Theoretical Comparison of Energy Harvesting Methods for Electret-free Variable-Capacitance Devices

Aaron L. F. Stein; Akshay Sarin; Heath F. Hofmann

doi:10.1515/ehs-2015-0020

Article Publicly Available

Theoretical Comparison of Energy Harvesting Methods for Electret-free Variable-Capacitance Devices

Aaron L. F. Stein , Akshay Sarin and Heath F. Hofmann

Published/Copyright: August 4, 2016

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From the journal Energy Harvesting and Systems Volume 3 Issue 3

Abstract

Electret-free variable-capacitance energy harvesters are micro-electromechanical systems (MEMs) that generate electrical power from mechanical vibrations. In order to effectively harvest energy from these devices, the power electronic circuitry is extremely important, and can be the difference between generating or losing energy during a harvesting cycle. Four methods of harvesting energy from these devices are known: the Constant Voltage Method, the Constant Charge Method, the Charge Pump Method, and the Constant Charge With Parallel Capacitance Method. All four methods have been reported; however, the literature is lacking a formal comparison of these methods. This paper evaluates these four methods and the new Voltage and Charge Constrained Method while considering power electronic circuit efficiency as a key parameter. By including efficiency as a parameter, new fundamental properties of these devices are derived: a threshold efficiency necessary for energy harvesting, analytical solutions for optimal harvesting conditions, and a realistic comparison of the four methods. A case study demonstrates the advantage of using the Charge Pump method for MEMs applications, and illustrates the use of the new fundamental properties in the design of a circuit topology that is practical for MEMs vibration energy harvesting applications.

Keywords: vibration energy harvesting; power electronic efficeincy; electrostatic devices; energy harvesting methods

1 Introduction

Recent advancements in communication and low-power sensor nodes have led to innovative data acquisition systems for applications such as heart monitoring, forest-fire detection, and building environmental controls. These sensor nodes play a vital role in human safety and comfort (Akyildiz et al. 2002; Tashiro et al. 2002; Mitcheson et al. 2008). Despite their high utility, sensor nodes are powered by batteries that have limited lifetimes due to finite energy storage. Many sensor networks require placement of nodes in remote locations characterized by limited access to electrical power sources and obstacles which would make replacement of batteries time-consuming and expensive. Harvesting energy from ambient sources such as human movement, acoustic noise, solar radiation, thermal gradients, wind, or vibrations has been shown to be an effective means for recharging sensor batteries (Roundy, Wright, and Rabaey 2003; Mateu and Moll 2005; Raghunathan et al. 2005; Weimer, Paing, and Zane 2006; Pereyma 2007; Chalasani and Conrad 2008; Agbossou et al. 2010). The effectiveness of each of the energy harvesting strategies depends on the device’s environment.

In some environments, mechanical vibration is the most accessible ambient energy source. The viability of a vibration energy source is determined by the magnitude of the acceleration and the frequency of the fundamental mode (Roundy, Wright, and Rabaey 2003). Vibration energy is typically converted into electrical energy using piezoelectric devices, electrostatic devices, or magnetic field-based generators (Roundy, Wright, and Rabaey 2003; Paradiso and Starner 2005; Wang et al. 2009). Some variable-capacitance devices can be easily integrated into microsystems, making them well-suited for harvesting energy for low-power sensor nodes. As discussed by Tiwari, Gupta, and Tiwary (2013), there are two different types of electrostatic devices: electret-free variable capacitance devices and electret-based devices.

The benefit of an electret-based energy harvesting system is that it does not require energy to initiate the energy harvesting cycle; however, electret materials have a finite lifetime (Mescheder et al. 2009). Successful electret-based energy harvesting designs have been demonstrated in Fu and Suzuki (2014a, 2014b). Electret-free variable-capacitance devices require charge to be inserted onto the device in order to initiate energy harvesting. However, they can be fabricated by a silicon process which is compatible with CMOS, allowing for close integration with CMOS electronics (Basset et al. 2009; Sheu, Yang, and Lee 2011; Cowan et al. 2014) and are not limited by the lifetime issues associated with the electret.

Electret-free variable-capacitance devices have many promising characteristics; however, practical difficulties have limited their use (Roundy, Wright, and Rabaey 2003). Challenges such as achieving a large capacitance ratio and a large maximum voltage are compounded by an incomplete understanding of the harvesting methods. In order to reach the full potential of these devices, there must be improvement in both the devices themselves and the harvesting methods by which energy is extracted from them.

