## 1 Introduction  
Wireless power transfer (WPT) systems allow elimination of cables, plugs and sockets, resulting in extended maintenance-free operation and increased reliability and safety [1]. In recent years, WPT became a hot topic due to the rapid growth of mobile devices and electric vehicles [2]. A great number of existing WPT systems utilize electromagnetic transmission techniques, but the effectiveness of these approaches in applications containing sealed metal containers (such as submarines, space crafts, planes, nuclear storage facilities, etc.) is limited by the Faraday shielding effect or the skin effect. As a kind of mechanical wave, ultrasound can penetrate metal walls. So, ultrasound has been suggested as effective means for passing power, as well as data, through metal barriers without physical penetration [3; 4; 5]. Ultrasound has also been demonstrated capable of safely and efficiently transferring energy through human tissue to power deeply implanted medical devices [6; 7; 8; 9]. In addition, airborne ultrasound has been shown to be a feasible alternative to microwave, capacitive or inductive coupling methods to transfer power wirelessly in air, when the transfer distance is above several times the transducer size [10; 11]. However, ultrasonic through-metal-wall power transfer (UTMWPT) systems usually achieve higher power transfer efficiency than ultrasonic through-air or through-non-metal-wall WPT systems, because the acoustic impedance of ultrasonic transducers is better matched to that of metal than air, non-metal or human tissue [12]. In general, a UTMWPT system uses a pair of piezoelectric transducers bonded on the opposite sides of the metal wall to generate and receive ultrasound. Besides, transducers in UTMWPT systems usually operate at frequencies between tens of kHz and 1 MHz, which range from the very low frequency (VLF) band through medium frequency (MF) band of radio spectrum [13]. An analytical solution for UTMWPT systems was proposed by [PERSON] et al., as early as 2003 [3]. In their later work [14], an alternating current to direct current (AC-DC) converter was employed at the receiving side of a UTMWPT system to convert the radio frequency (RF) alternating current (AC) output of the receiving transducer into a stable direct current (DC). The AC-DC converter was composed of a capacitor-filtered diode full-bridge rectifier (CF-DFBR) and a buck DC-DC converter. A rechargeable battery was applied at the output port of the AC-DC converter to store the transmitted energy. In addition, a synchronized switch harvesting on inductor (SSHI) in parallel with the receiving transducer was introduced to extend the closed interval of the AC-DC converter. Both analytical and numerical results of the system were presented. However, no experiments were shown and the system was greatly simplified that the electrodes of the piezoelectric transducers were considered as the metal wall. [PERSON] et al., presented two UTMWPT systems successively, which could transmit electric powers up to 100 W and 1 kW, respectively, through several-millimetre-thick titanium plates and light incandescent bulbs [15; 16]. The operating frequencies of these two UTMWPT systems are 747 kHz and 24.5 kHz, respectively. However, without the use of AC-DC converters, the output of these two UTMWPT systems was not directly suitable as a power supply for electronic circuits because of the high frequencies. [PERSON] et al., presented a UTMWPT system with a CF-DFBR as an AC-DC converter [17; 18]. The transducers operated at about 1 MHz. The thickness of the metal wall in the system reached up to 63.5 mm; and the material of it was steel, which was more widely used than titanium. [PERSON] et al. used simultaneous conjugate matching in their system to improve its power transfer efficiency. However, significant power mismatch loss was still caused by the CF-DFBR. DC power of about 19 W was output to a 50 \(\Omega\) resistor with an efficiency of only about 19%. [PERSON] et al.