# Magnetoelectric Transducer Designs for Use as Wireless Power Receivers in Wearable and Implantable Applications

^{1}

^{2}

^{*}

## Abstract

**:**

^{3}) size. The comparative study clearly demonstrates that under existing safety standards, the ME architecture is able to generate a significantly higher power density than the MME architecture. Analytical models for both types of transducers are developed and validated using centimeter scale devices. The Institute of Electrical and Electronics Engineers (IEEE) and the International Commission on Non-Ionizing Radiation Protection (ICNIRP) standards were applied to the lumped elements models which were then used to optimize device dimensions within a 2 mm

^{3}volume. An optimized ME device can produce 21.3 mW/mm

^{3}and 31.3 μW/mm

^{3}under the IEEE and ICNIRP standards, respectively, which are extremely attractive for a wide range of biomedical implants and wearable devices.

## 1. Introduction

^{3}or smaller). In light of these concerns, a Wireless Power Transfer (WPT) system would appear to be a promising solution.

_{2}O

_{3}[7]. Despite this breakthrough, subsequent research showed that at best the magnetoelectric coefficient for bulk materials such as Cr

_{2}O

_{3}was very low, on the order of 100 mV/(cm·Oe) [7]. This, along with other various complications, kept the materials from being used much in practical applications [6]. Before the ME effect was even observed in bulk materials, Tellegen suggested developing composites that demonstrated a cumulative ME effect [8]. The implication here is that by coupling two separate physical effects (piezoelectric (PE) and magnetostrictive (MS)) in two separate materials an equivalent ME effect could be obtained. In PE materials, the mechanical strain and electric field are coupled. In MS materials, the mechanical strain and magnetic field are coupled. By linking two such materials mechanically, the resulting pseudo ME effect can be demonstrated simply as [9]

^{3}receiver could generate 2 mW at a distance of 3 cm from a transmitting solenoid [19]. Citing O’Handley et al., Paluszek et al. make cases for how wireless endoscopy, brain imaging, and surgical tools might benefit from the use of ME based WPT [20]. Nonetheless, it would appear that with the exception of some finite element verification work, very little has been done to move the medical research forward [21].

## 2. Materials and Methods

#### 2.1. Lumped Element Model for ME Devices

_{m}, which is defined as

_{p}which is defined as

#### 2.2. Lumped Element Model for MME Devices

_{sub}), and another symmetric PE bottom layer. Strain is induced on the structure by anchoring the bending laminate at the center and adding oppositely oriented permanent magnets at its ends. When a magnetic field is applied along the length of the structure, the beam experiences a pure bending moment.

#### 2.3. Fabrication of Test Structures

^{®}Inc., Conway, SC, USA) and polyvinylidene fluoride (PVDF) laminate. Terfenol-D was avoided due to the difficulties associated with machining a brittle, pyrophoric material.

#### 2.4. Experimental Methods

## 3. Results

#### 3.1. Model Validation Results

#### 3.2. Comparative Analysis Results

^{3}. This constraint may seem somewhat arbitrary, but is meant to ensure applicability for minimally traumatic IMDs. The exact value of this constraint does not actually significantly alter the comparison results as long as the maximum size is on the order of 1–10 cubic millimeters. The maximum allowable magnetic field was determined using the IEEE standard on magnetic maximum permissible exposure (MPE) for the head and torso under controlled environmental conditions [22], [23], and the International Commission on Non-Ionizing Radiation Protection’s (ICNIRP) standard on maximum occupational exposure to magnetic fields [24]. Under both standards, the allowable MPE varies by frequency as shown in Figure 14. The ICNIRP standard is generally more conservative than the IEEE standard. Optimizations were performed separately using each standard. Finally, in most cases geometry constraints were coded as aspect ratio constraints to ensure reasonable device geometries for manufacture. A maximum aspect ratio of limit of 200:1 was set for the ratio of beam length (${l}_{0}$) to total beam thickness (${t}_{t}$) and for the ratio of beam width ($w$) to thickness (${t}_{t}$). A maximum aspect ratio limit of 10:1 and a minimum aspect ratio of 0.1:1 were set for the ratio of beam length (${l}_{0}$) to width ($w$). It should be noted that in both the aspect ratios, width refers to the entire structure width. However, the aspect ratios’ length, ${l}_{0}$ does not refer to the total structure length, but the length from both transducers’ center anchors to the free edges. This means for the ME transducer ${l}_{0}=0.5l$ and for the MME transducer ${l}_{0}=L$. Like the maximum volume constraint, these values are somewhat arbitrary based on the authors’ own experience. However, they do serve to keep device dimensions to values that could be manufactured and provide a reasonable basis for comparison of architectures.

