High Step-Up Ratio DC-AC Converter Using Fourth-Order LCLC Resonant Circuit for Ultrasonic Fingerprint-Sensor Drivers

Ultrasonic fingerprint sensors are becoming more widely used in thick or flexible displays. In order to better identify fingerprint information, ultrasonic sensors need to generate more ultrasonic energy, which can be transmitted to the display surface through media with higher acoustic impedance. In this paper, a DC-AC converter with a high lift ratio was proposed to enhance the transmission energy of the ultrasonic fingerprint sensor, thus helping to improve the identification. The converter comprises a full-bridge inverter and two LC resonant circuits. The introduction of an additional LC resonant circuit into the traditional Class-D LC resonant converter effectively increases the boost ratio of the proposed converter from 5 to 22. When used as a part of the ultrasonic fingerprint sensing system, the proposed converter can amplify the 20-V low-voltage DC required to drive the piezoelectric organic film to 376 V high-voltage AC. The voltage of the wave received from this new driver is equal to 970 mV, which greatly exceeds the 376 mV achieved by using the Class-D converter alone. In this paper, the topology proposed by the ultrasonic fingerprint sensor converter driver was experimentally verified, which greatly improved the boost ratio and can be considered suitable for wider applications.


Introduction
Ultrasonic fingerprint-identification technology [1][2][3][4][5][6][7] has been employed to realize under-screen fingerprint identification in intelligent devices such as mobile phones and laptops. To enhance the security of fingerprint identification, large-area ultrasonic fingerprint sensors capable of simultaneously detecting multiple fingers have been proposed [4][5][6]. As illustrated in Figure 1, a typical ultrasonic fingerprint sensor installed under an organic light-emitting diode (OLED) display module comprises a thin-film transistor backplane, transmitter (Tx) electrode (upper electrode), receiver (Rx) electrode (lower electrode), and poly(vinylidene fluoride) (PVDF) piezoelectric film [7]. Being a piezoelectric material, PVDF generates ultrasonic waves when driven by high-frequency voltage AC power [8]. Ultrasonic waves pass through intermediate media and reach the finger surface. Serrations on the finger surface result in the existence of two media types-air and skin-between the finger and fingerprint sensor ( Figure 1). Due to differences in acoustic impedances between the air and skin, waves reflecting from air and skin travel back to the same ultrasonic transducer, thereby causing a voltage difference across the PVDF film.
Typically, the Tx electrode is connected to a high-voltage signal, and the Rx electrode is connected to the ground. However, only low-voltage DC power is available in most mobile systems; therefore, a DC/AC converter must be used to drive ultrasonic fingerprint sensors. Due to the limited space in mobile devices, high-power and large-volume devices such as transformers cannot be used. PVDF also generates AC voltage signals on the Rx electrode when it receives echo ultrasound waves [9]. To achieve a high Rx voltage difference across mobile systems; therefore, a DC/AC converter must be used to drive ultraso sensors. Due to the limited space in mobile devices, high-power and large-v such as transformers cannot be used. PVDF also generates AC voltage sig electrode when it receives echo ultrasound waves [9]. To achieve a high Rx ence across the ultrasonic transducer, it is usually driven at high-voltage AC ever, most mobile systems can only supply low-voltage DC power; therefo quency DC-AC converter must realize a high step-up ratio to generate a hi signal to drive ultrasonic fingerprint sensors. An ultrasonic fingerprint sensor comprises thousands of pixels, and ea nected to the pixel circuit, as depicted in Figure 2. A Ag Tx electrode sp PVDF film connects to the resonant network through an anisotropic co (ACF) via a bonding process. The contact resistance R of ACF approximat The Rx electrode is made of indium tin oxide (ITO) manufactured via th Each switching cycle comprises two sub-modes-Tx and Rx. In the Rx mod trode is switched to ground, and the Rx electrode is connected to the thin-M2 and peak detect diode D. The voltage difference on the PVDF film gen ferent acoustic impedances between air and skin causes a drain-source cur in M2. Thus, the read-out current and ADC facilitate the accumulation o data via the detection of the drain-source current difference correspondin Tx mode, the DC-AC converter generates a high-voltage AC signal not ad the Tx and Rx electrodes; instead, it is passed through a thin-film transisto M1 must be connected to ground in light of the low normal operating volt Otherwise, TFT would burn out due to the application of excess voltage a Tx mode, the equivalent circuit of a pixel comprises a bonding-resistor R series with a PVDF capacitor CPVDF and TFT M1. In summary, the DC must be characterized by high-frequency operation, high step-up ratio, o CPVDF grounded, and small form-factor.  An ultrasonic fingerprint sensor comprises thousands of pixels, and each pixel is connected to the pixel circuit, as depicted in Figure 2. A Ag Tx electrode sputtered on the PVDF film connects to the resonant network through an anisotropic conductive film (ACF) via a bonding process. The contact resistance R of ACF approximately equals 5 Ω. The Rx electrode is made of indium tin oxide (ITO) manufactured via the TFT process. Each switching cycle comprises two sub-modes-Tx and Rx. In the Rx mode, the Tx electrode is switched to ground, and the Rx electrode is connected to the thin-film transistor M2 and peak detect diode D. The voltage difference on the PVDF film generated by different acoustic impedances between air and skin causes a drain-source current difference in M2. Thus, the read-out current and ADC facilitate the accumulation of finger-image data via the detection of the drain-source current difference corresponding to M2. In the Tx mode, the DC-AC converter generates a high-voltage AC signal not added directly to the Tx and Rx electrodes; instead, it is passed through a thin-film transistor. Meanwhile, M1 must be connected to ground in light of the low normal operating voltage of TFT [3]. Otherwise, TFT would burn out due to the application of excess voltage across it. In the Tx mode, the equivalent circuit of a pixel comprises a bonding-resistor R connected in series with a PVDF capacitor CPVDF and TFT M1. In summary, the DC-AC converter must be characterized by high-frequency