Open AccessArticle

Analysis and Design of Low-Power Piezoelectric Energy Harvesting Circuit for Wearable Battery-Free Power Supply Devices

Ivaylo Pandiev

^1,*

Hristo Antchev

²,

Nikolay Kurtev

Nikolay Tomchev

and

Mariya Aleksandrova

Department of Electronics, Faculty of Electronic Engineering and Technologies (FEET), Technical University of Sofia, Kliment Ohridski Blvd., 8, 1000 Sofia, Bulgaria

Department of Metallurgical Technologies, Electrical Engineering and Electronics, University of Chemical Technology and Metallurgy, Kliment Ohridski Blvd., 8, 1000 Sofia, Bulgaria

Department of Microelectronics, Faculty of Electronic Engineering and Technology, Technical University of Sofia, Kliment Ohridski Blvd., 8, 1000 Sofia, Bulgaria

Author to whom correspondence should be addressed.

Electronics 2025, 14(1), 46; https://doi.org/10.3390/electronics14010046

Submission received: 25 November 2024 / Revised: 18 December 2024 / Accepted: 24 December 2024 / Published: 26 December 2024

(This article belongs to the Special Issue Mixed Design of Integrated Circuits and Systems)

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Abstract

Improving microelectronic technologies has created various micro-power electronic devices with different practical applications, including wearable electronic modules and systems. Furthermore, the power sources for wearable electronic devices most often work with electrical energy obtained from the environment without using standard batteries. This paper presents the structure and electrical parameters of a circuit configuration realized as a prototype of a low-power AC-DC conversion circuit intended for use as a power supply device for signal processing systems that test various biomedical parameters of the human body. The proposed prototype has to work as a wearable self-powered system that transfers electrical energy obtained through mechanical vibrations in the piezoelectric generator. The obtained electrical energy is used to charge a single low-voltage supercapacitor, which is used as an energy storage element. The proposed circuit configuration is realized with discrete components consisting of a low-voltage bridge rectifier, a low-pass filter, a DC-DC step-down (buck) synchronous converter, a power-controlling system with an error amplifier, and a window detector that produces a “power-good” signal. The power-controlling system allows tuning the output voltage level to around 1.8 V, and the power dissipation for it is less than 0.03 mW. The coefficient of energy efficiency achieved up to 78% for output power levels up to 3.6 mW. Experimental testing was conducted to verify the proposed AC-DC conversion circuit’s effectiveness, as the results confirmed the preliminary theoretical analyses and the derived analytical expressions for the primary electrical parameters.

Keywords:

energy harvesting; medical applications; piezoelectric energy harvester; vibrations; rectifiers; buck synchronous converters; signal processing; testing

1. Introduction

In the past few years, low-power wearable electronic devices with biomedical applications have become relatively popular [1,2,3,4,5,6,7,8]. Moreover, such devices have been used to measure biomedical parameters indicating changes in the health status of the human body during physical activity. Power supply devices that provide electrical parameters with specific values are required to ensure the proper functioning of portable signal processing systems. The basic requirements for supply devices intended for portable electronic devices are [9,10,11,12]: (1) to provide electrical energy with precisely defined parameters—output voltage and current; (2) to maintain constant (stable) values of the output quantities when the load resistance and environmental parameters, such as ambient temperature or humidity, are changed; (3) to have a small consumption current (typically up to 10 μA) in static and dynamic operational mode and small power dissipation (typically up to 10 μW); (4) to be cheap to produce and to have a high energy efficiency coefficient value (>50%); (5) to be safe and durable in their operation in electronic devices. For the power supply devices intended for portable electronic devices, in some cases, it is inefficient to use conventional Li-ion batteries to supply electrical energy to wearable electronic devices as they require relatively frequent replacement (depending on the discharge current), or access to them may be limited. In the last few years, wearable electronic devices have been of particular interest, where electrical energy has been obtained through so-called energy harvesters, such as piezoelectric, electromagnetic, electrostatic, or tribo-electric elements. In our work, the research objects are piezoelectric elements (or generators) as sources, in which mechanical energy obtained from vibrations is converted into electrical energy that is used through a power management system to charge a low-power ultracapacitor (or supercapacitor).

The analysis of literary sources from the last ten years showed various energy-harvesting electronic circuits [13,14,15,16,17,18,19,20,21,22], some implemented as monolithic, laboratory-created integrated circuits [15,16,18]. The comparative analysis of the laboratory-created electronic circuits showed that most of them provide relatively high values for the output voltage (>2 V) and relatively low output current (≤0.5 mA) and achieve high values for the energy efficiency (>50%) but at relatively high values of the frequency (≥100 Hz) of the sinusoidal mechanical vibrations, which can be hard to supply when building wearable electronic devices. Also, a trend for the last few years has been for wearable electronic devices intended for data processing to use power supply voltages below 1.8 V. To obtain low, stable voltages, commercially available low-power energy harvesting integrated circuits (ICs) such as LTC3588-1 [23], LTC3255 [24], TPSM365R6 [25], and ADP5304 [26] can be used. The functionality of the commercially available ICs is maintained with a minimal number of external passive components, and an LC filter is added to the output port. Moreover, for available integrated circuits, the energy efficiency coefficient is obtained with a maximum value (typically more than 50%) at a particular value of the input and output signal parameters and for a selected mode of operation. Thus, the maximum value for energy efficiency is obtained at a relatively high level of the input voltage (>3 V) and a large value of the current through the load (>1 mA). Another feature of the low-power energy harvesting ICs is that only specific output voltage values can be obtained without the possibility of fine-tuning or forming an arbitrary value at a given external load. An interesting idea from an applied perspective is a piezoelectric energy harvesting circuit based on low-power-consumption synchronized switch technology [27]. In this circuit, a low-power-consumption microcontroller, the MSP430 (Texas Instruments, Dallas, TX, USA), with discrete components, is used to build the parallel synchronized switch harvesting on the inductor interface circuit (P-SSHI), as well as a commercial DC-DC converter, type LTC3388-1, from Analog Devices (Wilmington, MA, USA). An additional battery is used to provide a supply voltage for the MSP430 microcontroller, which works in low-power consumption modes. The microcontroller MSP430 switches (or “wakes up”) from low-power mode 4 to mode of operation 1 upon receiving a pulse from a zero-crossing comparator, and in mode 1, the internal RC oscillator is used, which operates at a frequency of 1 MHz, and the power consumption is up to about 600 μW. In low-power mode 4, the power consumption can be obtained with values even below 1 μW. As a result, the supply current can widely vary when switching and operating in different modes.

The presented work is an extended version of the conference paper [28] reported initially at the 31st International Conference on Mixed Design of Integrated Circuits and Systems—MIXDES 2024. Moreover, using the authors’ ideas for various functional stages and parts presented in [13,14,17], an improved form of a low-power electronic system for the conversion of energy from mechanical vibrations into electrical energy and further charging of a low-power supercapacitor has been developed. The developed prototype provides stabilized output DC voltage with a value equal to 1.8 V for output power levels up to 3.6 mW and a small value for power dissipation of the power-controlling system. The proposed prototype is intended to work as a power source for a precise wearable electronic system that acquires and processes information through biosensors [29].

This paper is systematized as follows: Section 2 presents the functional diagram for the proposed energy harvester circuit. Also, Section 2 explains the operational principle of the proposed AC-DC converter to obtain stable output voltage. The structure and the principle of operation of the proposed electronic circuits are given in Section 3, and the procedures and criteria for calculating the component parameters are shown. The experimental results of the study of the proposed circuit configuration are shown in Section 4. Moreover, a comparative analysis with known low-power AC-DC converters is also presented in the same section. Finally, Section 5 provides some highlights and directions for further work.