^{3}. As with the ME devices, the optimization was performed with the ICNIRP standard, IEEE standard, and a 1 Oe peak limitation at any frequency. The mechanical quality factor (${Q}_{m}$) was set to 42 based on experimental results. The results of the optimization are shown in Table 5.

## 4. Discussion

## 5. Conclusions

^{3}. Two different safety standards, the IEEE [22,23] and ICNIRP [24], were used as constraints to the optimization process. The results of this study reveal that the ME architecture is definitely preferable under the IEEE standard and given practical constraints is also preferable under the ICNIRP standard, although in the latter case, the estimated power produced by each type of structure is similar. The optimized ME devices are estimated to produce 42.7 mW (21.35 mW/mm

^{3}) and 62.6 µW (31.3 µW/mm

^{3}) under the IEEE and ICNIRP standard, respectively. Although much work needs to be done to implement transducers of this size and performance level, these results are very promising in the context of being able to wirelessly power very small biomedical implants.

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Song, S.H.; Kim, A.; Ziaie, B. Omni-Directional Ultrasonic Powering for mm-Scale Implantable Biomedical Devices. IEEE Trans. Biomed. Eng.
**2015**, 62, 2717–2723. [Google Scholar] [CrossRef] [PubMed] - Basaeri, H.; Christensen, D.B.; Roundy, S. A review of acoustic power transfer for bio-medical implants. Smart Mater. Struct.
**2016**, 25, 123001. [Google Scholar] [CrossRef] - Amar, A.B.; Kouki, A.B.; Cao, H. Power approaches for implantable medical devices. Sensors
**2015**, 15, 28889–28914. [Google Scholar] [CrossRef] [PubMed] - Abiri, P.; Abiri, A.; Packard, R.R.S.; Ding, Y.; Yousefi, A.; Ma, J.; Bersohn, M.; Nguyen, K.-L.; Markovic, D.; Moloudi, S.; et al. Inductively powered wireless pacing via a miniature pacemaker and remote stimulation control system. Sci. Rep.
**2017**, 7, 6180. [Google Scholar] [CrossRef] [PubMed] - Denisov, A.; Yeatman, E. Ultrasonic vs. Inductive Power Delivery for Miniature Biomedical Implants. In Proceedings of the 2010 International Conference on Body Sensor Networks, Singapore, 7–9 June 2010; pp. 84–89. [Google Scholar]
- Fiebig, M. Revival of the magnetoelectric effect. J. Phys. D Appl. Phys.
**2005**, 38, R123–R152. [Google Scholar] [CrossRef] - Dzyaloshinskii, I. On the magneto-electrical effect in antiferromagnets. Sov. Phys. JETP
**1959**, 37, 881. [Google Scholar] - Tellegen, B.D. The Gyrator, a New Electric Network Element. Philips. Res. Rep.
**1948**, 3, 81–101. [Google Scholar] - Nan, C.W. Magnetoelectric effect in composites of piezoelectric and piezomagnetic phases. Phys. Rev. B
**1994**, 50, 6082. [Google Scholar] [CrossRef] - Shin, K.H.; Inoue, M.; Arai, K.I. Preparation and properties of elastically coupled electro-magnetic elements with a bonding structure. IEEE Trans. Magn.
**1998**, 34, 1324–1326. [Google Scholar] [CrossRef] - Ryu, J.; Carazo, A.V.; Uchino, K.; Kim, H.E. Magnetoelectric properties in piezoelectric and magnetostrictive laminate composites. Jpn. J. Appl. Phys.
**2001**, 40, 4948. [Google Scholar] [CrossRef] - Zhai, J.; Xing, Z.; Dong, S.; Li, J.; Viehland, D. Magnetoelectric laminate composites: An overview. J. Am. Ceram. Soc.
**2008**, 91, 351–358. [Google Scholar] [CrossRef] - Dong, S.; Cheng, J.; Li, J.F.; Viehland, D. Enhanced magnetoelectric effects in laminate composites of Terfenol-D/Pb(Zr,Ti)O
_{3}under resonant drive. Appl. Phys. Lett.**2003**, 83, 4812–4814. [Google Scholar] [CrossRef] - Dong, S.; Li, J.F.; Viehland, D. Characterization of magnetoelectric laminate composites operated in longitudinal-transverse and transverse-transverse modes. J. Appl. Phys.