operation, high step-up ratio, one end of the CPVDF grounded, and small form-factor. such as transformers cannot be used. PVDF also generates AC voltage signals o electrode when it receives echo ultrasound waves [9]. To achieve a high Rx voltag ence across the ultrasonic transducer, it is usually driven at high-voltage AC powe ever, most mobile systems can only supply low-voltage DC power; therefore, a h quency DC-AC converter must realize a high step-up ratio to generate a high-vol signal to drive ultrasonic fingerprint sensors. An ultrasonic fingerprint sensor comprises thousands of pixels, and each pixe nected to the pixel circuit, as depicted in Figure 2. A Ag Tx electrode sputtered PVDF film connects to the resonant network through an anisotropic conduct (ACF) via a bonding process. The contact resistance R of ACF approximately equ The Rx electrode is made of indium tin oxide (ITO) manufactured via the TFT Each switching cycle comprises two sub-modes-Tx and Rx. In the Rx mode, the trode is switched to ground, and the Rx electrode is connected to the thin-film tr M2 and peak detect diode D. The voltage difference on the PVDF film generated ferent acoustic impedances between air and skin causes a drain-source current di in M2. Thus, the read-out current and ADC facilitate the accumulation of finge data via the detection of the drain-source current difference corresponding to M Tx mode, the DC-AC converter generates a high-voltage AC signal not added di the Tx and Rx electrodes; instead, it is passed through a thin-film transistor. Mea M1 must be connected to ground in light of the low normal operating voltage of Otherwise, TFT would burn out due to the application of excess voltage across i Tx mode, the equivalent circuit of a pixel comprises a bonding-resistor R conn series with a PVDF capacitor CPVDF and TFT M1. In summary, the DC-AC c must be characterized by high-frequency operation, high step-up ratio, one en CPVDF grounded, and small form-factor.   High-power inverters have already been used to drive ultrasonic transducers in recent studies [10,11]. However, these inverters usually consist of large-volume power devices and cannot be used in mobile phones. In our previous work [12,13], a Class-D inverter was proposed for inductor heating applications. This type of inverter is a classical DC/AC converter that can also be used to drive piezoelectric ultrasonic transducers [14][15][16][17], the output voltage of which is, however, insufficient due to its low step-up ratio. This induces a weak Rx signal on the PVDF ultrasonic sensor. To increase the voltage of the Rx signal, the step-up ratio of this DC/AC converter must be improved. The traditional Class-D LC resonant converter possesses only one LC resonant loop, the quality factor of which determines the step-up ratio of this converter. In this paper, a converter with two LC resonant circuits was proposed, the step-up ratio of which was approximately the product of the quality factors of two resonant loops. The step-up ratio of the proposed converter was found to be greater than that of traditional Class-D LC converters when the quality factor of the second resonant circuit exceeded one. This paper describes a high step-up ratio DC/AC converter using a fourth-order LCLC resonant circuit by adding another set of LC resonant circuits. The step-up ratio can be increased by approximately three times compared with that of the conventional Class-D LC resonant converter, which is expected to be sufficiently powerful to drive PVDF ultrasonic transducers.
The remainder of this paper is organized as follows. Section 2 presents the circuit configuration and operating principle of the proposed fourth-order LCLC resonant converter. Section 3 presents the equivalent circuit analysis of the proposed converter. Section 4 presents the experimental results based on the preliminary application of the proposed converter to a prototype ultrasonic fingerprint sensor. Section 5 concludes the paper. Figure 3 depicts the schematic of a Class-D inverter proposed in extant studies [13][14][15][16]. The output power stage comprises a signal-phase voltage-source half-bridge inverter comprising two MOSFET modules-Q 1 and Q 2 . The output from the inverter is connected to a LC resonant circuit comprising an ACF contact resistor R s , resonant inductor L, and PVDF ultrasonic transducer that can be modeled using a capacitor C. The parasitic resistance of inductor L is much lower compared to the ACF contact resistance. Therefore, in the proposed study, the same was not considered during the theoretical analysis. The piezoelectric thin film transducer is a key component in the ultrasonic fingerprint sensor, and its electrical characteristics can be modeled by a parallel plate capacitor. For a 150 mm 2 × 30 um PVDF thin film ultrasonic transducer, the equivalent capacitance was calculated as 500 pF. According to [12,13], the resonant frequency of the LC circuits, step-up ratio of the Class-D converter, current of the inductor, and voltage of the capacitor can be expressed as follows: High-power inverters have already been used to drive ultrasonic transducers in recent studies [10,11]. However, these inverters usually consist of large-volume power devices and cannot be used in mobile phones. In our previous work [12,13], a Class-D inverter was proposed for inductor heating applications. This type of inverter is a classical DC/AC converter that can also be used to drive piezoelectric ultrasonic transducers [14][15][16][17], the output voltage of which is, however, insufficient due to its low step-up ratio. This induces a weak Rx signal on the PVDF ultrasonic sensor. To increase the voltage of the Rx signal, the step-up ratio of this DC/AC converter must be improved. The traditional Class-D LC resonant converter possesses only one LC resonant loop, the quality factor of which determines the step-up ratio of this converter. In this paper, a converter with two LC resonant circuits was proposed, the step-up ratio of which was approximately the product of the quality factors of two resonant loops. The step-up ratio of the proposed converter was found to be greater than that of traditional Class-D LC converters when the quality factor of the second resonant circuit exceeded one. This paper describes a high step-up ratio DC/AC converter using a fourth-order LCLC resonant circuit by adding another set of LC resonant circuits. The step-up ratio can be increased by approximately three times compared with that of the conventional Class-D LC resonant converter, which is expected to be sufficiently powerful to drive PVDF ultrasonic transducers.

