A Novel and Cost-Effective Drive Circuit for Supplying a Piezoelectric Ceramic Actuator with Power-Factor-Correction and Soft-Switching Features

This paper proposes a novel and cost-effective drive circuit for supplying a piezoelectric ceramic actuator, which combines a dual boost AC-DC converter with a coupled inductor and a half-bridge resonant DC-AC inverter into a single-stage architecture with power-factor-correction (PFC) and soft-switching characteristics. The coupled inductor of the dual boost AC-DC converter sub-circuit is designed to work in discontinuous conduction mode (DCM), so the PFC function can be realized in the proposed drive circuit. The resonant tank of the half-bridge resonant inverter sub-circuit is designed as an inductive load, so that the two power switches in the presented drive circuit can achieve zero-voltage switching (ZVS) characteristics. A 50 W-rated prototype drive circuit providing a piezoelectric ceramic actuator has been successfully implemented in this paper. From the experimental results at 110 V input utility-line voltage, the drive circuit has the characteristics of high power factor and low input current total-harmonic-distortion factor, and two power switches have ZVS characteristics. Therefore, satisfactory outcomes from measured results prove the function of the proposed drive circuit.


Introduction
Piezoelectric ceramic actuators generate vibrations with a frequency above 20 kHz through the piezoelectric effect and have the characteristics of high accuracy, fast response, low power consumption, miniaturization, and high-density configuration. Piezoelectric ceramic actuators are widely used in low-power ultrasonic energy conversion circuits (such as ultrasonic beauty equipment, dental scalers, and atomizers) and high-power ultrasonic energy conversion circuits (such as ultrasonic cleaning machines, ultrasonic processing machines, and ultrasonic welding machines) [1][2][3][4][5][6][7]. Figure 1 shows a photo of a piezoelectric ceramic actuator. The equivalent circuit model of the piezoelectric ceramic actuator is shown in Figure 2, where the voltage source v OUT is the voltage output from the driving circuit to the piezoelectric ceramic actuator; the capacitance C p is the static capacitance of the piezoelectric ceramic actuator; the resistance R m is the mechanical equivalent resistance; L m is the mechanical equivalent inductance, and C m is the mechanical equivalent capacitance [8][9][10][11]. Figure 3 shows the conventional two-stage drive circuit for supplying a piezoelectric ceramic actuator applied with a DC input voltage source V IN-DC [12], which consists of a front-stage DC-DC boost converter (including an inductor L b , a power switch S b , a diode D b along with a DC-linked capacitor C b ), and a rear-stage DC-AC full-bridge resonant converter (including four power switches S 1 , S 2 , S 3 , and S 4 and a resonant inductor L r ) that provides rated power to the piezoelectric ceramic actuator.  Figure 3 shows the conventional two-stage drive circuit for supplying a piezoelectric ceramic actuator applied with a DC input voltage source VIN-DC [12], which consists of a front-stage DC-DC boost converter (including an inductor Lb, a power switch Sb, a diode Db along with a DC-linked capacitor Cb), and a rear-stage DC-AC full-bridge resonant converter (including four power switches S1, S2, S3, and S4 and a resonant inductor Lr) that provides rated power to the piezoelectric ceramic actuator. . The conventional two-stage drive circuit for supplying a piezoelectric ceramic actuator applied with a DC input voltage source [12].  Figure 3 shows the conventional two-stage drive circuit for supplying a piezoelectric ceramic actuator applied with a DC input voltage source VIN-DC [12], which consists of a front-stage DC-DC boost converter (including an inductor Lb, a power switch Sb, a diode Db along with a DC-linked capacitor Cb), and a rear-stage DC-AC full-bridge resonant converter (including four power switches S1, S2, S3, and S4 and a resonant inductor Lr) that provides rated power to the piezoelectric ceramic actuator. . The conventional two-stage drive circuit for supplying a piezoelectric ceramic actuator applied with a DC input voltage source [12].   Figure 3 shows the conventional two-stage drive circuit for supplying a piezoelectric ceramic actuator applied with a DC input voltage source VIN-DC [12], which consists of a front-stage DC-DC boost converter (including an inductor Lb, a power switch Sb, a diode Db along with a DC-linked capacitor Cb), and a rear-stage DC-AC full-bridge resonant converter (including four power switches S1, S2, S3, and S4 and a resonant inductor Lr) that provides rated power to the piezoelectric ceramic actuator.

