An Inductorless Self-Controlled Rectifier for Piezoelectric Energy Harvesting

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1 Sensors 2015, 15, ; doi: /s Article OPEN ACCESS sensors ISSN An Inductorless Self-Controlled Rectifier for Piezoelectric Energy Harvesting Shaohua Lu * and Farid Boussaid University of Western Australia, 35 Stirling Highway, Crawley, Western Australia 6009, Australia; farid.boussaid@uwa.edu.au * Author to whom corresondence should be addressed; @student.uwa.edu.au; Tel.: ; Fax: Academic Editor: Davide Brunelli Received: 23 June 2015 / Acceted: 13 November 2015 / Published: 19 November 2015 Abstract: This aer resents a high-efficiency inductorless self-controlled rectifier for iezoelectric energy harvesting. High efficiency is achieved by discharging the iezoelectric device (PD) caacitance each time the current roduced by the PD changes olarity. This is achieved automatically without the use of delay lines, thereby making the roosed circuit comatible with any tye of PD. In addition, the roosed rectifier alleviates the need for an inductor, making it suitable for on-chi integration. Reorted exerimental results show that the roosed rectifier can harvest u to 3.9 times more energy than a full wave bridge rectifier. Keywords: iezoelectric energy harvesting; AC-DC ower conversion; SSHI; rectifier 1. Introduction Harvesting ambient energy rovides an oortunity to enable self-owered wireless environmental sensing networks and embedded wearable microelectronic devices [1 3]. A number of techniques have been roosed to harvest ambient energy sources such as RF, solar, thermal, and vibration [4]. Among these energy sources, ambient vibrational energy has attracted much attention due to its high energy density (10 to 100 s µw) [5], high integration otential [6,7] and abundance [8 11]. High efficiency, stand-alone oeration and comatibility with semiconductor industry standard CMOS rocess are imortant requirements to achieve mass roduction of iezoelectric energy harvesting systems [12].

2 Sensors 2015, Such systems comrise a iezoelectric device (PD) to convert ambient vibrational energy into electrical energy, together with a rectifier. The latter is required because a vibrating iezoelectric device behaves as a caacitive ac current source in arallel with a caacitor and a resistor [13]. The simlest rectifier toology is the full-wave bridge rectifier [7,13 16]. However, it suffers from low ower conversion efficiency because the PD s internal caacitance is charged and discharged every half cycle [17,18]. In order to overcome this limitation, a high efficiency nonlinear technique Synchronized Switch Harvesting on Inductor (SSHI) was roosed by Guyomar et al. [19]. This oular technique uses a series connected switch and inductor in arallel with the iezoelectric device. Every half cycle, when the current roduced by PD changes olarity, the switch is closed. As a consequence, the inductor and the PD s internal caacitance form a LC oscillating network, allowing for the voltage across PD to be naturally inverted. The inversion time corresonds to half the eriod of the LC oscillating network. However, such a voltage inversion rocess is limited by the arasitic resistance along the LC oscillating network. The challenges associated to the imlementation of such a technique include: (i) the detection of the olarity change of the current roduced by the PD [20 23]; (ii) control of the inversion time given all the different ossible values of L and internal caacitance of PD [24]; and (iii) the ower required by the control circuits [25,26]. Figure 1. (a) Switch-only technique; (b d) Existing imlementations. In [27], we roosed a simle yet high efficient SSHI rectifier for iezoelectric energy harvesting. The roosed rectifier monitors the voltages at the two ends of the iezoelectric device (PD) to detect the olarity change of the current generated by the PD. The inversion rocess of the voltage across the PD is automatically controlled by diodes along the oscillating network. In contrast to rior works, the roosed rectifier combines a number of advantages including high ower efficiency, hardware simlicity, standalone oeration, but also comatibility with commercially available PDs. However, as the SSHI technique requires a large value for the inductor [24], the reviously roosed rectifier is not suitable for CMOS integration. One solution roosed to tackle this issue is to the emulate inductance