Circuit Description
The remainder of this paper is organized as follows. Section 2 presents the circuit configuration and operating principle of the proposed fourth-order LCLC resonant converter. Section 3 presents the equivalent circuit analysis of the proposed converter. Section 4 presents the experimental results based on the preliminary application of the proposed converter to a prototype ultrasonic fingerprint sensor. Section 5 concludes the paper. Figure 3 depicts the schematic of a Class-D inverter proposed in extant studies [13][14][15][16]. The output power stage comprises a signal-phase voltage-source half-bridge inverter comprising two MOSFET modules-Q1 and Q2. The output from the inverter is connected to a LC resonant circuit comprising an ACF contact resistor Rs, resonant inductor L, and PVDF ultrasonic transducer that can be modeled using a capacitor C. The parasitic resistance of inductor L is much lower compared to the ACF contact resistance. Therefore, in the proposed study, the same was not considered during the theoretical analysis. The piezoelectric thin film transducer is a key component in the ultrasonic fingerprint sensor, and its electrical characteristics can be modeled by a parallel plate capacitor. For a 150 mm 2  30 um PVDF thin film ultrasonic transducer, the equivalent capacitance was calculated as 500 pF. According to [12,13], the resonant frequency of the LC circuits, step-up ratio of the Class-D converter, current of the inductor, and voltage of the capacitor can be expressed as follows:   Figure 4 shows the simplified schematic of the fourth-order LCLC resonant converter circuit. The output power stage comprises a signal-phase voltage-source full-bridge inverter with four MOSFET modules Q 1 , Q 2 , Q 3 , and Q 4 . G 1 , G 2 , G 3 , and G 4 represent the driving signals of the MOSFETs. The output of the inverter is connected to the fourth-order LCLC resonant circuit, which consists of an ACF contact resistor R, two resonant inductors L 1 and L 2 , one resonant capacitor C 1 , and one ultrasonic transducer modeled by a capacitor C 2 .