Currently the literature provides four energy harvesting methods for these devices. For two of these methods either the voltage (Constant Voltage Method) or charge (Constant Charge Method) is held constant as the device capacitance transitions between its maximum and minimum values. These two methods are discussed at length in Meninger et al. (2001), Harb (2011), Torres et al. (2009), Roundy, Wright, and Rabaey (2004). Examples of circuit topologies that could be used to implement these methods are shown in Harb (2011), Meninger et al. (2001).

Next, the Charge Pump Method is comprised of two voltage sources connected to the device by rectifiers, as demonstrated in Roundy, Wright, and Rabaey (2003), Roundy, Wright, and Pister (2002), Roundy, Wright, and Rabaey (2004). This method was improved when the output voltage source was replaced with a dc-dc converter, eliminating the need for two voltage sources. Both a step-down converter and a flyback converter have been used in this application; however, both of these topologies require an inductor which makes integrating the circuit on a chip very difficult (Yen and Lang 2006; Cowan et al. 2014). To overcome this, (Yen and Lang 2006) propose the use of a switched-capacitor converter to allow a completely integrated energy harvesting system. To optimize the harvesting process (Roundy, Wright, and Rabaey 2003) finds an optimal input voltage for their system through simulation.

Finally, the Constant Charge with Parallel Capacitance Method (CCPC Method) is proposed by Meninger et al. (2001) where both the voltage and charge on the device change as the capacitance changes from its maximum to its minimum value. The CCPC Method is a modification of the Constant Charge Method, whereby an external capacitance is connected in parallel with the device. Through simulation, (Meninger et al. 2001) uncovered the existence of a relationship between circuit losses and the optimal parallel capacitance size. A power electronic interface that could be used to implement this method is proposed in Meninger et al. (2001).

The harvesting methods for electret-free variable-capacitance devices require energy to flow into the device in order to begin the harvesting process. It has been shown for piezoelectric devices, whose harvesting methods require energy flow into the device, that power electronic efficiency plays a large role in device performance and optimal operating conditions (Liu et al. 2009). However, the effect of circuit efficiency on variable-capacitance energy harvesting has not been formally examined in the literature for any of the above-mentioned harvesting methods.

The purpose of this paper is to determine how power electronic circuit efficiency affects energy harvesting for variable-capacitance devices. The energy harvesting capabilities of these devices are constrained by their physical limitations, as discussed in Section 2. While considering these limitations Section 3 uncovers the energy harvesting capabilities of existing harvesting methods and a new harvesting method, the Voltage and Charge Constrained (VCC) Method, as a function of power electronic circuit efficiency. This analysis reveals that each method has a threshold efficiency required to achieve energy harvesting. Furthermore, analytical solutions for computing the optimal parallel capacitance for the CCPC Method, and the optimal input voltage for the Charge Pump Method as a function of power electronic efficiency, provide insights into the design of effective energy energy harvesting systems. Finally, in Section 4, a micro-sized harvesting system is proposed. This system is based on the Charge Pump Method, which advances the system in Yen and Lang (2006) by providing a design which can be synthesized entirely in silicon and incorporates the optimal harvesting conditions derived in this paper.

2 Electret-Free Variable-Capacitance Devices

A variable-capacitance energy harvesting device is an electromechanical system in which a mass (M) is sprung between two conductive materials (electrodes) (Peano and Tambosso 2005). The capacitance of the device (C) is a function of the permittivity of air (ε0), the distance between electrodes (D), the width of the electrode (W), and the length of the overlapping area of the electrodes (L).

[1]C=ε0AD=ε0LWD

There are two common types of variable capacitance devices.

An area-overlap device, in which the mechanical vibrations cause the overlapping area of the electrodes to change; an example is shown in Figure 1(a) (Roundy, Wright, and Rabaey 2004). For this device, the length of the overlapping region changes as a function of the position of the mass (X).
A gap-closing device, in which the mechanical vibrations cause the distance D between the electrodes to change; examples are shown in Figure 1(b) and 1(c) (Roundy, Wright, and Rabaey 2004). For these devices, the distance between the electrodes changes as a function of the position of the mass (X).

