Bistable Wireless Power Transfer
The use of implanted biomedical devices has significantly increased in modern medicine. To supply these devices without requiring regular surgery, we focus on wireless power transfer through the human body.
Exposure to strong and high frequency magnetic fields induces eddy currents within the human body. If sufficiently large, these currents could cause unwanted stimulation of nerves and muscles and affect other biological processes. Another undesirable outcome is the patient's body warming up to the hyperthermia. This phenomenon is the result of eddy currents circulating through the body but might also come from the movement of water molecules subject to the magnetic field (like in a microwave oven) depending on its frequency. [1]
To prevent the use of dangerous magnetic fields, organizations like the ICNIRP suggest the use of norms and guidelines. [2]
As seen on the diagram, in order to use a magnetic field with a greater amplitude, the frequency of said magnetic field must be decreased to avoid any risk to the health of the patient.
Moreover, lower frequency magnetic fields will have an easier time passing through conductive materials like a steel housing of an implanted device and won't cause EMI in nearby electronic circuits.
The most traditional WPT transmitter technology works on the principle of electromagnetic induction. When a sinusoidal magnetic field passes through a coil, it produces a sinusoidal electric current of the same frequency.
Those receivers operate at a magnetic field of ~1 Mhz, which puts heavy constraints on the amplitude of the magnetic field used according to health standards.
To resolve this issue, some research groups proposed using electromechanical receivers instead. The simplest design works by replacing the coil with a cantilever beam with a magnet at its tip [3]. The sinusoidal magnetic field applies a force on the magnet that bends the beam. Then, a piezoelectric material converts the mechanical energy into electrical energy.
With this kind of receiver, the operating frequency of the system can go as low as 50-100 Hz which is still too high to use a magnetic field with a significant amplitude. To further decrease this frequency, the only way is to increase the magnetic mass and thus the volume. This is contradictory with the purpose of the receiver, which must be miniaturized to fit inside a human body.
To solve these issues, we aim to design a miniaturized receiver that works with a magnetic field of ~1 Hz, to limit the absorption into the body and allow greater efficiency at no risk to health.
The key limitation of the aforementioned receivers is their linear behaviour. This results in systems with a sinusoidal response with the same frequency as the excitation, which means that if a receiver works best for a certain frequency, the magnetic field must be of the same frequency for an optimal power transfer.
Since we have such a heavy constraint on the frequency of the magnetic field, we need a system that would still operate at its optimal frequency even when excited at a very low frequency. One way to achieve this is by using a non-linear electromechanical receiver.
The proposed receiver uses a buckled beam architecture that induces Duffing-type non-linearity. A magnet is placed at the center of the buckled beam to allow the system to tip over from a stable position to another with the variation of the magnetic field. An Amplified Piezoelectric Actuator (APA) is used to convert the mechanical energy of the system into electrical energy.
As said before, the main purpose of using an electromechanical non-linear receiver is to multiply the excitating frequency. As such, the displacement of the magnetic mass should illustrate this behaviour. Through analytical analysis, we calculate the governing differential equations of the system [4]. From these equations, we perform a numerical analysis to determine the response of the receiver to a sinusoidal excitation:
Even so the excitation is a sinusoidal wave, the behaviour of the receiver is close to a linear receiver impulse response. Therefore, the theoritical limits of energy harvesting from a linear harvester—from the need to preserve the sinusoidal steady state—no longer apply. Instead, the goals are to harvest all the available energy from the magnetic mass movement, and more importently, to optimize the design of the bistable receiver in order to get the highest energy impulse from the highest magnitude magnetic field—and thus the need to work at an extremly low frequency to comply with health guidelines—.