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

^{*}

## Abstract

**:**

## 1. Introduction

_{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].

_{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.

_{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 S

_{1}, S

_{2}, S

_{3}, 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.

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

#### 2.1. Introduction of Proposed Drive Circuit

_{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.

#### 2.2. Analysis of Operational Modes

- 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.

#### 2.2.1. Operational Mode 1 (t_{0} ≤ t < t_{1})

_{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.

#### 2.2.2. Operational Mode 2 (t_{1} ≤ t < t_{2})

_{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.

#### 2.2.3. Operational Mode 3 (t_{2} ≤ t < t_{3})

_{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 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.

#### 2.2.4. Operational Mode 4 (t_{3} ≤ t < t_{4})

_{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.

#### 2.2.5. Operational Mode 5 (t_{4} ≤ t < t_{5})

_{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.

#### 2.2.6. Operational Mode 6 (t_{5} ≤ t < t_{6})

_{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.

#### 2.3. Design Equations of Key Circuit Parameters

#### 2.3.1. Design Equation of the Coupled Inductors L_{B1} and L_{B2}

_{B1}and L

_{B2}can be represented by [15]:

_{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}.

_{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

_{B1}and L

_{B2}in the prototype drive circuit are 500 μH.

#### 2.3.2. Design Equation of the Resonant Inductor L_{r}

_{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]

_{in}of the equivalent circuit is expressed as

_{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]

_{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

_{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}.

_{r}can be expressed as [13]

_{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

_{1}and X

_{1}are respectively calculated as

_{DC}of 700 V and a I

_{rnv1-rms}of 1.414 A, the parameter |Z

_{in}| is calculated as

_{r}is calculated as

_{r}in the prototype drive circuit is 3.95 mH.

#### 2.3.3. Design of Input Low-Pass Filter

_{f}and a capacitor C

_{f}. The cut-off frequency f

_{cut-off}of the input low-pass filter is represented by

_{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

_{cut-off}of 4 kHz and selecting a capacitor C

_{f}of 470 nF, the inductor L

_{f}is determined by

## 3. Experimental Results of the Proposed Drive Circuit

_{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.

_{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

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 3.**The conventional two-stage drive circuit for supplying a piezoelectric ceramic actuator applied with a DC input voltage source [12].

**Figure 12.**Theoretical waveforms of the proposed drive circuit of the piezoelectric ceramic actuator during the positive half-cycle of the utility-line voltage.

**Figure 13.**The relationship between the coupled inductors L

_{B1}and L

_{B2}and the duty cycle D at different switching frequencies f

_{S}.

**Figure 14.**The equivalent circuit diagram of the resonant tank circuit combined with the piezoelectric ceramic actuator circuit model.

**Figure 15.**A photograph of the proposed prototype drive circuit for supplying a piezoelectric ceramic actuator.

**Figure 16.**(

**a**) Simulated and (

**b**) measured inductor current i

_{LB1}(1 A/div); time scale: 10 μs/div.

**Figure 17.**(

**a**) Simulated and (

**b**) measured switch voltage v

_{DS2}(200 V/div) and resonant inductor current i

_{Lr}(1 A/div); time scale: 10 μs/div.

**Figure 18.**(

**a**) Simulated and (

**b**) measured switch voltage v

_{DS1}(200 V/div) and switch current i

_{DS1}(2 A/div); time scale: 10 μs/div.

**Figure 19.**(

**a**) Simulated and (

**b**) measured output voltage v

_{O}(500 V/div) and current i

_{O}(0.5 A/div); time scale: 10 μs/div.

**Figure 20.**(

**a**) Simulated and (

**b**) measured input utility-line voltage v

_{AC}(50 V/div) and current i

_{AC}(1 A/div); time scale: 5 ms/div.

**Figure 21.**Measured harmonics of the input utility-line current in comparison with the IEC 61000-3-2 class C standard.

**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) |

**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 S_{1} | On | Off | Off | Off | Off | Off |

Switch S_{2} | Off | Off | Off | On | Off | Off |

Diode D_{1} | On | On | On | Off | Off | On |

Diode D_{2} | Off | Off | Off | Off | Off | Off |

Inductor L_{B1} | Charging | Discharging | Discharging | Discharging | Not Available | Charging |

Inductor L_{B2} | Not Available | Not Available | Not Available | Not Available | Not Available | Not Available |

Inductor L_{r} | Charging | Discharging | Discharging | Discharging | Discharging | Charging |

Capacitor C_{DC1} | Discharging | Discharging | Charging | Not Available | Discharging | Charging |

Capacitor C_{DC2} | Not Available | Charging | Charging | Discharging | Discharging | Not Available |

Parameter | Value |
---|---|

Resonant Frequency f_{r} | 40 kHz |

Mechanical Equivalent Resistance R_{m} | 25 Ω |

Static Capacitance C_{p} | 4000 pF |

Rated Power P_{O} | 50 W |

Parameter/Component | Value |
---|---|

Diode D_{1}, D_{2} | MUR460 |

Filter Inductor L_{f} | 3.36 mH |

Filter Capacitor C_{f} | 470 nF |

Coupled Inductor L_{B1}, L_{B2} | 500 μH |

DC-linked Capacitor C_{DC1}, C_{DC2} | 220 μF |

Power Switches S_{1}, S_{2} | W12NK90Z |

Resonant Inductor L_{r} | 3.95 mH |

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**MDPI and ACS Style**

Cheng, C.-A.; Cheng, H.-L.; Chang, C.-H.; Chang, E.-C.; Tsai, C.-Y.; Lan, L.-F.
A Novel and Cost-Effective Drive Circuit for Supplying a Piezoelectric Ceramic Actuator with Power-Factor-Correction and Soft-Switching Features. *Micromachines* **2021**, *12*, 1229.
https://doi.org/10.3390/mi12101229

**AMA Style**

Cheng C-A, Cheng H-L, Chang C-H, Chang E-C, Tsai C-Y, Lan L-F.
A Novel and Cost-Effective Drive Circuit for Supplying a Piezoelectric Ceramic Actuator with Power-Factor-Correction and Soft-Switching Features. *Micromachines*. 2021; 12(10):1229.
https://doi.org/10.3390/mi12101229

**Chicago/Turabian Style**

Cheng, Chun-An, Hung-Liang Cheng, Chien-Hsuan Chang, En-Chih Chang, Chih-Yang Tsai, and Long-Fu Lan.
2021. "A Novel and Cost-Effective Drive Circuit for Supplying a Piezoelectric Ceramic Actuator with Power-Factor-Correction and Soft-Switching Features" *Micromachines* 12, no. 10: 1229.
https://doi.org/10.3390/mi12101229