A. Circuit Description
Micromachines 2023, 14, x FOR PEER REVIEW 4 of 14 Figure 4 shows the simplified schematic of the fourth-order LCLC resonant converter circuit.   Figure 1 shows the schematic of an ultrasonic fingerprint sensor module. The ultrasound waves transmitted by the PVDF film pass through the OLED module to reach the finger and are reflected by the surface of the finger. The reflected waves pass through the OLED module again, and reach the piezoelectric PVDF film, which converts the received ultrasound waves into electrical voltage signals. The transmitting and receiving waveforms are shown in Figure 5. The receiving waves do not overlap with the transmitting waves if the transmission time T is less than the transfer time t.    Figure 1 shows the schematic of an ultrasonic fingerprint sensor module. The ultrasound waves transmitted by the PVDF film pass through the OLED module to reach the finger and are reflected by the surface of the finger. The reflected waves pass through the OLED module again, and reach the piezoelectric PVDF film, which converts the received ultrasound waves into electrical voltage signals. The transmitting and receiving waveforms are shown in Figure 5. The receiving waves do not overlap with the transmitting waves if the transmission time T is less than the transfer time t.  Figure 4 shows the simplified schematic of the fourth-order LCLC resonant converter circuit.   Figure 1 shows the schematic of an ultrasonic fingerprint sensor module. The ultrasound waves transmitted by the PVDF film pass through the OLED module to reach the finger and are reflected by the surface of the finger. The reflected waves pass through the OLED module again, and reach the piezoelectric PVDF film, which converts the received ultrasound waves into electrical voltage signals. The transmitting and receiving waveforms are shown in Figure 5. The receiving waves do not overlap with the transmitting waves if the transmission time T is less than the transfer time t.

B. Resonant Frequency
In Equation (2), the thickness of the OLED module s is approximately 1.5 mm. The transmission speed of ultrasound waves in the OLED module v is approximately 5000 m/s, considering that the majority of the OLED module is glass. Therefore, the switching frequency f must exceed N/0.6 MHz, which is approximately 12 MHz in this study.

Circuit State Analysis
The operating waveforms of the proposed fourth-order LCLC resonant converter are shown in Figure 6. The switch-mode transition and the resonant current pathway of the fourth-order LCLC resonant converter are depicted in Figure 7. In this converter, there are two resonant loops, which are shown in Figure 8, where one part of the inductor L 1 flows through the capacitor C 2 and the other flows through L 2 , R, and C 2 .
In Equation (2), the thickness of the OLED module s is approximately 1.5 mm. The transmission speed of ultrasound waves in the OLED module v is approximately 5000 m/s, considering that the majority of the OLED module is glass. Therefore, the switching frequency f must exceed N/0.6 MHz, which is approximately 12 MHz in this study.

C. Circuit State Analysis
The operating waveforms of the proposed fourth-order LCLC resonant converter are shown in Figure 6. The switch-mode transition and the resonant current pathway of the fourth-order LCLC resonant converter are depicted in Figure 7. In this converter, there are two resonant loops, which are shown in Figure 8, where one part of the inductor L1 flows through the capacitor C2 and the other flows through L2, R, and C2.    In Equation (2), the thickness of the OLED module s is approximately 1.5 mm. The transmission speed of ultrasound waves in the OLED module v is approximately 5000 m/s, considering that the majority of the OLED module is glass. Therefore, the switching frequency f must exceed N/0.6 MHz, which is approximately 12 MHz in this study.

C. Circuit State Analysis
The operating waveforms of the proposed fourth-order LCLC resonant converter are shown in Figure 6. The switch-mode transition and the resonant current pathway of the fourth-order LCLC resonant converter are depicted in Figure 7. In this converter, there are two resonant loops, which are shown in Figure 8, where one part of the inductor L1 flows through the capacitor C2 and the other flows through L2, R, and C2.

