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68 Journal Integrated Circuits and Systems 2011; v.6 / n.1:68-74

Energy Harvesting Circuit Using Variable Capacitorwith Higher Performance

1. INTRODUCTION

With the development of the micro and thenanotechnology, the electronic devices have been inrapid advancement. In this process, the size reductionis followed by the energy consumption reduction.Along with these advancements, new sources of ener-gy are also researched, in particular, the so-calledautonomous sources. These sources are integrated tothese devices in order to make them independentfrom the external energy sources [1]-[3].Autonomous sources are able to capture energy in dif-ferent ways, such as light, vibration, heat and electro-magnetic waves from the environment where they areinserted.

Among the autonomous devices, theautonomous sensors are pointed out once they aredevices able to act without the need of other compo-nents. They generate the necessary energy to feedtheir circuits; they read the sensors, process the signalsand send them via wireless by means of frequencyradio. The tendency of these technologies is that onlyone chip will be able to contain the autonomoussource, the sensor of the magnitude to be measured,the transmitter circuit and the control circuit to man-age the whole functioning process.

The autonomous sensors have great advantagesin relation to the conventional ones. First of all, thereis a reduction of the wire quantity used for the electri-cal connections between the source and the severalsensors. A second advantage is the fact that there is noneed for replacing the chemical batteries used forfeeding the sensors.

Many devices can have the mechanical vibra-tions as a single way of harvesting energy becausesuch devices can be inside machines, automobiles orspacecrafts in which there is no other way of harvest-ing. In these situations, the energy from the vibra-tions can be converted into electrical energy throughthe use of piezoelectric materials, electromagneticsystems, or by means of electrostatic charges usingvariable capacitors [1], [4]. This research focuses onthe energy conversion of mechanical vibrations intoelectrical energy with the use of an electrostatic trans-ducer, represented by a variable capacitor of MEMStechnology.

The harvesting of electrical energy through avariable capacitor is an alternative for attaining agreat quantity of energy in a reduced space. Theenergy harvesting in this system is proportional tothe square voltage over the variable capacitor and thenew technologies provide the use of higher and

ABSTRACT1

The search for compact autonomous devices has been increasing in the microelectronics industry.These devices have the capacity to generate their own energy in order to be charged. One of theways of harvesting environmental energy for charging such devices is by using mechanical vibra-tions through the use of variable capacitor. Taking this principle into account, this work presents abehavioral analysis of a system model of harvesting vibratory energy for low power, made up of acircuit which includes a variable capacitor. An architecture of a circuit which improves the relationconcerning the amount of harvested energy/circuit area in relation to conventional architectures isalso presented as well as a comparison between the circuit with the proposed architecture and theconventional circuit. In this way, it was verified that, under the same functioning conditions, the con-ventional circuit harvested a maximum power of 4,5 µW whereas the circuit with the new architec-ture harvested a 6,25 µW power.

Index Terms: Vibratory energy harvesting, variable capacitor, energy conversion, DC/DC powerconversion

Helder R. Florentino1, Dimitri Galayko2, Raimundo C. S. Freire1, Benedito A. Luciano3 and Caio Florentino3

1,3 Departamento de engenharia Elétrica, Universidade Federal de Campina Grande, PB, Brazil.2 LIP6 Laboratory, Paris VI, France.e-mail: [email protected]

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Energy Harvesting Circuit Using Variable Capacitor with Higher PerformanceFlorentino, Galayko, Freire, Luciano & Florentino

higher voltages. Integration becomes simpler as wellbecause the variable capacitors can be built in its cir-cuit substrate [4]-[7].

The architecture of energy harvesting circuit isobject of several studies with the intention to obtain ahigher energy amount [4]-[8]. In general, this archi-tecture is built from a charge pump and a flyback cir-cuit. Some critical points are verified in this architec-ture. One of them is the physical construction of theflyback circuit switch that consumes much energy dueto the high work voltage and its high commutation fre-quency. As to the second point, the control circuit con-struction is complex and it consumes much energy.

In this research, a new architecture of a circuitfor vibratory energy harvesting of low power by usingvariable capacitor is shown. The proposed architecturereduces the flyback circuit use by diminishing theswitch losses and simplifying the control circuit.Moreover, it attains a noteworthy increase in the ener-gy harvesting. The proposed architecture was com-pared to a conventional architecture and it harvesteda higher amount of energy. A model VHDL-AMS forthe transducer and a model for the ELDO for simu-lating the electrical circuit were used.

