Dual Piezoelectric Energy Investing and Harvesting Interface for High-Voltage Input

Abstract

A novel harvesting interface for multiple piezoelectric transducers (PZTs) is proposed for high-voltage energy harvesting. Pre-biasing a PZT prior to its mechanical deformation increases its damping force, resulting in higher energy extraction. Unlike the conventional harvesters where a PZT-generated output is assumed to be continuous sinusoidal and output polarity is assumed to be alternating every cycle, PZT-generated output from human motion is expected to be random. Therefore, in the proposed approach, energy is invested to the PZT only when PZT deformation is detected. Upon the motion detection, energy stored at a storage capacitor (C_STOR) from earlier energy harvesting cycle is invested to pre-bias PZT, enhancing energy extraction. The harvested energy is transferred to back C_STOR for energy investment on the next cycle and then excess energy is transferred to the battery. In addition, partial electric charge extraction (PECE) is adapted to extract a partial amount of charges from the PZT every time its voltage approaches the process limit of 40 V. Simulations with 0.35 µm BCD process show 7.61× (with PECE only) and 8.38× (with PECE and energy investment) improvement compared to the conventional rectifier-based harvesting scheme Proposed harvesting interface successfully harvests energy from excitations with open-circuit voltages up to 100 V.

1. Introduction

With ever-increasing interest in wearable electronics, many smart devices, such as smart watches, earphones, rings, and glasses, have been developed. Moreover, many devices for healthcare, such as human body posture, heart rate, blood pressure, sugar level, and wound monitors, have also been developed. These devices are usually powered with lightweight batteries having low capacity that require frequent battery re-charging or replacement, which is undesirable and sometimes difficult in the case of implantable devices. To achieve energy autonomy, widely investigated energy harvesting sources include RF [1,2,3,4], light [5], heat [6], and vibrations [7,8,9]. Among these sources, vibration energy has been extensively investigated due to the abundance of vibrations in the ambient environment. For this purpose, various electromechanical transducers, such as electromagnetic [10], triboelectric [11], and piezoelectric [12] transducers, are usually utilized.

Due to their light weight, flexibility, high energy density, and easy integration, piezoelectric transducers (PZTs) are widely used for kinetic energy harvesting. Multiple PZTs can be easily attached to human body joints, such as elbows or knees, to take advantage of vibrations resulting from human motion. As these vibrations are irregular, PZT generates irregular output with aperiodic pulses, which require a harvesting interface circuit for energy harvesting. Although many harvesting interface designs have been proposed to harvest energy from a single PZT [13,14,15,16,17], there has not been much work focused on harvesting energy from multiple PZTs attached to the human body. As energy generated by a single PZT could be insufficient to power wearable electronics, this work focuses on maximizing energy extraction from multiple PZTs.

Fabrication and characterization of multiple vibration transducers-based systems have been done in some of the prior works [18,19,20]. However, they only utilize simple circuits with discrete components or commercially available harvesting circuits to evaluate harvesting performance and did not present any optimized integrated circuit design for multiple transducers. Several investigations have been done on mathematical modelling of piezoelectric harvesters [21,22,23]. Cantilever beam configuration is the most commonly used configuration for piezoelectric energy harvesting. In this configuration, one end of PZT is fixed and a mass is attached to the other end. This can be represented as an electromechanical model [24]. In circuit domain, the PZT model can be simplified as a current source (PZT-generated current, I_P) in parallel with the PZT’s internal capacitance (C_P) [25], as shown in Figure 1a. The electromechanical model is utilized if accurate results in combination with interface circuits are required. If the focus lies exclusively on the designing interface circuit and resonance/feedback characteristics are not important, the simplified circuit (uncoupled model) can be used [26,27]. As focus of the proposed work is on harvesting circuit design, our analysis will be based on this electrical model of PZT.

When mechanical displacement (u) is applied to a PZT, I_P is generated, which charges C_P, and an output voltage (V_P) is developed across C_P. The generated charge (Q_P) is proportional to the physical deformation applied to the PZT. Therefore, for a given amount of physical deformation, Q_P remains the same even if the load capacitance (C_L) seen by the PZT changes [28]. PZT-generated energy (E_P) from a single deformation can be written as follows:

$$E_P= \frac{1}{2}\left(C_P+C_L\right)V_P^2=\frac{1}{2}\frac{Q_P^2}{C_P+C_L}$$

(1)

where V_P is the final (peak) PZT voltage at the maximum/minimum u. This implies that for any u applied to the PZT and generated Q_P, E_P is inversely proportional to load capacitance seen by the PZT. A smaller load capacitance allows the faster development of V_P and therefore makes the PZT damping force stronger [29,30]. Hence, for the same amount of u, more energy is required; therefore, more mechanical energy is converted to electrical energy. This means that to capitalize on the extractable energy from the PZT, the load capacitance seen by the PZT should be minimized [28].

