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

Abstract

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.

1. 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 S₁, S₂, S₃, and S₄ and a resonant inductor L_r) that provides rated power to the piezoelectric ceramic actuator.

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-factor-correction (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 S₁, S₂, S₃, and S₄; four diodes D₁, D₂, D₃, and D₄; and a resonant inductor L_r) that provides rated power to the piezoelectric ceramic actuator.

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.

2. The Proposed Drive Circuit for Supplying a Piezoelectric Ceramic Actuator

2.1. Introduction of Proposed Drive Circuit

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 v_AC and a filter (L_f and C_f), consists of two diodes (D₁ and D₂), a coupled-inductor (L_B1 and L_B2), two power switches (S₁ and S₂), and two DC-linked capacitors (C_DC1 and C_DC2). The half-bridge resonant inverter sub-circuit includes two switches (S₁ and S₂), 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.

Table 1. Comparisons between the conventional drive circuits and the proposed version for a piezoelectric ceramic actuator.

Item	Conventional Two-Stage Drive Circuit [12]	Conventional Two-Stage Drive Circuit [13,14]	Proposed Single-Stage Drive Circuit
Number of Required Power Switches	5	4	2
Number of Required Diodes	1	8	2
Number of Required Capacitors	1	1	3
Number of Required Magnetic Components	2	1	3
Input Voltage Source Suitable for the Application	DC Voltage	AC Voltage	AC Voltage
Function of Power-Factor-Correction	Not Available	No	Yes
Soft-Switching of Power Switches	Not All Switches	Yes (All Switches)	Yes (All Switches)

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.

2.2. 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 L_B1 and L_B2 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 Figure 6, Figure 7, Figure 8, Figure 9, Figure 10, Figure 11 and Figure 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 i_Lr drops to zero, the power switch S₁ 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 D₁ and the power switch S₁, 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 S₁ and provides energy to the piezoelectric ceramic actuator. When the power switch S₁ is turned off, the inductor current i_LB1 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 v_AC provides energy to the parasitic capacitance of the power switch S₁ through the inductance L_f and the capacitance C_f of the filter circuit, the diode D₁, 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 S₁ and provide energy to the piezoelectric ceramic actuator. The parasitic capacitance of the power switch S₂ 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 S₂ releases energy, the voltage v_DS2 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.

2.2.3. Operational Mode 3 (t₂ ≤ t < t₃)

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 DC-linked capacitors C_DC1 and C_DC2 through the inductance L_f and capacitor C_f of the filter circuit, the diode D₁, and the essential diode of the power switch S₂. 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 S₂ 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.

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 i_LB1 drops to zero, the power switch S₂ 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 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 L_r and the parasitic capacitance of the power switch S₁ 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 S₂ and provide energy to the piezoelectric ceramic actuator. When the parasitic capacitance energy of the power switch S₁ is released and the voltage v_DS1 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 v_DS1 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 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 D₁, and the coupled inductor current i_LB1 rises linearly from zero. In addition, through the essential diode of the power switch S₁, 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 S₁ is driven and turned on, Mode 6 ends and the circuit operation returns to Mode 1.

In addition,

Table 2. States of the main power devices in each operational mode during the positive half-cycle of the utility-line voltage.

Main Power Devices	Mode 1	Mode 2	Mode 3	Mode 4	Mode 5	Mode 6
Switch S1	On	Off	Off	Off	Off	Off
Switch S2	Off	Off	Off	On	Off	Off
Diode D1	On	On	On	Off	Off	On
Diode D2	Off	Off	Off	Off	Off	Off
Inductor LB1	Charging	Discharging	Discharging	Discharging	Not Available	Charging
Inductor LB2	Not Available	Not Available	Not Available	Not Available	Not Available	Not Available
Inductor Lr	Charging	Discharging	Discharging	Discharging	Discharging	Charging
Capacitor CDC1	Discharging	Discharging	Charging	Not Available	Discharging	Charging
Capacitor CDC2	Not Available	Charging	Charging	Discharging	Discharging	Not Available

shows states of the main power devices in each operational mode during the positive half-cycle of the utility-line voltage.

2.3. Design Equations of Key Circuit Parameters

2.3.1. Design Equation of the Coupled Inductors L_B1 and L_B2

The design equation of the coupled inductors L_B1 and L_B2 can be represented by [15]:

$$L_{B1}=\frac{\eta v_{\mathrm{AC}\text{-}\mathrm{rms}}{}^2{D}^2}{2P_O{f}_S}=L_{B2}$$

(1)

where η is the estimated efficiency of the proposed drive circuit; v_AC-rms is the root-mean-square (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.

With a η of 0.8, a v_AC-rms of 110 V, a D of 0.5, a P_O of 50 W, and a switching frequency f_S of 40 kHz, the inductances of the coupled inductors L_B1 and L_B2 are calculated as

$$L_{B1}=L_{B2}=\frac{\eta v_{\mathrm{AC}\text{-}\mathrm{rms}}{}^2{D}^2}{2P_O{f}_S}=\frac{0.8\cdot {110}^2\cdot {0.5}^2}{2\cdot 50\cdot 40k}=650 \mathsf{\mu }\mathrm{H}$$

In addition, the coupled inductors L_B1 and L_B2 in the prototype drive circuit are 500 μH.