**2004**, 95, 2625–2630. [Google Scholar] [CrossRef] - Dong, S.; Li, J.F.; Viehland, D. Longitudinal and transverse magnetoelectric voltage coefficients of magnetostrictive/piezoelectric laminate composite: Theory. IEEE Trans. Ultrason. Ferroelectr. Freq. Control
**2003**, 51, 794–799. [Google Scholar] [CrossRef] - Paprotny, I.; Xu, Q.; Chan, W.W.; White, R.M.; Wright, P.K. Electromechanical energy scavenging from current-carrying conductors. IEEE Sens. J.
**2013**, 13, 190–201. [Google Scholar] [CrossRef] - Han, J.; Hu, J.; Wang, Z.; Wang, S.X.; He, J. Enhanced performance of magnetoelectric energy harvester based on compound magnetic coupling effect. J. Appl. Phys.
**2015**, 117, 144502. [Google Scholar] [CrossRef] - Truong, B.D.; Roundy, S. Wireless Power Transfer System with Center Clamped Magneto-Mechano-Electric (MME) Receiver: Model Validation and Efficiency Investigation. Smart Mater. Struct.
**2018**, 28, 015004. [Google Scholar] [CrossRef] - O’Handley, R.C.; Huang, J.K.; Bono, D.C.; Simon, J. Improved Wireless, Transcutaneous Power Transmission for In Vivo Applications. IEEE Sens. J.
**2008**, 8, 57–62. [Google Scholar] [CrossRef] - Paluszek, M.; Avirovik, D.; Zhou, Y.; Kundu, S.; Chopra, A.; Montague, R.; Priya, S. Magnetoelectric composites for medical application. In Composite Magnetoelectrics: Materials, Structures, and Applications; Srinivasan, G., Priya, S., Sun, N.X., Eds.; Woodhead Publishing: Sawston, UK, 2005; p. 381. [Google Scholar]
- Yang, G.; Talleb, H.; Gensbittel, A.; Ren, Z. FEM Modeling of a Magnetoelectric Transducer for Autonomous Micro Sensors in Medical Application. Sens. Imaging
**2015**, 16, 12. [Google Scholar] [CrossRef] - IEEE C95.1-2005. IEEE Standard for Safety Levels with Respect to Human Exposure to Radio Frequency Electromagnetic Fields, 3 kHz to 300 GHz; IEEE: Piscataway, NJ, USA, 2006. [Google Scholar]
- IEEE International Committee and E. S. on N.-I. Radiation. IEEE Standard for Safety Levels with Respect to Human Exposure to Electromagnetic Fields, 0–3 kHz; IEEE: Piscataway, NJ, USA, 2007. [Google Scholar]
- International Commission on Non-Ionizing Radiation Protection. ICNIRP Guidelines for Limiting Exposure to Time-Varying Electric, Magnetic and Electromagnetic fields. Health Phys.
**1998**, 74, 494–522. [Google Scholar] - Zhai, J.; Dong, S.; Xing, Z.; Li, J.; Viehland, D. Giant magnetoelectric effect in Metglas/polyvinylidene-fluoride laminates. Appl. Phys. Lett.
**2006**, 89, 1–4. [Google Scholar] [CrossRef] - Zhou, Y.; Yang, S.C.; Apo, D.J.; Maurya, D.; Priya, S. Tunable self-biased magnetoelectric response in homogenous laminates. Appl. Phys. Lett.
**2012**, 101, 232905. [Google Scholar] [CrossRef] - Nan, C.W.; Bichurin, M.I.; Dong, S.; Viehland, D.; Srinivasan, G. Multiferroic magnetoelectric composites: Historical perspective, status, and future directions. J. Appl. Phys.
**2008**, 103. [Google Scholar] [CrossRef] - Bian, L.; Wen, Y.; Li, P.; Gao, Q.; Zheng, M. Magnetoelectric transducer with high quality factor for wireless power receiving. Sens. Actuators A Phys.
**2009**, 150, 207–211. [Google Scholar] [CrossRef] - Freeman, E.; Harper, J.; Goel, N.; Gilbert, I.; Unguris, J.; Schiff, S.J.; Tadigadapa, S. Improving the magnetoelectric performance of Metglas/PZT laminates by annealing in a magnetic field. Smart Mater. Struct.
**2017**, 26, 085038. [Google Scholar] [CrossRef] [PubMed] - Kornmann, X.; Huber, C. Microstructure and mechanical properties of PZT fibres. J. Eur. Ceram. Soc.
**2004**, 24, 1987–1991. [Google Scholar] [CrossRef]