Numerous harvesting interface circuits have been proposed [17,25,27,30,31,32,33,34] to efficiently harvest energy generated by vibrations applied to the PZT. Most of these prior works focus on harvesting energy from continuous (sinusoidal) or shock (decaying sinusoidal) excitations applied to the PZT. Some prior works, such as [21,22,23], rely on cantilever-beam configuration for measurement results for different operation frequencies (resonance and off-resonance), which is not applicable to the proposed work, which focuses on energy harvesting from random input pulses generated by human motion. Synchronous switch harvesting on inductor (SSHI) [17,25,31,32] is one of the most widely adopted piezoelectric energy-harvesting interface designs. A simplified circuit diagram of an SSHI-based harvesting interface is shown in Figure 1a. A rectifier is essential to convert PZT-generated alternating output voltage to the rectified V_RECT. Initially, input excitations applied to the PZT are assumed to be continuous, as shown in Figure 1b. The polarity of V_P is flipped (using an inductor) at every half cycle of I_P (maximum/minimum of u) to extract more energy from the PZT in the next half cycle. This means that the PZT voltage will be already at a higher value (behaving as pre-biased) as the next half cycle starts, which strengthens the damping force [30], and more energy is extracted from the PZT. However, these types of harvesters are not optimized for mechanical inactivity periods, which might be possible when the human body is at rest. During an inactive period, C_P will discharge (depending on the circuit/PZT resistance), which could compromise the harvesting interface circuit functionality. In addition, energy (E_PZT) extraction from the PZT will decrease during the next deformation as C_P would need to be charged from a lower voltage as the deformation starts. Therefore, bias-flipping at every maximum/minimum of u is not suitable for irregular human motion.

One solution to avoid a potential bias-flip circuit failure due to random input is a synchronous electric charge extraction (SECE) technique [27,33,34], in which bias-flip is not performed. In SECE-based PZT harvesting interface circuits [27,33,35], which can be simplified as shown in Figure 1c, V_P is increased to its peak before starting a complete electric charge extraction from C_P using an inductor. This means that the PZT-generated voltage starts from zero (without pre-bias) at the beginning of each deformation, which results in a lower damping force on the PZT [30] and hence limited energy extraction in each harvesting cycle. A variation of SECE, called delayed-SECE [36], aims at increasing energy extraction by sending part of the generated-energy back to the PZT at the end of one half-cycle of I_P with the help of an inductor. This way, V_P is already high at the start of the next half-cycle of I_P. However, circuit functionality (in case of random input) is compromised by doing bias-flip like operation (after peak detection) at the end of each deformation. Therefore, energy investment at the correct instant is critical for maximum energy extraction, and an optimized circuit needs to be designed for this purpose.

Moreover, as harvesting sources (piezo/tribo-electric transducers) are improved, higher energy can be extracted with higher input voltage [28,37,38,39,40]. Designing a circuit to harvest energy from these high-input voltages is a non-trivial challenge, and it becomes even more challenging when these output voltages can exceed the process limit. In SSHI-based harvesting interfaces, a large load (buffer) capacitor (C_L) is required at the output of the rectifier, as shown in Figure 1a. Typically, C_P of PZTs used for energy harvesting is in the order of 100 s of pF to 10 s of nF (in [17,27,28,29,31,32]). Whereas, typical value of C_L used by SSHI-based harvesters is in the order of 10s of µF (3.3 μF in [17,32] and 22 µF in [41]), which is very high compared to C_P. Due to this C_L, the PZT-generated voltage cannot exceed V_RECT much, as shown in Figure 1b. This C_L acts as protection against the strong input excitations, which can generate high piezoelectric open-circuit voltage (V_OC). Thus, V_RECT remains lower than the maximum voltage allowed by the process node (V_MAX). However, as discussed earlier, the addition of a large load capacitor significantly reduces energy extraction from the PZT [28]. In contrast, SECE-based harvesting interfaces can suffer from strong input excitations with high V_OCs of the PZT, where V_P is proportional to the strength of the input excitation applied to the PZT. For weak input excitations, PZT-generated peak voltage remains lower than V_MAX, but in the case of strong input excitations, V_P can exceed V_MAX (Figure 1d) and possibly damage the integrated circuit (IC).

To address all of the abovementioned challenges, a novel harvesting interface circuit is proposed. Unlike prior works [12,29,37], this work proposes an integrated-circuit-based harvesting solution for multiple PZTs. The power stage is designed using bi-directional switches, which enables bi-directional energy transfer for both energy investment and storage, while only using a single inductor. The energy from a PZT is deposited to a temporary storage capacitor (C_STOR) using an inductor at the peak voltage of V_P. A control circuit monitors the PZT deformation and activates the harvesting interface to invest energy stored on C_STOR back to the PZT (pre-biasing it) only when another deformation is detected. This energy-investment scheme is a new approach introduced in this work. Energy investment increases the PZT damping force, and more mechanical energy is converted to electrical energy. The PZT voltage keeps rising after this point until its peaking event is detected. In addition, to avoid IC damage due to strong excitations exceeding V_MAX, another harvesting approach called partial electric charge extraction (PECE) [29] is adopted. In PECE, charges are partially extracted from the PZT whenever V_P approaches V_MAX, thereby allowing the harvesting interface circuit to handle strong input excitations without needing any load capacitance, thereby maximizing energy extraction. A dedicated control circuit is designed to control PECE cycles for multiple PZTs and their different polarities. In addition, energy investment and PECE in the same circuit with multiple PZTs require a special control circuit and can result in many different operation cases. For this purpose, special control circuits and sub-blocks were designed in this work. All these cases and operation phases make this work unique from previous works.

The rest of this paper is organized as follows. In Section 2, the key approaches of the proposed harvesting interface circuit are described. In Section 3, the proposed harvesting interface implementation details are elaborated. The simulation results and comparison with prior works are reported in Section 4, and the paper is concluded in Section 5.

2. Proposed Maximum Energy Extraction Approach

PZTs can be easily attached to human body joints to convert vibrations generated by human motion into electrical energy. To maximize energy extraction from human body motion, multiple PZTs can be attached to human body joints or skin. As human motion can be irregular, a PZT-harvesting interface circuit should be optimized to deal with these vibrations of random amplitude and frequency. Therefore, the proposed energy-harvesting interface is designed to harvest energy from irregular motion applied to multiple PZTs simultaneously. To maximize the extractable energy, an energy-investment scheme is introduced. In addition, to handle strong input excitations, which can generate V_OCs greater than V_MAX, the harvesting interface utilizes a PECE scheme [29].