2. ENERGY HARVESTING THROUGHCIRCUITSWITH VARIABLE CAPACITOR

An option for producing electrical energythrough electrostatic charges is the use of two elec-trodes in parallel in order to form a capacitor. One ofthe electrodes is connected to a proof mass and it dis-places itself during the vibration in relation to the sec-ond electrode which is fixed in the substrate [6]. Inthis kind of transducer, the capacitance varies from amaximum value to a minimum one. It is representedin figure 1, the structure of the variable capacitor [9].

According to expression (1), the charge storedin a capacitor is function of its capacitance and its volt-age. By charging a variable capacitor with an initialcharge, and then, leaving its terminals open so that thevalue of this charge does not change, while a capaci-tance variation is taking place, there will also be a

change in voltage over the capacitor. The voltageincrease, which occurred in the variable capacitorwhen the capacitance value decreases, is used to boostelectrons in the circuit, working therefore as chargepump. The energy taken by each variation cycle of thecapacitor is given by the expression (2) in which Vin isthe initial voltage of the capacitor, Cmax and Cmin arethe maximum and minimum values of the variablecapacitor, respectively.

(1)

(2)

It is represented in Figure 2 the conventionalresonant circuit used for electrical energy harvestingthrough electrostatic charges. The circuit can bedivided into three parts: the first part is the chargepump which boosts the electrons to go round the cir-cuit, composed of Cres, Cvar, Cstore, D1 and D2; thesecond part is the flyback circuit which is responsiblefor the return from Cstore charges to Cres made up ofL, D3 and the Sw switch; and the third part is themechanical system composed of a spring and a proofmass connected to the variable capacitor [10].

The mechanical part was modeled by using aresonating dampened equation of second order asso-ciated to a capacitive transducer coupled to a proofmass. The proof mass is mechanically coupled to theexternal system by means of a bar which allows thetransmission of the external vibrations for the mass.The mechanical system is described by (3).

(3)

In this system, the following values were usedfor simulation: m = 46 µg, k=152,6 fo = 298 Hz, µ =2,185*10-3, Xmax = 50 um, Cmin = 150 pF, Cmax = 450pF. Where k is the stiffness coefficient of the spring, µis the damping coefficient, aext is the external acceler-ation, Ftransd is the force generated by the transducer,x is the displacement, m is the proof mass and fo is theresonance frequency of the mechanical system.

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Figure 1. Structure of variable capacitor [9] Figure 2. Circuit for energy harvesting [10]



In circuit of Figure 2, the Cvar capacitor is thevariable capacitor which has its value modified accor-ding to a mechanical vibration. The Cstore capacitorhas the function to store temporarily the charge sup-plied by Cvar and then send it to Cres. The Cres capaci-tor has the function to supply energy for the loadresistance, maintaining its voltage constant and thensupply charge to Cvar. [5].

In circuit of Figure 2, it can be initially adoptedthe condition that Vres = Vvar = Vstore and that Cvar isthe maximum. When the Sw switch is opened and acapacitance decrease occurs, caused by vibration, therewill be the increase in Cvar voltage. Consequently, theD2 diode will be directly polarized and the charge ofthis capacitor will be transferred to the Cstore, increa-sing the voltage over it. When the capacitance increa-ses, the voltage over the Cvar decreases, so it gets smal-ler than Vres. In this way, D1 remains directly polarizedtaking Cres charges to Cvar. This process repeats itselfduring the vibration.

When Cstore reaches the maximum value deter-mined by the logic of circuit control, the switch isclosed. The Cstore energy is transferred to Cres recharg-ing it. When the switch is opened, the inductor dis-charges its energy into Cres making up a serial circuitamong inductor, Cres and D3. From this point, the cir-cuit starts effectively to gain energy because Vres startsincreasing and its voltage will be higher than the volt-age it initially had.

Figure 3 represents the waveforms over the cir-cuit in which the Vstore voltage increases each time aCvar variation occurs. The bottom part of the Figurerepresents the current over the inductance due toCstore discharge, when the switch is opened.

When starting a cycle of the variable capacitor,Cvar starts decreasing its maximum value. Cvar voltagestarts to increase and the maximum value that Vvar canreach is given by the expression (4). Nevertheless, thisvalue is limited to a value a little higher than the Vstoredue to D2 conduction.

The transference of Cvar charges to Cstore takesplace when Vvar>Vstore. As in each cycle Vstore increas-es, it is necessary that Vvar reaches values higher and

higher so that the charge transference starts. In thisway, the first cycles of Cvar variation transfer morecharges to Cstore than the last ones, when Vstore is nearto the maximum value, that is, at each cycle fewercharges are transferred from Cvar to Cstore.