3 Sensors 2015, using a negative imedance [28,29]. In [29], the authors suggest the use of virtual grounded and floating inductors to achieve the required value of inductance. However, these tyes of imlementations remain oor reresentations of real inductors. In addition, they are large in size, sensitive to comonent variations and thus difficult to tune. Furthermore, they require the inclusion of additional active elements and external ower sources [23]. A switch-only technique solution that alleviates the need for an inductor was roosed in [24] (Figure 1a). This technique uts a switch M1 in arallel with the PD. When the olarity of current roduced by the PD changes (at the beginning of every half cycle), switch M1 closes. As a result, the voltage across the PD is discharged without drawing on the energy generated from the PD. [24] roosed an imlementation of the switch-only rectifier (Figure 1b), with two transistors imlementing switch M1. ON time is controlled by a digital inverter delay line comrising inverter chains searated by multilexers. By alying different control words to these multilexers, the delay line can roduce different ON times for switch M1. However, the control words are generated externally and need to be tuned for each secific PD so as to calibrate the correct ON time. A similar imlementation (Figure 1c) for switch M1 was resented in [30]. The rectifier also uses an inverter delay line to control the ON time of switch M1 but the delay line is not rogrammable. As a result, the ON time cannot be adjusted to different PDs. In [31], a rectifier (Figure 1d) uses four transistors controlled by custom designed reset dc offset o-ams and DSP to imlement switch M1. These custom designed o-ams revent the transistors turning ON before the current roduced by the PD changes olarity. However, the ON time of the transistors cannot accommodate different tyes of PDs, which would exhibit different internal caacitance values. To address these limitations, an inductorless self-controlled rectifier is roosed in this aer. The rectifier neither relies on external control signals, nor does it use an inverter chain to control the switch ON time. Furthermore, the rectifier offers high efficiency, low circuit comlexity while being fully comatible with CMOS technology as it does not use any inductor. The aer is organized as follows: Section 2 introduces the electrical model of a iezoelectric device. Section 3 resents the oeration and limitations of a conventional full wave bridge rectifier. Section 4 analyses the oeration, harvested energy and ower loss of the roosed rectifier. Section 5 discusses reorted exerimental results and rovides a erformance comarison with rior works. Section 6 concludes the aer. 2. Electrical Model of Piezoelectric Device Figure 2 shows the structure of a PD comosed of a cantilever beam, with two thin iezoelectric material films bonded on the to and bottom surfaces. When subject to vibration, the mechanical stress and strain develoed within the iezoelectric material are converted into electrical charge [24]. The electromechanical model (Figure 3a) of a iezoelectric device can be reresented as couling a mechanical system to electrical domain through a erfect transformer [32]. The rimary side of the transformer reresents the mechanical system, with Vm reresenting the inut vibration, Lm the mass, Cm the mechanical stiffness and Rm the mechanical loss. The secondary side of the transformer reresents the electrical load and characteristics of the iezoelectric device, with C reresenting its internal caacitance and R reresenting its internal resistance. Parameter Γ (Figure 3a) is a measure of the electromechanical couling of the iezoelectric element. This arameter rovides a measure of the

4 Sensors 2015, efficiency of energy conversion between mechanical and electrical domains. Because most iezoelectric devices have low couling coefficients, daming from the electrical side can often be neglected [33 35]. As a result, the equivalent circuit of the iezoelectric device can often be simlified to a current source i in arallel with the internal caacitance C (Figure 3b) [33 35]. This uncouled model assumes that the internal current source is mostly unaffected by the external load. This is equivalent to assuming that the vibration amlitude is indeendent of the external load [33 35]. For most ractical alications, the harvest ower can be boosted significantly by the interface circuits before i changes notably [34]. As a result, and for uroses of simlicity and clarity, the uncouled equivalent circuit model (Figure 3b) is widely used and adoted by all rior works (Table 1). Such a circuit often also takes into account the dielectric losses associated to C, by including a arallel resistor R (Figure 3b), whose value is usually very large (MΩ) [33 35]. This high internal resistance restricts the amount of outut current. Another non-ideal characteristic of the PD is its low outut voltage when the inut vibration level is low. This makes it difficult to design an efficient rectifier since the diodes in the rectifier usually have non-zero turn on voltages [24]. Figure 2. Structure of a iezoelectric device (PD) [36]. Figure 3. (a) Electromechanical model of the iezoelectric device; (b) Uncouled equivalent circuit of a iezoelectric device considering dielectric losses associated to C.