2.1. Energy Investment

As explained earlier, biasing a PZT to a higher voltage level prior to bending deformation results in a higher amount of energy extraction from the PZT during deformation. Therefore, in the proposed energy-harvesting interface, an energy-investment scheme is introduced. In this scheme, energy is invested to a PZT at the start of its bending deformation, which increases the bias voltage across the PZT and makes its damping force stronger, resulting in higher energy extraction from the PZT.

The conceptual waveform of the proposed energy investment-based harvesting scheme is shown in Figure 2. A storage capacitor (C_STOR) is utilized to temporarily store the PZT-generated energy and invest it back to the PZT when required. For weak input excitations (assuming C_STOR is not fully charged initially), V_P is maximized until it reaches its peak (V_A), at which point some energy is transferred to C_STOR through the inductor until it becomes fully charged and the remaining energy is harvested to the battery. The energy generated by the PZT till this point can be written as

$$E_A= \frac{1}{2}{C}_P{V}_A^2$$

(2)

When the next deformation is detected, the energy from C_STOR is invested to the PZT (using the inductor), which increases the PZT voltage by ∆V_i, resulting in more energy extraction from the PZT until peak voltage (V_B) is detected. The energy at this point (V_B) can be written as

$$E_B= \frac{1}{2}{C}_P{V}_B^2$$

(3)

Assuming that the same amount of deformation is applied to PZT in the second half cycle and the energy (∆V_i = V_A ideally) is invested as soon as PZT deformation starts, Equation (3) can be written as

$$E_B= \frac{1}{2}{C}_P{\left(\Delta V_i+V_A\right)}^2=4\times E_A$$

(4)

E_B is ideally the maximum harvestable energy, which is significantly higher than E_A, thanks to energy investing. In a non-ideal situation, energy will be invested when V_P has already increased to a threshold voltage (determined by the harvesting interface), as shown in the second half cycle in Figure 2. This means that the actual E_B will not have reached a maximum amount as in (4), but still it would be significantly higher than E_A. Therefore, in the proposed energy-investment scheme, the energy generated by the PZT is maximized by the energy investment to the PZT.

2.2. Partial Electric Charge Extraction (PECE)

PZT-generated energy is inversely proportional to the load capacitance seen by the PZT [28,29]. As the load capacitance is reduced, E_PZT increases, but the resultant V_P also increases. The IC could be damaged if this V_P exceeds V_MAX. At this point, the PZT needs to be discharged to protect the IC, but it is also desirable to maintain the PZT voltage as high as possible for maximum energy extraction, as explained earlier. Therefore, a PECE scheme is adopted in which once the PZT voltage approaches V_MAX, charges are partially extracted from the PZT, thereby decreasing V_P by PECE step voltage (∆V_PH) after a single PECE cycle, as shown in Figure 2. Following a PECE cycle, the PZT voltage keeps increasing until another PECE condition (V_P >= V_MAX) is achieved or the peak voltage (V_PK) is detected. Once V_PK is detected, the charges are completely extracted from the PZT. By using this approach, energy extraction is maximized by load capacitance minimization while avoiding V_MAX. This allows the IC to tolerate strong input excitations that can generate V_OCs higher than V_MAX.

Determining the optimal value of ∆V_PH is critical for achieving maximum energy extraction from the PZT. Assuming a strong input excitation, if ∆V_PH is too small, PECE will be activated many times before peak detection. This means that the harvesting interface will need to be activated multiple times to extract a partial amount of charges from the PZT, incurring switching losses and thereby reducing the net amount of harvested energy (E_HRV). Whereas, if ∆V_PH is too large, V_P will drop to a low voltage, decreasing the damping force on the PZT and hence lowering the energy extraction from it. Therefore, determining the optimal value of ∆V_PH is very important for maximum energy extraction from the PZT. A ∆V_PH of 8 V was chosen based on simulations.

3. Multiple Piezoelectric Energy-Harvesting Interface Implementation

To maximize the energy extraction from human body joints, multiple PZTs are utilized in this work. A simplified circuit diagram of the proposed piezoelectric energy-harvesting interface circuit is shown in Figure 3. For conceptual verification of high-voltage energy-harvesting using multiple PZTs, two PZTs are used in this work to harvest energy using a shared single inductor (L₁). This inductor is used to transfer energy from the PZTs to the battery and/or storage capacitor (C_STOR). Energy harvesting from C_P to C_STOR (or battery) and energy investment from C_STOR to C_P requires bidirectional power switches. Therefore, two switches per PZT, S_Pi1 and S_Pi2, are used for the positive half cycle of PZT-generated output voltage. Similarly, two switches per PZT, S_Ni1 and S_Ni2, are used for the negative half cycle. Altogether, these four switches act as a rectifier and are only activated according to the PZT-generated voltage polarity.

The proposed harvesting interface operation phases are shown in Figure 4, and the corresponding conceptual waveforms are shown in Figure 5. For convenience, in the harvesting operation explanation, only a single PZT (PZT₁) is assumed to undergo deformation; therefore, the circuit configurations in Figure 4 and Figure 5 correspond to PZT₁ only. Whenever mechanical deformation is applied to PZT₁, the generated I_P1 starts charging C_P (Phase I). V_P1 keeps rising until the peak voltage (V_PK) is detected (at time t₀), as shown in Figure 5a. At this point, S_P11/S_P22/S₂ are turned on and the charges are completely extracted from C_P to the inductor (L₁) (Phase II). This will be referred to as full electric charge extraction (FECE) in the remainder of the paper. In Phase III, S_P11/S_P22/S₂ are turned off and S₃/S_STOR are turned on to transfer energy from L₁ to C_STOR (Figure 5b) until V_STOR reaches the desired maximum value (V_STOR(MAX)). The remaining energy on the inductor (if any) is delivered to the battery in Phase IV by turning on S₃/S_BAT. Once this energy transfer is complete, S₃/S_BAT are turned off to mark the completion of a harvesting cycle.