Lr Boost Converter
Full-Bridge Resonant Inverter Lb Db Cb VIN-DC Sb S1 S2 S3 S4 Piezoelectric Ceramic Actuator Figure 3. The conventional two-stage drive circuit for supplying a piezoelectric ceramic actuator applied with a DC input voltage source [12]. Figure 3. The conventional two-stage drive circuit for supplying a piezoelectric ceramic actuator applied with a DC input voltage source [12]. Figure 4 shows the conventional two-stage drive circuit for supplying a piezoelectric ceramic actuator applied with a AC input voltage source v AC and without power-factorcorrection (PFC) [13,14], which consists of a front-stage AC-DC full-bridge rectifier (including four diodes D R1 , D R2 , D R3 , and D R4 along with a DC-linked capacitor C DC ) and a rear-stage DC-AC full-bridge resonant converter (including four power switches S 1 , S 2 , S 3 , Micromachines 2021, 12, 1229 3 of 17 and S 4 ; four diodes D 1 , D 2 , D 3 , and D 4 ; and a resonant inductor L r ) that provides rated power to the piezoelectric ceramic actuator.
Micromachines 2021, 12,1229 3 of 17 Figure 4 shows the conventional two-stage drive circuit for supplying a piezoelectric ceramic actuator applied with a AC input voltage source vAC and without power-factorcorrection (PFC) [13,14], which consists of a front-stage AC-DC full-bridge rectifier (including four diodes DR1, DR2, DR3, and DR4 along with a DC-linked capacitor CDC) and a rear-stage DC-AC full-bridge resonant converter (including four power switches S1, S2, S3, and S4; four diodes D1, D2, D3, and D4; and a resonant inductor Lr) that provides rated power to the piezoelectric ceramic actuator.  . The conventional two-stage drive circuit for supplying a piezoelectric ceramic actuator applied with an AC input voltage source without PFC [13,14].
The traditional driving circuit that supplies power to the piezoelectric ceramic actuator requires more power switches, and the switching loss and conduction loss generated by the power switches are relatively large, which will affect the overall efficiency of the circuit. In response to these challenges, this paper presents a novel and cost-effective drive circuit for providing a piezoelectric ceramic actuator with PFC and soft-switching functions, which integrates a dual boost converter with a coupled inductor and a half-bridge resonant inverter. Descriptions of the operational modes and design equations along with experimental results of the proposed drive circuit are demonstrated in what follows. Figure 5 shows the proposed drive circuit with PFC, which integrates a dual boost converter with a coupled inductor and a half-bridge resonant inverter, for supplying a piezoelectric ceramic actuator. The dual boost converter with a coupled-inductor sub-circuit, which is followed by an input AC voltage vAC and a filter (Lf and Cf), consists of two diodes (D1 and D2), a coupled-inductor (LB1 and LB2), two power switches (S1 and S2), and two DC-linked capacitors (CDC1 and CDC2). The half-bridge resonant inverter sub-circuit includes two switches (S1 and S2), two DC-linked capacitors (CDC1 and CDC2), and a resonant inductor (Lr) along with the piezoelectric ceramic actuator. In addition, the coupledinductor (LB1 and LB2) is designed to be operated in discontinuous-conduction mode (DCM) in order to accomplish input-current shaping. Table 1 shows comparisons between the conventional two-stage drive circuits in References [12][13][14] and the proposed single-stage one for the piezoelectric ceramic actuator. It can be seen that the proposed drive circuit has the characteristics of power-factor-correction and soft switching and requires fewer power switches than in References [12][13][14], so it can be a cost-effective alternative version for supplying a piezoelectric ceramic actuator. . The conventional two-stage drive circuit for supplying a piezoelectric ceramic actuator applied with an AC input voltage source without PFC [13,14].

