INCREASED POWER OUTPUT FROM PIEZOELECTRIC ENERGYHARVESTERS BY PRE-BIASING

J. Dicken, P.D. Mitcheson, I. Stoianov and E.M. YeatmanDepartment of Electrical Engineering, Imperial College London, UK.

Abstract: This paper presents, for the first time, experimental results demonstrating a new approach to increasingthe power output of piezoelectric energy harvesters by applying a bias charge at the beginning of each half cycleof motion. Ultimate power limits of inertial energy harvesters depend only on the device size and nature of theexcitation, rather than on the transduction mechanism. However, practical devices generally perform well belowthe theoretical limit, often because a sufficiently high transducer damping force cannot be achieved. For suchcases, we show that the generator effectiveness is improvedby a pre-biasing technique, and present simulationresults with experimental verification. These results showthat the effectiveness of the piezoelectric generator isimproved by more than 10 times compared to an optimised purely resistive load. In practice our gains werelimited by the voltage breakdown of the components used.

Keywords: Energy harvesting, pre-biasing, piezoelectric

INTRODUCTIONPiezoelectric transduction is very popular for

inertial energy harvesters [1], but due to lowelectromechanical coupling the achievable electricaldamping forces are low. When a microgeneratormust operate with a low ratio ofZl/Y0 the electricaldamping must be high in order that the proofmass does not hit the generator end-stops so that themaximum possible power density can be achieved [2].Piezoelectric transducers operated with a resistive loadare generally unable to provide sufficient dampingforce under such circumstances [3]; this limitation isprimarily caused by the intrinsic shunt capacitance,which limits the real power transfer capability of thetransducer into a resistive load. Several techniqueshave been proposed to overcome this limitation, suchas the SSH techniques described by Guyomar [4].In this paper we present a generalised solution topreviously presented work and show that by using acombination of pre-biasing and synchronous chargeextraction a significant improvement can be made tothe output power of piezoelectric harvesters operatingat low Zl/Y0 ratios where large electrical dampingis required. As the electrical damping force in apiezoelectric generator is equal to the cell voltagetimes the piezoelectric force factorα, it is possibleto increase the damping force presented by thepiezoelectric material and to increase output power,by placing a bias charge on the piezoelectric whenthe mass is at its maximum displacement in eitherdirection. In this paper we demonstrate our methodfor improving the power output of such a device by

Fig. 1. Pre-bias of piezo to increase damping force

simulation and the construction of a prototype thatimproves the power output of the generator by afactor of 10 over an optimal resistive load.

PRE-BIASINGWhen a piezoelectric material is strained in one

direction in open circuit, the resulting charge displace-ment causes a force which tries to move the materialback to an unstrained state, and some work is done instraining the material. If a charge is placed onto thematerial forcing it to become strained in one directionbefore the material is forced to move in the otherdirection by an external force, more mechanical workcan be done as the force presented by the piezoelectricmaterial is increased. Therefore more electrical energycan be be generated. This is illustrated graphically inFig. 1. When the piezo cantilever is strained upwardat maximum displacement such that a positive chargewould be generated by the deflection of the material ifin open circuit, a negative pre-bias voltage is appliedto the material allowing increased mechanical work to

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Fig. 2. Ideal waveform with synchronous charge extraction andpre-biasing

be done as the cantilever free end moves downwards.The opposite applies when the free end of the piezocantilever is at the maximum downwards position.

If the applied biasVB is large compared to the piezo-electrically induced voltage change∆Vp, the forcemagnitude will now be constant at≈ αVB, rather thanoscillating in the range±α∆Vp. The output voltagewaveform will be as sketched in Fig. 2. This canbe seen as a generalisation of the method developedby Guyomar et al. [3] in which the cell voltage isinverted synchronously. In that case the explanationof improved power output is given in terms of thenonlinear functioning of the circuit, but it is theincreased mechanical force due to the resultant cellbiasing that is the essential origin of the increasedoutput power. Therefore this bias can be implimentedin any way, but must be delivered efficiently to give anet power benefit.

Use of the dedicated biasing circuit presented herein Fig. 4 allows the damping force to be adapteddynamically to the source amplitude, providing maxi-mum power point tracking. The output stage shown inFig. 4 allows the piezo capacitor to be synchronouslydischarged to the load at the end of a generation cyclejust before pre-biasing occurs as illustrated in Fig. 2.