Figure 1:

Physical model of an area-overlap and a gap-closing variable-capacitance energy harvesting devices. (a) Area-overlap Device (b) Out-Of-Plane Gap-closing Device (c) In-Plane Gap-closing Device.

As either the area of overlap or distance between the electrodes change, so too does the capacitance of the device. Based on the magnitude of the ambient vibrations, the variable capacitance device will achieve a maximum capacitance (Cmax) and a minimum capacitance (C_min). The ratio of Cmax to Cmin is an important device parameter, hereafter denoted by Rc:

[2]Rc=CmaxCmin.

The literature provides expressions for the ideal energy harvested per mechanical cycle for each of the four methods of energy harvesting. These equations are derived after making a quasi-static assumption, meaning here that the electrical energy harvesting does not affect the mechanical displacement. This assumption does not prohibit dynamic analysis: redefining Cmax and Cmin to values achieved by the dynamic excitation will maintain the validity of this theory.

2.1 Variable-Capacitance Device Constraints

To estimate the energy harvesting capabilities of a variable-capacitance device, appropriate constraints must be considered. These constraints are inherent to the devices, and are necessary for understanding the energy harvesting limitations of said devices.

In many cases, the energy harvesting capabilities of variable-capacitance devices are limited by its structural properties. Stored energy in the variable-capacitance device creates an electrostatic force between the electrodes. As the energy in the device increases, so too does the force on the electrodes of the device. If the stored energy becomes too large, the resulting force on the electrodes could cause physical deformation of the device (e. g., pull-in effect) (Mescheder et al. 2012).

In order to avoid device failure and harvest energy, force constraints must be placed on the device. The force in a variable capacitance device is derived from the co-energy of the electric field (Wfld′) (Melcher 1981), and is

[3]Fes=∂W′fld(V,X)∂X=12∂C∂XV2.

Deriving the electrostatic force expression for each device will illuminate the electrical constraints that must be considered in order to avoid mechanical failure. The electrical constraint which must be applied to each device considered in this manuscript can be found in Table 1.

2.1.1 Area-Overlap Electrical Device Constraint

For an area-overlap device, such as the one depicted in Figure 1(a), the maximum allowable voltage across the device is an important device constraint. Assuming linear motion of parallel plates, the device capacitance changes as a function of position (X) as follows:

[4]C=2ε0(Xo−X)WD.

Substituting the capacitance equation into eq. [3], the electrostatic force is given by

[5]Fes=∂∂XWε0(X0−X)DV2=−ε0WDV2.

The force between the electrodes in an area-overlap device is therefore dependent on the physical device parameters and the voltage on the device (V). For a given area-overlap device, ε0WD is independent of the state of the device; i. e., it is constant. Therefore, to limit the maximum force and avoid the pull-in effect, the maximum voltage (Vmax) applied to the device should be limited (Meninger 1999; Meninger et al. 2001; Roundy, Wright, and Rabaey 2003; Despesse et al. 2005; Torres et al. 2009).

The maximum voltage limitation on a area-overlap device constrains the energy storage capabilities of the device. For a given Vmax, the maximum energy that can be stored in the device is

[6]Emax=12CmaxVmax2.

The maximum energy that can be stored in the device provides an upper bound on the amount of energy that can be harvested. This is established in Section 3.5, where it is shown that for certain harvesting methods, as Rc→∞ and η=1, the harvested power approaches 12CmaxVmax2 for an area-overlap device.

2.1.2 Gap-Closing Electrical Device Constraint

Let us first consider an out-of-plane gap-closing device, such as the one depicted in Figure 1(b). The capacitance in this device is given by

[7]C=ε0LWX.

Assuming linear motion of parallel plates, and using eq. [3], the electrostatic force in the device is

[8]Fes=∂∂Xε0LW2XV2=−ε0LW2X2V2=−Q22ε0LW.

For a given out-of-plane gap-closing device, 12ε0LW does not change with the state of the device; therefore, it is constant. Thus, to mitigate the pull-in effect on a out-of-plane gap-closing device, the maximum charge (Qmax) should be limited.

For an in-plane gap-closing device such as the one illustrated in Figure 1(c) the capacitance of the device is given by

[9]C=ε0LW1(X0−X)+1(X0+X).

The largest electrostatic force will occur when the mass is significantly displaced; i. e., when X approaches X0 or −X0. Consider the case when X approaches X0. In this case the capacitance can be approximated by

[10]C≈ε0LW(X0−X).