2. Functional Diagram for the Proposed Energy Harvester Circuit

Figure 1 shows the functional diagram of the proposed energy-harvesting circuit. Some leading topological structures of portable electronic devices with low power dissipation and, respectively, a high value of energy efficiency were used as a basis for the construction of the functional diagram. When choosing functional blocks and electrical connections between them, the primary goal is to figure out how to store the small electrical energy obtained as a result of mechanical vibrations that occurred spontaneously and then how to achieve a desired value of stabilized output DC voltage, which in turn can be used as a supply voltage, as well as how to obtain a high value of energy efficiency for the selected circuit configuration. The main reason for defining the above-described objective is that the single piezoelectric generator has a relatively large internal resistance, and the generated current has a small value (up to about milliamps). Furthermore, based on the proposed functional diagram, an electronic circuit was synthesized, which can be used depending on the parameters of the input signal and the requirements of the external load, or, in other words, according to the parameters of the powered electronic device. The advantages and disadvantages of the proposed electronic circuit are systematized in the following subsections, where the structure and principle of operation of the specific configuration are considered.

For the circuit configuration shown in Figure 1, a bridge rectifier is cascaded after the piezoelectric generator, and a low-power supercapacitor is connected with a charge balancing system. Also, a Zener diode with breakdown voltage V_Z is connected to the supercapacitor for protection in case of voltage peaks. Compared to rechargeable batteries, using supercapacitors as energy storage elements allows a greater number of charge and discharge cycles to be formed. This is particularly important for wearable electronic devices since mechanical vibrations in piezoelectric elements are spontaneous and occur repeatedly but, in some cases, at longer intervals.

The proposed block diagram in Figure 1 is constructed so that the harvested electrical energy can be stored on the input supercapacitor and the output capacitor C_o. Moreover, at the beginning of the mode of operation, it is intended that the upper pMOS transistor M₂ of the step-down (buck) converter is turned on and the lower nMOS transistor M₁ is turned off. The extremely low value of the current consumption and the provision of a smooth approach to the minimum input voltage at which the reference voltage source starts to work determine the possibility of initially accumulating a charge on the output capacitors. By using a reference voltage source, a stable supply voltage

V_{D D}^{+}

is provided for the micro-power pulse oscillator (or multivibrator), the PWM (pulse-width modulation) comparator, and the error amplifier. The step-down converter starts to transfer part of the stored energy to the output. Furthermore, a small value for the consumption current is obtained in the regulation mode. In operation, the buck converter uses pulse-width modulation and an internal oscillator, providing control of the output voltage V_o by controlling its value via internal negative feedback. More specifically, a part of the output voltage V_o is applied to one input terminal of the error amplifier, and the reference voltage V_ref is applied to the other input. As a result of the amplification and filtering of the signal, the v_control is obtained. The level of the v_control at the output of the error amplifier is compared with the instantaneous value of the triangular voltage v_tr, forming the voltage v_d for controlling the driver stage. A delay circuit is used to obtain non-overlapping pulse sequences to control the MOS transistors of the buck converter. As a result of the operation of the converter, charging of the output capacitor C_o through the inductor L_o is provided at a voltage slightly greater or slightly less than the regulation point. For the electronic circuit, the DC output voltage is regulated by changing the duty cycle δ of the rectangular voltage v_d.

In addition to the proposed energy-harvesting circuit, a window comparator (undervoltage/overvoltage detector) is designed to produce a signal indicating that the output voltage level has reached within ±10% of the desired value. As a result of the comparator’s operation, a “power-good” or logic high signal is formed, which indicates to the surrounding digital and other circuits that the supply voltage has reached a set value, and those circuits can proceed to startup and operation.

3. Circuit Description

Based on the block diagram presented in Figure 1, a circuit configuration, shown in Figure 2, was synthesized. The schematic for each active element shows the type of integrated circuit used, as well as the values of the majority of the passive RC components. The principle of calculation and the concrete values for the remaining passive components are given in the text below. The description of the structure and principle of operation of the proposed prototype is presented sequentially (from the input to the output network) in the following subsections.

3.1. Full-Bridge Rectifier at a Non-Sinusoidal Input Signal—Input Stage

The electronic circuit of a rectifier in Figure 3a connected to the piezoelectric element was implemented using four micro-power Schottky diodes of type PMEG3002TV with a forward voltage of up to 150 mV and one low-power supercapacitor of type SCMR22G105SRBA0 (from KYOCERA^® (Kyoto, Japan)) with a capacity of 1 F and a maximum voltage equal to 7.5 V. By using a single supercapacitor, greater compactness and smaller sizes of the entire electronic device can be obtained. For protection against peak values of the input voltage, a Zener diode type BZX84-A6V2 with a stabilization voltage of 6.2 V with low leakage current (up to 3 μA) is connected in parallel to the chosen supercapacitor [10,23,30]. To illustrate the structure and the principle of operation of the proposed prototype, Figure 3a shows the schematic configuration of only the input (first) stage. In it, the piezoelectric generator is presented as a current source (Norton’s equivalent circuit) i_p with an equivalent resistance r_p and an equivalent capacitance C_p connected in parallel [13,31]. This way of representing the piezoelectric element as an equivalent electrical circuit provides an opportunity to evaluate its influence on the operation of subsequent stages and blocks in the electronic system.

Typical timing diagrams of the input voltage v_p and the

i_{C_{p}}

through the piezoelectric capacitance at resonance operational mode are given in Figure 3b. In Figure 3b,

T = 1 / f

is the period of the input signal,

f = ω / 2 π

is the frequency of the mechanical vibrations, and

ω

is the value of the angular frequency of the vibrations. This input stage of the proposed prototype is the basic functional block, as it has to ensure the storage of the electrical energy, which will then be used in the mode of operation of the supercapacitor C_STO. In this case, the output voltage V_STO at no-load (R_L → ∞) has the following form [32]:

V_{S T O, 0} = V_{p, m} - 2 V_{D},

(1)

where V_p_,m = I_p/ωC_p is the piezoelectric no-load voltage, and V_D is the voltage drop in the used Schottky diodes (for the chosen diodes, the voltage drop is ≈100 mV at a forward current ≈ 100 μA).

When an external load R_L is connected, a current flows in the circuit’s output network, and the capacitors’ discharge begins as the output voltage starts to decrease. At a steady state operation in the circuit, i.e., when the incoming charge of the capacitor is equal to the outgoing charge, the output voltage has a value equal to the following [32]:

V_{S T O, \infty} \approx V_{S T O, 0} (1 - \sqrt{\frac{r_{p}}{2 R_{L}}}) .

