4–1.6 MRayls) [16] when implantedin the body, and the receiver is designed with air backing(Zair � 400 Rayls) to minimize the effect of mechanicaldamping. Using this model, we investigate four different mate-rials, PZT4, PZT5H, barium titanate (BaTiO3), and lithiumniobate (LiNbO3), and compare their performances as ultra-sonic receivers for IMDs. PZT4 and PZT5H are commonpiezoelectric materials widely utilized in imaging and sensortransducers. BaTiO3 and LiNbO3 are lead-free piezoelectricmaterials and are potentially biocompatible [34], [35]. Thematerial properties, assuming a length expander bar mode (LEmode) operation, are listed in Table I. The LE mode is utilizedhere as it provides better approximation when the aspect ratioof the receivers (G = w/t) is constrained below unity in orderto reduce the overall implant volume [36], [37].

B. Selection of Dimensions and Materials for Receiver

The thickness of the receivers t and the sound velocityof the piezoelectric materials v are the main parameters forpositioning the fundamental resonance. foc and fsc for G � 1are given as [33]

foc = v

2t(3)

fsc �√

1 − 8k233

π2 foc (4)

TABLE I

MATERIAL PROPERTIES FOR LE MODE [33]

TABLE II

CALCULATED RESONANCE AND IMPEDANCE

where fsc is lower in frequency than foc, and they are relatedby k33, which in turn determines the span of the IB. Theresonance frequencies are inversely proportional to thicknessof the material; thus, thinner devices have higher operatingfrequency. Due to mode coupling from finite width, thefundamental resonances will shift to slightly lower values fora practical aspect ratio. A correction factor of 1 to 0.7 forG ≤ 1 can be inserted into (3) and (4) for more accuratedetermination of resonances [36]–[39]. Nonetheless, this smallshift does not have significant impact on the design process.

We aim to operate the devices with an IB between∼1 and 2 MHz as a tradeoff between acoustic propagationlosses through soft tissue (∼1 dB · MHz/cm) and overallimplant thickness. Based on (3) and (4), and the materialvelocities listed in Table I, we can position the IB suffi-ciently close to the target range for all four materials using athickness of 1.5 mm. Table II shows the calculated 1-D reso-nance frequencies for different materials. Receivers made fromPZT4 and PZT5H have lower resonance frequencies than thosemade from BaTiO3 and LiNbO3 due to lower sound velocity.

The area of the ultrasonic receiver and piezoelectric materi-als offers another tradeoff between implant size and powercapture area. As an example demonstration, we choose alateral dimension w of 1.1 mm and use material as a designparameter to achieve the desired impedance range. Shown inFig. 2, the off-resonance resistance in the IB is bounded by ashort-circuit resistance Rsc and an open-circuit resistance Roc.Using the chosen dimensions, acoustic loadings, and thematerial properties in Table I, Rsc and Roc can be calculatedwith the following equations derived from the series circuitmodel:

Rsc ∼= 1

8k233 fscC0

Z F + Z B

Zc∝ 1

ρv2εT k233

(1 − k2

33

) 32

t2

w2 (5)

Roc ∼= 2k233 fsc

π2 f 2ocC0

Zc

Z F + Z B∝ ρk2

33

εT(1 − k2

33

) 12

t2

w2 . (6)

CHANG et al.: DESIGN OF TUNABLE ULTRASONIC RECEIVERS FOR EFFICIENT POWERING OF IMDs 1557

Equations (5) and (6) also show the direct relationship ofRsc and Roc to the material properties under the assumptionof given acoustic loadings (i.e., tissue and air for front andbacking loading, respectively). The calculated values for athickness of 1.5 mm and width of 1.1 mm are shown inTable II. Rsc and Roc are similar for receivers made fromPZT4, PZT5H, and BaTiO3; in addition, these materials offeran off-resonance resistance range that is well matched tothe desired Rin from Section II. Conversely, the resistancesfor receivers made from LiNbO3 are nearly two orders ofmagnitude higher due to drastically lower relative permittivity,as captured by (5) and (6). Although increasing the area ofthe piezoelectric receivers can be used to lower impedancerange, this is undesirable for the purpose of miniaturization.Therefore, LiNbO3 is not a preferred material for millimeter-sized implants of the specific targeted power range in thispaper, while PZT4, PZT5H, and BaTiO3 are well suited forour applications.