Introduction of Proposed Drive Circuit
The traditional driving circuit that supplies power to the piezoelectric ceramic actuator requires more power switches, and the switching loss and conduction loss generated by the power switches are relatively large, which will affect the overall efficiency of the circuit. In response to these challenges, this paper presents a novel and cost-effective drive circuit for providing a piezoelectric ceramic actuator with PFC and soft-switching functions, which integrates a dual boost converter with a coupled inductor and a halfbridge resonant inverter. Descriptions of the operational modes and design equations along with experimental results of the proposed drive circuit are demonstrated in what follows. Figure 5 shows the proposed drive circuit with PFC, which integrates a dual boost converter with a coupled inductor and a half-bridge resonant inverter, for supplying a piezoelectric ceramic actuator. The dual boost converter with a coupled-inductor subcircuit, which is followed by an input AC voltage v AC and a filter (L f and C f ), consists of two diodes (D 1 and D 2 ), a coupled-inductor (L B1 and L B2 ), two power switches (S 1 and S 2 ), and two DC-linked capacitors (C DC1 and C DC2 ). The half-bridge resonant inverter sub-circuit includes two switches (S 1 and S 2 ), two DC-linked capacitors (C DC1 and C DC2 ), and a resonant inductor (L r ) along with the piezoelectric ceramic actuator. In addition, the coupled-inductor (L B1 and L B2 ) is designed to be operated in discontinuous-conduction mode (DCM) in order to accomplish input-current shaping.

Analysis of Operational Modes
When analyzing the operational modes of the piezoelectric ceramic actuator drive circuit, the assumptions made for some circuit components are as follows: • The control signals of the power switches S1 and S2 are in a complementary state, and the essential diodes and parasitic capacitances on the power switches are considered.
• The two coupled inductors LB1 and LB2 in the drive circuit are designed to operate in discontinuous-conduction Mode (DCM).
• The equivalent resistance of diodes D1 and D2 and the forward bias voltage drop are ignored in the analysis.
• The remaining circuit components are assumed to be ideal. The operating modes and theoretical waveforms of the proposed piezoelectric ceramic driver drive circuit during the positive half-cycle of the utility-line voltage are shown in Figures 6-12, respectively. The circuit analysis and operating modes of the drive circuit during the positive half-cycle of the utility-line voltage are described and discussed in detail below.
2.2.1. Operational Mode 1 (t0 ≤ t < t1) Figure 6 shows the operational Mode 1 of the new piezoelectric ceramic actuator drive circuit with PFC. In the previous operation mode, the essential diode of the power switch S1 is forward-biased conduction. When the resonant inductor current iLr drops to zero, the power switch S1 is driven on and has ZVS. The voltage source vAC provides energy to the  Table 1 shows comparisons between the conventional two-stage drive circuits in References [12][13][14] and the proposed single-stage one for the piezoelectric ceramic actuator. It can be seen that the proposed drive circuit has the characteristics of power-factorcorrection and soft switching and requires fewer power switches than in References [12][13][14], so it can be a cost-effective alternative version for supplying a piezoelectric ceramic actuator.

Analysis of Operational Modes
When analyzing the operational modes of the piezoelectric ceramic actuator drive circuit, the assumptions made for some circuit components are as follows:

•
The control signals of the power switches S 1 and S 2 are in a complementary state, and the essential diodes and parasitic capacitances on the power switches are considered.

•
The two coupled inductors L B1 and L B2 in the drive circuit are designed to operate in discontinuous-conduction Mode (DCM).

•
The equivalent resistance of diodes D 1 and D 2 and the forward bias voltage drop are ignored in the analysis.