(2)

During every recharge period, the peak current is

I_{o} \approx V_{S T O, 0} / \sqrt{2 r_{p} R_{L}}

[32]. As can be seen, the internal resistance r_p of the piezoelectric element significantly influences the peak value of the output current and determines the value of the output power

P_{o} = V_{S T O, \infty} I_{o}

3.2. Step-Down (Buck) Synchronous Converter and Switching Circuit

The electronic circuit of the converter is synthesized based on the basic structures of buck/boost converters, presented in [12,32], and the circuit configurations of switching circuits, presented in [13,14,16]. The proposed synchronous buck regulator is implemented with a driver stage consisting of two analog comparators of type LPV7215 (from Texas Instruments^® (Dallas, TX, USA)) supplied by V_STO, two electronic switches, two capacitors (one of which is used as an electrical energy storage element), and a single inductor. Additionally, for the correct operation of the two analog comparators so that the pulse signals controlling the electronic switches do not overlap (i.e., obtaining non-overlapping pulse signals with a “dead zone” [12] on the rising and falling edges), two reference voltages and one input RC group forming a smooth rise of the square-wave control signal are used. The two electronic switches are realized with the pair of low-power complementary MOS (CMOS) transistors of type BSD235C (from Infineon Technologies AG^® (Munich, Germany)). In the first operation phase, the upper transistor M₂ is turned on, and the lower transistor M₁ is turned off. The inductor L_o is connected to the rectified voltage, with the current flowing from the V_STO to the load. In this case, the current through the load increases approximately linearly. In the second phase, M₁ is on and M₂ is off. In this case, the inductor L_o is connected to the ground, with the current flowing from the ground to the load. The current through the load decreases approximately linearly as the electromotive voltage of the inductor decreases. In the next phase, the processes are repeated, increasing the tension on the load. In this case, the synchronous converter works in continuous conduction mode (CCM), which means that the current through the inductor does not drop to zero. The current fluctuations through the load should be small values around the regulation point to ensure a relatively constant voltage across the load.

Calculating the L_o and C_o values is of particular importance for the proposed prototype since, on the one hand, they reduce output voltage and current ripples. On the other hand, these passive LC components affect the input impedance of the error amplifier and influence the frequency compensation of the loop. Based on the recommendations defined in [31], the necessary value of the smoothing capacitor C_o is obtained as follows:

C_{o} = T_{s} \frac{I_{o, \min}}{4 Δ V_{o}} \approx 20 μ F,

(3)

where

I_{o, \min} = I_{o} - Δ I_{o} = 1.98

mA (

Δ I_{o} = 0.01 \times I_{L, \max}

) is the minimum value of the output current compared to the maximum value of the output current

I_{L, \max}

through the load, and

Δ V_{o}

is the output voltage ripple, chosen equal to

5 mV

(in this case, the output voltage ripple is less than 1%).

The inductor value can be calculated using the following expression [32,33]:

L_{o} = \frac{V_{i n} - V_{o}}{I_{o, \min}} \frac{V_{o u t}}{V_{i n}} T_{s} \approx 127 mH,

(4)

where

V_{i n} \approx 6 V

is the maximum value of the input voltage of the synchronous converter.

For the proposed prototype based on the calculations performed above, standard values

C_{o} = 100 μ F \pm 10 %

and

L_{o} = 200 mH \pm 10 %

were chosen. These values are relatively larger than calculated, providing a smoother waveform output voltage (

V_{o} = 1.8 V \pm 5 mV

) and output current (

I_{o} = 2 mA \pm 20 μ A

R_{L} = 900 Ω

) in the presence of relatively large input voltage fluctuations. Achieving the indicated values of the electrical parameters allows the developed prototype to provide electrical power for precise wearable electronic devices that process signals when acquiring information through biosensors [29].

To generate rectangular pulses for the switching circuit of the synchronous converter in Figure 2, an oscillator circuit was used, implemented with a micro-power analog comparator without hysteresis, type LPV7215, with a typical value of the supply current approximately equal to 0.8 μA. In this circuit, the timing group (R and C) was included in the negative feedback circuit, and constant positive feedback was formed through resistors R₁, R₂₁, and R₂₂. If, at the time of turning on the supply voltage, the comparator establishes itself in the state v_r = V_DD, in this case, for the high trigger level (switch-off level) of the analog comparator, the equivalent circuit of the pulse oscillator was drawn up, shown in Figure 4. In Figure 4, the resistances R₂₁ and R₂₂ are represented as

R_{21} | | R_{22}

, and an ideal voltage source

0.5 V_{D D}^{+}

is added in series to them since

R_{21} = R_{22} = 1 M Ω

is chosen. Then, for the current i through the resistors forming a positive feedback loop, the following was written:

i = \frac{v_{r} - 0.5 V_{D D}^{+}}{R_{1} + R_{21} | | R_{22}} .

(5a)

According to Ohm’s law for the voltage at the non-inverting input of the analog comparator, the following is obtained:

V_{T H}^{+} = (R_{21} | | R_{22}) i + 0.5 V_{D D}^{+} .

(5b)

After substituting (5a) into (5b) for the high trigger level, the following expression is found:

V_{T H}^{+} = \frac{R_{21} | | R_{22}}{R_{1} + R_{21} | | R_{22}} (V_{D D}^{+} - 0.5 V_{D D}^{+}) + 0.5 V_{D D}^{+} \approx 1.875 V,

(6)

where

R_{1} = 500 k Ω

Since the voltage at the inverting input is still zero (capacitor C is not charged when the supply voltage is turned on), the state of the comparator is self-sustaining. However, the capacitor C begins to charge from the output voltage through the resistor R, and when

v_{C} \approx V_{T H}^{+}

, the comparator operates and switches, where

v_{r} = 0 V

. The voltage at the non-inverting input also changes with a switch to the low trigger level (or switch-on level), and the expression is found in a similar way to the expression for the high trigger level, i.e.,

V_{T H}^{-} = \frac{R_{21} | | R_{22}}{R_{1} + R_{21} | | R_{22}} (0 V - 0.5 V_{D D}^{+}) + 0.5 V_{D D}^{+} \approx 0.625 V

(7)

and the comparator remains in the new state. The capacitor C begins to discharge through R to zero, and when

v_{C} \approx V_{T H}^{-}

, the comparator switches again. The processes are periodically repeated, and since both half-periods are determined by the same time constant, the generated pulses have a duty cycle of 0.5. The following expression determines their switching frequency [11]:

f_{S} = \frac{1}{T_{S}} = \frac{1}{2 R C \ln [1 + 2 (R_{21} | | R_{22}) / R_{1}]} .

(8)

For the proposed prototype, the switching frequency is chosen to be equal to 5 kHz (

T_{S} = 200 μ s

and

0.5 T_{S} = 100 μ s

). For this value, the switching frequency is significantly higher than the possible frequency of the mechanical vibrations, which, depending on the activity of a person, can be from several tens of Hertz to about 100 Hz. In this case, the passive elements have the following values:

R = 1 M Ω \pm 1 %

and

C = 100 pF \pm 5 %

An integrating circuit in Figure 5 consisting of R₃, R₄, and C₁ obtained a triangular signal in Figure 6 from the rectangular pulses. To analyze the time-domain behavior of the integrator under a rectangular pulse, the output voltage v_tr can be found from the following differential equation [32]:

\frac{R_{3} + R_{4}}{R_{4}} (R_{34} C_{1} \frac{d v_{t r}}{d t} + v_{t r}) = v_{r}, R_{34} = R_{3} | | R_{4} .

(9)

Based on differential Equation (9) at the rising and falling edges of the input voltage, the output voltage is as follows:

v_{t r} (t) = V_{r, m} \frac{R_{4}}{R_{3} + R_{4}} (1 - e^{- t / R_{34} C_{1}}) — at the rising edge

(10a)

and

v_{t r} (t) = V_{r, m} \frac{R_{4}}{R_{3} + R_{4}} e^{- t / R_{34} C_{1}} — at the falling edge .