The above arguments are not meant to be a comprehensiveanalysis of all piezoelectric materials and sizing, but are addedto demonstrate various tradeoffs for the given target powerlevel and volume. Depending on the requirements of theapplication, a similar analysis can be carried out to inves-tigate the feasibility of different materials and dimensions.For example, with the given dimensions, single crystallinepiezoelectric materials such as PMN-PT are more suitablefor applications requiring a higher power range (>1 mW)due to their large εT (∼5000) and k33(∼0.9) [40]. One can alsotune the properties of the piezoelectric materials by utilizinga composite piezoelectric transducer [41]. Additionally, forshallow IMDs (<5 cm), a shorter link reduces the acousticloss through tissue, and thus, higher frequency operation canbe used to further scale down the thickness and width of thereceiver while maintaining the desired impedance range.

IV. CHARACTERIZATION OF RECEIVERS

Ultrasonic receivers were built using PZT4, PZT5H, andBaTiO3 to compare the general impedance behavior with thefirst-order analysis. We also measured acoustic-to-electricalPCE across the IB for each material. The PCE is definedmathematically as

PCE = Pav,ele

Pacou= Pav,ele

I0 A(7)

where Pav,ele is the available electrical power and Pacou isthe incident acoustic power, which is the product of incidentacoustic intensity on top of the receiver characterized by ahydrophone I0 and physical area of the receiver A. PCE isthe acoustic-to-electrical efficiency analogous to the apertureefficiency of an antenna [23]. It varies across frequency anddoes not depend on electrical loading or characteristics ofthe ultrasonic transmitter as long as the receiver is in the farfield [23], [24].

All piezoelectric receivers having a thickness of 1.5 mmwere diced to a width of 1.1 mm, as shown in Fig. 4(a), andpackaged on top of a print circuit board (PCB). We designedthe package to minimize the total volume of the device.A bond wire and a copper sheet were used to establish

Fig. 4. (a) PZT4, PZT5H, and BaTiO3 with dimensions of 1.5 mm ×1.1 mm × 1.1 mm. (b) Diagram and photo of ultrasonic receiver’s package.(c) Setup for ultrasonic power transferring measurement. The ultrasonictransmitter is centered above the ultrasonic receiver in an oil tank. I0 is theacoustic intensity on top of the receiver characterized by the hydrophone.

top and bottom electrical connections to the receivers’ elec-trodes. Air backing was created by sealing the via hole onthe PCB. The experimental setup is shown in Fig. 4 (c). Thereceiver was immersed in a custom tank filled with mineraloil (1.16 MRayls) in order to minimize electrical parasiticsand mimic the acoustic loading of body tissue. The ultrasonictransmitter (Olympus A303S) and the receiver were spaced ata distance of 6.0 cm to ensure both devices are in the far-field region. In practice, one would use a focusing array toget higher link efficiency, but here, we are interested onlyin characterizing the ultrasonic receivers, independent of thetransmitter.

A. Measured Resonances and Impedances of Receivers

We characterized the impedance profile of the ultrasonicreceivers using an impedance analyzer (Agilent 4294A). Fig. 5shows the measured and calculated Rpiezo from the seriescircuit model with a correction factor of 0.93 (for G ∼ 0.7)to correct resonance frequency, which is consistentwith [38, Fig. II-7]. The measured IB is highlighted in greenand the values of the resonance frequencies Rsc and Rocare listed in Table III. We omit the reactance across the IBsince we can utilize a capacitor-only matching network tocancel the reactance as described in Section V. The measuredRpiezo curve has lower mechanical quality factor comparedwith the first-order model since the model does not take intoaccount the loss from material and package. Nonetheless, therange of measured Rpiezo agrees reasonably well with thefirst-order model. For each material, Rpiezo spans much of

1558 IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL, VOL. 63, NO. 10, OCTOBER 2016

Fig. 5. Measured Rpiezo (blue solid line), the calculated Rpiezo from the series circuit model (blue dashed line), and the measured PCE (red solid line) ofthe receivers made from (a) PZT4, (b) PZT5H, and (c) BaTiO3. The IB is highlighted in green.