ANALYSISEnergy stored on the capacitance of the piezoelec-

tric cell is proportional to the square of the voltage.Therefore, if there already exists a charge on thematerial before charge is added due to mechanicalstrain, more work is done to charge the piezoelectricinternal capacitance because that charge is driven intoa higher voltage than in the case where no initialcharge was present. Therefore, after synchronouslydischarging the energy generated in the previous half

Fig. 3. Theoretical power enhancement relative to conventionalpiezoelectric cell vs. efficiency of pre-biasing

cycle, the piezoelectric cell should be pre-charged ateach extremmity of position before movement occursin the opposite direction.

The gain in energy by applying the pre-bias cannow be readily calculated. If we define efficienciesfor the charging and discharging process asηc andηd

respectively, then the energy that must be supplied tocharge the piezo to a voltageVB is CVB

2/2ηc, whilethe energy that is usefully obtained at discharge is1/2×C[ηd(VB+∆V)2]. This gives a net energy outputof:

E =12

C[ηd(VB +∆V)2−V2/ηc] (1)

The optimum value forVB in terms of∆V is foundby settingdE/dVB = 0:

VB =ηcηd

1−ηcηd∆V (2)

From this we can derive an expression for theoptimum energy gain vs. efficiency. Taking the casewhere ηc = ηd = η and combining (1) and (2), weobtain an energy gain factor (the ratio of energygenerated for synchronous extraction with zero pre-bias to energy generated with the optimal pre-bias fora given efficiency) of:

fE =E(η)

E(VB = 0)=

3η3

(1−η2)+η (3)

This function is plotted in Fig. 3, and shows thathigh output gain is obtained for efficiencies above90%.

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SDGSDGSDGSDG

V c cS DGS DG +

Fig. 4. Piezo Pre-Bias H-Bridge Circuit

CIRCUITRYThe charging circuit shown in Fig. 4 comprises

an H-bridge with an inductor after the collector ofthe top two FETs. The inductor enables near-losslescharging of the piezo capacitor, with current allowed tofreewheel between VCC and ground via two diodes.The gates are controlled as per a normal H-Bridgeconfiguration with FETs 1 and 4 allowing per-chargingin one direction and 2 and 3 in the reverse direction.FETs 5 and 6 are used for synchronous discharge ofthe piezoelectric capacitance in an interlieved buckconfiguration.

The circuit as described was simulated usingPSpiceusing inductors of 15 mH with a 350mΩ seriesresistance and the capacitors were modelled as ideal.Real semicondictor models were used.

SIMULATION RESULTSThe piezoelectric device used for experimentation

was a Kingsgate KPSG-100 Loudspeakeras usedGuyomar et. al. in [4]. The data-sheet states a piezo-electric capacitance of 65 nF, although our sample wasmeasured as 50 nF. Our simulation was set up so thatthe device, being excited so it produces a current ofmagnitude 122µA at 105 Hz was connected to anoptimal load resistance of 30.3 kΩ [3]. In simulation,this resistor dissipates 0.1 mW. The was taken as abase case.

In order to test the likely practical effectiveness ofour pre-biasing technique a simulation was run withthe piezo excited with the same mechanical motion.The circuit of Fig. 4 was implemented in PSpice using2N7000 MOSFETS and ZC5800 Schottky diodes. Inthe simulation the pre-bias technique was shown togenerate up to 6.25 mW net power, a factor of 62.5more than the optimised resistive load. In a second

simulation (this time with an 80 Hz excitation anda piezo current magnitude of 500µA) the ideal load(30.6kΩ) developed 0.6 mW. Synchronous extractionwith an 18 V pre-bias voltage developed 7 mW netpower output.

It was noted that the system is particularly sensitiveto the relative values of the charge extraction pulselength and the output inductor size due to the res-onant nature of the charging circuit. The system issurprisingly insensitive to the series resistance of theinductor and the system still performed within 50% ofthe stated power gain values with a series resistanceas high as 2Ω - although better practical componentscan be sourced.