C. Circuit State Analysis
The operating waveforms of the proposed fourth-order LCLC resonant conv shown in Figure 6. The switch-mode transition and the resonant current pathwa fourth-order LCLC resonant converter are depicted in Figure 7. In this converter, t two resonant loops, which are shown in Figure 8, where one part of the inductor through the capacitor C2 and the other flows through L2, R, and C2.    The resonant circuit shown in Figure 8 can be described by the following parameters. The output voltage of C 2 is given by where and E is the amplitude of the input power. Therefore, the open loop transfer function of V c2 and E can be represented as The peak-to-peak voltage of V c2 and the step-up ratio of the full bridge fourth-order LCLC resonant converter are If the number of pulses is N, a transmitter cycle operation can be divided into 2N sub-modes, as shown in Figure 6. There are two sub-modes in one switching cycle: charge and discharge. The operating principles of the charge and discharge modes are as follows.
(1) Mode 1 [0, T/2]: The circuit mode of the fourth-order LCLC resonant converter enters the charge mode. Q 1 and Q 4 are conducted, and the capacitors C 1 and C 2 start charging. According to the KVL law, the initial values of i 1 , i 2 , V c1 , and V c2 are zero, and the state equations of this mode are expressed as follows: (2) Mode 2 [T/2, T]: At T/2, Q 1 and Q 4 are turned off, and Q 2 and Q 3 are turned on. The circuit mode of the fourth-order LCLC resonant converter switches to the discharge mode. The discharge mode initiates at the end of the charge mode. Therefore, the state equations of this mode are expressed as follows: In one switching cycle, the converter transitions from Mode 1 to Mode 2, and then back to Mode 1 in the next switching cycle. If the system transmits N pulses, the converter repeats this action N times. Thus, Modes 3, 5, 7, and 9 have the same state equations as Mode 1, and Modes 4, 6, 8, and 10 have the same state equations as Mode 2. However, the initial value of each state differs because the end value of the previous state will be different. The state Equations (6) and (7) have the same characteristic equation: The characteristic roots of Equation (8) are a 1 ± b 1 i and a 2 ± b 2 i. The voltage and current waveforms of Mode n in the time domain can be obtained by solving Equations (6)- (8).
When n is an odd number, V c2 is When n is an even number, V c2 is The initial value of each Mode is where A, B, C, and D can be obtained by solving the initial (11). i 1 , i 2 , V c1 can be obtained by solving Equations (6), (7), (9) and (10), which are described as follows:

Analysis of Step-Up Ratio
When the switching frequency f = 12 MHz and load capacitor C 2 = 500 pF, the stepup ratio of the Class-D converter can be calculated by substituting Equation (13) into Equation (1).
Similarly, when the inductors in the fourth-order LCLC converter L 1 = 100 nH and L 2 = 110 nH, the step-up ratio can be calculated by substituting Equation (13) into Equation (5).
By comparing the step-up ratios of the fourth-order LCLC converter D c2 and the Class-D converter D c , we observed that the step-up ratio of the proposed converter was approximately four times larger than that of the Class-D inverter. According to previous studies in [12,13], the peak-to-peak voltage of the resonant capacitor cannot exceed 106 V with the resonant parameters proposed in this paper. However, in this proposed converter, the peak-to-peak voltage of the resonant capacitor was considerably greater than 106 V. Figure 9 shows the resonant voltage waveforms of V c2 , which were obtained by solving Equations (9)-(12) in MATLAB. The peak-to-peak voltage of V c2 gradually increased from 0 to 420 V as the number of pulses increased from 0 to 5. This indicates that the proposed fourth-order LCLC converter is a high step-up ratio converter.
in [12] and [13], the peak-to-peak voltage of the resonant capacitor cannot exceed 106 V with the resonant parameters proposed in this paper. However, in this proposed converter, the peak-to-peak voltage of the resonant capacitor was considerably greater than 106 V. Figure 9 shows the resonant voltage waveforms of Vc2, which were obtained by solving Equations (9), (10), (11), and (12) in MATLAB. The peak-to-peak voltage of Vc2 gradually increased from 0 to 420 V as the number of pulses increased from 0 to 5. This indicates that the proposed fourth-order LCLC converter is a high step-up ratio converter.

B. Analysis of Resonant Circuit Parameters
The proposed fourth-order LCLC resonant converter can be considered as two resonant circuit loops connected in series. One resonant loop comprises an inductor L1 and a capacitor C1, and the other loop comprises two inductors L1 and L2, two capacitors C1 and C2, and a serial resistor R. The value of C2 is determined by the device structure, which is 500 pF. The fourth-order LCLC resonant converter has two resonant frequency points, which can be expressed as follows.
The resonant circuit analysis in our previous works [12] and [13] revealed that the voltage on the resonant capacitor was the maximum when the switching frequency was approximately equal to the resonant frequency. Thus, the step-up ratio Dc2 has two maximum points, as shown in Figure 10. When L1 and L2 increase from 50 nH and C2 = 500 pF, R = 5, f = 12 MHz, and C1 = 980 pF, the resonant frequency f2 in Equation (13) is approximately equal to the switching frequency f. At this time, the step-up ratio Dc2 reaches the first maximum point P1. As L1 and L2 increase further, the resonant frequency f1 is approximately equal to the switching frequency f. The step-up ratio Dc2 reaches the second maximum point P2.