TABLE III

MEASURED RESONANCE FREQUENCIES AND IMPEDANCES

the ∼2–200 k� targeted range in the IB suitablefor IMDs.The measurement results demonstrate the utility of the seriescircuit model as a first-order design tool for IMD’s receivers.

B. Measured PCE of Receivers

PCE is computed from measured open circuit ac voltageacross the terminals of the receiver along with the measuredimpedance for a given I0. Measured PCE in the IB is alsoplotted in Fig. 5. Measurements for receivers of three differentmaterials all present high PCE with variation across theentire IB. Similar to the aperture efficiency of antenna, thePCE larger than unity is possible for small resonators [23].As an example, even with a worst case PCE of 30%, we arestill able to obtain 1 mW of time-averaged available powerwith less than 40% of the FDA limit (7.2 mW/mm2). The PCEplots indicate that off-resonance operation can be utilized totransfer power efficiently for various Pload values.

V. ADAPTIVE MATCHING TO MAXIMIZE EFFICIENCY

With the favorable impedance profile designed and mea-sured in the previous sections, we now demonstrate how tooperate these piezoelectric receivers efficiently for a dynam-ically varying Pload. The total implant efficiency ηimplantfrom (1) is maximized by utilizing the full span of Rpiezoacross the IB with capacitive-only matching networks. A trulydynamic design would implement a programmable capacitivematching network, such as switchable capacitor banks, tomatch the inductive reactance from the receiver at differentoperating frequencies. A closed-loop system with data uplinkis needed to adaptively change the transmit frequency andacoustic intensity for various Pload values. Fig. 6 shows a

Fig. 6. Conceptual diagram of the proposed dynamic system with aprogrammable capacitive matching network and a closed-loop data linkbetween IMDs and the external transmitter.

conceptual diagram of a closed-loop system with an adaptivepower recovery chain.

Series and L matching networks, shown in Fig. 7, areused in this paper to increase ηimplant. More complicatedschemes can also be chosen for the same purpose. Measuredcharacteristics of the PZT4 receiver in Section IV are used toillustrate the operation and efficiency gain of the two matchingnetworks compared with a nonadaptive system. As seen inFig. 7, the receiver is represented as a Thévenin modelwith an open-circuit root-mean-squared voltage Voc equalto (4Pav,ele Rpiezo)

1/2. A commercial full-wave bridge recti-fier [42] is selected as an example of the power recovery circuitin the power recovery chain in Fig. 1. Due to the nonlinearityin the power recovery circuit, a more accurate characterizationof Rin looking into the rectifier and load requires an iterativeapproach [43]. Therefore, circuit simulations were performedusing Keysight Advanced Design System (ADS) to obtain theoptimal adaptive matching parameters at various load powers.In the simulations, the output voltage is constrained to be2 V and different load resistors are used to model differentPload values. Measurements on matching networks are alsoperformed to verify the simulation results using the samecomponents.

CHANG et al.: DESIGN OF TUNABLE ULTRASONIC RECEIVERS FOR EFFICIENT POWERING OF IMDs 1559

Fig. 7. Schematics of the power recovery chain for off-resonance operationwith series or L matching networks. The ultrasonic receiver is represented asa Thévenin’s model. Z ′

in is the effective load impedance that the receiver seesbefore the matching network and Z ′

piezo is the input impedance seen from thenonlinear power recovery circuit and loads.

Fig. 8. (a) Simulated values of Rpiezo (blue solid line), required Rin (greendashed line) for optimal matching, and capacitance Cs (red solid line), as afunction of Pload using series matching network with the PZT4 receiver inSection IV. (b) Optimized PME with adaptive matching (blue solid line) andthe PME without adaptive matching (red dashed line) versus Pload.

A. Series Matching Network

Fig. 7(a) shows a series matching network, the simplestimplementation of a programmable matching network. In orderto maximize PME, Z ′

piezo and Rin after the series matchingnetwork or, equivalently, Zpiezo and Z ′

in before the matchingnetwork must be complex conjugate pairs, respectively [31].A series matching network can be easily understood as match-ing Z ′

piezo to Rin. As Pload varies, the operating frequency isselected such that Rpiezo is close to Rin. The series capacitorCs is then configured to cancel out the remaining inductivepart of the receiver, making Z ′

piezo matched to Rin. The seriesmatching network is most effective when the range of Rpiezoin the IB is large enough to cover all possible Rin values.