5 Sensors 2015, Conventional Rectifier The conventional full wave bridge rectifier (Figure 4a) is traditionally used to convert the AC outut voltage of a iezoelectric device into a DC voltage. The outut caacitor Crect is chosen to be large enough to make the outut voltage Vrect constant. The corresonding inut and outut waveforms of current and voltage are shown in Figure 4b. The oeration of the full wave bridge rectifier can be divided into two regions: (i) from time t0 to t1, voltage Vb is smaller than the outut voltage Vrect (voltage across the caacitor Crect) and all diodes are reverse biased. Current i cannot thus flow to the outut caacitance Crect. On the other hand, the internal caacitance C is charged u; (ii) from time t1 to tπ, Vb is first equal then higher than the value of outut voltage. Therefore current i flows into Crect until current i changes olarity. In the first region, the energy generated by PD is dissiated on the internal caacitance C and resistance R. As a result, the energy generated in this region cannot be harvested. The energy harvested in the second region is reresented by the shaded area in Figure 4b. To calculate the harvested energy, one needs first to determine the average outut current iout, which can be exressed as: 1 V + 2V i I tdt t t ( ) tπ rect D = sin out, average ω π 1 t t 1 R π 1 cosωt cosωt V + 2V = + t ω ω R π ( ) π 1 rect D I t t π 1 (1) where I and ω are the amlitude and angular frequency of inut current i, resectively. The energy harvested by the full wave bridge rectifier is thus: V cosωt cosωt V + 2V P = I + t t t ω ω R π ( ) rect π 1 rect D full _ bridge π 1 (2) Since ωtπ = π, hence: V I V + 2V P = + t t t t ω R π ( 1 cosω ) ( ) rect rect D full _ bridge 1 π 1 (3) where: t 1 = ( ) 2 V + 2V ωc 1 rect D cos 1 I (4) ω The maximum ower harvested by the full wave bridge rectifier is obtained when [32]: with the maximum ower given by: V rect I = VD (5) ωc 2 I P C V ωc = 2 full _ bridge,max D 2 ω 2π (6)

6 Sensors 2015, Figure 4. (a) Conventional full wave bridge rectifier; (b) Inut and outut waveforms. 4. Proosed Inductorless Self-Controlled Rectifier 4.1. Oeration Princile The major limitation of the full wave bridge rectifier was shown to be with the fact that the charge generated by the PD cannot be harvested when the outut voltage is higher than the voltage across the PD (Figure 4b). This is because the internal caacitance of the PD needs to be first discharged and then charged again at a voltage higher than the outut voltage for the generated charge to flow to the outut. To address this issue, we roose an inductorless self-controlled rectifier which can short both ends of the PD to ground at the beginning of every half cycle. As a result, the energy generated by the PD only needs to charge u the internal caacitance, thereby saving significant energy. Figure 5a shows the roosed rectifier, which has a switch M1 connected in arallel with the PD. At the beginning of every half cycle, the current i roduced by the PD changes olarity, the switch M1 is turned ON. As a consequence, the charges stored in the PD s internal caacitance C are immediately discharged to ground through switch M1. As soon as C becomes fully discharged, switch M1 is turned OFF. As a result, current source i only needs to charge u C from ground to ±(Vrect + 2VD), before the current starts flowing to the outut. The corresonding voltage and current waveforms are shown in Figure 5b. Every half cycle, the total charge delivered to the outut by the roosed rectifier is the total charge roduced by the PD minus the charge loss on the internal comonents C and R of the PD and on the diodes. The latter is given by:

7 Sensors 2015, Q = Q Q Q harvest total loss, C loss, R (7) The total charge roduced by the PD every half cycle is thus: Q = 2C V (8) total where V is the oen circuit voltage of the PD, which is given by: V I = (9) ωc Figure 5. (a) Proosed rectifier scheme; (b) Associated voltage and current waveforms. Since the internal caacitance C is discharged through M1 in a very short time interval [t0, t1] comared to the half cycle of current i, the charge lost in time interval [t0, t1] can be neglected. The charge lost on the internal caacitance C from t1 to t2 is thus: ( ) [( 2 ) 0] Q = V V C loss, C final initial = V + V C rect D ( 2 ) = V + V C rect D (10)

8 Sensors 2015, The charge lost on the internal resistance R can be divided into two regions: (1) Vb is smaller than outut voltage Vrect from t1 to t2; (2) Vb is greater than Vrect from t2 to tπ. In the first region, the charge lost on R is: where: t2 t2 b Qloss, R, region1 = ir, region1dt = dt t1 t1 R v (11) 1 t v = I sinωtdt + v t b b t C 1 ( ) I = ( cosωt cos ωt 1 ) + v ( t ) b 1 ωc ( cosω cosω ) ( ) = V t t + v t 1 b 1 1 (12) Since Vb(t1) = Vinitial = 0 and ωt1 is aroximately equal to 0, hence: ( 1 cosω ) v V t b = (13) Bringing Vb back to Equation (11): Q loss, R, region1 = t2 t1 V ( 1 cosωt) R [( ) ω + sin ω sin ω ] ( ω sin ω ) 2 2 dt V t t t t = ωr V t t = ωr (14) Taking the boundary conditions for Vb at time t2: Hence: ( ) 2 ( 1 cosω ) v t = V + V = V t b 2 rect D 2 (15) t 2 = 1 V + 2V rect D cos 1 V (16) ω In second region [t2, tπ], the charge lost on R is: V + 2V Q = ( t t ) (17) rect D lost, R, region2 π 2 R where: Finally, the harvested ower is thus: t π π = (18) ω Pharvest = 2 fvrectqharvest (19)