Therefore the electrostatic force can be approximated by

[11]Fes≈∂∂Xε0LW2(X0−X)V2=−ε0LW(X0−X)2V2=−Q22ε0LW.

Once again, 12ε0LW does not change with the state of the device; therefore, to mitigate the pull-in effect on an in-plane gap-closing device, the maximum charge (Qmax) should again be limited.

The maximum charge limitation on a gap-closing device constrains the energy storage capabilities of the device. For a given Qmax, the maximum energy that can be stored in the device is

[12]Emax=Qmax22Cmin.

Once again, the maximum energy that can be stored in the device provides an upper bound on the amount of energy that can be harvested. This is also confirmed for gap-closing devices in Section 3.5 of the sequel.

Table 1:

Variable-capacitance device constraints.

Device type	Constraint	Maximum energy
Area-overlap device	Voltage	1 2 C m a x V m a x 2
Out-of-plane gap-closing device	Charge	1 2 C m i n Q m a x 2
In-plane gap-closing device	Charge	1 2 C m i n Q m a x 2

2.1.3 Efficiency-Based Analytical Tools

To understand the energy harvesting capabilities of these devices, first consider the amount of energy that can be extracted assuming 100 % efficient power electronics (ideal energy harvested). The expression for the ideal energy harvested over an energy harvesting cycle is given by:

[13]Eideal=∮V(Q)dQ=Eout−Ein,

The ideal energy harvested accounts for the electrical energy supplied to the harvesting device, Ein, to initiate harvesting and the electrical energy removed from the device, Eout.

For each harvesting method a voltage versus charge plot will be shown. The net area enclosed by the voltage versus charge plot is Eideal, which is the difference between the area enclosed by Eout and the area enclosed by Ein.

In order to take into account losses in the power electronic circuitry, the input and output energy of the device are penalized by an efficiency η. Using efficiency, as opposed to specific loss models, allows the analysis to be generalized for all circuits. Furthermore, it is assumed that the efficiency of inserting Ein, and removing Eout, is the same. Although some circuits might present conditions where the input and output efficiencies would be different, using a single efficiency yields more tractable mathematical expressions that provide intuition into the design of variable-capacitance energy harvesting systems without significantly altering the results. The net energy harvested (Enet) is therefore given by:

[14]Enet=ηEout−1ηEin

The net energy equation is normalized by the maximum the maximum possible energy that can be extracted from the device. The normalized net energy NEnet is

[15]NEnet=EnetEmax=ηEout−1ηEinEmax.

The normalized net energy equation is derived to illustrate the energy harvesting capabilities of each method independent of specific device parameters. It should be noted that NEnet is not a function of either the maximum voltage or the maximum charge and, for a given device architecture, the normalization energy Emax is constant between methods and therefore allows direct comparisons of the methods. This can be seen in the sequel by comparing the normalized net energy plots presented in Section 3.5 with the results from the case study in Section 4.

Comparisons between voltage-limited and charge-limited devices are also possible, assuming the maximum energy harvesting densities of the devices are identical. In Roundy, Wright, and Rabaey (2004) it is claimed that the energy harvesting density of area-overlap devices and gap-closing devices are roughly the same, while in Lee et al. (2009) it is claimed that area-overlap devices have a slightly higher energy density. Either way, the normalized net energy harvested provides a basis for comparison between the different energy harvesting methods and device architectures.

As will be shown, each method has a threshold power electronic efficiency, ηthresh, which must be exceeded in order to harvest energy. To solve for ηthresh, Enet is set to zero in eq. [14] and solved for η:

[16]ηthresh=EinEout.

3 Efficiency-based Analysis for Energy Harvesting Methods

3.1 Constant Voltage Method

The Constant Voltage Method charges the capacitive device to a voltage V_max when the capacitance is at its maximum value so that the charge on the device is given by:

[17]Qmax=CmaxVmax.

As the device’s capacitance is reduced to its minimum value, the voltage across it is held constant at Vmax. Charge is extracted from the device, until the remaining charge is:

[18]Qmin=CminVmax.

Finally, once the device reaches its minimum capacitance, the voltage on the device is reduced to zero (Meninger et al. 2001). The voltage and charge fluctuations of this process are illustrated in Figure 2.