Fig. 8(a) shows the simulated values of Rpiezo and Rinfor optimal impedance matching as a function of Pload from10 μW to 1 mW. As anticipated from (2), Rpiezo follows Rinand moves inversely with Pload. The range of Rpiezo limits theload power for which optimal matching can be obtained. ForPload lower than 25 μW, required Rin becomes too large to bematched by Rpiezo in the IB of the receivers; as a result, theoptimal operating frequency stays at foc and the PME drops.The capacitance values used for Cs , also shown in Fig. 8(a),range from 1 to 15 pF, which is easily achieved using on-chipcapacitors for miniaturization. Fig. 8(b) shows the comparison

Fig. 9. Simulated total implant efficiency calculated from (1) with optimiza-tion of only PME (blue solid line) and co-optimization considering both PMEand PCE (red dashed line).

of the PME between an adaptive system with a series matchingnetwork and a nonadaptive system. PME with series matchingis able to reach almost 100% because of the presence ofthe tuned network [44]. For the nonadaptive case, a staticresonance frequency operation (at fsc) is assumed; its PMEdrops significantly at lower load powers due to mismatch.

The analysis so far has considered only Rpiezo and neglectedthe PCE, but the PCE could be taken into account since ηimplantis related to the product of PCE and PME by (1). Fig. 9 showsthe simulated ηimplant of the power recovery chain includingefficiency of the rectifier ηac−dc when PCE is consideredin the optimization process. Note that ηac−dc is about 80%over the entire range of load power. The result shows thatco-optimizing PCE and PME together produces a higherηimplant for some Pload. For the PZT4 receiver, the difference ismost prominent at higher Pload, from 100 μW to 1 mW, witha boost of nearly 10 percentage points at 1 mW. Therefore,maintaining an operating frequency in a high PCE region butwith a suboptimal PME can increase overall efficiency. Thisimprovement is significant because at higher power levels,higher efficiency can reduce the required transmitted power.

B. L Matching Network

As seen in the comparison between simply maximizingPME and co-optimizing PME and PCE together, the efficiencyfor the co-optimized case is larger for some Pload. To decouplethese two parameters, we can introduce an additional degreeof freedom into the system, allowing for better optimizationof ηimplant.

An L matching network provides an additional degreeof freedom with the extra shunt capacitor in the matchingnetwork. It can be used to transform Rin to a higher or lowervalue depending on the topology and quality factor of thematching network [31], [32]. Here, the network is designed totransform Rin to match Rpiezo at the frequency where PCE isoptimal—concurrently maximizing both PCE and PME. Forthe L matching network scheme shown in Fig. 7, the PMEis maximized when Z ′

in is the complex conjugate of Zpiezo.Rin is transformed down to a lower effective resistance byCL1 to match Rpiezo. CL2 is then used to cancel out residualinductance from the piezoelectric receiver such that an optimal

1560 IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL, VOL. 63, NO. 10, OCTOBER 2016

Fig. 10. (a) Measured Xpiezo and Qpiezo of the PZT4 receiver. (b) Com-parison of ηimplant from simulation of system using the L matching network(blue solid line), series matching network (red dashed line), and nonadaptivesystem (green dotted line). A boost in efficiency is observed throughout theinterested range of Pload. Measurements at six different Pload values arerepresented by circles. The ADS simulation and measurement are in goodagreement.

match is obtained. This transformation ratio is approximatelybounded by the frequency dependent quality factor of thereceiver Qpiezo defined as Qpiezo = Xpiezo/Rpiezo. The ratiois given as

Rin

Rpiezo< 1+Q2

piezo. (8)

A meaningful transformation ratio thus can be achieved withlarger Qpiezo. From the series circuit model as well asimpedance measurement of the receiver, it can be observed thatmaterials with high k33 result in higher Qpiezo in the middleof the IB; therefore, using an L matching network is moreadvantageous for material with high k33. Fig. 10(a) shows themeasured reactance and Qpiezo of the PZT4 receiver in the IB.A comparison of optimized ηimplant for L matching, seriesmatching, and nonadaptive systems is plotted in Fig. 10(b).An increase of as much as 20 points in ηimplant is observed forthe L matching network in comparison with series matching,while a nearly 50 point efficiency boost is obtainable comparedwith a nonadaptive system operating at fsc. The capacitancesused in the network are about 2–20 pF. Depending on thecharacteristics of the receiver, one can choose the appropriatematching networks to increase the total implant efficiency.