Analysis of Resonant Circuit Parameters
The proposed fourth-order LCLC resonant converter can be considered as two resonant circuit loops connected in series. One resonant loop comprises an inductor L 1 and a capacitor C 1 , and the other loop comprises two inductors L 1 and L 2 , two capacitors C 1 and C 2 , and a serial resistor R. The value of C 2 is determined by the device structure, which is 500 pF. The fourth-order LCLC resonant converter has two resonant frequency points, which can be expressed as follows.
The resonant circuit analysis in our previous works [12,13] revealed that the voltage on the resonant capacitor was the maximum when the switching frequency was approximately equal to the resonant frequency. Thus, the step-up ratio D c2 has two maximum points, as shown in Figure 10. When L 1 and L 2 increase from 50 nH and C 2 = 500 pF, R = 5, f = 12 MHz, and C 1 = 980 pF, the resonant frequency f 2 in Equation (13) is approximately equal to the switching frequency f. At this time, the step-up ratio D c2 reaches the first maximum point P 1 . As L 1 and L 2 increase further, the resonant frequency f 1 is approximately equal to the switching frequency f. The step-up ratio D c2 reaches the second maximum point P 2 .  Figure 11 presents the change in the step-up ratio Dc2. The step-up ratio Dc2 initially increased and then decreased as the value of C1 increased from 800 pF to 1200 pF. The value of C2 was determined by the structure of the ultrasonic fingerprint sensor, which was 500 pF. The step-up ratio Dc2 was the maximum when C1 was 980 pF.  Figure 11 presents the change in the step-up ratio D c2 . The step-up ratio D c2 initially increased and then decreased as the value of C 1 increased from 800 pF to 1200 pF. The value of C 2 was determined by the structure of the ultrasonic fingerprint sensor, which was 500 pF. The step-up ratio D c2 was the maximum when C 1 was 980 pF.  Figure 11 presents the change in the step-up ratio Dc2. The step-up ratio Dc2 initially increased and then decreased as the value of C1 increased from 800 pF to 1200 pF. The value of C2 was determined by the structure of the ultrasonic fingerprint sensor, which was 500 pF. The step-up ratio Dc2 was the maximum when C1 was 980 pF.

Experimental Results
To evaluate the feasibility of the proposed fourth-order LCLC converter, circuit experiments were conducted. A full bridge LCLC resonant converter prototype was designed to drive an ultrasonic fingerprint sensor, as shown in Figure 12. The major experimental parameters are listed in Table 1. The generalized control strategy of the prototype was implemented in FPGA EP4CE75F23C8N (Altera) using Verilog HDL. Figure 11. Effect of C 1 and C 2 on the step-up ratio D c2 .