(10b)

As can be seen from the solution of the differential equation, the output voltage

v_{t r} (t)

of the integrator asymptotically approaches the values

v_{t r, 0} = [R_{4} / (R_{3} + R_{4})] V_{r, m}

\approx 1.25 V

and 0 V, respectively. In order to obtain the maximum dynamic operating range, 3τ (where

τ = R_{34} C_{1}

is the time constant of the integrator corresponding to the length of the segment from 0 to the intersection of the subtangent and the x-axis) is chosen to be approximately equal to T_S/2. Thus, according to an approximately exponential law, the voltage v_tr at the output of the integrator will, in this case, reach a value approximately equal to V_DD/2.

For the implementation of pulse-width modulation (PWM) in the step-down converter, an analog comparator of type TLV3012 (from Texas Instruments^® (Dallas, TX, USA)) was used. The triangle signal v_tr was applied to the inverting input terminal of the comparator, and the control voltage V_control, generated by the error amplifier, was applied to the non-inverting input terminal. Depending on the level of the control voltage, for the voltage ratio of the v_d (or v_{pwm_control}), the following is obtained:

δ = \frac{t_{o n}}{T} \approx \frac{V_{c o n t r o l}}{v_{t r, 0}} .

(11)

As a result of comparing the two voltages, the width of the pulses changed bilaterally (Figure 6—the second graph). The two edges were shifted symmetrically according to the control signal. The average output voltage can be calculated in terms of the switch duty ratio as follows:

V_{o, a v} = \frac{1}{T_{S}} (\int_{0}^{t_{o n}} V_{d, m} d t + \int_{t_{o n}}^{T_{S}} 0 d t) = \frac{t_{o n}}{T_{S}} V_{d, m} = δ V_{d, m} .

(12)

Substituting Formula (10) in expression (11) yields the following:

V_{o, a v} \approx \frac{V_{d, m}}{v_{t r, 0}} V_{c o n t r o l} = k V_{c o n t r o l},

(13)

where

k = V_{d, m} / v_{t r, 0}

The duty ratio t_on/T_S of the used dual comparator and MOSFET switches, and V can be controlled by varying V_o_,av. Also, the average output voltage V_o_,av varied approximately linearly with the V_control, as is the case in linear amplifiers.

3.3. Structure of the Error Amplifier and the Compensator

The error amplifier and compensator in Figure 7 of the switching circuit are implemented with a single micro-power operational amplifier (op-amp) of type AD8500 (from Analog Devices^® (Wilmington, MA, USA)) (the supply current has a typical value equal to 1.2 μA) and frequency-dependent negative feedback, including R_F, R_N, R₅, C₂, and C₃, as well as the values of the L_o and C_o at the output port. The voltage amplification for low frequencies was determined by the voltage divider consisting of two resistors, R_F and R_N, with fixed values equal to 560 kΩ and one trimming potentiometer R_V with a nominal value equal to 2 MΩ. The R_V is used to fine-tune the output voltage through the DC voltage

V_{r e f}^{'} \approx 0.9 V

formed from the reference voltage V_ref = 1.242 V ± 1% of the voltage source included in the integrated comparator TLV3012. Thus, the low-frequency value of the amplification coefficient was obtained as

A_{U, 0} = V_{o} / V_{r e f}^{'} \approx 1 + R_{F} / R_{N}

To ensure stable operation (or frequency compensation) in a wide frequency range according to analytical expressions given in [34], the values of the RC components, connected directly between the inverting input and the output of the op-amp, are calculated in the following sequence:

(1): The double poles frequency determined by $L_{o} = 200 mH$ and $L_{o} = 100 μ F$ in the output port is calculated as follows:

$f_{L C} = \frac{1}{2 π \sqrt{L_{o} C_{o}}} \approx 35.6 Hz;$

(14)
(2): The zero frequency $f_{Z 1}$ and the pole frequency $f_{p 2}$ of the compensating circuit are determined (for the selected circuit configuration of the compensator circuit, the following condition has to be fulfilled: $f_{Z 1} < f_{p 2}$ ; otherwise, self-oscillation can occur at the output): $f_{Z 1} = 0.75 f_{L C} \approx 26.7 Hz$ and $f_{p 2} = 0.5 f_{s} = 2.5 kHz$ ;
(3): The value of the resistor R₅ equal to 560 kΩ ± 1% is selected, and then the required value of the capacitor C₃ is calculated as follows:

$C_{3} = \frac{1}{2 π f_{Z 1} R_{5}} \approx 10 nF,$

(15)

where a standard value is selected, $C_{3} = 10 nF \pm 5 %$ ;
(4): The required value of the capacity C₂ is calculated as follows:

$C_{3} = \frac{1}{2 π f_{p 2} R_{5}} \approx 114 pF,$

(16)

where a standard value is selected, $C_{2} = 100 pF \pm 5 %$ .

The supply voltage for the switching circuit’s active components is 2.5 V, provided by a precision voltage reference source of type ISL60002-25 (from Renesas Electronics^® (Tokyo, Japan)) with a typical supply current value of 350 nA.

3.4. Structure of a Low-Power Driver Stage for the Synchronous Converter

As written above, the driver stage in Figure 8 has to provide non-overlapping pulse sequences with a certain amplitude to control the electronic switches, implemented through the complementary pair of MOS transistors BSD235C (Infineon Tech. AG, Munich, Germany). Moreover, the two pulse sequences are periodic square-wave signals and have a constant frequency equal to 5 kHz and a variable duty cycle with value according to the presented analytical expression (9). In order to obtain two non-overlapping pulse sequences, the pulse-width modulated signal v_d from the output of the analog comparator U₅ is applied to a delay circuit implemented with the resistor R_D and the capacitor C_D. The time constant τ of this delay circuit is more than 10 times smaller than T_s/2. At this selection of the τ, over a wide range (approximately from 10% to 90%) of variation in the duty cycle δ, the square wave of the voltage can be maintained. After the delay circuit, the signal is applied to the non-inverting inputs of the analog comparators U₆ and U₇, implemented with ICs LPV7215. By the trimming potentiometer R_T, a part of the reference voltage V_ref (not more than 1/3 of V_ref) is supplied to the inverting input terminal of the comparator U₆, and the entire voltage equal to 1.242 V is applied to the inverting input of U₇. As a result, two pulse sequences are obtained at the output terminals of U₆ and U₇, with the square-wave voltage at node TP3 having a shorter pulse duration and the square-wave voltage at node TP2 having a longer pulse duration. Therefore, two non-overlapping pulse sequences are obtained, which will cause the two transistors to switch correctly without having time intervals when both transistors are turned on.

This technique of obtaining the two control signals ensures minimum consumption with a minimum number of passive components used without limiting the functionality of the proposed electronic circuit. To illustrate the above description of the driver stage circuit, Figure 9 gives the timing diagrams of the signals before and after the delay circuit, as well as the received signals at nodes TP2 and TP3 of the two analog comparators U₆ and U₇.

As can be seen in Figure 9, by moving the middle point (or wiper) of the R_T (see Figure 2), the value of the reference voltage V_ref₁ can be changed (the value of the V_ref₂ is approximately constant and equal to 1.242 V). In this way, the distance between the two reference voltages can be changed, and hence, the time interval of the non-overlapping of the two pulse sequences can be changed. Simultaneously, the amplitude of the square-wave voltages is preserved, having a value equal to the voltage V_STO to which the supercapacitor is charged.

3.5. Structure of the Window Detector Produces the “Power-Good” Signal

To obtain a “power-good” signal, a window comparator with a dual analog comparator of type MAX9020 (from Analog Devices^® (Wilmington, MA, USA)) was developed Figure 10, which selects voltages in the range from 1.782 V (defined as the under-voltage threshold) to 1.89 V (defined as the over-voltage threshold) or approximately from −1% up to +5% of the nominal value of the output voltage V_o equal to 1.80 V.