C. Measurement With Two Matching Networks

We performed wireless power transfer measurements forthe power recovery chain at various load powers to verifythe results obtained from ADS simulations for both matchingnetworks. The photo of the measurement package is shown inFig. 11. A full-wave bridge rectifier (the same as the one used

Fig. 11. Photo of the PZT4 ultrasonic receiver package with a rectifier anddiscrete capacitors for implementing series or L matching networks.

in the simulation) and discrete capacitors for implementingmatching networks are added to the PCB board. Both therectifier and programmable capacitors can be designed on-chipfor further miniaturization. Different load resistors modelingPload are connected off the board. The dc output voltage ofthe rectifier is measured through an oscilloscope. Measuredefficiencies at six different Pload values for the three differentconfigurations are shown in Fig. 10(b) in circles. The mea-surement results are in good agreement with the simulation,demonstrating the capability of using matching networks forefficient power transfer.

VI. CONCLUSION

We utilize the off-resonance operation of millimeter-sizedultrasonic receivers to maximize the power transfer efficiencyof IMDs with a wide range of power levels. The piezoelec-tric receivers are designed to meet millimeter-dimensionalrequirements while also achieving a favorable impedancerange for efficient power delivery. Materials and dimensionsare identified as two of the major design variables to obtainthe desired impedance range for typical implant applications.Theoretical analysis and experimental verification to comparethe performance of several different materials—PZT4, PZT5H,and BaTiO3—were concluded to be well suited for IMDpowering and to achieve high PCE. Using a capacitive-onlymatching network ηimplant for various load powers can bemaximized by utilizing the IB impedance of the receiver andthus avoiding the use of conventional bulky inductors. Bothseries and L matching networks are analyzed and comparedwith the typical resonance-based operation. The simulationand measurement results show significant increases in the totalimplant efficiency for a miniaturized implant with an ultrasonicreceiver and a proper matching network.

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Ting Chia Chang (S’11) received the B.S. degreein electrical engineering and computer science fromthe University of California at Berkeley, Berkeley,CA, USA, in 2012, and the M.S. degree in electricalengineering from Stanford University, Stanford, CA,USA, in 2015, where he is currently pursuing thePh.D. degree in electrical engineering.

During his undergraduate study, he worked onnanoelectronic devices. He was an Intern at theMicroelectronic Research Center, University ofTexas at Austin, Austin, TX, USA, in 2011. His

current research interests include wireless power delivery, wireless commu-nication, acoustics applications, implantable medical devices, and digital andanalog low power integrated circuit design.

Mr. Chang received Honorable Mentions from the National Science Foun-dation Graduate Research Fellowship in 2014.

1562 IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL, VOL. 63, NO. 10, OCTOBER 2016

Marcus J. Weber (S’10) received the B.S. degreein electrical engineering from the University ofWisconsin–Madison, Madison, WI, USA, in 2012,and the M.S. degree in electrical engineering fromStanford University, Stanford, CA, USA, in 2014,where he is currently pursuing the Ph.D. degree inelectrical engineering.

In 2008, he was a Software Engineer Intern atGE Healthcare. He was an Electrical Engineer inthree cooperative education semesters at the NASAJohnson Space Center, Houston, TX, USA, from

2009 to 2011. From 2010 to 2012, he performed research at the Universityof Wisconsin–Madison, investigating the atmospheric effects on terahertzwave propagation. His current research interests include implantable devices,biosensing, wireless power, energy harvesting, low power electronics, andanalog and RF circuit design.

Mr. Weber was a recipient of the Stanford Graduate Fellowship and theNational Science Foundation Graduate Research Fellowship.

Max L. Wang (S’15) received the B.S. degree inelectrical engineering from the California Institute ofTechnology (Caltech), Pasadena, CA, USA, in 2015.He is currently pursuing the M.S. and Ph.D. degreesin electrical engineering with Stanford University,Stanford, CA, USA.

He interned at Caltech investigating antireflectioncoatings for solar cells, The Aerospace Corporation,El Segundo, CA, USA, researching carbon nanotubetransistors, and Intel, Santa Clara, CA, USA, val-idating high-speed I/O blocks from 2012 to 2014.