EXPERIMENTATIONA PCB of Fig. 4 was manufactured and the

Kingsgate piezo element mounted on a shaker. Thevibration level was increased at a set freqency untilthe piezo voltage under open-circuit matched that ofthe simulation. In practice the position measurementsfor the synchronisation of the pre-bias and dischargegate pulses were difficult to generate directly fromthe measured piezo voltage since as soon as a chargeis placed on the piezo the voltage changes. Thereforethe position was sensed by measuring the voltageof the shaker coil and a suitable phase shift added.This waveform was fed into a DSP chip and a peakrate-of-change detection algorithm determined thefrequency and amplitude and hence the appropriatecharge/discharge instants. The DSP then drove theMOSFET gate drivers. Scope traces are shown inFig. 6.

RESULTS & VERIFICATION OF MODELThe open-circuit output voltage was 5Vp−p, which

given an ideal 50 nF shunt capacitor equates to anoptimal load resistor of(2π fC)−1 = 30.3 kΩ. Thisresistive load gave an output power (PR) of 0.103 mW(calculated by measuring the voltage across the resis-tor). This agrees with the value for the same test foundin PSpice. The power into the pre-biasing systemwas calculated using a sense resistor. A measurementwas taken for each pre-charge voltage and the energyextracted per cycle was calculated from12CV2

PEAK atthe peak of the cycle. The results are promising: thepower gain increases as a function of pre-bias voltageas predicted, suggesting the limit of the method isthe voltage the piezo can support. Figure 7 showsthe output power improvement ratio (when compared

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Fig. 5. Circuit Implementation

Fig. 6. Experimental waveform with positive and negative pre-bias firing angles highlighted

to the optimal shunt resistor case) for different pre-bias voltages. It can be seen that in the case wherethe pre-bias voltage is zero (synchronous extractionalone) the power output doubles. In our experimentthe MOSFETs broke down at around 35 V causingthe efficiency to drop sharply as the piezo capacitorbegan to discharge directly through ground and pre-biasing was no longer achieved.

CONCLUSIONSWe have shown that greater electro-mechanical

coupling can be achieved by pre-biasing the internalcapacitance of a piezo-electric device, and that doingso improves the overall power output of the system byan order of magnitude compared to an ideal resistiveload on the same device. It was demonstrated thatthe method works in practice and effectively extractsmore energy from a source of excitation than the

Fig. 7. Output power improvement compared to ideal resistiveload

optimal shunt load resistor. The method is primarilysuitable for applications where the source excitationis un-dampable (e.g engines, foot-traffic etc.), and forlow-frequency but high source amplitude operationsince the efficacy is heavily dependent on theamplitude of the excitation.

FURTHER WORKThe next stage is to develop a standalone circuit that

derives the pre-bias voltage from the output. Self-startcircuitry will be needed, as it may be the case thatthe piezo alone will not charge the reservoir capacitorsufficiently to power the gate drives. The amount bywhich the pre-bias method increases power output willdepend on the load placed upon the system by signalprocessing and pre-charging and discharging circuitry.This means the system may be unsuitable for operationat very low power although this is a matter for furtherinvestigation.

REFERENCES[1] S. R. Anton and H. A. Sodano, “A review of power harvesting

using piezoelectric materials (2003-2006),”Smart Materialsand Structures, vol. 16, no. 3, pp. R1–R21, 2007.

[2] P. D. Mitcheson, T. C. Green, E. M. Yeatman, and A. S.Holmes, “Architectures for vibration-driven micropower gen-erators,”Microelectromechanical Systems, Journal of, vol. 13,no. 3, pp. 429–440, 2004.

[3] P. D. Mitcheson, E. K. Reilly, T. Toh, P. K. Wright, and E. M.Yeatman, “Performance limits of the three mems inertial en-ergy generator transduction types,”Journal of Micromechanicsand Microengineering, vol. 17, no. 9, pp. S211–S216, 2007.

[4] M. Lallart, L. Garbuio, L. Petit, C. Richard, and D. Guyomar,“Double synchronized switch harvesting (dssh): a new energyharvesting scheme for efficient energy extraction,”Ultrason-ics, Ferroelectrics and Frequency Control, IEEE Transactionson, vol. 55, no. 10, pp. 2119–2130, October 2008.

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