The values of the under-voltage and over-voltage thresholds were selected depending on the parameters of the load, which was intended to be a low-voltage microcontroller signal processing circuit with biomedical applications [29]. The IC MAX9020 uses a reference voltage V_ref of the TLV3012 equal to 1.242 V. Also, for the MAX9020, the output MOS transistor has an open drain. As a result, without additional external logic elements, an AND logic function can be implemented by adding a single 100 kΩ pull-up resistor, with the upper pin connected to the output voltage of the converter. Then, to obtain the under-voltage and over-voltage thresholds, the values of the resistors, R₆, R₇, and R₈, that form the voltage divider are determined according to the design procedure given in [35], with the following sequence:

(1): The input bias current of the MAX9020 is below 2 nA, so the current through R₈ has to be at least 200 nA to minimize errors caused by the non-idealities of the used active devices. In this case, the resistor R₈ is selected with a value of 2.2 MΩ ± 1% standard value (the current through R₈ has to exceed 200 nA for the thresholds to be accurate, or R₈ = V_ref/I_R₈ = 1.242 V/0.6 μA (the current I_R₈ is chosen to be 0.6 μA));
(2): The sum of the resistances R₆ + R₇ is calculated assuming the over-voltage threshold is V_oth = 1.89 V, i.e., $R_{6} + R_{7} = R_{8} [(V_{o t h} / V_{r e f}) - 1] \approx$ $1.165 M Ω$ ;
(3): The resistance R₇ is calculated assuming the under-voltage threshold is V_uth = 1.78 V, i.e., $R_{7} = (R_{6} + R_{7} + R_{8}) (V_{r e f} / V_{u t h}) -$ $R_{8} \approx 146 k Ω$ (a standard value equal to R₇ = 150 kΩ ± 1% is selected);
(4): The resistance R₆ is determined: $R_{6} = (R_{6} + R_{7}) - R_{7} \approx 1.02 M Ω$ (a standard value equal to R₆ = 1 MΩ ± 1% is selected).

Then, the standard values of the voltage divider’s resistances are R₆ ≈ 1 MΩ ± 1%, R₇ = 150 kΩ ± 1%, and R₈ = 2.2 MΩ ± 1%.

4. Experimental Results and Discussion

To verify the efficiency of the proposed low-power AC-DC converter and to confirm the results of the theoretical analysis, the results and discussions of the experimental study of sample circuits are given in this section. The first variant (Figure 11a) of a printed circuit board (PCB) was realized based on the circuit configuration [28] with the selected passive and active components. Based on an experimental study of the electronic circuit in static and dynamic modes of operation, the primary electrical parameters were determined, and topological and parametric optimization criteria were defined. As a result of implementing some improvements, the circuit diagram in Figure 2 was obtained, and in Figure 11b, a top view of the corresponding PCB (variant 2) is represented. For the realization of the PCB, surface mount components were used, which allowed for obtaining smaller sizes of the individual functional blocks and reducing some parasitic effects. Also, to obtain a prototype with smaller dimensions and a small height for the printed circuit board components, the two trimming potentiometers (R_V and R_T) in Figure 11b are implemented with a pair of resistors with fixed resistance. The values of these resistors were determined during the preliminary testing of the circuit, represented in Figure 11a. For the circuit in Figure 11b,

R_{V 1} = 511 k Ω

and

R_{V 2} = 1.62 M Ω

, as well as

R_{T 1} = 1.58 M Ω

and

R_{T 2} = 442 k Ω

, are used. In addition, as shown in Figure 11b, the energy storage element is located along its length, which significantly reduces the maximum height of the components of the printed circuit board. For the selected supercapacitor, a “window” is formed in the printed circuit board where it is placed.

To illustrate the principle of operation of the proposed low-power AC-DC converter (Figure 2), Figure 12, Figure 13, Figure 14, and Figure 15 present timing diagrams of the voltages

v_{r}

v_{t r}

v_{c o n t r o l}

, and

v_{d}

, respectively. Moreover, the timing diagrams were captured at the no-load output (Figure 12) and three different external ohmic loads, respectively, 3.6 kΩ (Figure 13), 1.8 kΩ (Figure 14), and 900 Ω (Figure 15). In addition, in Figure 16, the timing diagrams for the pulse-width modulated signal

v_{d}

, the non-overlapping pulse signals (

v_{T P 2}

and

v_{T P 3}

) at the gates of the M₂ and M₁, and the output voltage level

V_{o}

are presented at the no-load output. The timing diagrams were captured at a DC voltage at the rectifier output equal to 3.5 V. As can be seen in Figure 16, two non-overlapping pulse signals are received at the two gates of the MOS transistors, which ensures the formation of a “dead zone.” As a result, the switching circuit’s current consumption is below 35 μA, which provides a small power dissipation value. Also, the output voltage was obtained with the required value of 1.8 V. As can be seen, visible fluctuations in the voltage level are not noticeable. When connecting an external load (Figure 13, Figure 14 and Figure 15) R_L to the output port of the proposed electronic circuit, the level of the output voltage V_o is maintained due to the action of the negative feedback. Furthermore, when the value of the load resistance R_L decreases,

V_{o}^{'} < V_{r e f}^{'}

, the pulse width decreases, and as a result, the time interval during which M₂ is turned on increases. The level of the control voltage V_control increases, and as a result, the decrease in the output voltage is compensated, according to Formula (13). For a load resistance of 900 Ω, the load current reaches 2 mA, and the output power on the load is 3.6 mW. During the regulation process, the frequency

f_{S}

of the switching signal remains a constant value.

To graphically illustrate the process of reaching a steady state, a sinusoidal generator with a small internal resistance, an amplitude of 4 V, and a frequency of 30 Hz is connected between terminals PZ1 and PZ2 in place of the piezoelectric element. In this way, the process of charging the supercapacitor and establishing the output voltage

V_{o}

and the “power-good” signal

V_{P G O O D}

can be traced. The start-up profile of the proposed energy-harvesting circuit is presented in Figure 17. The timing diagrams represent the process of starting and establishing the output voltage at the no-load output. More specifically, Figure 17 shows the voltage

v_{S T O}

on the supercapacitor, the output voltage

V_{o}

, and the

V_{P G O O D}

signal at the output of the window detector that produces a “power-good” signal. As shown in Figure 17, the output voltage was initially equal to zero since there was still no charge on the capacitor C_o. At the beginning of the operation process, since the output voltage is equal to zero (or there is no charge over the output capacitor C_o), the control voltage V_control is equal to 2.5 V. Moreover, the op-amp U₃ is initially without feedback. As a result, a voltage approximately equal to zero is obtained at the output of the analog comparator U₅. Then, at the output terminals of U₆ and U₇, voltages approximately equal to zero will be obtained. The nMOS transistor M₁ is turned off, and the pMOS transistor M₂ is turned on (

V_{G S 2} < V_{T H 2}

, where

V_{T H 2} < 0 V

is the threshold voltage of the pMOS transistor). After the initial moment, the capacitor C_o begins to charge, the feedback is closed, and the output voltage V_o smoothly rises. At the same time, the V_control decreases, and when its level reaches the level of the triangular voltage, a rectangular voltage begins to form with a decreasing duty cycle δ until the required value is reached. The V_control decreases to its required value, according to analytical expressions (12) and (13). At

k = \frac{V_{d, m}}{v_{t r, 0}} \approx \frac{2.5 V}{1.16 V} \approx 2.16

, for the control voltage produced by the error amplifier, the following is obtained:

V_{c o n t r o l} \approx \frac{V_{o, a v}}{k} \approx \frac{1.79 V}{2.16} \approx 0.83 V

In addition to the description of the principle of establishing a steady state of the prototype, Figure 18 shows the timing diagrams of the voltage drop

V_{S T O}

over the supercapacitor, the output voltage

V_{o}

, and the “power-good” signal

V_{P G O O D}

under the condition that the initial voltage drop over the supercapacitor is 1.5 V and higher than the value of the internal resistance. In this case, in about 650 s, an output voltage of 1.8 V is reached, and a “power-good” signal is obtained. As can be seen in Figure 18, the voltages change monotonically without intermediate spikes, and in the initial time interval, the output voltage is equal to zero. When the voltage on the supercapacitor reaches approximately 1.5 V (see Figure 17), an output voltage of about 1.2 V is reached with a jump. After this moment, the output voltage gradually reaches its established value equal to 1.8 V. The

V_{P G O O D}

signal reaches its setpoint value with a jump at the moment when the output voltage reaches a value of approximately 1.782 V or 1% of the setpoint value of the output voltage. When the voltage on the supercapacitor is further increased, no change in the output voltage occurs due to the action of the negative feedback of the DC-DC converter.

To evaluate the functionality of the proposed low-power DC-DC converter, the overall electrical energy efficiency (or power conversion efficiency) coefficient, which can be calculated based on the measured values of the average currents at certain nodes, is obtained from the following:

η = \frac{P_{L}}{P_{i n}} \times 100 %,

(17)

where

P_{i n}

is the power of the input signal produced by the DC power supply of type 2281S, and

P_{L} = P_{O S} - P_{C}

is the output power of the DC-DC converter (

P_{O S}

is the output power after the output LC filter, and

P_{C}

is the power consumption of the PWM controller circuit) over the load R_L.

As a result of the measurement procedure, Figure 19 shows the overall electrical energy efficiency (or power conversion efficiency)

η

under various piezoelectric excitation levels V_p_,m while the output voltage is V_o = 1.8 V. The tests are conducted for three values of the external load resistance R_L with values of 900 Ω, 1.8 kΩ, and 3.6 kΩ. The energy efficiency coefficient’s maximum value is approximately 78% at a piezoelectric voltage of 3 V and a load resistance of 3.6 kΩ. As the piezoelectric voltage increases, the polarization current flow decreases due to the regulating action of the negative feedback of the DC-DC converter, resulting in a reduction in the energy efficiency to a value approximately equal to 73%. As the load resistance decreases, the input polarization current is obtained with a larger value. Then, when the piezoelectric voltage increases, the polarizing current decreases again due to the action of the control circuit. Hence, the energy efficiency coefficient decreases (65% to 63% at R_L = 900 Ω). An advantage of the proposed circuit is the relatively small change in the coefficient of energy efficiency with relatively wide ranges of change in the resistance of the external load.

Based on the performed experimental study of a sample electronic circuit built on PCB in Figure 11b, according to the circuit configuration in Figure 2, the main electrical parameters are given in Table 1. Also, the main parameters of some representative self-powered energy harvesting circuits [15,18,22,36,37,38,39,40,41,42] published in the last five years are added. In addition to the values for the electrical parameters in Table 1, some comments are also given on the type of conversion circuit chosen, the start-up requirements when applying an input signal, the type of energy storage element used, the type of technology used to implement the certain electronic circuit, the type of piezoelectric generator used, and the chosen piezoelectric material.

The comparison of the proposed prototype and other previously published self-powered energy harvesting circuits shows that for most of them [15,18,22,37,38,39,40], the electrical parameters are obtained at a frequency of mechanical vibrations higher than 100 Hz. Thus, a relatively large average value of the generated electrical energy is obtained. For wearable electronic devices, the frequency of mechanical vibrations is usually in the order of several Hertz to several tens of Hertz, not exceeding 30–40 Hz. Furthermore, for some of the known circuit configurations [15,37,42], electrical energy is obtained by operating several piezoelectric elements, which is not always possible to apply, especially for wearable devices used by elderly and infirm patients. In the circuit configurations using commercially available specialized circuits of electronic converters [38,39,41] or built as custom monolithic integrated circuits (ICs) [15,18,36,37,40], the degree of miniaturization is significant, i.e., the devices are small in size and use several external discrete components. Also, in this case, the power dissipation is below 20 μW. However, for most of them, it is relatively complex to change the values of the output electrical parameters depending on the change in the parameters of the piezoelectric generator or the external load. For this type of electronic circuit, the output power has a relatively small value and does not exceed 500 μW. In contrast to the IC-based converters in the proposed prototype and other circuits with discrete components [22,38,41,42], high stability and relatively easy adjustment of the output signal parameters can be obtained. Also, for the circuits with discrete components, a larger value of the load current (>0.1 mA) can be produced for a given value of the load, which allows us to obtain both a larger output power and a higher value of Figure of Merit (FoM; this parameter is defined as

F o M = P_{o} / (C_{p} f V_{p, \max}^{2})

, where

P_{o} = V_{o}^{2} / R_{L}

is the power that can be delivered from the storage element (rechargeable battery or supercapacitor). Since the conversion of mechanical energy into electrical energy is obtained through a piezoelectric generator, the output power is strongly dependent on the operating conditions of the input source. For our work, the proposed prototype was designed to operate with a piezoelectric generator of type PPA-2011 (Mide Technology^®, Woburn, MA, USA) [43], which can provide an output current of up to 2 mA at a frequency of 25 Hz and an acceleration amplitude of up to 2 g. As a result, as well as due to the low self-consumption for the proposed prototype, a FoM is obtained with a value higher than 10. In comparison with the electronic circuits employing discrete components, a smaller number of passive and active components were used for the realization of the proposed prototype, and a significant part of the functionality was realized by specialized integrated circuits (such as op-amps and analog comparators), which have relatively simple topologies and contain a small number of integrated transistors.

5. Conclusions

A low-power piezoelectric energy harvesting circuit was designed and implemented using discrete passive components and several specialized analog integrated circuits. The proposed circuit configuration has functionality for converting electrical energy obtained through a single piezoelectric generator and is intended for use as a wearable battery-free power supply device. Based on the presented structure, the described principle of operation, and the experimental results, the following highlights of achievement can be defined for the proposed circuit: (1) a small number of active and passive components, as well as relatively easy tuning of the output voltage level; (2) a current consumption in idle operation no higher than 35 μA; (3) a coefficient of energy efficiency that can be achieved with a value greater than 75% for power dissipation below 30 μW, respectively; (4) a stabilized small output DC voltage with a value equal to

1.8 V \pm 5 mV

; (5) it achieved a good value for the power supply rejection ratio (PSRR) in the working range of input voltages; and (6) the output current value can reach 2 mA at a certain ohmic load without changing the level of the output voltage.

Along with the presented achievements, the future work of the authors is related to the following directions of improvement of the proposed prototype: (1) Expansion of the dynamic range of control, because for the presented electronic circuit, the triangular voltage that is applied to the non-inverting input terminal of the pulse-width modulator changes from 0 to about 0.5 V_DD. Furthermore, when passive RC components are used to form an integrator, the output voltage has an approximately exponential variation. This can be overcome by replacing the passive integrator with an active integrator circuit. In this way, approximately linear variation in the triangular voltage in the range from 0 to V_DD can be obtained. This, in turn, will lead to a certain increase in current consumption and a decrease in the energy efficiency factor. (2) Providing a functional possibility to obtain several output voltages depending on the type of external load. This possibility requires some complexity of the circuit structure and the addition of new passive and active components, but it can lead to an expansion of the efficiency of the proposed power supply device. (3) In the process of implementation, circuit configuration on a flexible printed circuit board is optimized, which provides an opportunity for better integration with the human body so that the electronic device does not create discomfort when worn and used for a long time.