•
The remaining circuit components are assumed to be ideal.
The operating modes and theoretical waveforms of the proposed piezoelectric ceramic driver drive circuit during the positive half-cycle of the utility-line voltage are shown in Figures 6-12, respectively. The circuit analysis and operating modes of the drive circuit during the positive half-cycle of the utility-line voltage are described and discussed in detail below. coupled inductor LB1 through the inductance Lf and the capacitor Cf of the filter circuit, the diode D1 and the power switch S1, and the coupled inductor current iLB1 presents a linear increase. The DC-linked capacitor CDC1 charges the resonant inductor Lr through the power switch S1 and provides energy to the piezoelectric ceramic actuator. When the power switch S1 is turned off, the inductor current iLB1 rises to the maximum value. At time t1, Mode 1 ends. 2.2.2. Operational Mode 2 (t1 ≤ t < t2) Figure 7 shows the operational Mode 2 of the new piezoelectric ceramic actuator drive circuit with PFC. The voltage source vAC provides energy to the parasitic capacitance of the power switch S1 through the inductance Lf and the capacitance Cf of the filter circuit, the diode D1, and the coupling inductor LB1, and the coupling inductor current iLB1 begins to decrease linearly. The DC-linked capacitor CDC1 and the resonant inductor Lr charge the parasitic capacitance of the power switch S1 and provide energy to the piezoelectric ceramic actuator. The parasitic capacitance of the power switch S2 and the resonant inductance Lr provide energy to the load and provide energy for the DC-linked capacitor CDC2. When the parasitic capacitance of the power switch S2 releases energy, the voltage vDS2 of the power switch S2 drops to zero, and the essential diode of the power switch S2 is forwardly biased and turned on. At time t2, Mode 2 ends.   Figure 7 shows the operational Mode 2 of the new piezoelectric ceramic actuator drive circuit with PFC. The voltage source vAC provides energy to the parasitic capacitance of the power switch S1 through the inductance Lf and the capacitance Cf of the filter circuit, the diode D1, and the coupling inductor LB1, and the coupling inductor current iLB1 begins to decrease linearly. The DC-linked capacitor CDC1 and the resonant inductor Lr charge the parasitic capacitance of the power switch S1 and provide energy to the piezoelectric ceramic actuator. The parasitic capacitance of the power switch S2 and the resonant inductance Lr provide energy to the load and provide energy for the DC-linked capacitor CDC2. When the parasitic capacitance of the power switch S2 releases energy, the voltage vDS2 of the power switch S2 drops to zero, and the essential diode of the power switch S2 is forwardly biased and turned on. At time t2, Mode 2 ends.  2.2.4. Operational Mode 4 (t3 ≤ t < t4) Figure 9 shows the operational Mode 4 of the new piezoelectric ceramic actuator drive circuit with PFC. When the coupled inductor current iLB1 drops to zero, the power switch S2 is driven to turn on and has a ZVS characteristic. The DC-linked capacitor CDC2 charges the resonant inductor Lr through the power switch S2 and provides energy to the piezoelectric ceramic actuator. When the power switch S2 is turned off, Mode 4 ends.   Figure 9 shows the operational Mode 4 of the new piezoelectric ceramic actuator drive circuit with PFC. When the coupled inductor current iLB1 drops to zero, the power switch S2 is driven to turn on and has a ZVS characteristic. The DC-linked capacitor CDC2 charges the resonant inductor Lr through the power switch S2 and provides energy to the piezoelectric ceramic actuator. When the power switch S2 is turned off, Mode 4 ends. 2.2.5. Operational Mode 5 (t4 ≤ t < t5) Figure 10 shows the operational Mode 5 of the new piezoelectric ceramic actuator drive circuit with PFC. The resonant inductor Lr and the parasitic capacitance of the power switch S1 charge the DC-linked capacitor CDC1 and provide energy to the piezoelectric ceramic actuator. At the same time, the resonant inductor Lr and the DC-linked capacitor CDC2 charge the parasitic capacitance of the power switch S2 and provide energy to the piezoelectric ceramic actuator. When the parasitic capacitance energy of the power switch S1 is released and the voltage vDS1 of the power switch S1 drops to zero, the essential diode of the power switch S1 is forwardly biased and turned on. At time t5, Mode 5 completes. 2.2.6. Operational Mode 6 (t5 ≤ t < t6) Figure 11 shows the operational Mode 6 of the new piezoelectric ceramic actuator drive circuit with PFC. In the previous operational mode, the energy of the parasitic capacitance of the power switch S1 is released, the voltage vDS1 of the power switch S1 drops to zero, and the essential diode of the power switch S1 is turned on in a forward bias. The voltage source vAC provides energy to the coupled inductor LB1 through the inductance Lf and the capacitor Cf of the filter circuit and the diode D1, and the coupled inductor current iLB1 rises linearly from zero. In addition, through the essential diode of the power switch S1, the resonant inductor Lr and the voltage source vAC provide energy to the DC-linked capacitor CDC1 and the piezoelectric ceramic actuator. When the resonant inductor current iLr drops to zero and the power switch S1 is driven and turned on, Mode 6 ends and the circuit operation returns to Mode 1.  2.2.6. Operational Mode 6 (t5 ≤ t < t6) Figure 11 shows the operational Mode 6 of the new piezoelectric ceramic actuator drive circuit with PFC. In the previous operational mode, the energy of the parasitic capacitance of the power switch S1 is released, the voltage vDS1 of the power switch S1 drops to zero, and the essential diode of the power switch S1 is turned on in a forward bias. The voltage source vAC provides energy to the coupled inductor LB1 through the inductance Lf and the capacitor Cf of the filter circuit and the diode D1, and the coupled inductor current iLB1 rises linearly from zero. In addition, through the essential diode of the power switch S1, the resonant inductor Lr and the voltage source vAC provide energy to the DC-linked capacitor CDC1 and the piezoelectric ceramic actuator. When the resonant inductor current iLr drops to zero and the power switch S1 is driven and turned on, Mode 6 ends and the circuit operation returns to Mode 1.  In addition, Table 2 shows states of the main power devices in each operational mode during the positive half-cycle of the utility-line voltage.  2.2.1. Operational Mode 1 (t 0 ≤ t < t 1 ) Figure 6 shows the operational Mode 1 of the new piezoelectric ceramic actuator drive circuit with PFC. In the previous operation mode, the essential diode of the power switch S 1 is forward-biased conduction. When the resonant inductor current i Lr drops to zero, the power switch S 1 is driven on and has ZVS. The voltage source v AC provides energy to the coupled inductor L B1 through the inductance L f and the capacitor C f of the filter circuit, the diode D 1 and the power switch S 1 , and the coupled inductor current i LB1 presents a linear increase. The DC-linked capacitor C DC1 charges the resonant inductor L r through the power switch S 1 and provides energy to the piezoelectric ceramic actuator. When the power switch S 1 is turned off, the inductor current i LB1 rises to the maximum value. At time t 1 , Mode 1 ends. Figure 7 shows the operational Mode 2 of the new piezoelectric ceramic actuator drive circuit with PFC. The voltage source v AC provides energy to the parasitic capacitance of the power switch S 1 through the inductance L f and the capacitance C f of the filter circuit, the diode D 1 , and the coupling inductor L B1 , and the coupling inductor current i LB1 begins to decrease linearly. The DC-linked capacitor C DC1 and the resonant inductor L r charge the parasitic capacitance of the power switch S 1 and provide energy to the piezoelectric ceramic actuator. The parasitic capacitance of the power switch S 2 and the resonant inductance L r provide energy to the load and provide energy for the DC-linked capacitor C DC2 . When the parasitic capacitance of the power switch S 2 releases energy, the voltage v DS2 of the power switch S 2 drops to zero, and the essential diode of the power switch S 2 is forwardly biased and turned on. At time t 2 , Mode 2 ends. Figure 8 shows the operational Mode 3 of the new piezoelectric ceramic actuator drive circuit with PFC. The voltage source v AC and the coupled inductor L B1 charge the DClinked capacitors C DC1 and C DC2 through the inductance L f and capacitor C f of the filter circuit, the diode D 1 , and the essential diode of the power switch S 2 . At this time, the coupled inductor current i LB1 shows a linear decrease. The resonant inductor L r charges the DC-linked capacitor C DC2 through the essential diode of the power switch S 2 and provides energy to the piezoelectric ceramic actuator. When the coupled inductor current i LB1 and the resonant inductor current i Lr drop to zero, Mode 3 ends. Figure 9 shows the operational Mode 4 of the new piezoelectric ceramic actuator drive circuit with PFC. When the coupled inductor current i LB1 drops to zero, the power switch S 2 is driven to turn on and has a ZVS characteristic. The DC-linked capacitor C DC2 charges the resonant inductor L r through the power switch S 2 and provides energy to the piezoelectric ceramic actuator. When the power switch S 2 is turned off, Mode 4 ends. Figure 10 shows the operational Mode 5 of the new piezoelectric ceramic actuator drive circuit with PFC. The resonant inductor L r and the parasitic capacitance of the power switch S 1 charge the DC-linked capacitor C DC1 and provide energy to the piezoelectric ceramic actuator. At the same time, the resonant inductor L r and the DC-linked capacitor C DC2 charge the parasitic capacitance of the power switch S 2 and provide energy to the piezoelectric ceramic actuator. When the parasitic capacitance energy of the power switch S 1 is released and the voltage v DS1 of the power switch S 1 drops to zero, the essential diode of the power switch S 1 is forwardly biased and turned on. At time t 5 , Mode 5 completes.

