Power management of magnetoelectric transducer 

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Piezoelectric material

Piezoelectric materials have the ability to generate an electric field under applied mechanical stress (direct effect). Inversely, they are also able to develop internal stress when they are exposed to electric field (converse effect). The direct effect was discovered by the Curie brothers (Pierre and Jacques Curie) in 1880 and the converse effect by Gabriel Lippmann in 1881 [46, 47]. The mechanical stress could be generated by ultrasound waves or mechanical contact. Fig. I-13 illustrates an idealized response of a piezoelectric cube in the two effects (direct and converse). Hence, piezoelectric materials are used for actuation and sensing applications as energy harvesters [48] [49] for many applications such as motors and actuators [50], frequency standards (e.g. crystal oscillator) [51] and sonar [52].

Acoustic power transfer based on piezoelectric transducer

Typically, acoustic power transfer (APT) uses a pair of piezoelectric transducers (a transmitter and a receiver) to transfer energy in the form of ultrasound waves. A fundamental schematic of the APT technology is shown in Fig. I-18. This APT system (transmitter and receiver) can be represented as an equivalent lumped circuit as shown in Fig. I-19.
The acoustic wave behaves differently in two region denoted by: near-field and far-field [1]. The near-field is when the receiver (RX) is close to the transmitter (TX). This region is defined as the region where the acoustic beam is convergent. This zone only exists as long as the diameter of the emitter is larger than the wavelength of the acoustic wave. The other is the far-field region where the acoustic wave is spherical an where the acoustic beam diverges. Hence, in this region, the wave amplitude decreases when the distance between RX and TX increases. The transition region between near and far fields is the best location where the receiver should be installed, to get the largest density of acoustic energy. This distance is known as Rayleigh distance [58] and is defined by I.4. 𝐿 = 𝐷2 − 𝜆2 4𝜆 (𝑚).

Comparison between the WPT techniques

To compare the different WPT applications we have built a graph, reported in Fig. I- 22. It represents the amount of power transferred in each application as a function of the surface of the receiver. Since the operating frequency is also an important parameter to take into account, we indicate it also (when the technology is not DC).
These applications are divided into three categories depending on the energy transmitted to the implants: electromagnetic, acoustic and light. We can notice that the techniques that rely on EM sources are positioned at the top of the graph which means that, these techniques show a great potential. However, the operating fre-quency of these application tends to be large (>5MHz). We will keep this in mind for our investigations. Acoustic power transfer delivers a decent amount of power at large dimensions (receiver of around 1cm² typically). However, this power decreases significantly if one tries to reduce the size of the receiver.This gives an advantage for acoustic power transfer technologies. Another drawback of APT is that it requires a precise orientation and alignment of the receiver with the transmitter to be at the optimal position [65]. Light-based sources are positioned at the low part of the graph which means that one can expect very low power from these techniques. As illustrated on the graph, recent works based on light power transfer have still managed to achieve a good amount of power (typically 10mW with small receivers) so it seems that these solutions may have a promising future. As discussed previously, acoustic sources present one advantage compared to EM sources : they reach a decent amount of power for relatively small devices at low frequencies (generally lower than 1MHz) while EM sources require frequencies larger than 10MHz to bring out sufficient power transfer. In this thesis, we try to find the best of both worlds : a hybrid technology combining acoustic power transfer (mechanical vibrations) and EM power transfer (transfer via electromagnetic waves) which combines a high output power with small receiver surface for relatively low frequencies and being less sensitive to the orientation of the emitter compared to EM or acoustic competitors.

Magnetoelectric transducers for wireless charging

The magnetoelectric materials exhibit two effects direct and reverse. The direct effect was discovered in 1888 when the physicist Wilhelm Röntgen found that if a dielectric moves in an electric field it becomes magnetized. The reverse effect came 17 years later when it was discovered that if a dielectric moves in a magnetic field it becomes polarized [73]. The material that has these two properties are called magnetoelectric material. Fig. I-25 shows different applications based on ME composites [74]. Magnetoelectric transducer can be manufactured using ME materials or composite systems like 𝐶𝑟2𝑂3. In Fig. I-26 we show the most three commonly used ME architectures: particulate composites(0-3), layered composites(2-2) and rod composites(1-3) [74]. Another way to build ME transducers is by joining piezoelectric and magnetostrictive materials. We have introduced the piezoelectric effect in section 3.3.2 of acoustic power transfer solution. The magnetostriction effect of magnetostrictive materials was discovered in 1842 by the english physicist James Prescott Joule. This effect was observed on materials that changed their length (L) in the presence of magnetic field (H). The first observation was on an iron sample [75]. The magnetostriction coefficient 𝜆 = Δ𝐿/𝐿 is defined to quantify this effect. Δ𝐿 is the material deformation when it is exposed to magnetic field [76, 77]. The cause of this MS effect is explained as a result of the rotation of small magnetic domains in the material. This re-orientation causes internal strains in the material structure [78]. The strains can lead to the stretching, in the case of positive magnetostriction (𝜆 > 0), and the shrinking in the case of negative magnetostriction (𝜆 < 0) as shown in Fig. I-27. For instance, when positive magnetisation material are exposed to an AC magnetic field (H) the material will stretch for positive and negative magnetic field 𝐻 as shown in Fig. I-28(b).

