Design of High-Efficiency Miniaturized Ultrasonic

Receivers for Powering Medical Implants with

Reconfigurable Power Levels

Ting Chia Chang, Marcus Weber, Jayant Charthad, Amin Nikoozadeh, Pierre T. Khuri-Yakub, Amin Arbabian

Department of Electrical Engineering, Stanford University, Stanford, CA USA

Abstract—Miniaturized ultrasonic receivers are designed for

high efficiency ultrasonic powering of implants. Several

piezoelectric materials are investigated for their practicality in

designing millimeter-sized ultrasonic receivers. Piezoelectric

receivers were built from these materials and measurements

were performed in order to characterize their impedance and

efficiency. We show operation of the piezoelectric receivers in an

inductive frequency band, near resonance, allowing for

impedance matching to typical implant loads. Finally, adaptive

matching and frequency tuning techniques are demonstrated

showing high power matching efficiencies across variable

implants loads.

Keywords—Ultrasonic receiver, wireless power transfer,

ultrasonic power delivery, piezoelectric material, adaptive

matching, implantable medical devices.

I. INTRODUCTION

Millimeter and sub-mm sized implantable medical devices (IMDs) with high available power are attractive for many novel therapeutic applications [1]. In order to shrink down to these sizes, replacement of bulky batteries with wireless power delivery is necessary. As we have described in previous studies [2], ultrasonic power delivery, due to small wavelengths (e.g. 1.5 mm at 1 MHz), has several key advantages over RF wireless powering when shrinking down to the mm-scale: high acoustic-electrical power conversion efficiency, superior energy focusing down to mm-spots, and favorable impedance to interface with power recovery circuits. In addition, ultrasound has relatively small propagation losses through tissue (~ 1dB MHz ∙ cm⁄ ) and a high FDA allowed intensity (7.2 mW/mm2) allowing for efficient power transmission at great depths (> 5cm) [3], [4]. To utilize and extend the scope of applications that can be enabled by ultrasonic power delivery, ultrasonic receivers must be designed and operated in an efficient manner. In this paper, we will discuss designing miniaturized ultrasonic receivers with favorable impedances, and we will present techniques on how to operate with maximum efficiency for powering IMDs with variable power levels.

II. IMPLANT POWER RECOVERY CHAIN

In order to harvest ultrasonic power, an ultrasonic receiver and power recovery circuits must be employed. A schematic diagram of an ultrasonic power recovery chain is shown in Fig. 1(a). Current and future IMDs may be equipped with several functionalities, such as electrical or optical stimulation, neural recording, and temperature and pressure sensing, within one module [1]; these functions require a large range of power

loads typically ranging from 10 µW to 1 mW. The varying power level can be abstracted to an effective load impedance (RL), looking into the power recovery circuits, using the time-averaged power and an assumed rectified voltage [2]. For instance, as a first-order estimation, assuming a 1V peak input rectified voltage and 50% AC to DC conversion efficiency [2], the effective resistance can be computed to be between 100 kΩ and 1 kΩ for 10 µW to 1 mW load powers. Fig. 1(b) shows the power recovery chain with the modeled load impedance. Since the load impedance varies over a large range, an energy receiver capable of matching to these loads is preferred to achieve high power matching efficiencies (PME) over any potential loading. Conventionally, passive magnetic reactive components are used in order to perform impedance matching. Though capacitance is easy to obtain in a small form factor, large inductance around MHz is not possible when volume is limited to mm-dimensions. Fortunately, we can leverage the inherent inductive nature of a piezoelectric receiver when operating near mechanical resonance. With careful design, this mechanically derived inductance can be used, along with capacitive only matching networks, to maximize PME over a wide range of electrical loadings.

The piezoelectric receiver acts as an available power source

with a frequency dependent effective power aperture [5], [6]. We define power conversion efficiency (PCE) as the electrical available power divided by the product of the incident acoustic intensity and the physical area (𝑃𝐶𝐸 = 𝑃𝑎𝑣/(𝐼0𝐴)). In order to design a high efficiency implant, both the PCE and PME need to be taken into account. Some matching and frequency-tuning techniques are demonstrated to achieve this goal.

Fig. 1. Schematic diagram of (a) an ultrasonic power recovery chain and

(b) a power recovery chain with Thevenin model of piezoelectric receiver

and modeled RL.