Author Contributions

Conceptualization, I.P., H.A., N.T., N.K. and M.A.; methodology, I.P. and H.A.; formal analysis, I.P., N.K. and M.A.; investigation, I.P., H.A., N.K. and N.T.; resources, I.P., N.T. and N.K.; writing—original draft preparation, I.P., N.T., N.K. and M.A.; writing—review and editing, I.P., H.A., N.T., N.K. and M.A.; visualization, I.P., N.K. and N.T.; supervision, I.P. All authors have read and agreed to the published version of the manuscript.

Funding

This work has been accomplished with financial support from the European Regional Development Fund within the Operational Programme “Bulgarian National Recovery and Resilience Plan”, the procedure for the direct provision of grants ”Establishing of a network of research higher education institutions in Bulgaria”, and under Project BG-RRP-2.004-0005 “Improving the research capacity and quality to achieve international recognition and resilience of TU-Sofia (IDEAS)”.

Data Availability Statement

The data presented in this study are available on request from the authors.

Acknowledgments

The authors wish to thank L. V. Bogdanov, V. V. Dimitrov, and the reviewers for their helpful comments and suggestions.

Conflicts of Interest

The authors declare no conflicts of interest.

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Figure 1. Functional diagram of the proposed circuit prototype.

Figure 2. Schematic diagram of the proposed low-power energy-harvesting circuit.

Figure 3. A detailed schematic of the input stage for the schematic diagram in Figure 2—a full-bridge rectifier with an energy storage element: (a) schematic diagram; (b) typical signal waveforms of the input voltage v_p and the

i_{C_{p}}

through the piezoelectric capacitance at resonance operational mode.

i_{C_{p}}

through the piezoelectric capacitance at resonance operational mode.

Figure 4. An equivalent circuit of the pulse oscillator (or multivibrator), based on the multivibrator given as a part of the schematic diagram in Figure 2.

Figure 5. A configuration of the integrating circuit from the schematic diagram in Figure 2.

Figure 6. Signal waveforms of the input and output voltages for the proposed pulse-width modulator.

Figure 7. A configuration of the error amplifier and compensator from the schematic diagram in Figure 2.

Figure 8. A configuration of the low-power driver stage for the synchronous converter from the schematic diagram in Figure 2.

Figure 9. Signal waveforms at the input and output voltages for the proposed low-power driver stage of the synchronous converter.

Figure 10. A configuration of the window detector producing the “power-good” signal for the synchronous converter from the schematic diagram in Figure 2.

Figure 11. The low-power AC-DC converter construction prototype board: (a) variant 1 (top view); (b) variant 2 (top view).

Figure 12. Captured waveforms from the experimental study (CH1:

v_{r}

, CH2:

v_{t r}

, CH3:

v_{c o n t r o l}

, and CH4:

v_{d}

in Figure 2) at the no-load output (R_L → ∞).

Figure 12. Captured waveforms from the experimental study (CH1:

v_{r}

, CH2:

v_{t r}

, CH3:

v_{c o n t r o l}

, and CH4:

v_{d}

in Figure 2) at the no-load output (R_L → ∞).

Figure 13. Captured waveforms from the experimental study (CH1:

v_{r}

, CH2:

v_{t r}

, CH3:

v_{c o n t r o l}

, and CH4:

v_{d}

in Figure 2) at external load R_L = 3.6 kΩ.

Figure 13. Captured waveforms from the experimental study (CH1:

v_{r}

, CH2:

v_{t r}

, CH3:

v_{c o n t r o l}

, and CH4:

v_{d}

in Figure 2) at external load R_L = 3.6 kΩ.

Figure 14. Captured waveforms from the experimental study (CH1:

v_{r}

, CH2:

v_{t r}

, CH3:

v_{c o n t r o l}

, and CH4:

v_{d}

in Figure 2) at external load R_L = 1.8 kΩ.

Figure 14. Captured waveforms from the experimental study (CH1:

v_{r}

, CH2:

v_{t r}

, CH3:

v_{c o n t r o l}

, and CH4:

v_{d}

in Figure 2) at external load R_L = 1.8 kΩ.

Figure 15. Captured waveforms from the experimental study (CH1:

v_{r}

, CH2:

v_{t r}

, CH3:

v_{c o n t r o l}

, and CH4:

v_{d}

in Figure 2) at external load R_L = 900 Ω.

Figure 15. Captured waveforms from the experimental study (CH1:

v_{r}

, CH2:

v_{t r}

, CH3:

v_{c o n t r o l}

, and CH4:

v_{d}

in Figure 2) at external load R_L = 900 Ω.

Figure 16. Captured waveforms for the pulse-width modulated signal

v_{d}

(CH1), the non-overlapping pulse signals (

v_{T P 3}

(CH2) and

v_{T P 2}

(CH3)) at the gates of the M₂ and M₁ (see Figure 2), and the level of the output voltage

V_{o}

(CH4) from the experimental study at the no-load output.

Figure 16. Captured waveforms for the pulse-width modulated signal

v_{d}

(CH1), the non-overlapping pulse signals (

v_{T P 3}

(CH2) and

v_{T P 2}

(CH3)) at the gates of the M₂ and M₁ (see Figure 2), and the level of the output voltage

V_{o}

(CH4) from the experimental study at the no-load output.

Figure 17. Start-up profile of the DC-DC converter circuit from the experimental study using an input sinusoidal generator with a low internal resistance at

C_{S T O} = 1 F

C_{o} = 100 μ F

, and

R_{L} \to \infty

(no-load output) (CH1:

v_{S T O}

(a yellow curve), CH2:

V_{o}

(a blue curve), and CH3:

V_{P G O O D}

(a red curve)).

Figure 17. Start-up profile of the DC-DC converter circuit from the experimental study using an input sinusoidal generator with a low internal resistance at

C_{S T O} = 1 F

C_{o} = 100 μ F

, and

R_{L} \to \infty

(no-load output) (CH1:

v_{S T O}

(a yellow curve), CH2:

V_{o}

(a blue curve), and CH3:

V_{P G O O D}

(a red curve)).

Figure 18. Captured waveforms from the experimental study at an initial voltage of

V_{S T O} = 1.5 V

C_{S T O} = 1 F

C_{o} = 100 μ F

R_{L} \to \infty

(no-load output), and

I_{p, m} \approx 2 mA

(CH1:

v_{S T O}

(a yellow curve), CH2:

V_{o}

(a blue curve), and CH3:

V_{P G O O D}

(a red curve)).

Figure 18. Captured waveforms from the experimental study at an initial voltage of

V_{S T O} = 1.5 V

C_{S T O} = 1 F

C_{o} = 100 μ F

R_{L} \to \infty

(no-load output), and

I_{p, m} \approx 2 mA

(CH1:

v_{S T O}

(a yellow curve), CH2:

V_{o}

(a blue curve), and CH3:

V_{P G O O D}

(a red curve)).

Figure 19. Measured overall electrical energy efficiency under various piezoelectric excitation levels V_p_,m while the output voltage is V_o = 1.8 V.

Table 1. A comparison between the proposed prototype and selected self-supplied energy harvesting circuits reported during the last five years.