9 Sensors 2015, with the ower losses due to diodes being aroximately equal to: P 2V i (20) lost, diodes D out, average 4.2. Imlementation The imlementation of the roosed inductorless self-controlled rectifier is given in Figure 6. To detect the olarity change of i, the voltages V and Vn are comared with a reference voltage Vref, chosen to be slightly higher than the negative value of diodes forward voltage VD. When i is ositive (before t0) and diodes 1 and 4 are ON, V is close to Vrect + VD and Vn is close to VD but lower than Vref. Comarators CMP1 and CMP2 evaluate V and Vn against Vref. As a consequence, the oututs of comarators OUT1 and OUT2 are low and high resectively, since V is higher than Vref and Vn is lower than Vref. As a result, the outut of the NOR gate Nout is low. Once current i becomes negative at t0+, the voltage Vn increases and reaches the value of Vref. As a result, OUT2 toggles from high to low while OUT1 stays low. Figure 6. (a) Imlementation of roosed self-controlled inductorless rectifier; (b) associated voltage and current waveforms. This makes the outut Nout of the NOR gate toggles from low to high. Therefore, a ulse is generated for detecting the olarity change of i. A similar rocess occurs when i changes olarity again. Signal Nout is then assed to the digital control block (Figure 7) to generate two olarity change detecting signals. These signals control the ON and OFF time of the transistors M1 M4. At time t0, i changes olarity from ositive to negative, the signals Ph1 and Ph1inv are firstly generated to turn on transistors M1 and M3. At this time, a discharging ath is formed by transistors M1, M3 and diode D5. As a result, the charge stored in internal caacitance C is discharged through this ath. This discharging rocess lasts from t0 to t1 and is automatically terminated by diode D5. Subsequently, the current i charges C from about VD to (Vrect + 2VD) in time interval [t1, t2] and then delivers ower to the outut. When i changes olarity again from negative to ositive, a similar rocess occurs for transistors M2, M4 and diode D6.

10 Sensors 2015, Figure 7 shows the imlementation of the digital control block with inut Nout and oututs Ph1, Ph1inv, Ph2 and Ph2inv. Signal Nout is used as the CLK inut for the ositive edge triggered D fli-flo. With the D fli-flo s comlemented outut connected to its D inut, oututs Q and Q bar have both a frequency that is half that of the inut Nout signal. They also have the same ulse width, which is double that of the Nout signal. Giving that oututs Q and Q bar are ANDed with the delayed version of Nout signal, signals Ph1 and Ph2 have the same ulse width than inut signal Nout and half its frequency. Ph1inv and Ph2inv are inverted forms of signals Ph1 and Ph2. 5. Exerimental Results and Discussion Figure 7. Digital control block. The roosed rectifier was demonstrated using ultra-low ower off-the-shelf ICs. Two ultra-low ower comarators (LTC1540 Linear Technology, Militas, CA, USA, 680 na max quiescent suly current) were used to imlement comarators CMP1 and CMP2 (Figure 6a). Standard 4000 series CMOS gates with low inut current leakage were used to build NOR gate and the frequency divider (Figure 7). Switches in the discharging ath were imlemented using two tyes of MOSFETs (VN0104 and VP0104 Microchi, Chandler, AZ, USA), with on resistance of 3 Ω and 11 Ω for a gate voltage of 5 V, resectively. All diodes in the roosed rectifier are Schottky diodes (BAT54 Fairchild Semiconductor, San Jose, CA, USA). Exeriments were carried out to evaluate the erformance of the roosed rectifier imlementation. In our exerimental Labworks setu, only the vibration frequency and acceleration amlitude can be set. The PD (V21B Mide Technology, Medford, OR, USA) is screwed on an aluminium late, which is mounted (using screws) on an electrodynamic shaker (ET-126B-4 Labworks Inc., Costa Mesa, CA, USA). The shaker is driven by a sine wave generator (SG-135 Labworks Inc., Costa Mesa, CA, USA) amlified through a ower amlifier (PA-138 Labworks Inc., Costa Mesa, CA, USA). The outut signal of a vibration acceleration sensor (model J352C33 PCB Piezotronics, Deew, NY, USA), fixed on the shaker late, is fed to a controller unit, which ensures that the acceleration amlitude of the shaker late is ket constant, regardless of the electromechanical feedback introduced by the electrical load. When the PD vibrates at or close to its resonant frequency, the current generated by the PD is roortional to the acceleration [33]. By measuring the oen-circuit voltage V, it is then ossible to deduce the current I using Equation (9). The acceleration can be adjusted on the signal wave generator (SG-135 Labworks Inc., Costa Mesa, CA, USA) to achieve the required values of V and thus I. When setting the vibration frequency to 246 Hz and the acceleration to 0.9 g (1 g = 9.8 m/s 2 ) on the sine wave generator (SG-135 Labworks Inc., Costa Mesa, CA, USA), the amlitude of the resulting current generated by the PD is about 390 µa. Figure 8 shows the resulting oscilloscoe waveforms for the