978-1-4799-8182-3/15/$31.00 ©2015 IEEE 2015 IEEE International Ultrasonics Symposium Proceedings

10.1109/ULTSYM.2015.0215

III. ULTRASONIC RECEIVER DESIGN FOR IMDS

The design of an efficient, miniaturized ultrasonic receiver for wirelessly powered IMDs needs to address the size constraint and total power delivery efficiency, simultaneously. First, receivers with mm-dimension and resonance frequency ~1 MHz are preferred when operating at large depths to minimize loss through tissue. Second, we focus on designing receivers in mm-sized form factor to have a favorable impedance, ZPIEZO, for matching to typical implant loads. We want the real part, RPIEZO, to mimic typical implant loads in the inductive frequency band (IB), between the fundamental series and parallel resonances (fsc and foc), alleviating the design constraint on the matching network, leading to higher efficiencies. With programmable capacitors matching networks, along with the receiver’s inductive impedance, XPIEZO, we can maximize PME over a wide range of implant loadings. Figure 2 shows an example impedance plot of a piezoelectric receiver sized to 1.5 mm × 1.1 mm × 1.1 mm with PZT5H material (sizing and material are addressed in later sections). fsc and foc are labeled and the IB is shaded in green. As desired, the range of RPIEZO coincides well with the range of implant loads. We will introduce a first-order circuit model, and design procedure, that can be used in order to create mm-sized devices with favorable impedance characteristics.

A. Ultrasonic Receiver Modeling and Materials

In order to get the insight into designing ultrasonic receivers, we use an equivalent series circuit model shown in Fig. 3 [7]. This model assumes one dimensional operation when the transducer is in either thickness expander mode if the aspect ratio, defined as width over thickness, is extremely large or length expander bar mode if the aspect ratio is extremely small [7]. In our case, we will investigate receivers with aspect ratios close to unity, as described later. Therefore, they do not fully fall into either category of one dimensional transducer; nonetheless, other studies have shown that aspect ratios near unity operate with characteristics (e.g. resonance frequency and electromechanical coupling coefficient) closely approximated by the length expander bar mode [6], so we can still use the model for first order analysis. In addition, we perform finite element method (FEM) analysis, using COMSOL Multiphysics, to simulate receivers to further verify measurement results in section IV. Using these design and analysis tools, we will compare four different materials to

determine their practicality for piezoelectric receiver design. Lead Zirconate Titanate 4 (PZT4), Lead Zirconate Titanate 5H (PZT5H), Barium Titanate (BaTiO3), and Lithium Niobate (LiNbO3) are chosen for comparison. PZT4 and PZT5H are common piezoelectric materials while BaTiO3 and LiNbO3 are potentially bio-compatible [8]. Material properties for length expander bar mode modeling are shown in Table I for each material [7].

B. Resonance Frequency and Size Constraint

The length expander bar open-circuit and short-circuit

resonance frequencies of a piezoelectric receiver are given as

follows [6], [7]

𝑓𝑜𝑐 =

𝑣

2𝑡

(1)

𝑓𝑠𝑐 = √1 − 𝑘33

2 𝑓𝑜𝑐. (2)

As stated previously, we aim to operate ~1 MHz in order to

reduce tissue losses. As seen in (1) and (2), the IB frequency

span is largely determined by the thickness of the piezoelectric

device. We also want to keep device dimensions on the mm-

scale. Based on the velocities seen in Table I, using a thickness

of 1.5 mm positions the IB of all materials sufficiently close to

the ~1 MHz target – small deviations from 1 MHz do not have

significant impact on our design. We chose a cross-sectional

dimensions of 1.1 mm, giving an area of 1.21 mm2, as a trade-

off between power receiving aperture and implant size (i.e.

maintaining mm-dimensions).

C. Resonant Frequency Impedances

The equivalent series circuit elements are determined as a function of the piezoelectric receiver dimensions and material properties. ZF and ZB are front and back acoustic impedances loading to the receivers; and ZC is the acoustic impedance of the piezoelectric material [7]. In this study, we use mineral oil (1.16 MRayls) for front loading since it closely mimics tissue impedances (~1.4-1.6 MRayls) [4] without introducing

Fig. 2. Impedance of 1.5 mm thick piezoelectric receiver made of

PZT5H. RPIEZO mimics typical implant loads and positive reactive part,

XPIEZO, is utilized for matching. Shaded region indicates inductive band.