(4)

The voltage that Vstore reaches for each vibrationcycle is given by the expressions (5) and (6), where nis the number of times that the capacitor varies.

(5)

(6)

The energy amount that the system gained in aspecific interval of time can be found by subtractingthe final energy over Cres and Cstore from the initialenergy over these capacitors. The expressions (7) and(8) show the calculus of the total gain of energy.

(7)

(8)

Where the f and ini rates indicate the end andinitial values, respectively, of each variable.

In the conventional resonant circuit, shown inFigure 2, the increase of voltage over Cstore, due to thevibration, serves as potential energy for the flyback cir-cuit functioning, once the real energy gain of the res-onant depends on this circuit.

The disadvantage of this circuit is that parts ofthe energy that Cstore gained with the vibration arewasted in the process of sending back the Cstorecharges to Cres. Thus, only the energy accumulated inthe inductor which is transferred to Cres, when theswitch is opened, is used by the load resistance.Besides this factor, the higher frequency of switchcommutation impels the increase of the losses as wellas it makes the control circuit of switch more complex.

A. New resonant circuit for energy harvesting

In this circuit, the load resistance is put betweenCstore and Cres, according to Figure 4. As occurs in thecircuit of Figure 2, voltage over the Cstore capacitorincreases due to the Cvar vibration which takes chargesfrom Cres and puts them in Cstore. The higher voltageof Cstore enables it to supply energy to the load resist-ance and the same current which will feed such resist-ance sends back the charges to Cres. In this way, it is theCstore itself that supplies the charge current, therefore itdoes not need the flyback circuit to supply energy to


Figure 3. Voltage waveform over Cstore



the resistor. This circuit can have an energy efficiencyhigher than the original resonator.

The current which is produced by the Cvar vari-ation divides itself between the load resistance and theCstore capacitor. When the current produced by Cvar ishigher than the current consumed by the load resist-ance, the difference between these currents goes tothe Cstore capacitor, causing an increase in voltage.

Supposing that the variation value of the vari-able capacitance and the frequency are constant, aftera determined time interval, voltage over Cstore andover the load resistance stabilizes.

Disregarding the losses due to leakage currentand taking over that the Vstore value is constant, con-sequently the current generated by Cvar is completelytransmitted to the load resistance.

The charge supplied by the Cvar capacitor for avibration cycle is given by the expression (9):

(9)

The current supplied by Cvar is given by theexpression (10):

(10)

The current supplied by Cva, ivar current, canbe expressed by equation (11).

(11)

Where f is the vibration frequency of the vari-able capacitor. The charge current iRL is given by theexpressions (12) and (13). The iRL charge can beequaled to ivar current, when Vstore is constant, result-ing in the expression (10) which shows theRLoad value.

(12)

(13)

The power over RLoad is calculated by theexpression (14).

(14)

As the circuit is presented in Figure 4, its energywill disappear due to the capacitor losses represented bythe resistors in parallel with each capacitor. The energyof this circuit will decrease because the capacitor chargeis slowly drained to the ground. It is represented inFigure 5 the behavior of the circuit voltages in whichthe Rload voltage, Vres and Vstore decrease slowly.

B. New circuit proposed with flybqck

In order to make up for the leakage currentlosses of the capacitors, we coupled to the circuit ofFigure 4 a flyback circuit. In this way, the equationsfrom the previous section are still valid because thecircuit losses are disregarded by the energy gain of theflyback circuit. The load resistance is now attachedbetween the new point, over C3 and the Cres capaci-tor. Such change is shown in Figure 6. Again, it isCstore that supplies energy for the flyback circuit.Equation (15) describes the functioning of the flyback

71Journal Integrated Circuits and Systems 2011; v.6 / n.1:68-74

Figure 4. Representation of the capacitor leakage

Figure 5. Vres, Vstore and load resistance voltages

Figure 6. New Circuit proposed with Flyback



circuit. The advantage of using the flyback, in thisway, is that it is only activated to make up for lossesdue to leakage current, resulting in a low frequency ofswitch commutation, which reduces the losses by theswitching and makes the control circuit easy. The Swswitch is activated every time Vres voltage decreases 2%of its nominal value resulting in the flyback circuitfunctioning until Cres voltage returns to its referencevalue. This circuit represents a new version of the res-onant circuit. It is able to harvest a higher amount ofenergy than the circuit presented in Figure 2.