Parameter	This Work	(Peng et al.) [36]	(Du et al.) [15]	(Li et al.) [37]	(Chew et al.) [38,39]	(Çiftci et al.) [18]	(Chamanian et al.) [40]	(Huet et al.) [41]	(Ben Ammar et al.) [42]	(Costanzo et al.) [22]
Piezoelectric element
Piezoelectric generator	MIDE PPA-2011 ⁽⁴⁾	MIDE PPA-1022	Custom MEMS harvester 1.0 g	MIDE PPA1021 and PPA1011	1 Smart Material MFC8528-P2	Custom MEMS harvester with a footprint of 36 mm²	MIDE V22BL	MIDE PPA-1014	AB4113BLW100-R	MIDE PPA-4011
Excitation frequency	10–30 Hz	53–85 Hz	219 Hz	100–140 Hz	>100 Hz	450 Hz	208 Hz	<100 Hz	1 Hz	232 Hz
Maximum average power (or raw power)	205 μW	>300 μW	186 μW	160–200 μW	0.5 mW	n.a.	n.a.	>5 mW	85.53 μW ⁽⁵⁾	>100 μW
Piezoelectric capacitance	190 nF	7 nF	1.94 nF	20 and 100 nF	n.a.	2 nF	4.66 nF	40 nF	150 nF	415 nF
Open circuit voltage amplitude	up to 6 V	0.85–2.13 V	up to 7 V	1.6–2.66 V	1.2–20 V	<3.2 V	0.87 V	<8 V	7.2 V	<4 V
Piezoelectric material	PZT-5H	PZT-5H	N/A	PZT-5H	Micro Fiber Composite material (MFC)	N/A	PZT-5H	PZT-5H	PZT	PZT-5H
Controlling circuit
Type of conversion circuit	Bridge rectifier; DC-DC step-down synchronous converter and power-controlling system	Sense-and- set (SaS) rectifier with a static power of 7 nW	Split-electrode SSHC (SE-SSHC) rectifier	Parallel-SSHI Rectifier; buck-boost DC-DC converter	Voltage doubler; analog control circuit LTC3388-3, buck converter, and LTC2934-2	SSHC circuit utilizing a flipping inductor; DC-DC converter; LDO	Enhanced SSHI system (used external inductor in the range of μHs)	LTC3588-1 extraction circuit; balancing system ALD810023 for ultra caps	Self-Powered (SP P-SSHI ⁽⁶⁾) energy management circuit	Energy Harvester Power Optimizer (EHPO)
Type of realization	Discrete components	Process: 180 nm CMOS; Chip-area: 0.47 mm²	Process: 180 nm CMOS; Chip-area: 3.9 mm²	Process: 130 nm CMOS; Chip-area: 1.07 mm²	Discrete components	Process: 180 nm CMOS; Chip-area: 1.23 mm²	Process: 180 nm CMOS; Chip-area: 0.28 mm²	Discrete components	Discrete components	Discrete components
Power consumption	≈30 μW	≈10 μW ⁽¹⁾	≈2.9 μW ⁽¹⁾	5 μW ⁽¹⁾	≤80 μW	≈18 μW ⁽¹⁾	3.84–26.37 μW	50 μW	n.a.	n.a.
Output DC voltage	1.8 V ± 5 mV	up to 2 V	up to 6 V	≤3 V	≤3.3 V	≤3 V	2.68 V optimum value	2.8–3.6 V	3.6 V	up to 4 V
Output power	3.6 mW	15 μW	16.1 μW	120–200 μW	2.43 mW	24.2 μW	3.84 μW	213.2 mW	3.6 mW	2.81 mW
FoM ⁽³⁾	>10	up to 7.8	n.a.	8.47	4.86	2.62	up to 5.23	n.a.	n.a.	1.9 ⁽⁵⁾
Maximum overall electrical energy efficiency	78%	42%	>80%	78%	75.6%	83% (L = 100 μH)	93% (L = 820 μH)	36%	83.02%	n.a.
Start-up requirements	Self-powered; supercapacitor 1 F/7.5 V at the output of the rectifier ⁽²⁾	Self-powered; battery at the output port ⁽²⁾	Self-powered; storage capacitor at the output port ⁽²⁾	Self-powered; supercapacitor 4.7 mF at the output port ⁽²⁾	Self-powered; supercapacitor 22 mF at the output port ⁽²⁾	Self-powered; storage capacitor 453 nF at the output port ⁽²⁾	Self-powered; storage capacitor 449 nF at the output port ⁽²⁾	Self-powered; supercapacitors 8 × 1 F at the output of the rectifier ⁽²⁾	Self-powered; ML 2032 cell Lithium battery at the output port ⁽²⁾	Self-powered; aluminum electrolytic capacitors at the output port
Year	2024	2019	2019	2019	2020	2021	2021	2022	2023	2023

⁽¹⁾ Calculated from the paper; ⁽²⁾ A battery or capacitor is connected as an energy storage element; ⁽³⁾ Figure of Merit:

F o M = P_{o} / (C_{p} f V_{p, \max}^{2})

, where

P_{o} = V_{o}^{2} / R_{L}

is the power that can be delivered from the storage element (rechargeable battery or supercapacitor); ⁽⁴⁾ The proposed electronic circuit of the AC-DC converter is intended to work with the PPA-2011 [43]; ⁽⁵⁾ Estimated from graphs in the paper; ⁽⁶⁾ Parallel Synchronized Switch Harvesting on Inductor (P-SSHI). n.a. = data not available.

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Pandiev, I.; Antchev, H.; Kurtev, N.; Tomchev, N.; Aleksandrova, M. Analysis and Design of Low-Power Piezoelectric Energy Harvesting Circuit for Wearable Battery-Free Power Supply Devices. Electronics 2025, 14, 46. https://doi.org/10.3390/electronics14010046

AMA Style

Pandiev I, Antchev H, Kurtev N, Tomchev N, Aleksandrova M. Analysis and Design of Low-Power Piezoelectric Energy Harvesting Circuit for Wearable Battery-Free Power Supply Devices. Electronics. 2025; 14(1):46. https://doi.org/10.3390/electronics14010046

Chicago/Turabian Style

Pandiev, Ivaylo, Hristo Antchev, Nikolay Kurtev, Nikolay Tomchev, and Mariya Aleksandrova. 2025. "Analysis and Design of Low-Power Piezoelectric Energy Harvesting Circuit for Wearable Battery-Free Power Supply Devices" Electronics 14, no. 1: 46. https://doi.org/10.3390/electronics14010046

APA Style

Pandiev, I., Antchev, H., Kurtev, N., Tomchev, N., & Aleksandrova, M. (2025). Analysis and Design of Low-Power Piezoelectric Energy Harvesting Circuit for Wearable Battery-Free Power Supply Devices. Electronics, 14(1), 46. https://doi.org/10.3390/electronics14010046

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Analysis and Design of Low-Power Piezoelectric Energy Harvesting Circuit for Wearable Battery-Free Power Supply Devices

Abstract

1. Introduction

2. Functional Diagram for the Proposed Energy Harvester Circuit

3. Circuit Description

3.1. Full-Bridge Rectifier at a Non-Sinusoidal Input Signal—Input Stage

3.2. Step-Down (Buck) Synchronous Converter and Switching Circuit

3.3. Structure of the Error Amplifier and the Compensator

3.4. Structure of a Low-Power Driver Stage for the Synchronous Converter

3.5. Structure of the Window Detector Produces the “Power-Good” Signal

4. Experimental Results and Discussion

5. Conclusions

Author Contributions

Funding

Data Availability Statement

Acknowledgments

Conflicts of Interest

References

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