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

Abstract

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.

1. 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 the ultrasonic transducer, it is usually driven at high-voltage AC power. However, most mobile systems can only supply low-voltage DC power; therefore, a high-frequency DC-AC converter must realize a high step-up ratio to generate a high-voltage AC signal to drive ultrasonic fingerprint sensors.

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.

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.

2. Fourth-Order LCLC Resonant Converter

2.1. Circuit Description

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 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 mm² × 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:

$$\left\{\begin{array}{l}f=1/(2\pi \sqrt{LC})\\ D_c=V_c/V_{in}=1/(2\pi fCR)\end{array}\right.$$

(1)

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 Q₁, Q₂, Q₃, and Q₄. G₁, G₂, G₃, and G₄ 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 L₁ and L₂, one resonant capacitor C₁, and one ultrasonic transducer modeled by a capacitor C₂.

2.2. Resonant Frequency

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.

$$\left\{\begin{array}{l}T<t\\ T=N/f\\ t=2s/v\end{array}\right.$$

(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.

2.3. 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.

The resonant circuit shown in Figure 8 can be described by the following parameters. The output voltage of C₂ is given by

$$\left\{\begin{array}{l}{V}_{L1}+V_{c1}=E\\ V_{L1}+V_{L2}+V_R+V_{c2}=E\end{array}\right.$$

(3)

where $\left\{\begin{array}{l}{V}_{L1}=i_{1}j\omega L_1,V_{c1}=i_1/(j\omega C_1),V_{c2}=i_2/(j\omega C_2)\\ V_{L2}=i_{1}j\omega L_2,V_R=i_2\times R,i=i_1+i_2\end{array}\right.$ and E is the amplitude of the input power. Therefore, the open loop transfer function of V_c2 and E can be represented as

$$\left\{\begin{array}{l}H(j\omega )=V_{c2}(j\omega )/E(j\omega )=1/(a+bj)\\ a=[L_1{C}_1{L}_2{C}_2{\omega }^4-(L_1{C}_1+L_1{C}_2+L_2{C}_2){\omega }^2+1]\\ b=(R{C}_2\omega -L_1{C}_{1}R{C}_2{\omega }^3)\end{array}\right.$$

(4)

The peak-to-peak voltage of V_c2 and the step-up ratio of the full bridge fourth-order LCLC resonant converter are

$$V_{C2}=2E\times \left|H(j\omega )\right|,D_{c2}=2/\left|H(j\omega )\right|=2/\sqrt{a^2+b^2}$$

(5)

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. Q₁ and Q₄ are conducted, and the capacitors C₁ and C₂ start charging. According to the KVL law, the initial values of i₁, i₂, V_c1, and V_c2 are zero, and the state equations of this mode are expressed as follows:

$$\left\{\begin{array}{l}\frac{L_{1}d(C_1\frac{d{V}_{c1}}{dt}+C_2\frac{d{V}_{c2}}{dt})}{dt}+V_{c1}=E\\ \frac{L_{1}d(C_1\frac{d{V}_{c1}}{dt}+C_2\frac{d{V}_{c2}}{dt})}{dt}+\frac{L_2{C}_2{d}^2{V}_{c2}}{d{t}^2}+\frac{R{C}_{2}d{V}_{c2}}{dt}+V_{c2}=E\\ V_{c1}(1,0)=0\\ V_{c2}(1,0)=0\end{array}\right.$$

(6)

(2) Mode 2 [T/2, T]: At T/2, Q₁ and Q₄ are turned off, and Q₂ and Q₃ 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:

$$\left\{\begin{array}{l}\frac{-L_{1}d(C_1\frac{d{V}_{c1}}{dt}+C_2\frac{d{V}_{c2}}{dt})}{dt}=V_{c1}+E\\ \frac{-L_{1}d(C_1\frac{d{V}_{c1}}{dt}+C_2\frac{d{V}_{c2}}{dt})}{dt}-\frac{L_2{C}_2{d}^2{V}_{c2}}{d{t}^2}-\frac{C_{2}Rd{V}_{c2}}{dt}=V_{c2}\\ V_{c1}(2,0)=V_{c1}(1,T/2)\\ V_{c2}(2,0)=V_{c2}(1,T/2)\end{array}\right.$$

(7)