(15)

Figure 7 represents the waveform over Vnovo,Vstore, Vres and VRLoad for the circuit of Figure 6. Inthis circuit, the voltage over the load resistance sets updue to the increase of Vnovo and the decrease of Cresvoltage which occurs naturally in function of the valueof the load resistance. The higher the load resistanceis, the higher the voltage over it will be. Notice thatcontrary to the waveform, presented in Figure 5, thevoltages over RLoad and Cres remain stable.

3. MODEL FOR HARVESTING ENERGY ANDRESULTS

The conventional system presented in Figure 2was modeled by using VHDL_AMS for the electrome-chanical transducer, the resonant and the switch. AnELDO model for the electrical part was used. Themodels were presented in literature [5], [7].

For the circuit of Figure 6, it was used the samemodel making the changes in the electrical ELDOmodel and in the VHDL-AMS model of the switch sothat the new circuit works properly.

The result of a simulation, for the circuit inFigure 6, is represented in Figure 8, in which we havethe following initial conditions: Vres = Vstore =5 V, Rloadvoltage of VRLoad = 0 V and load resistances of 6 MΩ.A model of an exponential diode with inverse satura-

tion current of 10 pA was used. After the simulationbeginning, V store increases and it stabilizes near 8,5V. The Vres, however, decreases a little due to the char-ges which are taken initially from Cres. The Rload vol-tage gets near to 3,2 V.

A. Power harvested by the proposed circuit

For the resonant circuit proposed in Figure 6,it was noted that the output voltage varies in functionof the load resistance and so does the harvestedpower. The amount of harvested power also dependson the initial Cres voltage, once the higher the Vres is,the higher the maximum voltage in the variable capa-citor and the energy harvesting will be.

Three simulations in VHDL – AMS for this cir-cuit were accomplished. It had the purpose to verify theamount of harvested energy for the different initial volta-ges of Vres taking several values of the load resistance. Foreach simulation, it was previously supplied an initial vol-tage for the Cres capacitor. It is represented in Figure 8the graph of harvested power for the Vres of 5, 8, and 10V in function of the load resistance. It is represented inTable 1 the maximum value of the harvested power foreach Vres of the two circuits.

B. Comparison between the proposed resonantcircuit and the conventional one

While taking the conventional resonant circuitand comparing it with the new resonant circuit pro-posed and by using the same parameters for the twocircuits with maximum and minimum values of thevariable capacitor, vibration frequency and Cres volta-ge, it can be observed a meaningful power gain of theresonant circuit proposed in relation to the conven-tional resonant circuit.

72

Figure 7.Waveform over Vnew, Vstore, Vres and VRLoad Figure 8.Graph of harvested power for the 5, 8 and 10 V voltages

Table 1. Harvested power

The first res(V) RLoad power (µW)5 1,748 4,6910 8,04

Journal Integrated Circuits and Systems 2011; v.6 / n.1:68-74



It is represented in Figure 9 the harvestedpower for both circuits in function of Cres voltage.Table 2 illustrates the maximum harvested value forthe initial voltage of Vres for the two circuits.

C. Experimental Part

Aiming to accomplish the experiments, a vari-able capacitor using two copper plates measuring20X20 cm, in parallel, was built. A thin layer of micaas dielectric was used. The bottom plate was fixed in awooden structure whereas the upper one was mobileand it moved by means of a DC motor. The move-ment velocity of the upper board was determined bythe value of DC voltage applied over the motor.

An experiment was carried out in order to ver-ify the increase of voltage over the capacitor when thecapacitance decreases. For fulfilling this experimentthe TLC27L2 amplifier of input impedance around1012 Ω was used to make up the voltage measure overthe capacitor, according to the diagram illustrated inFigure 10.

Initially the variable capacitor was adjusted forits maximum capacitance. The SW switch was closedso that the capacitor could be charged with 5 V. Afterthat, the switch was opened and the capacitor changedto the minimum capacitance. The voltage measure-ment of the capacitor which had its value varying from5V to 13,82 V was accomplished.

D. Power harvesting proof

To verify the amount of harvested power, thecircuit presented in Figure 11 was built. The Crescapacitor of 1µF, the Cnew capacitor f 27 nF, both ofpolyester, were used, as well as a Rloud of 14 MΩ. Thediodes were of the 1N4148 type which presents areverse current lower than 10 nA at a temperature of25ºC. Voltage over Cres was measured with a digitalvoltmeter and the Cnew voltage with a digital oscillo-scope. For these voltage measurements, the buffer useby means of an operational TLC 27L2. amplifier wasnecessary.