Operational Mode 5 (t 4 ≤ t < t 5 )
2.2.6. Operational Mode 6 (t 5 ≤ t < t 6 ) Figure 11 shows the operational Mode 6 of the new piezoelectric ceramic actuator drive circuit with PFC. In the previous operational mode, the energy of the parasitic capacitance of the power switch S 1 is released, the voltage v DS1 of the power switch S 1 drops to zero, and the essential diode of the power switch S 1 is turned on in a forward bias. The voltage source v AC provides energy to the coupled inductor L B1 through the inductance L f and the capacitor C f of the filter circuit and the diode D 1 , and the coupled inductor current i LB1 rises linearly from zero. In addition, through the essential diode of the power switch S 1 , the resonant inductor L r and the voltage source v AC provide energy to the DC-linked capacitor C DC1 and the piezoelectric ceramic actuator. When the resonant inductor current i Lr drops to zero and the power switch S 1 is driven and turned on, Mode 6 ends and the circuit operation returns to Mode 1.
In addition, Table 2 shows states of the main power devices in each operational mode during the positive half-cycle of the utility-line voltage. The design equation of the coupled inductors L B1 and L B2 can be represented by [15]: where η is the estimated efficiency of the proposed drive circuit; v AC-rms is the root-meansquare (rms) value of the input utility-line voltage v AC ; D and f S are the duty ratio and switching frequency of the power switches, respectively; P O is the output power. From the Formula (1), it can be drawn that Figure 13 shows the relationship between the coupled inductors L B1 and L B2 and the duty cycle D at different switching frequencies f S .