**Figure 1.**Four bimorph laminate orientation combinations. Orange indicates magnetostrictive (MS) material, blue the piezoelectric (PE) material, and black the location of the PE electrodes. Additionally, the letters in the mode names, T for transverse and L for longitudinal, indicate the orientation of the MS material and PE material, respectively. (

**a**): L-T Mode; (

**b**) T-T Mode; (

**c**) L-L Mode; (

**d**) T-L Mode. Compiled from [12,13,14,15].

**Figure 2.**Geometry layout for L-T mode bimorph. Arrows M and P show the magnetization and polarization orientation. Adapted from [13].

**Figure 3.**Magnetoelectric equivalent circuit with added load resistor. Adapted from [13].

**Figure 4.**A typical magnetostriction profile and its derivative. Adapted from [25].

**Figure 5.**Geometry layout for the double cantilever mechano-magnetoelectric (MME) structure. Arrows marked P indicate PE poling directions and arrows marked H

_{DC}indicate the orientation of the permanent magnetic fields.

**Figure 7.**Images of fabricated test structures. (

**a**) Galfenol-lead zirconate titanate (PZT) laminate. (

**b**) Metglas-polyvinylidene fluoride (PVDF) ME laminate. (

**c**) MME structure.

**Figure 9.**Biasing magnet arrangement and resulting field lines. Transducer is shown in between the two magnets.

**Figure 10.**Repeated open circuit voltage vs frequency. Experimental Average, upper and lower deviation, and model prediction shown.

**Figure 12.**(

**a**) Power output vs. load resistance for Galfenol-PZT device operating at 70.7 kHz. (

**b**) Power output vs. load resistance for Metglas-PVDF device operating at 99.3 kHz.

**Figure 13.**(

**a**) Experimental and modeled MME transducer power output across frequency. (

**b**) Experimental and modeled MME transducer power output under varying magnetic field at 350 Hz operating frequency. (Reproduced from [18], with permission from © 2018 IOP Publishing.).