TABLE I

BASIC MATERIAL PROPERTIES FOR LENGTH EXPANDER BAR

PZT4 PZT5H BaTiO3 LiNbO3

Density, ρ (kg/cm3) 7500 7500 5700 4640

Velocity, v (m/s) 4100 3850 5000 6400

Acoustic Impedance, ZC (MRayls) 30.8 28.9 28.5 29.7

Electrical-Mechanical Coupling

Coefficient, k33 0.70 0.71 0.5 ~0.5

Relative Permittivity, εT 1300 3400 1700 30

Mechanical Quality 600 75 300 >1000

Fig. 3. Schematic diagram of the equivalent series circuit model and

relationship between circuit parameters and piezoelectric material.

electrical parasitics. We use air-backing in order to reduce mechanical damping and to increase PCE [2], [7]. The circuit model is more accurate when ZF and ZB are significant lower than ZC, as is the case for our loadings.

From the circuit, the resulting short-circuit (Rsc) and open-circuit (Roc) resistances are approximately equal to

𝑅𝑠𝑐 ≅1

8𝑘332 𝑓𝑠𝑐𝐶0

𝑍𝐹 + 𝑍𝐵

𝑍𝑐 (3)

𝑅𝑜𝑐 ≅2𝑘33

2 𝑓𝑠𝑐

𝜋2𝑓𝑜𝑐2 𝐶0

𝑍𝑐

𝑍𝐹 + 𝑍𝐵. (4)

Using our chosen dimensions, Rsc and Roc can be calculated with material properties given in Table I. As shown in Table II, PZT4, PZT5H, and BaTiO3 exhibit a favorable impedance range between Rsc and Roc, meaning high impedance matching efficiency can be obtained with mm-sized dimensions. LiNbO3, on the other hand, has a significantly higher range of impedance, and is not favorable for matching to higher power loads (lower RL). It is expected that Rsc and Roc are similar for PZT4, PZT5H, and BaTiO3 as they have similar material properties; while a higher range of impedance for LiNbO3 is obtained because of its low relative permittivity, which is almost two orders of magnitude smaller than other three materials. Increasing the area of the piezoelectric receivers can be used to further decrease the Rsc, but this is undesirable for miniaturization. As a result, LiNbO3 is not a desirable material for mm-sized implants while PZT4, PZT5H, and BaTiO3 are well-suited for typical miniaturized implants. Depending on the requirement, one can tune the cross section of the receiver or choose the proper material for different applications. This is not meant to be a comprehensive analysis of all piezoelectric materials, but similar analysis can be carried to investigate the feasibility of other materials for implant applications.

IV. MEASURMENT AND SIMULATION RESULTS

Ultrasonic receivers with PZT4, PZT5H, and BaTiO3 were

built to compare with the first-order analysis shown in section

III. As stated previously, all piezoelectric receivers were diced

to 1.5 mm × 1.1 mm × 1.1 mm. The package for measurement

is shown in Fig. 4(b). The piezoelectric block is placed on top

of print circuit board (PCB). Electrical connections are

established using a bondwire and copper sheet, and air backing

is achieved by sealing the via hole on PCB. The package is

immersed in mineral oil during all the measurement. A custom

tank was built to allow external access to the receiver

electrodes. We used an impedance analyzer for impedance

measurements. In our simulation setup, using the COMSOL

Acoustics Module, we modeled just the piezoelectric block

along with the air backing, since we found the other features

of the packaging did not significantly influence the impedance.

A. Measured Resonance and Impedance of Receivers

Fig. 4(c)(d)(e) show measured and simulated RPIEZO of the

receivers made from the different piezoelectric materials. The

shaded regions on the plots correspond to IB for each material.

BaTiO3 has a higher measured resonance frequency than

PZT4 and PZT5H as BaTiO3 has slightly higher sound

velocity. The measurement and simulation of RPIEZO are in

good agreement, covering most of the interesting range for RL.

The resonance frequencies and impedances for the different

materials are shown in Table III, and they show reasonable

agreeance with the first-order model predictions,

demonstrating the utility of the series circuit model.

B. Measured PCE of the Receivers

We also used the custom tank to measure the PCE of our

receivers. We used a characterized ultrasonic transmitter to

beam ultrasonic energy to the receivers, and then measured the

available power of the piezoelectric receiver to compute PCE.

The PCE of the receivers, over the IB, are shown in Fig. 4

(c)(d)(e). We achieved high efficiency with variation from

30% to 70% across the IB for different materials. With a worst

case PCE of 30%, we are still able to obtain 1 mW of

available power with less than 40% of the FDA limit.