Assuming there is no input excitation (between Phase IV and V in Figure 5a) applied to the PZT₁ for a while, the circuit remains idle. Once another (second) deformation is applied to the PZT1 in the opposite direction, I_P1 starts charging C_P1 with opposite polarity (Phase V). As soon as this deformation is detected by the circuit, an energy investment cycle is initiated (at time t₁ in Figure 5a). The zoomed energy investment phases VI–VII are shown in Figure 5c. In Phase VI, the energy stored on C_STOR is transferred to the inductor by closing S₃/S_STOR. To invest this energy into C_P1, the circuit is configured as shown in Phase VII in Figure 4, where the inductor charges C_P1 until I_L becomes 0, which marks the end of the energy investment. During energy investment, V_P1 increases by ∆V_i, as the waveform shows in Figure 5a. Due to this increased voltage, the damping force of the PZT increases, and more energy is extracted from PZT until V_P1 reaches the peak voltage (Phase VIII). After peak voltage detection (at time t₃), similar steps (II–IV) as those performed for the 1st deformation for energy transfer to C_STOR and battery are repeated. In the case of multiple PZTs, energy will be invested/harvested to/from whichever PZT deforms first or detects V_PK first, while accounting for PZT voltage polarity.

In some cases, after energy investment, V_P can rise faster due to strong input excitations and can approach V_MAX (as shown in the 2nd deformation in Figure 5a). In that case, PECE is activated (at time t₂) and PZT voltage is decreased by ∆V_PH, and thereby V_P keeps increasing until V_PK. PECE also repeats the same energy-harvesting steps (II–IV) as in the 1st deformation, as shown in Figure 5d. In another possible scenario (not shown in Figure 5) of strong input excitations where there is no energy available to invest at the start of the second deformation, the PZT voltage will keep rising until either the PECE condition is achieved or peak voltage is detected. For strong excitations, multiple PECE cycles can be activated before a peaking event is detected.

The top-level implementation details of the proposed piezoelectric energy-harvesting interface circuit are presented in Figure 6. A full-bridge rectifier (FBR) is used to rectify the PZT alternating output to V_RECT. This rectifier is essential to interface the wakeup-controller (WUC) [37] with the PZT, which is used to monitor and detect PZT deformation. The WUC is implemented using all low-voltage (LV) devices except a high-voltage capacitor C_i1. The V_RECT is capacitively coupled using C_i1, which is necessary to deal with the high output voltages of the PZT. This rectifier is not used for actual energy transfer to/from the PZT and is not required after PZT deformation has been detected. Once a deformation is applied to the PZT, the WUC monitors the rise in PZT-generated voltage. As V_RECTi starts to increase, V_WUCi starts to increase as well. The WUC triggers TRIG_i signal only when V_WUCi (V_P) exceeds a certain threshold voltage level. After the trigger, one of the terminals in C_i1 connected to WUC is grounded to avoid damaging WUC with increasing V_P input.

TRIG_i is used to activate other sub-blocks using a specially designed harvest and invest control circuit (HIC). First of all, TRIG_i activates the polarity detection controller (PDC), which determines the polarity of the PZT voltage by comparing V_Pi and V_Ni. Polarity is termed as positive (V_POL = 1) for V_Pi > V_Ni; otherwise it is negative (V_POL = 0). Along with the PDC, the WUC activates a storage level comparator (SLC), which is a clocked comparator, where clock in this case is a single pulse (TRIG_i). The SLC is utilized to check the voltage level of the storage capacitor (C_STOR). V_STOR > V_REF means the capacitor is charged with a certain voltage level and energy can be invested to the PZT, where V_REF (internally generated reference voltage) in this case is 3.3 V. The SLC is time shared by both PZTs depending on whichever triggers first. In addition, TRIG_i also activates a clock generator (CLK Gen.) [42] to generate a clock that is necessary for the operation of other sub-blocks. The activation and operation of other sub-blocks are explained in the following sub-sections.

3.1. Energy Investment Control

For maximum energy extraction from the PZT, energy investment to the PZT is carried out. Before energy investment, the SLC compares V_STOR and V_REF and determines if there is enough energy in C_STOR available to invest. If V_STOR > V_REF condition is met, the energy investment cycle starts. In this cycle, energy is initially transferred from C_STOR to L₁ by closing S₃ and S_STOR, as explained earlier in Figure 4. A zero-crossing detector (ZCD_B) (derived from [43]) is activated to monitor this energy transfer. ZCD_B keeps comparing V_L2 with GND, and energy transfer to L₁ is stopped when V_L2 <= 0 V condition is met. At this point, energy can be invested from the inductor to the PZT by turning on power switches according to the polarity of the PZT. For positive polarity, S_Pi1/S_Pi2 are closed along with S₂, and energy starts transferring from L₁ to the PZT. Here, V_L1 starts rising and so does V_Pi. As both of these voltages can be higher than 5 V, they cannot be handled with LV switches. To handle these higher voltages, V_L1 is divided by R₅ and R₆ to V_LDIV, and V_Pi is divided by R_i1 and R_i2, and then this divided voltage is fed to a 2 × 1 analog multiplexer (M_i1) whose output (V_RDIV) is selected by V_POL. A comparison of V_RDIV with V_LDIV is performed by an investment-tracking comparator (ITC), which keeps tracking these voltages until V_LDIV becomes lower than V_RDIV, which means V_L1 < V_Pi and I_L becomes ~0 A. At this point, the investment cycle is completed and S_Pi1/S_Pi2/S₂ are opened. I_Pi keeps charging C_Pi after this point until the end of deformation.