**Table 1.**Lumped parameter equations for L-L magnetoelectric (ME) laminate. Adapted from [15].

Lumped Parameter Variable | Constitutive Equation |
---|---|

Characteristic Mechanical Impedance, ${Z}_{0}$ | ${Z}_{0}={\rho}_{avg}v\ast \left({A}_{1}+{A}_{2}\right)\left[\frac{\mathrm{kg}}{\mathrm{s}}\right]$ |

Average Laminate Density, ${\rho}_{avg}$ | ${\rho}_{avg}=\frac{{\rho}_{ms\text{}}{A}_{2}+{\rho}_{me}{A}_{1}}{{A}_{1}+{A}_{2}}\left[\frac{\mathrm{kg}}{{\mathrm{m}}^{3}}\right]$ |

Magnetoelectric Wave Speed, $v$ | $v=\sqrt{\frac{n}{{s}_{33}^{H}}+\frac{\left(1-n\right)}{{s}_{11}^{D}}}\text{}\left[\frac{\mathrm{m}}{\mathrm{s}}\right]$ |

Volumetric Layer Ratio, $n$ | $n=\frac{{A}_{2}}{{A}_{2}+{A}_{1}}$ |

Fundamental Frequency, ${\omega}_{s}$ | ${\omega}_{s}=\frac{\pi v}{l}\text{}\left[\frac{rad}{s}\right]$ |

Effective Laminate Quality Factor, ${Q}_{m}$ | ${Q}_{m}={\left(\frac{n}{{Q}_{ms}}+\frac{1-n}{{Q}_{me}}\right)}^{-1}$ |

Magnetostrictive Material Density, ${\rho}_{ms}$ | Material property |

Piezoelectric Material Density, ${\rho}_{pe}$ | Material property |

Magnetostrictive Quality Factor, ${Q}_{ms}$ | Material property |

Piezoelectric Quality Factor, ${Q}_{pe}$ | Material property |

Lumped Parameter Variable | Constitutive Equation |
---|---|

Bean Length, $L$ | Dimension |

Beam Length up to Magnet, ${L}_{0}$ | Dimension |

Beam Substrate Thickness, ${t}_{s}$ | Dimension |

PE Layer Thickness, ${t}_{p}$ | Dimension |

Magnet Mass, $M$ | $M={\rho}_{M}{V}_{M}\text{}[\mathrm{kg}]$ |

Magnet Mass, $M$ | $M={\rho}_{M}{V}_{m}\text{}[\mathrm{kg}]$ |

Beam Mass, ${m}_{b}$ | ${m}_{b}={\rho}_{s}{V}_{s}+{\rho}_{PE}{V}_{PE}\text{}[\mathrm{kg}]$ |

Equivalent Mass, $m$ | $m=M+\frac{33}{140}{m}_{b}$ [m] |

Equivalent Moment Force, ${F}_{m}$ | ${F}_{M}=\frac{3{M}_{b}}{2{l}_{eff}}[\mathrm{N}]$ |

Short-circuit Stiffness, ${K}_{0}$ | ${K}_{0}=\frac{3{\left(YI\right)}_{c}}{{l}_{eff}^{3}}\text{}\left[\frac{\mathrm{N}}{\mathrm{m}}\right]$ |

Open-circuit Stiffness | ${K}_{1}={K}_{0}+\Delta K\left[\frac{\mathrm{N}}{\mathrm{m}}\right]$ |

Piezoelectric Capacitance, ${C}_{0}$ | ${C}_{0}=\frac{wL}{{t}_{p}{\beta}_{p}}\text{}[\mathrm{F}]$ |

Open-circuit resonance Frequency, ${\omega}_{1}$ | ${\omega}_{1}=\sqrt{\frac{{K}_{1}}{m}}\text{}\left[\frac{\mathrm{rad}}{\mathrm{s}}\right]$ |

Property | Value |
---|---|

Piezo Systems PZT-5A4E | |

Piezoelectric voltage coefficient, ${g}_{31,p}$ | −11.6 × 10^{-3} $\mathrm{Vm}/\mathrm{N}$ |

Density, ${\rho}_{pe}$ | 7800 $\mathrm{kg}/{\mathrm{m}}^{3}$ |

Piezoelectric compliance, ${s}_{11,p}$ | 15 × 10^{−12} ${\mathrm{m}}^{2}/\mathrm{N}$ |

Relative Dielectric constant, ${K}_{3}^{T}$ or ($1/({\beta}_{p}{\u03f5}_{0})$) | 1800 |