11 Sensors 2015, voltage across PD when attached to the roosed rectifier and full wave bridge rectifier, resectively. Measurements showed that the PD s oen circuit voltage is 1.7 V and its oen-circuit frequency is 246 Hz. The obtained waveforms are consistent with the described oerations of the roosed rectifier scheme shown in Figure 6b. The roosed rectifier is seen to automatically discharge the voltage across PD to ground at the beginning of every half cycle. As can be observed in Figure 8 (to), the voltage Vb does not fully discharge to 0. This is due to the forward voltage of diodes and arasitic resistance along the discharging ath. Figure 8. Measured waveforms of the outut voltages across PD for the roosed rectifier (to) and the full wave bridge rectifier (bottom). Figure 9 reorts the measured outut ower as a function of the outut voltage. The curve at the bottom with star symbols is the outut ower of a full wave bridge rectifier. Note that the maximum outut of 40 µw is achieved for an outut voltage of 0.51 V and diodes forward voltage of 0.3 V. The curve with square symbols is the outut ower of the roosed rectifier. The maximum ower of 156 µw is here achieved when the outut voltage reaches 1.5 V. Reorted measurements show that the roosed rectifier can imrove the harvested ower by 3.9 times comared to the full wave bridge rectifier.

12 Sensors 2015, Figure 9. Measured outut ower. Figure 10. Power measurements of control circuit elements against outut ower of roosed rectifier. Figure 10 reorts the measured outut ower of the roosed rectifier together with the ower consumtion of the control circuit elements. Exerimental results are given for the case where the roosed rectifier is self-owered by Vrect but also for the case where it is externally owered. It can be seen from Figure 10 that: (i) for outut voltages Vrect < 1.7 V, the roosed rectifier works as a assive rectifier since Vrect is less than the minimum ositive voltage suly requirement for the comarators and (ii) for outut voltage Vrect > 1.7 V, the control circuits are enabled and the outut ower is greatly increased, while a certain amount of harvested energy is used to ower the control circuits. The ower consumtion of control circuit elements was obtained by measuring the average suly current and voltage across each comonent using a Rigol DM3068 digital multimeter. The results show that the