Experimental Results
To evaluate the feasibility of the proposed fourth-order LCLC converter, circuit experiments were conducted. A full bridge LCLC resonant converter prototype was designed to drive an ultrasonic fingerprint sensor, as shown in Figure 12. The major experimental parameters are listed in Table 1. The generalized control strategy of the prototype was implemented in FPGA EP4CE75F23C8N (Altera) using Verilog HDL.  The MOSFET driving signals G1, G2, G3, and G4 were generated via FPGA (see Figure 13). The blue waveform is the driving waveform of MOSFET Q1 and Q4 and the light green waveform is the driving waveform of MOSFET Q2 and Q3 in Figure 7. When G1 and G4 are high level, G2 and G3 are low level, MOSFET Q1 and Q4 are open, MOSFET Q2 and Q3 are closed, and the converter is in charge mode; when G1 and G4 are low level, G2 and G3 are high level, then MOSFET Q1 and Q4 are closed, Q2 and Q3 are open, and the converter is in discharge mode. At this time, the converter has completed a cycle of charging and discharging. In Figure 13, there are five pulse drives in total, so after five charging and discharging cycles, the MOSFETs are all closed.  The MOSFET driving signals G 1 , G 2 , G 3 , and G 4 were generated via FPGA (see Figure 13). The blue waveform is the driving waveform of MOSFET Q 1 and Q 4 and the light green waveform is the driving waveform of MOSFET Q 2 and Q 3 in Figure 7. When G 1 and G 4 are high level, G 2 and G 3 are low level, MOSFET Q 1 and Q 4 are open, MOSFET Q 2 and Q 3 are closed, and the converter is in charge mode; when G 1 and G 4 are low level, G 2 and G 3 are high level, then MOSFET Q 1 and Q 4 are closed, Q 2 and Q 3 are open, and the converter is in discharge mode. At this time, the converter has completed a cycle of charging and discharging. In Figure 13, there are five pulse drives in total, so after five charging and discharging cycles, the MOSFETs are all closed. The MOSFET driving signals G1, G2, G3, and G4 were generated via FPGA (see Figure 13). The blue waveform is the driving waveform of MOSFET Q1 and Q4 and the light green waveform is the driving waveform of MOSFET Q2 and Q3 in Figure 7. When G1 and G4 are high level, G2 and G3 are low level, MOSFET Q1 and Q4 are open, MOSFET Q2 and Q3 are closed, and the converter is in charge mode; when G1 and G4 are low level, G2 and G3 are high level, then MOSFET Q1 and Q4 are closed, Q2 and Q3 are open, and the converter is in discharge mode. At this time, the converter has completed a cycle of charging and discharging. In Figure 13, there are five pulse drives in total, so after five charging and discharging cycles, the MOSFETs are all closed. The resonant voltages of the proposed converter Vc1 and Vc2 are depicted in Figure  14, where the blue waveform is the voltage of capacitor c1, and the green waveform is the voltage of capacitor c2. In the charging mode, Vc1 and Vc2 gradually increased, while in the discharge mode, Vc1 and Vc2 gradually decreased. After five charging and discharging cycles, Vc1 and Vc2 gradually increased the maximum value. With all MOSFETs Figure 13. Waveforms of the MOSFET driving signals (100 nS/div 5 V/div).
The resonant voltages of the proposed converter V C1 and V C2 are depicted in Figure 14, where the blue waveform is the voltage of capacitor c1, and the green waveform is the voltage of capacitor c2. In the charging mode, V C1 and V C2 gradually increased, while in the discharge mode, V C1 and V C2 gradually decreased. After five charging and discharging cycles, V C1 and V C2 gradually increased the maximum value. With all MOSFETs closed, the resonant capacitor enters the free damping oscillation state. Under the effect of damping, V C1 and V C2 gradually decays from the highest point to 0. The experimental waveforms are identical to the theoretical waveforms, as predicted in Figure 6. The peak-to-peak voltage of V C2 was 376 V, which was less than the theoretical voltage 420 V. This is mainly because the parasitic resistor of MOSFET is not considered in the theoretical calculation. In the experimental circuits, these parasitic resistors can induce a reduction in the resonant voltage. Thus, the resonant voltage tested in the experimental circuits is expected to be lower than the theoretical value. closed, the resonant capacitor enters the free damping oscillation state. Under the effect of damping, Vc1 and Vc2 gradually decays from the highest point to 0. The experimental waveforms are identical to the theoretical waveforms, as predicted in Figure 6. The peakto-peak voltage of Vc2 was 376 V, which was less than the theoretical voltage 420 V. This is mainly because the parasitic resistor of MOSFET is not considered in the theoretical calculation. In the experimental circuits, these parasitic resistors can induce a reduction in the resonant voltage. Thus, the resonant voltage tested in the experimental circuits is expected to be lower than the theoretical value. The resonant voltage of the Class-D resonant converter Vc is shown in Figure 15. The blue waveform is the voltage output by the Class-D converter in the resonant state. The peak-to-peak voltage of Vc2 was 86 V, which was less than the resonant voltage of the proposed converter at 376 V. This proves that the step-up ratio in the proposed fourthorder LCLC resonant converter is far greater than that in the Class-D resonant converter. The resonant voltage of the Class-D resonant converter V c is shown in Figure 15. The blue waveform is the voltage output by the Class-D converter in the resonant state. The peak-to-peak voltage of V C2 was 86 V, which was less than the resonant voltage of the proposed converter at 376 V. This proves that the step-up ratio in the proposed fourth-order LCLC resonant converter is far greater than that in the Class-D resonant converter. VPP = 376 V) and Vc1 (sky blue Vpp = 260 V).
The resonant voltage of the Class-D resonant converter Vc is shown in Figure 15. The blue waveform is the voltage output by the Class-D converter in the resonant state. The peak-to-peak voltage of Vc2 was 86 V, which was less than the resonant voltage of the proposed converter at 376 V. This proves that the step-up ratio in the proposed fourthorder LCLC resonant converter is far greater than that in the Class-D resonant converter. In addition, Figure 16 and Figure 17 display the receiving ultrasonic waveforms of the proposed converter and the Class-D resonant converter. The start pulse is the amplified waveform of the Vc2 voltage in Figure 14 (blue). Under the excitation of this waveform, the piezoelectric material vibrates the ultrasonic wave, so this waveform is also called Tx. The ultrasonic wave bounces back after passing through the medium, and the piezoelectric material receives the echo and converts it into an electrical signal, which is the first RX envelope waveform shown in the figure. After the echo is transmitted back through the medium again, similarly, the electrical signal generated by the piezoelectric materials can be the second echo, that is, the second Rx envelope waveform shown in the In addition, Figures 16 and 17 display the receiving ultrasonic waveforms of the proposed converter and the Class-D resonant converter. The start pulse is the amplified waveform of the Vc2 voltage in Figure 14 (blue). Under the excitation of this waveform, the piezoelectric material vibrates the ultrasonic wave, so this waveform is also called Tx. The ultrasonic wave bounces back after passing through the medium, and the piezoelectric material receives the echo and converts it into an electrical signal, which is the first RX envelope waveform shown in the figure. After the echo is transmitted back through the medium again, similarly, the electrical signal generated by the piezoelectric materials can be the second echo, that is, the second Rx envelope waveform shown in the figure. The larger the echo, the better for the subsequent circuit, which can be seen from the comparison of the echoes generated under the drive of two different converters. figure. The larger the echo, the better for the subsequent circuit, which can be seen from the comparison of the echoes generated under the drive of two different converters. The peak-to-peak voltages of the waveforms in Figure 16 and Figure 17 were 980 mV and 360 mV, respectively. The magnitude of the voltage in the receiving waveforms further proves that the fourth-order LCLC resonant converter is a high step-up ratio converter. Figure 16. Experimental results of the receiving ultrasonic waveforms (400 nS/div 500 mV/div Rx Vpp = 970 mV). Figure 16. Experimental results of the receiving ultrasonic waveforms (400 nS/div 500 mV/div Rx V PP = 970 mV).
The peak-to-peak voltages of the waveforms in Figures 16 and 17 were 980 mV and 360 mV, respectively. The magnitude of the voltage in the receiving waveforms further proves that the fourth-order LCLC resonant converter is a high step-up ratio converter.