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:

$$\begin{array}{l}{s}^4+\frac{R}{L_2}{s}^3+\frac{(L_1{C}_1+L_1{C}_2+L_2{C}_2)}{L_1{C}_1{L}_2{C}_2}{s}^2\\ +\frac{R}{L_1{C}_1{L}_2}s+\frac{1}{L_1{C}_1{L}_2{C}_2}=0\end{array}$$

(8)

The characteristic roots of Equation (8) are a₁ ± b₁i and a₂ ± b₂i. 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

$$\begin{array}{l}{V}_{c2}(n,t)=e^{a_{1}t}[A\times \sin (a_{1}t)+B\times \cos (b_{1}t)]\\ +e^{a_{2}t}[C\times \sin (a_{2}t)+D\times \cos (b_{2}t)]+\mathrm{E}\end{array}$$

(9)

When n is an even number, V_c2 is

$$\begin{array}{l}{V}_{c2}(n,t)=e^{a_{1}t}[A\times \sin (a_{1}t)+B\times \cos (b_{1}t)]\\ +e^{a_{2}t}[C\times \sin (a_{2}t)+D\times \cos (b_{2}t)]-\mathrm{E}\end{array}$$

(10)

The initial value of each Mode is

$$\begin{array}{l}\left\{\begin{array}{l}{i}_{L1}(n,0)=i_{L1}(n-1,0.5T)\\ i_{L2}(n,0)=i_{L2}(n-1,0.5T)\\ V_{C1}(n,0)=V_{C1}(n-1,0.5T)\\ V_{C2}(n,0)=V_{C2}(n-1,0.5T)\end{array}\right.,(n>1)\\ \left\{\begin{array}{l}{i}_{L1}(n,0)=0,i_{L2}(n,0)=0\\ V_{C1}(n,0)=0,V_{C2}(n,0)=0\end{array}\right.,(n=1)\end{array}$$

(11)

where A, B, C, and D can be obtained by solving the initial (11). i₁, i₂, V_c1 can be obtained by solving Equations (6), (7), (9) and (10), which are described as follows:

$$\left\{\begin{array}{l}{i}_2(n,t)=C_2{y}^{\prime };y=V_{c2}(n,t)\\ V_{c1}(n,t)=L_2{C}_2{y}^{″}+R{C}_2{y}^{\prime }+y\\ i_1(n,t)=C_1{L}_2{C}_2{y}^{\prime ″}+R{C}_1{C}_2{y}^{″}+C_1{y}^{\prime }\\ i(n,t)=C_1{L}_2{C}_2{y}^{\prime ″}+R{C}_1{C}_2{y}^{″}+(C_1{+C}_2)y^{\prime }\end{array}\right.$$

(12)

3. Analysis of Fourth-Order LCLC Resonant Converter

3.1. Analysis of Step-Up Ratio

When the switching frequency f = 12 MHz and load capacitor C₂ = 500 pF, the step-up ratio of the Class-D converter can be calculated by substituting Equation (13) into Equation (1).

$$D_C=1/(2\pi fCR)=5.3052$$

Similarly, when the inductors in the fourth-order LCLC converter L₁ = 100 nH and L₂ = 110 nH, the step-up ratio can be calculated by substituting Equation (13) into Equation (5).

$$D_{c2}=2/\left|H(j\omega )\right|\approx 22>D_C=5.3052$$

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.

3.2. 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.

$$f_1\approx 1/(2\pi \sqrt{L_1{C}_1}),f_2\approx 1/[2\pi \sqrt{(L_1+L_2)C_2}]$$

(13)

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 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 D_c2 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 D_c2 reaches the second maximum point P₂.

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 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 D_c2 was the maximum when C₁ was 980 pF.

4. 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. Parameters of the prototype.

Parameters	Symbols	Value
Input voltage	Vin	20 V
Equivalent effective inductance 1	L1	100 nH
Equivalent effective inductance 2	L2	110 nH
Resonant capacitors 1	C1	980 pF
Resonant capacitors 2	C2	500 pF
ACF contact resistance	R	5 Ω
Switching frequency	f	12 MHz
Thickness of glass cover	s	2 mm
MOSFET switches	Q1, Q1, Q3, Q4	WSP4620

. 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 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.

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.

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 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.

5. 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.