Design Equation of the Coupled Inductors LB1 and LB2
The design equation of the coupled inductors LB1 and LB2 can be represented by [15]: where η is the estimated efficiency of the proposed drive circuit; vAC-rms is the root-meansquare (rms) value of the input utility-line voltage vAC; D and fS are the duty ratio and switching frequency of the power switches, respectively; PO is the output power. From the formula (1), it can be drawn that Figure 13 shows the relationship between the coupled inductors LB1 and LB2 and the duty cycle D at different switching frequencies fS.
In addition, the coupled inductors L B1 and L B2 in the prototype drive circuit are 500 µH.

Design Equation of the Resonant
Inductor L r Figure 14 shows the equivalent circuit diagram of the resonant inductor combined with the piezoelectric ceramic actuator circuit model; v inv and i inv respectively represent the input voltage and current of the equivalent circuit; Z PCA represents the equivalent circuit model of the piezoelectric ceramic actuator; Z in represents the input impedance of the equivalent circuit. The output power P O of the piezoelectric ceramic actuator is provided by the fundamental component of the input current i inv of the resonant tank circuit, and the switching frequency f S of the power switch is designed to be equal to the resonant frequency f r of the piezoelectric ceramic actuator. In addition, at the resonance frequency of the piezoelectric ceramic actuator, the equivalent series impedance in the right branch of the Z PCT resonance tank circuit is reduced to only the resistance R m . The rms value I inv1-rms of the fundamental component of the current i inv can be expressed as [13] The input impedance Z in of the equivalent circuit is expressed as where R 1 and X 1 are the equivalent resistance and reactance of the piezoelectric ceramic actuator impedance Z PCA , and they can be respectively expressed as [13] After dividing the maximum value of the input voltage V inv1-max by the maximum value of the input current √ 2I inv1-rms of the equivalent circuit, the amplitue of the input impedance Z in can be expressed as where V inv1-max is the maximum level of the fundamental component V inv1 of the input voltage v inv of the resonant tank circuit; V DC is the voltage level of the DC-linked capacitors C DC1 and C DC2 . By combining (3) with (6), the design formula of the resonant inductor L r can be expressed as [13] With a R m of 25 Ω, a C p of 4000 pF, a P O of 50 W, and a resonant frequency f r of 40 kHz, the parameter I inv1-rms is calculated as The parameters R 1 and X 1 are respectively calculated as With a V DC of 700 V and a I rnv1-rms of 1.414 A, the parameter |Z in | is calculated as Therefore, the parameter L r is calculated as In addition, the resonance inductor L r in the prototype drive circuit is 3.95 mH.
In addition, the resonance inductor Lr in the prototype drive circuit is 3.95 mH.

