A computationally efficient technique to model depth, orientation and alignment via ray tracing in acoustic power transfer systems

Abstract

In acoustic power transfer systems, a receiver is displaced from a transmitter by an axial depth, a lateral offset (alignment), and a rotation angle (orientation). In systems where the receiver's position is not fixed, such as a receiver implanted in biological tissue, slight variations in depth, orientation, or alignment can cause significant variations in the received voltage and power. To address this concern, this paper presents a computationally efficient technique to model the effects of depth, orientation, and alignment via ray tracing (DOART) on received voltage and power in acoustic power transfer systems. DOART combines transducer circuit equivalent models, a modified version of Huygens principle, and ray tracing to simulate pressure wave propagation and reflection between a transmitter and a receiver in a homogeneous medium. A reflected grid method is introduced to calculate propagation distances, reflection coefficients, and initial vectors between a point on the transmitter and a point on the receiver for an arbitrary number of reflections. DOART convergence and simulation time per data point is discussed as a function of the number of reflections and elements chosen. Finally, experimental data is compared to DOART simulation data in terms of magnitude and shape of the received voltage signal.

Miniaturised Wireless Power Transfer Systems for Neurostimulation: A Review

“…Another important issue of focused acoustic beams is the effect of angular rotation and misalignment on both the PTE and PCE [98]. Beam-forming systems were recently demonstrated to be an interesting and efficient strategy to minimise the negative effect of misalignment on the PTE [99].…”

Acoustic power transfer for biomedical implants using piezoelectric receivers: effects of misalignment and misorientation

“…As the frequency goes up, the wavelength becomes shorter, and more elements are needed in meshing the geometry. In order to efficiently model the effects of orientation and alignment in high frequencies, we employed a modeling technique that models the effect of depth, orientation, and alignment via ray tracing (DOART) as presented in [39]. This technique uses Huygens principle to discretize the face of the transmitter into spherically radiating pressure sources.…”

Non-dimensional analysis of depth, orientation, and alignment in acoustic power transfer systems

“…Material properties of the assumed piezoelectric material and titanium matching layer are given in table 1. To model this system efficiently, the DOART modeling technique as described in [27] is used to obtain simulation data. DOART approximates the behavior of the TX and RX using circuit equivalent models.…”

“…Table 3 provides a reference of non-dimensional expressions for system parameters. The variables used are consistent with the variables in [27] and are summarized as follows:  is the depth or axial separation distance between the TX and RX, X q is the angle between the TX and RX faces,  is the offset or lateral offset distance between the TX and RX, D TX is the diameter of the TX, D RX is the diameter of the RX, f is the operating frequency of the TX, c is the speed of sound in the medium, l is the acoustic wavelength in the medium, R L is the impedance of the load, R L,opt,avg is the fixed-average optimal load resistance, V is the RMS voltage measured across the RX load, and P is the average power delivered to the RX load. The non-dimensional expressions given in table 3.…”

“…However, this approach is not trivial to solve analytically for non-simple cases and does not account for pressure reflections between the TX and RX or the effect of electronics attached to the TX and RX. In order to efficiently model the effects of orientation and alignment while accounting for reflections and electronics, this paper employs a modeling technique that models the effect of depth, orientation, and alignment via ray tracing (DOART) as presented in [27]. DOART provides a reduction in computational cost that enables a more thorough exploration of the design and operational space of acoustic power transfer systems.…”