TdVib Galfenol | |

Piezomagnetic coefficient, ${d}_{33,m}$ | 15–30 $\mathrm{nm}/\mathrm{A}$ (15 used) |

Density, ${\rho}_{ms}$ | 7800 $\mathrm{kg}/\mathrm{m}$ |

Magnetostrictive compliance, ${s}_{33}^{H}$ | 12.5–25.0 × 10^{−12} ${\mathrm{m}}^{2}/\mathrm{N}$ (16.7 used) |

Property | Value |
---|---|

TE Metallized PVDF | |

Piezoelectric voltage coefficient, ${g}_{31,p}$ | 216 × 10^{−3} $\mathrm{Vm}/\mathrm{N}$ |

Density, ${\rho}_{pe}$ | 1780 $\mathrm{kg}/{\mathrm{m}}^{3}$ |

Piezoelectric compliance, ${s}_{11,p}$ | 3.7 × 10^{−10} ${\mathrm{m}}^{2}/\mathrm{N}$ |

Relative Dielectric constant, ${K}_{3}^{T}$ or ($1/({\beta}_{p}{\u03f5}_{0})$) | 12 |

Metglas 2605SA1 | |

Piezomagnetic coefficient, ${d}_{33,m}$ | 25–50 $\mathrm{nm}/\mathrm{A}$ (25 used) |

Density, ${\rho}_{ms}$ | 7180 $\mathrm{kg}/\mathrm{m}$ |

Magnetostrictive compliance, ${s}_{33}^{H}$ | 9.09 × 10^{−12} ${\mathrm{m}}^{2}/\mathrm{N}$ |

Optimized Parameter | ME Galfenol-PZT | ME Metglas-PZT | MME PZT Bimorh | |||
---|---|---|---|---|---|---|

ICNIRP | IEEE | ICNIRP | IEEE | ICNIRP | IEEE | |

$l=2{l}_{0}$ | 21.5 mm | 2 mm | 25.2 mm | 2 mm | NA | NA |

${t}_{P}$ | 15.9 µm | 19.4 µm | 18.1 µm | 25.5 µm | 10 µm | 10 µm |

${t}_{m}$ | 33.5 µm | 40.3 µm | 22.4 µm | 37.3 µm | NA | NA |

$w$ | 1.1 mm | 10 mm | 1.26 mm | 10 mm | 0.4 mm | 0.51 mm |

${H}_{p}$ | 0.44 Oe | 2.89 Oe | 0.40 Oe | 2.89 Oe | 5.56 Oe | 38.39 Oe |

$2L$ | NA | NA | NA | NA | 8.0 mm | 8.0 mm |

${L}_{m}$ | NA | NA | NA | NA | 0.48 mm | 0.39 mm |

$h$ | NA | NA | NA | NA | 5.0 mm | 5.0 mm |

${\omega}_{1}$ | 65 kHz | 698 kHz | 71.9 kHz | 915 kHz | 61 Hz | 325 Hz |

${P}_{avg}$ | 15.6 µW | 7.4 mW | 62.6 µW | 42.7 mW | 120 µW | 8.7 mW |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Rupp, T.; Truong, B.D.; Williams, S.; Roundy, S.
Magnetoelectric Transducer Designs for Use as Wireless Power Receivers in Wearable and Implantable Applications. *Materials* **2019**, *12*, 512.
https://doi.org/10.3390/ma12030512

**AMA Style**

Rupp T, Truong BD, Williams S, Roundy S.
Magnetoelectric Transducer Designs for Use as Wireless Power Receivers in Wearable and Implantable Applications. *Materials*. 2019; 12(3):512.
https://doi.org/10.3390/ma12030512

**Chicago/Turabian Style**

Rupp, Tyrel, Binh Duc Truong, Shane Williams, and Shad Roundy.
2019. "Magnetoelectric Transducer Designs for Use as Wireless Power Receivers in Wearable and Implantable Applications" *Materials* 12, no. 3: 512.
https://doi.org/10.3390/ma12030512