3.2. Peak Voltage Detection Control

Once the investment has been completed, the PZT voltage must increase to its peak to maximize energy extraction. V_PK can be detected by a clocked voltage peak detector (VPD_i) (based on [37]), which is activated by the PDC. Each PVD (just like WUC) is implemented using all LV devices except a high voltage capacitor. The PZT voltage is capacitively coupled using this capacitor, which is necessary to handle the high output voltages of the PZT. Therefore, two capacitors, C_i2 and C_i3, are utilized to deal with the positive and negative polarity of the PZT voltage, respectively. V_POL determines the output (V_PDIV) of another 2 × 1 analog Multiplexer (M_i2) for VPD_i. V_PDIV is injected to VPD_i, which keeps tracking the PZT voltage for V_PK. VPD_i determines the V_PK by comparing the slope of PZT voltage during two consecutive clock cycles. At the end of a single deformation, I_Pi becomes ~0 A and PZT voltage slope becomes negative, which signals peak detection. Voltage at the output of the capacitor (either C_i2 / C_i3) is repeatedly reset to ground at the end of every clock cycle to keep their voltage within the range of 0 V-V_DD, preventing damages on IC due to high voltages. The HIC also keeps monitoring the output of the VPDs of both PZTs in case both of them are pressed together. If the V_PKs of both PZTs are detected at the same time, the first PZT to transfer energy to storage/battery through the inductor is selected by a priority bit. Following the energy transfer from the first PZT, energy is extracted from the second PZT immediately. To avoid false peak detection, the HIC stops peak voltage detection during the energy investment/harvesting cycles of either PZT. This does not affect the overall performance of the system as energy investment/harvesting cycles are completed within a few micro-seconds.

3.3. PECE Control

Partial electric charge extraction (PECE) control has also been adopted to extract more energy from the PZT for V_OCs greater than the maximum tolerable voltage (V_MAX). The supply voltage (V_DD) used for control circuits in this work is 3.3 V. The transistors used for control circuits can only handle up to 5 V. Along with VPD, a clocked high-voltage tracker (HVT) is also activated to track V_Pi for V_MAX. A resistive divider is utilized to generate fractional PZT voltage (V_DIV) with a division ratio of 13:1, which is necessary to keep divided V_RECT (V_DIV) within the range of V_DD. Here, V_DIV is also generated through resistive dividers just like R_1i-R_4i, followed by a V_POL-controlled (2 × 1) analog multiplexer, which are not shown here to avoid figure complexity. The HVT keeps comparing V_DIV with V_MAX /13 until the V_DIV >= V_MAX /13 condition is met, which initiates a PECE cycle. During PECE, the PZT voltage is decreased by PECE step voltage (∆V_PH) during energy transfer to L₁. A clocked low-voltage tracker (LVT) is activated to keep monitoring the PZT voltage and detect the point where V_DIV becomes lower than ((V_MAX − ∆V)/13). At this point, energy transfer to the inductor is stopped and PZT voltage keeps rising until another PECE condition is met or V_PK is detected.

3.4. Harvesting and Storage Control

Once a PECE condition is met or peak voltage is detected, all of the energy from the PZT is transferred to the inductor. A zero-crossing detector (ZCD_A) is utilized to monitor this energy transfer. A capacitive divider (C₄, C₅) is necessary here to generate a low voltage (V_Z) from high voltage (V_L1) as ZCD_A consists of LV transistors. The ZCD keeps comparing this V_Z with GND until the V_Z <= 0 V condition is achieved, which indicates peak inductor current (I_PK). After this, the HIC determines whether energy will be transferred to C_STOR and/or the battery. As soon as energy transfer to the inductor is started, the HIC starts evaluating C_STOR with the SLC. The harvesting and storage decisions made by the HIC based on this evaluation are explained with the following 2 cases, and the conceptual waveforms are shown in Supplementary Figure S1.

3.4.1. Case1: C_STOR Not Fully Charged

In case ①, where C_STOR is not fully charged (V_STOR < V_REF), energy is transferred from the inductor to C_STOR. Here, a storage-level tracker (SLT) is activated to keep monitoring V_STOR until V_STOR >= V_REF condition is achieved. At this point, the remaining energy (if any) on the inductor is transferred to the battery. Energy transfer to the battery is monitored by a reverse current detector (RCD_H), which blocks reverse current and detects the point where I_L becomes ~0 A, marking the completion of a harvesting cycle. However, if the energy on the inductor is not enough to fully charge C_STOR, the V_STOR >= V_REF condition will never be achieved, and reverse energy transfer from C_STOR to L₁ can happen, which can waste energy. Therefore, to prevent this situation, another reverse current detector (RCD_S) is utilized. HIC activates RCD_S along with SLT, where RCD_S continues monitoring the energy transfer from the inductor to C_STOR and detects the point where V_L2 becomes lower than V_STOR, which means that I_L is ~0 A. Here the energy transfer to C_STOR is stopped and a single harvesting cycle (or PECE cycle) is completed.