Design of Input Low-Pass Filter
A low-pass filter is usually added to the AC input power terminal, which is composed of an inductor Lf and a capacitor Cf. The cut-off frequency fcut-off of the input lowpass filter is represented by In order to filter high-frequency switching noise, the design consideration of the cutoff frequency fcut-off of the input low-pass filter is determined as one-tenth of the switching frequency fS. Rearranging (8), the design equation of the inductor Lf is given by With a cut-off frequency fcut-off of 4 kHz and selecting a capacitor Cf of 470 nF, the inductor Lf is determined by Figure 14. The equivalent circuit diagram of the resonant tank circuit combined with the piezoelectric ceramic actuator circuit model.

Design of Input Low-Pass Filter
A low-pass filter is usually added to the AC input power terminal, which is composed of an inductor L f and a capacitor C f . The cut-off frequency f cut-off of the input low-pass filter is represented by In order to filter high-frequency switching noise, the design consideration of the cutoff frequency f cut-off of the input low-pass filter is determined as one-tenth of the switching frequency f S . Rearranging (8), the design equation of the inductor L f is given by With a cut-off frequency f cut-off of 4 kHz and selecting a capacitor C f of 470 nF, the inductor L f is determined by

Experimental Results of the Proposed Drive Circuit
In this paper, a prototype of the proposed drive circuit for supplying a 50 W-rated piezoelectric ceramic actuator has already been implemented and testified. A photograph of the proposed prototype drive circuit for supplying a piezoelectric ceramic actuator is shown in Figure 15, and the key circuit components have been indicated in the photograph. The parameters of the utilized piezoelectric ceramic actuator are shown in Table 3. In addition, the components utilized in the prototype drive circuit for the piezoelectric ceramic actuator are shown in Table 4.

Experimental Results of the Proposed Drive Circuit
In this paper, a prototype of the proposed drive circuit for supplying a 50W-rated piezoelectric ceramic actuator has already been implemented and testified. A photograph of the proposed prototype drive circuit for supplying a piezoelectric ceramic actuator is shown in Figure 15, and the key circuit components have been indicated in the photograph. The parameters of the utilized piezoelectric ceramic actuator are shown in Table 3. In addition, the components utilized in the prototype drive circuit for the piezoelectric ceramic actuator are shown in Table 4.

