Design and Optimization of Ultrasonic Links With Phased Arrays for Wireless Power Transmission to Biomedical Implants

Abstract

Ultrasound (US) is an attractive modality for wireless power transfer (WPT) to biomedical implants with millimeter (mm) dimensions. To compensate for misalignments in WPT to a mm-sized implant (or powering a network of mm-sized implants), a US transducer array should electronically be driven in a beamforming fashion (known as US phased array) to steer focused US beams at different locations. This paper presents the theory and design methodology of US WPT links with phased arrays and mm-sized receivers (Rx). For given constraints imposed by the application and fabrication, such as load (R_L) and focal distance (F), the optimal geometries of a US phased array and Rx transducer, as well as the optimal operation frequency (f_c) are found through an iterative design procedure to maximize the power transfer efficiency (PTE). An optimal figure of merit (FoM) related to PTE is proposed to simplify the US array design. A design example of a US link is presented and optimized for WPT to a mm-sized Rx with a linear array. In measurements, the fabricated 16-element array (10.9×9×1.7 mm³) driven by 100 V pulses at f_c of 1.1 MHz with optimal delays for focusing at F = 20 mm generated a US beam with a pressure output of 0.8 MPa. The link could deliver up to 6 mW to a ∼ 1 mm³ Rx with a PTE of 0.14% (R_L = 850 Ω). The beam steering capability of the array at -45^o to 45^o angles was also characterized.

Fig. 1.

Conceptual schematic of a US WPT link for powering mm-sized implants uisng a US phased array as the power transmitter (Tx).

Fig. 2.

A linear US phased array with a conceptual beam shape, consisting of near- and far-field zones.

Fig. 3.

k-Wave simulation setup used to optimize an array for US WPT. The array surface is parallel to the yz plane and centered at the origin x = y = z = 0. Both the xy and xz planes were defined as sensors for recording US pressure.

Fig. 4.

Iterative optimization flowchart of a US link with a phased array for efficient WPT to mm-sized biomedical implants. The proposed procedure needs to be completed in COMSOL and k-Wave.

Fig. 5.

Geometry optimization of the US array at f_c =1.4 MHz, F = 30 mm, and $P_{{\theta }_{s,\mathit{\text{max}}}}/P_0\ge 0.7$ at θ_s,max = 45°, showing (a) normalized FoM vs. L, (b) normalized FoM vs. d and a, (c) $P_{{\theta }_{s,\mathit{\text{max}}}}/P_0$ at θ_s,max = 45° vs. d, (d) normalized FoM vs. N, and (e) array element impedance vs. frequency to find optimal t.

Fig. 6.

Simulated beam profiles of the optimal array in the xy and yz planes when the beam was focused at F = 30 mm and θ_s = 0° (f_c = 1.4 MHz).

Fig. 7.

(a) Fabrication procedure of the linear US array using a dicing machine. (b) Fabricated mm-sized US receiver (Rx).

Fig. 8.

(a) Block diagram of the TX7316EVM evaluation board for driving the US array in our measurements. (b) Ultrasonic WPT link measurement setup inside a water tank without and with a chicken breast mimicking tissue.

Fig. 9.

Measured impedance profile of (a) all 16 elements of the fabricated linear US array at a frequency range of 0.6–1.5 MHz, and (b) Rx transducer at a frequency range of 0.8–2 MHz.

Fig. 10.

(a) Measured US pressure output at 20 mm axial distance (20 V peak-peak sinusoids) of individual elements in the fabricated 16-element array, and (b) measured electrical input power of each element at the same conditions.

Fig. 11.

Optimal delay patterns of each element of US array obtained from k-Wave simulations for beamforming (a) at different focal depths F with θ_s = 0°, and (b) at different steering angles θ_s with F = 20 mm.

Fig. 12.

Measured transient waveforms of the driver board across 4 US elements (# 2, 5, 12, 15 in Fig. 7) for beamforming at F = 20 mm with (a) θ_s = 0° and (b) θ_s = 45°. (c) Burst-mode signal generated by the driver and the received voltage by the Rx transducer (F = 20 mm, θ_s = 0°).

Fig. 13.

Simulated and measured beam profiles of the 16-element array in the xy plane at F = 20 mm with different θ_s of a) 0°, b) 45°, and c) −45°

Fig. 14.

Simulated and measured beam profiles of the 16-element array in the xy plane at F = 20 mm (θ_s = 0°) in the presence of the chicken breast.

Fig. 15.

Measured received power P_L (θ_s = 0°) by the Rx transducer vs. R_L at a depth of F = 20 mm while driving the array at different voltages.

Fig. 16.

Measured highest PTE of the US WPT link for different RL, when the beam was focused at F = 20 mm (θ_s = 0°).

Fig. 17.

Measured P_L with beam focusing and steering at different F and θ_s (R_L = 850 Ω). (a) P_L at different axial distances at different F. (b) P_L at different lateral distances at different F. (c) P_L at different axial distances at different θ_s, and (d) P_L at different lateral distances at different θ_s.

Fig. 18.

Measured PL along the axial axis x at zero and 13.2 mm lateral (y) distances when the beam was focused at F = 20 mm and θ_s = 0° and 45°.