2.3.2. 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]

$$I_{\mathrm{inv}1\text{-}\mathrm{rms}}=\frac{R_m-j\left(\frac{1}{2\pi f_r{C}_p}\right)}{-j\left(\frac{1}{2\pi f_r{C}_p}\right)}\left(\sqrt{\frac{P_O}{R_m}}\right)$$

(2)

The input impedance Z_in of the equivalent circuit is expressed as

$$Z_{\mathrm{in}}=Z_{\mathrm{PCA}}+j{Z}_{\mathrm{Lr}}=(R_1+j{X}_1)+j2\pi f_r{L}_r$$

(3)

where R₁ and X₁ are the equivalent resistance and reactance of the piezoelectric ceramic actuator impedance Z_PCA, and they can be respectively expressed as [13]

$$R_1=\frac{R_m}{1+{(2\pi f_r)}^2{C}_p^2{R}_m^2}$$

(4)

$$X_1=\frac{2\pi f_r{C}_p{R}_m^2}{1+{(2\pi f_r)}^2{C}_p^2{R}_m^2}$$

(5)

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

$${|Z}_{in}|=\frac{V_{\mathrm{inv}1\text{-}\max }}{\sqrt{2}{I}_{\mathrm{invl}\text{-}\mathrm{rms}}}=\frac{{8V}_{\mathrm{DC}}}{\sqrt{2}\pi I_{\mathrm{invl}\text{-}\mathrm{rms}}}$$

(6)

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]

$$L_r=\frac{1}{2\pi f_r}\left(X_1+\sqrt{|Z_{\mathrm{in}}{|}^2-R_1^2}\right)$$

(7)

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

$$I_{\mathrm{inv}1\text{-}\mathrm{rms}}=\frac{R_m-j\left(\frac{1}{2\pi f_r{C}_p}\right)}{-j\left(\frac{1}{2\pi f_r{C}_p}\right)}\left(\sqrt{\frac{P_O}{R_m}}\right)=\frac{25-j\left(\frac{1}{2\pi \cdot 40k\cdot 4000p}\right)}{-j\left(\frac{1}{2\pi \cdot 40k\cdot 4000p}\right)}\left(\sqrt{\frac{50}{25}}\right)=1.414\angle {1.432}^0\mathrm{A}$$

The parameters R₁ and X₁ are respectively calculated as

$$R_1=\frac{R_m}{1+{(2\pi f_r)}^2{C}_p^2{R}_m^2}=\frac{25}{1+{(2\pi \cdot 40k)}^2\cdot {\left(4000p\right)}^2\cdot {25}^2}=24.98 \mathsf{\Omega }$$

$$X_1=\frac{2\pi f_r{C}_p{R}_m^2}{1+{(2\pi f_r)}^2{C}_p^2{R}_m^2}=\frac{2\pi \cdot 40k\cdot 4000p\cdot {25}^2}{1+{(2\pi \cdot 40k)}^2\cdot {\left(4000p\right)}^2\cdot {25}^2}=0.625 \mathsf{\Omega }$$

With a V_DC of 700 V and a I_rnv1-rms of 1.414 A, the parameter |Z_in| is calculated as

$${|Z}_{in}|=\frac{V_{\mathrm{inv}\text{-}\max }}{\sqrt{2}{I}_{\mathrm{invl}\text{-}\mathrm{rms}}}=\frac{{8V}_{\mathrm{DC}}}{\sqrt{2}\pi I_{\mathrm{invl}\text{-}\mathrm{rms}}}=\frac{8\cdot 700}{\sqrt{2}\pi \cdot 1.414}=891.4 \mathsf{\Omega }$$

Therefore, the parameter L_r is calculated as

$$L_r=\frac{1}{2\pi f_r}\left(X_1+\sqrt{|Z_{\mathrm{in}}{|}^2-R_1^2}\right)=\frac{1}{2\pi \cdot 40k}\left(0.625+\sqrt{{891.4}^2-{24.98}^2}\right)=3.55 \mathrm{mH}$$

In addition, the resonance inductor L_r in the prototype drive circuit is 3.95 mH.

2.3.3. 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

$$f_{\mathrm{cut}\text{-}\mathrm{off}}=\frac{1}{2\pi \sqrt{L_f{C}_f}}$$

(8)

In order to filter high-frequency switching noise, the design consideration of the cut-off 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

$$L_f=\frac{1}{4{\pi }^2{f}_{\mathrm{cut}\text{-}\mathrm{off}}{}^2{C}_f}$$

(9)

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

$$L_f=\frac{1}{4{\pi }^2{f}_{\mathrm{cut}\text{-}\mathrm{off}}{}^2{C}_f}=\frac{1}{4{\pi }^2\cdot {\left(4\mathrm{kHz}\right)}^2\cdot 470n}=3.36 \mathrm{mH}$$

3. 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. Parameters of the utilized piezoelectric ceramic actuator.

Parameter	Value
Resonant Frequency fr	40 kHz
Mechanical Equivalent Resistance Rm	25 Ω
Static Capacitance Cp	4000 pF
Rated Power PO	50 W

. In addition, the components utilized in the prototype drive circuit for the piezoelectric ceramic actuator are shown in

Table 4. Components utilized in the prototype of the proposed drive circuit.

Parameter/Component	Value
Diode D1, D2	MUR460
Filter Inductor Lf	3.36 mH
Filter Capacitor Cf	470 nF
Coupled Inductor LB1, LB2	500 μH
DC-linked Capacitor CDC1, CDC2	220 μF
Power Switches S1, S2	W12NK90Z
Resonant Inductor Lr	3.95 mH

.

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.

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.

4. 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.