V. ADAPTIVE MATCHING TO MAXIMIZE EFFICIENCY

In order to adaptively match over a wide range of implant power loads, we propose implementing a programmable capacitive matching network and a closed-loop data link with

TABLE II

CALCULATED RSC AND ROC

PZT4 PZT5H BaTiO3 LiNbO3

Rsc (kΩ) 2.69 1.18 2.00 85.1

Roc (kΩ) 225 89.7 54.9 2530

Fig. 4. (a) Diced piezoelectric receivers. (b) Diagram of measurement

pacakge. (c)(d)(e) Measured (solid blue curve) and simulated (dashed

blue curve) RPIEZO and PCE (red curve) for receivers made from PZT4,

PZT5H, and BaTiO3. Shaded region indicates inductive band.

TABLE III

MEASURED AND SIMULATED RESONANCE FREQUENCY AND IMPEDANCE

PZT4 PZT5H BaTiO3

Mea Sim Mea Sim Mea Sim

fsc (MHz) 0.95 0.93 0.83 0.82 1.46 1.39

Rsc (kΩ) 5.04 4.06 1.71 1.97 4.22 2.10

foc (MHz) 1.19 1.20 1.18 1.16 1.58 1.56

Roc (kΩ) 161.6 225.6 89.5 65.5 49.4 55.7

the external transmitter. Fig. 5 shows a conceptual diagram of the proposed system. By re-configuring the matching network, and tuning the ultrasonic transmitter frequency and output power (i.e. minimum required power), PME can be maximized over the entire range of load powers. For instance, we can use a reconfigurable series capacitor, Ca, for matching in the power recovery chain, as shown in Fig. 6(a). In order to increase overall efficiency for different RL values, the transmitted frequency is tuned within the IB such that RPIEZO is close to RL. Ca is then configured to conjugate match to the inductive part of the receiver’s impedance. This allows for perfect power matching based on maximum power transfer theorem (𝑃𝑀𝐸 =1). Additionally, the power level transmitted by the external source is adjusted such that the available power from the receiver is at the minimum level required to support the load. Without this configurability, PME could decrease significantly; for example, with RPIEZO of 5 kΩ, when the effective RL of an implant moves from 5 kΩ to 50 kΩ, PME would experience a huge drop from 100 % to 33 %.

In order to illustrate the efficiency gains of adaptively

matching to the load, we use the measured PZT4 data to

compute the total power delivery efficiency, defined as the

product of PCE and PME, with and without matching. Fig.

6(b) shows the comparison over a range of load impedances.

Here, we show from Rsc to 100 kΩ because we cannot

impedance match to loads smaller than Rsc with a simple series

matching network. The solid blue line shows the efficiency if

the piezoelectric receiver is adaptively matched, and the

dashed blue line shows the efficiency if the device is operated

at fsc throughout the load range. For load impedances above

the Rsc, we can achieve a perfect impedance match meaning

the efficiency is dependent only on the PCE. The efficiency

improvement is significant and the total efficiency achieved

spans from 35% to 70% over the load range. Fig. 6(b) also

shows the Ca required for the match varies between 3 pF and

100 pF, which are practical on chip. For further optimization of the implant efficiency, multi-

capacitor matching networks could be implemented to increase the degrees of freedom. Using more complex matching networks, the effective implant load can be passively transformed to higher or lower impedances. For example, a two capacitor L-match is shown in Fig. 6(c), which can be used increase the effective load impedance (RLeff). Added impedance transformation flexibility can be coupled with the frequency dependence of PCE in order to find the optimal frequency of operation in the IB.

VI. CONCLUSION

We have demonstrated that mm-sized piezoelectric receivers can be designed to enable high efficiency ultrasonic power delivery for implant applications. A first-order model is used to evaluate the practicality of using several different materials for power recovery. FEM simulations and measurements were performed to validate the models and PZT4, PZT5H, and BaTiO3 were identified as one of the optimal materials for implant powering. The inherent inductive behavior of the piezoelectric receivers, near resonance, allows for efficient impedance matching across variable load impedances. Finally, adaptive matching techniques are shown to drastically increase the power recovery efficiency over varying implant loads.

ACKNOWLEDGEMENTS

This material is based upon work supported by the National Science

Foundation Graduate Research Fellowship Program under Grant No. DGE-

114747 and the DARPA Young Faculty Award (YFA).

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Fig. 5. Conceptual diagram of proposed system with a capacitive matching network and a closed-loop data link with the external transmitter.

Fig. 6. (a) Circuit diagram for single series capacitor matching (b) Total power delivery efficiency with (solid blue line) and without (dashed blue line) matching, and required capacitance for Ca. (c) A two capacitor L-match circuit diagram for optimization.