If the V_STOR >= V_REF condition is detected by the SLT while I_L is non-zero, this means that there is still some energy on the inductor, which can be transferred to the battery. However, in some cases, this energy can be very low, and as soon as S_BAT is closed, the circuit will only see reverse current, which makes RCD_H detection impossible and the circuit fails. Therefore, V_BAT (3 V) is intentionally kept lower than V_STOR (3.3 V) to avoid circuit failure in the case of lower energy on the inductor during case ①. In this case, RCD_H is activated together with the SLT and RCD_S. During energy transfer from L₁ to C_STOR, V_L2 starts rising slowly until it becomes >3 V. RCD_H detects this point, and its output (V_RCDH) becomes low, which means even if there will be little or no energy available on the inductor, once the energy transfer to C_STOR is complete, RCD_H will still detect I_L becoming ~0 A (by detecting V_RCDH high at V_L2 < V_BAT). This will de-activate RCD_H and mark the completion of a harvesting cycle.

3.4.2. Case2: C_STOR Fully Charged

In case ②, where C_STOR is already fully charged, the V_STOR >= V_REF condition is detected by the HIC. Therefore, in this case, all of the energy on the inductor needs to be transferred to the battery. Here only RCD_H is activated to block reverse current by detecting the point where I_L becomes ~0 A.

The HIC plays a vital role in determining energy transfer cycles. In another case, where both PZTs are pressed together, energy is only invested to the one whose WUC triggers first, and only the VPD of the second PZT is activated. The inductor is time shared between both PZTs for energy transfer in case both PZTs detect V_PK or meet the PECE condition at the same time. Similarly, the inductor is also time-shared in case the PECE condition is achieved by one PZT and voltage peak is detected by the other PZT. This time sharing is possible because energy transfer to/from the inductor to/from the PZT only takes a few µs. This makes the circuit reliable for irregular human motion conditions. To deal with the high voltage of PZTs, S_Pi1/S_Pi2/S_Ni1/S_Ni2/S₃ are designed using high-voltage (HV) transistors, whereas S₂/S_BAT/S_STOR are designed using LV transistors to minimize conduction loss.

3.5. Bi-Directional Control

For the proposed dual-PZT harvesting circuit, S_Pi1/S_Pi2/S_Ni1/S_Ni2 need to be bi-directional for energy investment and harvesting. Therefore, bi-directional transistors, as shown in Figure 7a, were utilized for these switches. Depending on energy investment to the PZT_i or energy extraction from the PZT_i, the voltage on either side of the switch can be higher. This means that the body of these switches cannot be tied to either side. Therefore, each switch consists of two transistors, S_P (PZT side) and S_L (inductor side). A carefully designed high-voltage level shifter (HVLS) is used to control these switches, as shown in Figure 8. These two switches (with HVLS) are necessary for (1) blocking current from PZT_i to the inductor when V_Pi is increasing, (2) blocking current from PZT₁ to/from PZT₂, and (3) blocking current to PZT₁ during energy investment to PZT₂ and vice versa. The V_H node in the HVLS is interfaced with the PZT or the inductor to generate a gate control voltage (V_G) to turn on/off these power switches with full voltage swing. V_Pi1 is the trigger signal (for HVLS) to turn on/off S_Pi1. Similarly, V_Pi2, V_Ni1, and V_Ni2 (shown in Figure 6) are trigger signals used for S_Pi2, S_Ni1, and S_Ni2, respectively. All these signals are activated by HIC for harvesting/storage/invest operation.

S_STOR is a low-voltage switch that needs to be bi-directional for energy transfer to/from the inductor. Voltage on either side of S_STOR (and S_BAT) can be high; therefore, the body of these switches also needs to be attached to the high-voltage side. In this case, a bulk regulator [27] (Figure 7b) is utilized to connect the high voltage to the body of the switch to block the reverse current.

As stated earlier, HVLS is needed to generate a gate control voltage with full voltage swing (up to 40 V). Whereas, supply voltage used to control HVLS is <5 V, which is necessary to minimize switching losses. The low-voltage input signals cannot be directly applied to the high-voltage transistors of HVLS, which are at a different potential. That is why a capacitively cross-coupled HVLS is utilized. M_B is intentionally kept larger than M_A. Initially, IN_B is kept high. As V_H starts to increase, OUT_B becomes high, which keeps M_A remained closed. Diodes D₁-D₄ are used to charge C_A to maintain OUT_A high enough to keep voltage across M_A < 5 V, as M_A and M_B are made with LV devices. Similarly, D₅-D₈ are utilized for C_B and M_B. As OUT_B follows V_H, M_C remains closed and V_FS remains low, V_G keeps following V_H. To pull down V_G, IN_B is turned low, which pulls down OUT_B and enough gate-source voltage difference is created to turn on M_C. V_FS quickly rises to the (high voltage) level of V_H, which triggers inverters to invert V_G value as well. Inverters/buffers on the right side of Figure 8 are made with HV transistors; therefore, they can handle full voltage swing.

The main target of this work was to perform efficient harvesting operation while assuming external power supply is available. Therefore, this work mainly focused on high-voltage energy harvesting challenges using multiple PZTs and cold-start circuit implementation is not considered.

4. Results and Discussion

The proposed energy-harvesting interface was designed and simulated in 350 nm BCD process. Figure 9a shows the layout of the proposed harvesting interface, which occupies an active area of 16.81 mm². Figure 9b shows the values of components used for proposed harvesting interface. For simulations, a PZT electrical model with 20 nF internal capacitance (C_P) was utilized. Figure 10 shows the simulation results of the proposed energy-harvesting interface with different input excitations to demonstrate the reliability of the harvesting controller (HIC). Initially, only PZT₁ is pressed (assumed); therefore, V_PZT1 (PZT₁-generated voltage) increases and energy is harvested at every peak. The harvesting cycle activation for PZT₁ is represented by the V_HRV1 signal in Figure 10a. During weaker input excitations, V_PZT1 remains lower than V_MAX, and the charges are completely extracted at the peak voltage. Similarly, weak input excitations are applied to only PZT₂, which triggers V_HRV2 for harvesting at the peak of V_PZT2 (PZT₁-generated voltage). After that, weak input excitations are applied to both PZTs simultaneously to verify the effectiveness of the HIC to handle both PZTs at the same time. V_INVST here refers to the activation of an energy investment cycle, where energy is invested to only one of the PZTs if both PZTs are pressed together.