13 Sensors 2015, difference in outut ower between externally owered and self-owered rectifiers corresonds to the total ower consumtion of the control circuits. As observed in Figure 10, when the outut voltage Vrect is less than 0.4 V, the outut ower is the same for both externally owered rectifier and self-owered rectifiers. This is because in this range, the voltage across the PD is smaller or slightly over the forward voltage of diodes along the discharging ath. As a result when the switch is turned ON, the charge stored in the internal caacitance is blocked by diodes along the discharging ath and cannot flow to ground. Table 1 comares the erformance of the roosed rectifier with reorted inductorless rectifiers for iezoelectric energy harvesting [24,30,31]. As in rior works, we comare the roosed rectifier against a conventional full bridge rectifier using the same PD oerated in the same exerimental conditions. This is done because the actual harvested ower cannot be used as a erformance metric given that the inut ower rovided by the PD is a function of its mechanical roerties, dimensions, resonant frequency, internal caacitance and resistance but also on exerimental conditions (e.g., tye of shakers, PD ositioning onto the shaker). Each of these arameters greatly affects the ower generated by the PD. The rectifiers in [24,30,31] and this work both use iezoelectric cantilever beams as PDs for testing the erformance of the rectifiers. This tye of PD is not suitable for broadband iezoelectric energy harvesting when the ambient vibration frequencies cover a wide range. This is because the PD can only reach its maximum outut when it vibrates at or close to its resonant frequency. The resonant frequency of the PD can be adjusted by attaching a roof mass. The works in [30,31] use equivalent circuits to mimic the PD. The amlitude I of current roduced by PD is roortional to the vibration amlitude. Getting a high value of I results in a PD roducing more energy, as shown in Equation (8). However, the harvested energy does not deend only on the amlitude I but also on the internal caacitance C. When two different PDs roduce the same amlitude I, the one with the smaller internal caacitance C can be used to harvest more energy, as shown in Equation (10). Therefore, the internal caacitance of the PD should be made as small as ossible. The forward voltage of diodes is a major source of ower loss for rectifiers. The voltage dro across diodes should be as low as ossible to reduce their energy loss. Schottky diodes were used for [30,31] and this work because they have lower voltage dros and higher switching seed. In addition, Schottky diodes can be imlemented in standard semiconductor industry CMOS rocess [37]. To get a voltage dro lower than that of Schottky diodes, authors in [30,31] imlemented custom designed o-am based diodes. The custom designed o-ams were designed to have a reset dc offset voltage that revents toggling before the olarity change of the current roduced by the PD. This was achieved by alying different asect ratios to o-am s inut transistors. However, the mismatch of the reset offset voltages associated to rocess variations degrades the erformance of the rectifier [30]. Furthermore, these custom designed o-ams require constant current inut, as well as a custom designed suly indeendent bias circuit to act as the start-u circuit for the rectifier. Due to the use of discrete comonents for control circuits in this work, the maximum quiescent current consumtion is much higher than other works. However, it can significantly be lowered once the comlete rectifier is integrated onto a chi. Eliminating the requirement of inductor (external or internal) makes the roosed rectifier fully comatible with semiconductor industry standard CMOS rocess. The efficiency of the rectifier, defined as the ratio of the measured maximum outut ower to the theoretical maximum ower (Figure 9), is 91.23%. The ratio of measured maximum harvested ower

14 Sensors 2015, of the roosed rectifier to that of the full wave bridge rectifier was found to be 3.9 times. The roosed rectifier shows several advantages over other designs listed in Table 1, including efficiency, standalone oeration, circuit simlicity, comatibility with standard semiconductor industry CMOS rocess and comatibility with different tyes of PDs. Table 1. Performance comarison with inductorless rectifiers for iezoelectric energy harvesting. Publication [24] [30] [31] This Work Technology Integrated Integrated Integrated Discrete Piezoelectric Device (PD) Mide Technology Equivalent Mide Technology Equivalent Circuit (V22B) Circuit (V21B) Amlitude I of current roduced by PD 63 µa 88 µa 94 µa µa Internal Caacitance C 18 nf 25 nf 25 nf 52 nf Vibration Frequency 225 Hz 200 Hz 200 Hz 246 Hz Diode Forward Voltage 0.05 V 0.01 V 0.01 V 0.1 V Start-u circuit No Yes Yes No Max Quiescent Current Consumtion >220 na 180 na >180 na 4900 na External Inductor Required No No No No Efficiency Not shown 90% 91.2% 91.23% Performance comared with a Full Wave Bridge Rectifier 1.9 times 3.4 times 3.5 times 3.9 times 6. Conclusions An inductorless self-controlled rectifier for iezoelectric energy harvesting has been resented in this aer. It overcomes the limitations of existing high erformance inductorless rectifiers, which rely on comlex DSP and or external control signal circuitry to detect the occurrence of the olarity change of the PD outut current but also to control the time required to discharge the internal caacitance of the PD. Furthermore, the roosed rectifier alleviates the need for an inductor, making it suitable for chi integration. This was achieved by using two voltage comarators at the two ends of the PD to monitor olarity change of its outut current. The switch ON time is automatically controlled by the diodes along the discharging ath. Although the roosed inductorless self-controlled rectifier was imlemented using discrete comonents, it still can imrove the harvested energy by u to 3.9 times comared to that of a conventional full wave bridge rectifier. Acknowledgments This research was suorted under Australian Research Council s Discovery Projects funding scheme (roject number DP ). Author Contributions Shaohua Lu: Rectifier design, exeriments, data analysis and aer writing; Farid Boussaid: Rectifier design and aer writing.

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