Piezoelectric Ceramic Actuator
Lf Cf LB1&LB2 D1 D2 S1 S2 CDC1 CDC2 Lr Figure 15. A photograph of the proposed prototype drive circuit for supplying a piezoelectric ceramic actuator.     Figure 16a,b presents the simulated and measured inductor current i LB1 , and it can be seen that the current i LB1 is operated in DCM. Figure 17a,b shows the simulated and measured switch voltage v DS2 and resonant inductor current i Lr . It can be seen that the inductor current i Lr lags with respect to voltage v DS2 so that the series resonant circuit is similar to an inductive load. Figure 18a,b presents the simulated and measured switch voltage v DS1 and switch current i DS1 ; thus, ZVS occurred on the power switch for lowering the switching losses. Figure 19a,b depicts the simulated and measured output voltage v O and output current i O . It can be seen from the waveform that the output voltage v O lags the output current i O , so the piezoelectric ceramic actuator has capacitive characteristics.
Micromachines 2021, 12, 1229 13 of 17 Figure 16a,b presents the simulated and measured inductor current iLB1, and it can be seen that the current iLB1 is operated in DCM. Figure 17a,b shows the simulated and measured switch voltage vDS2 and resonant inductor current iLr. It can be seen that the inductor current iLr lags with respect to voltage vDS2 so that the series resonant circuit is similar to an inductive load. Figure 18a,b presents the simulated and measured switch voltage vDS1 and switch current iDS1; thus, ZVS occurred on the power switch for lowering the switching losses. Figure 19a,b depicts the simulated and measured output voltage vO and output current iO. It can be seen from the waveform that the output voltage vO lags the output current iO, so the piezoelectric ceramic actuator has capacitive characteristics.  Figure 16a,b presents the simulated and measured inductor current iLB1, and it can be seen that the current iLB1 is operated in DCM. Figure 17a,b shows the simulated and measured switch voltage vDS2 and resonant inductor current iLr. It can be seen that the inductor current iLr lags with respect to voltage vDS2 so that the series resonant circuit is similar to an inductive load. Figure 18a,b presents the simulated and measured switch voltage vDS1 and switch current iDS1; thus, ZVS occurred on the power switch for lowering the switching losses. Figure 19a,b depicts the simulated and measured output voltage vO and output current iO. It can be seen from the waveform that the output voltage vO lags the output current iO, so the piezoelectric ceramic actuator has capacitive characteristics.   The simulated and measured waveforms of input utility-line voltage vAC and current iAC are respectively shown in Figure 20a,b, and it can be seen that PFC is achieved in the proposed drive circuit. Figure 21 shows the use of a power analyzer (Tektronix PA 4000) to measure the harmonic components of the AC input current and compare it with the IEC 61000-3-2 class C standard. From the figure, it is known that all current harmonics meet the requirements. Additionally, the measured power factor and the input utility-line current total-harmonic distortion (THD) of the proposed drive circuit are 0.8683 and 3.4927%, respectively. The simulated and measured waveforms of input utility-line voltage v AC and current i AC are respectively shown in Figure 20a,b, and it can be seen that PFC is achieved in the proposed drive circuit. Figure 21 shows the use of a power analyzer (Tektronix PA 4000) to measure the harmonic components of the AC input current and compare it with the IEC 61000-3-2 class C standard. From the figure, it is known that all current harmonics meet the requirements. Additionally, the measured power factor and the input utility-line current total-harmonic distortion (THD) of the proposed drive circuit are 0.8683 and 3.4927%, respectively.
iAC are respectively shown in Figure 20a,b, and it can be seen that PFC is achieved in the proposed drive circuit. Figure 21 shows the use of a power analyzer (Tektronix PA 4000) to measure the harmonic components of the AC input current and compare it with the IEC 61000-3-2 class C standard. From the figure, it is known that all current harmonics meet the requirements. Additionally, the measured power factor and the input utility-line current total-harmonic distortion (THD) of the proposed drive circuit are 0.8683 and 3.4927%, respectively.

Conclusions
This paper proposes a novel and cost-effective drive circuit, which combines a dual boost converter with a coupled inductor and a half-bridge resonant inverter, with PFC and soft-switching features for providing a piezoelectric ceramic actuator. A 50W-rated prototype drive circuit has been implemented and tested with an input utility-line voltage of 110 V. From the experimental results at a 110V input utility-line voltage, the driving circuit developed in this thesis has as characteristics a high power factor (>0.86) and a low input current total-harmonic-distortion factor (<4%), and two power switches possess the ZVS feature.

Conclusions
This paper proposes a novel and cost-effective drive circuit, which combines a dual boost converter with a coupled inductor and a half-bridge resonant inverter, with PFC and soft-switching features for providing a piezoelectric ceramic actuator. A 50W-rated prototype drive circuit has been implemented and tested with an input utility-line voltage of 110 V. From the experimental results at a 110V input utility-line voltage, the driving circuit developed in this thesis has as characteristics a high power factor (>0.86) and a low input current total-harmonic-distortion factor (<4%), and two power switches possess the

Conclusions
This paper proposes a novel and cost-effective drive circuit, which combines a dual boost converter with a coupled inductor and a half-bridge resonant inverter, with PFC and soft-switching features for providing a piezoelectric ceramic actuator. A 50 W-rated prototype drive circuit has been implemented and tested with an input utility-line voltage of 110 V. From the experimental results at a 110 V input utility-line voltage, the driving circuit developed in this thesis has as characteristics a high power factor (>0.86) and a low input current total-harmonic-distortion factor (<4%), and two power switches possess the ZVS feature.