For the experiment fulfillment, the switch wasinitially closed and charging Cres with 6V and after-wards it was opened. The variable capacitor had vibra-tion in 100 Hz frequency produced by the DC motor.The upper plate of the capacitor was pushed down-wards, decreasing the distance between the two plates,resulting in the increase of the capacitance. The capac-itance value varied between 650 pF and 1,85 nF.These values were found by using an RC series circuit.

During the measurements, voltage over Cresremained practically constant in 6V and voltage of the“new” point attained a value approximately of 11V, asshown in Figure 12. The Rload had a 5V voltage andthe harvested power was approximately 1.8 µW.

73

Figure 9. Harvested power for the two circuits in Vres function

Figure 10. Diagram for variation measurement of the capacitorvoltage

Figure 11. Diagram of the harvesting power circuit using variablecapacitor

Figure 12. Graph of voltage of the new point obtained by a digi-tal oscilloscope

Table 2. Maximum harvest value for each circuit.

Vres (v) Conventional New resonatorresonator power (µW) power (µW)

5 0,96 1,746 1,72 2,667 2,45 3,678 3,42 4,839 4,5 6,25

Journal Integrated Circuits and Systems 2011; v.6 / n.1:68-74



4. CONCLUSION

As a result of the comparison between the twoarchitectures, we can conclude that the amount ofharvested energy by the resonant circuit with the pro-posed architecture (maximum power 6,25 µW) issuperior in relation to the architecture of the conven-tional resonant circuit (maximum power 4,5 µW).This occurs for the entire Vres variation band having asresult a better use of vibration energy by the proposedcircuit than by the harvesting circuit of conventionalenergy.

We could corroborate, through the experi-ments, the power harvesting with the use of variablecapacitor. As concerns the charge resistance, it wasobtained a harvested power of 1,8 µW, for a capaci-tance variation from 650 pF to 1.85 nF, in a 100 Hzfrequency, what proves the model efficacy.

REFERENCES

[1] T. Le, J. Han, A. von Jouanne, K. Mayaram, and T.S. Fiez,“Piezoelectric power generation interface circuits,” in Proc. ofIEEE Custom Integrated Circuit Conf. (CICC), pp. 489-492,Sep. 2003.

[2] T. Le, K. Mayaram, T. S. Fiez, Efficient far-field radio fre-quency power conversion system for passively poweredsensor networks, IEEE Custom Integrated CircuitsConference (CICC), pp. 293-296, Sept. 2006.

[3] F. Lu, H. P. Lee, and S. P. Linn, “Modeling and analysis ofmicro piezoelectric power generators for micro-electro-mechanical systems,” Electronic Journals,Smart Materialsand Structures, vol. 13, pp. 57-63, February 2004.

[4] B. C. Yen, J. H. Lang, “A variable-capacitance vibration-to-electric energy harvester”, IEEE transactions on Circuits andSystems – I: Régular Papers, vol. 53, pp. 288-295, February2006.

[5 D. Galayko, Philippe Basset, Ayyaz Mahmood Paracha, “Optimization and AMS Modeling for Design of anElectrostatic Vibration Energy Harvester’s ConditioningCircuit with an Auto-Adaptive Process to the ExternalVibration Changes” DTIP 9-11 April 2008.

[6] Y Chiu and V Tseng F G., “A capacitive vibration-to-electri-city energy converter with integrated mechanical switches”.Journal of Micromechanics and Microenginnering, IOPPublishing. 2008.

[7] A. M. Paracha, P. Basset, P. Lim, F. Marty and P. Bourouina,“A bulk silicon-based vibration-to-energy converter using anin-plan plate (IPOP) mechanism”, Proc. Of Power MEMS2006, pp. 169-172, 2006.

[8] M. Khbeis, J. McGee, C.Richardson, and R Ghodssi. “Designof a Hybrid Ambient Low Frequency, Low Intensity VibrationEnergy Scavenger”, The Sixth International Workshop onMicro and Nanotechnology for Power Generation andEnergy Conversion Applications, Berkeley, U.S.A. 2006.

[9] A. M Paracha. “Design and Fabrication Issues of a Silicon-Based Vibration Powered Electric Energy Generator UsingParallel Plate and In-Plane Mechanism”. IEEE transactionson Circuits and Systems, 2006.

[10] D. Galayko, R. Pizarro, P. Basset, A. M. Paracha, PillesAmándola, “AMS modeling of controlled switch for designoptimization of capacitive vibration energy harvester”, pro-ceeding of BMAS conference, september 2007, San José,California, 2007.



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Energy Harvesting Circuit Using Variable Capacitor with ... · Energy Harvesting Circuit Using Variable Capacitor ... micro piezoelectric power generators for micro-electro -