As stronger input excitations are applied to PZT₁, V_PZT1 can exceed V_MAX. Therefore, PECE is initiated to keep V_PZT1 below V_MAX and maximize energy extraction from PZT₁. V_HRV1 here represents the activation of a PECE cycle as well, which is basically a partial harvesting cycle. Therefore, V_HRV1 can be seen as activated multiple times in Figure 10a as PECE is initiated a few times. Similar steps are repeated for PZT₂ with stronger input excitations. In the end, both PZTs are pressed simultaneously with stronger input excitations. It can be concluded from Figure 10a that the proposed HIC effectively differentiates between different voltage polarities of both PZTs to initiate energy investment or harvesting cycles accordingly.

Figure 10b shows a zoomed waveform of the case where both PZTs are pressed simultaneously. Initially, (for positive polarity) V_PZT1 rises faster than V_PZT2; therefore, energy is invested to PZT₁, and V_PZT1 keeps rising until the V_OC >= V_MAX condition is met. At this point, charges are partially extracted (PECE) from PZT₁. Multiple PECE cycles are activated (represented by V_HRV1) until the peak detection of V_PZT1. V_PZT2 also keeps rising without energy investment with a few PECE cycles (represented by V_HRV2) until its peak voltage is detected.

Once the peak voltage is detected, charges are completely extracted from both PZTs. The similar operation of energy harvesting is shown for both PZTs when their output voltages have negative polarity. PECE as well as FECE takes a very short time (a few μs) for completion. A zoomed version of FECE activation for both PZTs sharing a single inductor is shown in Figure 10c. In the given case, the V_PZT2 peak is detected earlier than the V_PZT1 peak, and therefore, V_HRV2 triggers to perform FECE on PZT₂. Following V_PZT1 peak detection, V_HRV1 is activated to perform FECE on PZT₁, as well.

The zoomed waveform of an energy investment cycle of PZT₁ is shown in Figure 10d. As the WUC triggers TRIG₁, the HIC starts the evaluation of C_STOR using the SLC, which triggers V_INVST only after assuring that C_STOR is fully charged. Energy is extracted from C_STOR using the inductor, where ZCD_B monitors this energy transfer to stop it once V_L2 <= 0 V is detected. Later, this energy on the inductor is transferred (invested) to PZT₁, where V_PZT1 can be seen rising by ∆V_i) in Figure 10d at the end of the transfer. Whereas, for PZT₂ (in Figure 10b), after the WUC triggers TRIG₂, the SLC does not trigger V_INVST because the energy from C_STOR has already been invested to PZT₁. In that case, VPD₂ immediately starts tracking the peak of V_PZT2.

After energy investment to PZT₁, VPD₁ also keeps tracking the peak of V_PZT1. At the same time, HVT₁ of PZT₁ and HVT₂ of PZT₂ are also active to track the respective PZT’s voltage for V_MAX. Due to stronger input excitation applied to PZT₁, HVT₁ detects the V_PZT1 > V_MAX condition earlier, and PECE cycles are activated multiple times before the PZT₁ peak voltage is detected by VPD₁. During a PECE cycle, charges are partially extracted from a PZT using the inductor, as shown in Figure 10e. In PECE, energy is transferred from a PZT to the inductor for a short duration, during which V_PZT1 decreases by PECE step voltage (∆V_PH). The LVT keeps monitoring V_PZTi to stop this energy transfer once V_PZTi decreases by ∆V_PH. This energy on the inductor is later transferred to the storage, which marks the end of a single PECE cycle.

Once either a PECE activation condition or peaking event is detected, energy needs to be harvested to C_STOR and/or the battery, as explained earlier in Section 3.4. Figure 10f shows a case where energy is stored to both C_STOR and the battery since the C_STOR is not fully charged. After peak detection, the charges are completely extracted from PZT₁ using the inductor (V_PZT1 becomes ~0 V at the peak of i_L1). After that, energy is harvested to the C_STOR first, until the V_STOR >= V_REF condition is met. The remaining energy on the inductor is transferred to the battery. The inductor current during energy transfer to C_STOR (i_STO) is denoted by the dashed blue line, whereas, the inductor current during energy transfer to the battery (i_BAT) is denoted by the dashed red line in Figure 10f.

The performance and effectiveness evaluation of the proposed piezoelectric energy-harvesting interface is carried out with simulations with varying strengths of input excitations. Figure 11 shows the simulation results of the proposed harvesting interface for quantitative analysis. Unlike most of the prior works, this work deals with the discontinuous input pulses; therefore, quantitative analysis could be carried out in terms of energy, as presented in some of the recent works [28,29,37,44]. The energy harvested using the proposed harvesting interface in a single deformation cycle is represented as E_HRV, and the energy consumed during this single harvesting operation is termed E_LOSS. The E_HRV can be calculated with the following equation:

$$E_{HRV}= V_{BAT}{{\displaystyle \int }}_{to}^{tf}{I}_{BAT} dt$$

(5)

where i_BAT is current transferred to the battery. The V_BAT is assumed fixed and the i_BAT is integrated for the duration (time t_o to t_f) of energy transfer from inductor to the battery. For indirect comparison with state-of-the-art works, an FBR-based harvester is utilized. Energy harvested using this FBR-based harvester is indicated as E_FBR. The results were recorded for harvesting operation with energy investment as well as without energy investment. The proposed harvesting interface maintains a good end-to-end conversion efficiency of >80% for almost all input excitation values, as shown in Figure 11a. The proposed harvesting interface harvests the PZT energy with PECE for input excitations when V_OC >= 40 V; otherwise PECE is not used. With very weak input excitations (V_OC < 15 V), without any energy investment, the conversion efficiency remains lower than when energy is invested. This is because the overall generated and transferred energy values are lower (without energy investment), and hence losses dominate.