From 2014 to 2015, he was a Researcher at Caltech, where he helped todesign a wireless power transfer system. His current research interests includebiomedical devices, electromagnetic and acoustic fundamentals, and integratedcircuit systems.

Mr. Wang was a recipient of the Stanford Graduate Fellowship and theNational Science Foundation Graduate Research Fellowship.

Jayant Charthad (S’13) received the B.Tech.degree in electrical engineering from IIT Bom-bay, Mumbai, India, in 2009, and the M.S. degreein electrical engineering from Stanford University,Stanford, CA, USA, in 2013, where he is currentlypursuing the Ph.D. degree in electrical engineering.

From 2009 to 2011, he was with Texas Instru-ments, Bangalore, India, where he designed low-dropout regulator ICs. He was with the SAR ADCteam at Linear Technology, Milpitas, CA, USA, in2012. His current research interests include wireless

power transfer, implantable medical devices, biosensing, and integrated circuitand system design.

Mr. Charthad was a recipient of the Analog Devices Outstanding StudentDesigner Award in 2014, the Centennial Teaching Assistant Award in 2015,and the 2015 James F. Gibbons Outstanding Student Teaching Award inElectrical Engineering at Stanford University.

Butrus (Pierre) T. Khuri-Yakub (S’70–M’76–SM’87–F’95) received the B.S. degree in electri-cal engineering from the American University ofBeirut, Beirut, Lebanon, the M.S. degree in electricalengineering from Dartmouth College, Hanover, NH,USA, and the Ph.D. degree in electrical engineeringfrom Stanford University, Stanford, CA, USA.

He is a Professor of Electrical Engineering atStanford University. He has authored over 600 publi-cations and has been principal inventor or coinventorof 97 U.S. and international issued patents. His

current research interests include medical ultrasound imaging and therapy,ultrasound neurostimulation, chemical/biological sensors, gas flow and energyflow sensing, micromachined ultrasonic transducers, and ultrasonic fluidejectors.

Prof. Khuri-Yakub was awarded the Medal of the City of Bordeaux in1983 for his contributions to Nondestructive Evaluation, the DistinguishedAdvisor Award of the School of Engineering at Stanford University in 1987,the Distinguished Lecturer Award of the IEEE UFFC Society in 1999, theStanford University Outstanding Inventor Award in 2004, the DistinguishedAlumnus Award of the School of Engineering of the American Universityof Beirut in 2005, the Stanford Biodesign Certificate of Appreciation for thecommitment to educate, mentor, and inspire Biodesgin Fellows in 2011, andthe IEEE Rayleigh Award in 2011, and was elected Fellow of the AIMBE in2015.

Amin Arbabian (S’06–M’12) received the Ph.D.degree in electrical engineering and computer sci-ence from the University of California at Berkeley,Berkeley, CA, USA, in 2011.

In 2007 and 2008, he was a part of the initialengineering team at Tagarray, Inc., Palo Alto, CA,USA. He was with Qualcomm’s Corporate Researchand Development Division, San Diego, CA, USA,designing circuits for next-generation ultralow powerwireless transceivers in 2010. In 2012, he joinedStanford University, Stanford, CA, USA, as an

Assistant Professor of Electrical Engineering, where he is also the FrederickE. Terman Fellow with the School of Engineering. His current researchinterests include high-frequency circuits, systems and antennas, medicalimaging, and ultralow power sensors.

Prof. Arbabian was a recipient/corecipient of the 2015 NSF CAREERAward, the 2014 DARPA Young Faculty Award, the 2013 Hellman FacultyScholarship, the 2010–2011, 2014–2015, and 2016–2017 Qualcomm Inno-vation Fellowships, and best paper awards at the 2016 IEEE Conferenceon Biomedical Wireless Technologies, Networks, and Sensing Systems, the2014 IEEE Very Large Scale Integration Circuits Symposium, the 2013IEEE International Conference on Ultra-Wideband, the 2010 IEEE Jack KilbyAward for Outstanding Student Paper at the International Solid-State CircuitsConference, and second place for the Best Student Paper Awards twice atthe 2008 and 2011 RFIC symposiums. He currently serves on the TPC forthe European Solid-State Circuits Conference and the IEEE Radio-FrequencyIntegrated Circuits Symposium.