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Magnetoelectric transducer samples

Our magnetoelectric transducers are composed of two materials: a magnetostrictive (MS) and a piezoelectric (PE) layer. The MS material converts the magnetic energy into mechanical energy and the PE material converts the mechanical energy into electrical energy. The material layers are glued together with epoxy glue. This makes both layers vibrate together when the magnetostrictive layer is exposed to alternative magnetic fields (sinusoidal). To enhance the performance of the transducer, the magnetostrictive layer needs to be magnetized by exposing it to a DC magnetic field. The main possible configurations for the magnetization and the polarization of the transducer are shown in Fig. II-1 . Based on previous work [95], one of the most promising configuration is the L-T type which is used for our samples.
Moreover in [96, 95], 45 piezoeletric materials were tested to evaluate their performance when glued to the same magnetrostrictive material. This study showed that the combination between the piezoelectric material PZT-5H with the magnetostrictive material (Terfenol-D) transfers the highest power. Note that Terfenol-D is a magnetostrictive material known for its high strain capabilities and therefore it is relatively common in the industry [95], which makes it easy to purchase. The main samples that we used in our study are:
1. « PZT-5H/Terf-D »: One magnetostrictive layer of Terfenol-D longitudinallypolarized (7𝑚𝑚 × 14𝑚𝑚 × 1𝑚𝑚) glued to a piezoelectric layer of PZT-5longitudinally-polarized (7𝑚𝑚 × 20𝑚𝑚 × 1𝑚𝑚), (see Fig. II-2).
2. « P51/2×Terf-D »: Two magnetostrictive layers (Terfenol-D longitudinally-polarized) of the same dimensions (10𝑚𝑚 × 14𝑚𝑚 × 1𝑚𝑚) glued to a piezoelectric plate of P51 longitudinally-polarized (10𝑚𝑚 × 20𝑚𝑚 × 1𝑚𝑚), (see Fig. II-3).

Table of contents :

Résumé en français
Acknowledgments
Abbreviation
I Wireless power transmission: a review 
1 Introduction
2 Evaluation criteria for wireless power transmission
3 Wireless power transmission techniques
3.1 Electromagnetic field sources
3.1.1 Inductive power transfer
3.1.2 Capacitive power transfer
3.2 Light sources
3.3 Acoustic sources
3.3.1 Piezoelectric material
3.3.2 Acoustic power transfer based on piezoelectric transducer
3.4 Comparison between the WPT techniques
4 Study case: wireless charging of implants
4.1 Implantable medical devices
4.2 Magnetoelectric transducers for wireless charging
5 Conclusion
II Characterization of magnetoelectric transducers 
1 Introduction
2 Overview on magnetoelectric transducer modeling
3 Experimental setup
3.1 Magnetoelectric transducer samples
3.2 Characterization procedures
3.2.1 Introduction
3.2.2 Characterization in the absence of AC magnetic fields
3.2.2.i Introduction
3.2.2.ii System-level model
3.2.2.iii Admittance measurements
3.2.2.iv Parameter identification
3.2.2.v Results and Discussion
3.2.2.vi Conclusion
3.2.3 Characterization in the presence of AC magnetic fields
3.2.3.i Introduction
3.2.3.ii Characterization setup
3.2.3.iii First assumption: predominant magnetic losses
a Introduction
b The magnetoelectric transducer model
c Measurement acquisition
d Experimental results
e Discussion and observations
f Conclusion: failure of the first assumption
3.2.3.iv Second assumption: predominant mechanical losses
a Introduction
b Characterization setup
c Presumption based on admittance measurements
d Linear model with variable parameters
e Experimental results
f Further analysis and validation
g Discussion about the physical origin of power losses
4 Conclusion
IIIPower management of magnetoelectric transducer 
1 Introduction
2 Output power of magnetoelectric transducer
2.1 Power limit of the magnetoelectric transducer
2.1.1 Definition of the power limit
2.1.2 Conditions to reach the power limit
2.1.3 Figure-of-merit of the magnetoelectric transducer
2.1.4 The power limit formula
2.1.5 Impact of parameter variations on circuit design
2.2 Power management circuits for magnetoelectric transducer .
2.2.1 Introduction
2.2.2 Power terms in the system
2.2.3 Selection criteria of the power management circuits .
2.2.4 Power management circuit simulation
2.2.4.i Standard energy harvesting circuit
a State-of-the-art : Description of the
SEH circuit topology and impedance
matching condition
b Implementation proposed for the SEH circuit
2.2.4.ii Unipolar synchronized electric charge extraction circuit
a State-of-the-art : Description of the
USECE circuit topology and impedance
matching condition
b USECE implementation with RS latch
2.2.4.iii LTSpice Simulation
a Operating points of the simulations .
b Extracted power with respect to the
power limit
c Efficiency of the circuit
d Autonomous circuit for implants
2.2.4.iv Conclusion
3 Conclusion
Appendices
List of Figures
List of Tables
Bibliography

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