Conclusions
A high step-up ratio DC-AC converter based on a fourth-order LCLC circuit was proposed in this paper. The proposed converter had two resonant loops. The theoretical calculations agreed well with the experimental results, indicating that the step-up ratio of the proposed converter is considerably higher than that of the conventional Class-D converter. Under the same input voltage condition, the Class-D converter had a limited output voltage multiple in the resonant state, which was lower than the LCLC converter proposed in this paper. The higher the output voltage, the higher the vibration amplitude of piezoelectric materials, the greater the ultrasonic energy generated, and the thicker the media that can be penetrated.
In this paper, an ultrasonic fingerprint sensor prototype was constructed to verify that the proposed fourth-order LCLC resonant converter can be used in mobile phones to drive the organic piezoelectric thin film-based ultrasonic fingerprint sensors. The proposed converter enables ultrasonic fingerprint sensors to be applied to a wider range of Figure 17. Experimental results of the receiving ultrasonic waveforms of the Class-D resonant converter (400 nS/div 500 mV/div Rx V PP = 360 mV).

Conclusions
A high step-up ratio DC-AC converter based on a fourth-order LCLC circuit was proposed in this paper. The proposed converter had two resonant loops. The theoretical calculations agreed well with the experimental results, indicating that the step-up ratio of the proposed converter is considerably higher than that of the conventional Class-D converter. Under the same input voltage condition, the Class-D converter had a limited output voltage multiple in the resonant state, which was lower than the LCLC converter proposed in this paper. The higher the output voltage, the higher the vibration amplitude of piezoelectric materials, the greater the ultrasonic energy generated, and the thicker the media that can be penetrated.
In this paper, an ultrasonic fingerprint sensor prototype was constructed to verify that the proposed fourth-order LCLC resonant converter can be used in mobile phones to drive the organic piezoelectric thin film-based ultrasonic fingerprint sensors. The proposed converter enables ultrasonic fingerprint sensors to be applied to a wider range of media with higher acoustic impedances. This study also provides theoretical guidance for future applications of large-area ultrasonic sensors in different scenarios.