E_HRV is compared with E_FBR in Figure 11b. E_HRV remains well above E_FBR for different values of V_OCs for harvesting with or without energy investment. To verify the effectiveness of the proposed harvesting circuit with strong excitations, PECE is performed with a V_OC of 100 V. The difference between E_HRV with and without energy investment can be seen as increasing up till 40 V, which verifies effectiveness of energy investment. However, this difference remains almost the same once V_MAX is reached, as from this point, the energy extracted during each PECE cycle remains almost same.

Energy extraction improvement using the proposed harvesting interface is compared with an FBR-based harvester in Figure 11c. Without energy investment (PECE for V_OC > 40 V), the proposed circuit achieves up to 7.61× energy extraction improvement compared to an FBR-based harvester. In contrast, operating with both energy investment and PECE results in an energy extraction improvement of up to 8.38×. As V_OC increases, the difference between improvement with and without energy investment decreases as energy extracted by PECE cycles starts to dominate.

Table 1. Comparison with prior arts.

	This Work	[17] ESSCIRCʹ 18	[25] JSSCʹ 10	[25] ISSCCʹ 19	[33] ISSCCʹ 18	[36] ISSCCʹ 18	[13] VLSIʹ 15
Process	350 nm BCD (40 V)	130 nm CMOS (Standard Voltage)	350 nm (Standard Voltage)	350 nm (Standard Voltage)	40 nm CMOS (10 V)	350 nm (Standard Voltage)	250 nm CMOS (40 V)
Active Area (mm2)	4.1 × 4.1	0.53	4.25	1.4 × 2.9	1.1 × 0.5	0.27	2 × 1.2
Harvesting Technique	Energy Invest + PECE	SSHI	SSHI	Reconfigurable VM-SECE	SECE	Delayed-SECE	Series-Parallel SC
Harvesting Source	PZT	PPA1022	MIDE V22B	Custom PZT/Nickel/PZT	MIDE PPA1011	MIDE V21B	PMN-PT On disc
Source Capacitance (CP)	20 nF (each PZT)	14 nF	12 nF	17 nF–49 nF	43 nF	-	150 nF
Inductor	220 μH	47 μH	0.82 mH	2.2 mH	2.2 mH	-	470 μH
Excitation Type	Irregular Pulse	Periodic	Periodic	Periodic & Shock	Periodic & Shock	Periodic	Irregular Pulse
Input Voltage	>100 V * (Theoretically unlimited)	2.5 V	2.4 V	<5 V **	<6 V **	<4 V **	35 V
Max. Improvement ***	7.61× (PECE only) 8.38× (PECE+ Invest)	3.85×	4×	5.11×	4.2×	-	-

* Open-circuit voltage. ** Estimated from paper. *** (E_HRV − E_LOSS)/E_FBR.

summarizes the comparison between the proposed harvesting interface and state-of-the-art harvesting circuits [13,17,25,33,35,36]. To handle irregular input excitations, instead of flipping C_P polarity in every half cycle to extract more energy in the next cycle [32] or using no flipping at all in [33], the proposed circuit temporarily stores energy on a storage capacitor and waits for the next vibration cycle to invest the stored energy to the PZT. In addition, prior works lack any kind of circuit in case the PZT-generated voltage exceeds the maximum voltage tolerated by the technology used. Therefore, PECE is utilized in this work for overvoltage protection as well as to ensure maximum energy extraction by keeping the PZT voltage high. With the help of PECE, the proposed harvesting interface can harvest from theoretically unlimited open-circuit voltages generated by the PZT, assuming that the input current remains within the manageable range. PECE performance is also limited by clock frequency used for tracking PZT voltage for V_MAX. In addition, energy transfer time (from PZT to the inductor and then inductor to the battery) is also an important factor to determine maximum voltage limit, as there can be only so many energy-transfer cycles (of few µs) during a single deformation. With the help of energy investment and PECE, the proposed harvesting interface successfully harvests energy from excitations with V_OC up to 100 V and achieves 8.38× energy extraction improvement compared to an FBR-based harvesting circuit.

5. Conclusions

A novel dual piezoelectric energy investment and harvesting scheme is introduced in this work. An efficient harvesting controller is designed to time-share a single inductor for both energy extraction and investment to/from both PZTs. A WUC is utilized to monitor the PZT-generated output voltage and detect and trigger once this voltage approaches a certain threshold level. The WUC triggers the harvesting controller to start energy investment to the PZT using a temporary storage capacitor. Following energy investment, the PZT voltage continues to rise until a PECE condition (the PZT voltage exceeds the maximum tolerable voltage) is achieved or peak voltage is detected. In both conditions, energy is transferred to the inductor, keeping account of the correct polarity of the PZT-generated voltage. The proposed harvesting interface circuit was designed in 350 nm process. Without energy investment (PECE for V_OC > 40 V), the proposed circuit achieves up to 7.61× energy extraction improvement compared to an FBR-based harvester. In contrast, operating with both energy investment and PECE results in an energy extraction improvement of up to 8.38×. With the help of energy investment and PECE, the proposed harvesting interface successfully harvests energy from excitations with V_OC up to 100 V.