Figure 2:

Voltage versus charge plot for the Constant Voltage Method.

3.1.1 Voltage-Limited

Using eq. [13], the energy into and out of a voltage-limited device can be derived directly from the shaded areas shown in Figure 2:

[19]Ein=12QmaxVmax=12CmaxVmax2,

[20]Eout=(Qmax−Qmin)Vmax+12QminVmax=(Cmax−12Cmin)Vmax2,

[21]⇒Eideal=Ein−Eout=12(Cmax−Cmin)Vmax2.

The net energy harvested is therefore:

[22]Enet=ηEout−1ηEin=η(Cmax−12Cmin)Vmax2−12ηCmaxVmax2.

Using eq. [15], the normalized energy harvested is derived:

[23]NEnet=2η−ηRc−1η.

The normalized net energy is plotted in Figure 3 and illustrates how efficiency affects energy harvesting for the voltage limited Constant Voltage Method. Given highly efficient power electronics and a device with a large Rc, the Constant Voltage Method’s net energy harvested becomes 12CmaxVmax2.

$Figure 3: The voltage-limited normalized net energy harvested, NEnet${N_{Enet}}$, using the Constant Voltage Method is plotted as a function of efficiency (η$\eta $) for various values of capacitance ratio (Rc${R_c}$).$

Figure 3:

The voltage-limited normalized net energy harvested, NEnet, using the Constant Voltage Method is plotted as a function of efficiency (η) for various values of capacitance ratio (Rc).

3.1.2 Charge-Limited

Using eq. [13], the ideal energy harvested from a charge-limited device using the Constant Voltage Method is

[24]Eideal=12(Qmax−Qmin)Vmax=Qmax22Cmax1−1Rc.

Including the efficiency of the power electronics, the net energy harvested is

[25]Enet=Qmax2Cmaxη−η2Rc−12η.

The normalized net energy NEnet is therefore

[26]NEnet=2ηRc−ηRc2−1Rcη.

$Figure 4: The charge-limited normalized net energy harvested, NEnet${N_{Enet}}$, using the constant voltage method is plotted as a function of efficiency (η$\eta $) for various values of capacitance ratio (Rc${R_c}$).$

Figure 4:

The charge-limited normalized net energy harvested, NEnet, using the constant voltage method is plotted as a function of efficiency (η) for various values of capacitance ratio (Rc).

The normalized net energy is plotted in Figure 4, and illustrates how efficiency affects energy harvesting for the Constant Voltage Method on a charge-limited device. As the capacitance ratio increases, the Constant Voltage Method harvests only a small fraction of the available energy independent of power electronic efficiency.

3.1.3 Threshold Efficiency

The threshold efficiency for the Constant Voltage Method is given by:

[27]ηthresh=EinEout=Rc2Rc−1.

A good variable-capacitance harvesting device has a Cmax that is much larger than Cmin. Setting Rc to infinity shows the behavior of the best possible device. The limit of eq. [27] as Rc goes to infinity provides the threshold efficiency for energy harvesting from an ideal device.

[28]limRc→∞ηthresh=limRc→∞Rc2Rc−1=12=70.71%

A capacitance ratio of 25 or higher is sufficiently large for eq. [28] to be a good approximation of the threshold efficiency.

3.2 Constant Charge Method

The Constant Charge Method of energy harvesting charges the device to a voltage Vinit while the device is at Cmax. The device is then left in an open-circuit configuration such that charge on the device is constant. Once the device reaches Cmin, the voltage across the device reaches Vmax, and the energy is harvested from the device by discharging the capacitor (Meninger et al. 2001). Figure 5 helps elucidate the Constant Charge Method by showing the variations of both the voltage and the charge on the device during the harvesting process.

Figure 5:

Voltage versus charge plot for the Constant Charge Method.

The voltage on the device is inversely proportional to the capacitance during the constant charge part of the cycle. The maximum voltage experienced by the device is derived in eq. [29].

Qmax=CmaxVinit=CminVmax

[29]⇒Vmax=CmaxCminVinit

3.2.1 Voltage-Limited

In order to prevent the voltage from exceeding the voltage limit, Vinit must be selected according to eq. [29]. Using the V–Q plot shown in Figure 5, Ein, Eout, and Eideal are derived:

[30]Ein=12QmaxVinit=12Cmin2CmaxVmax2,

[31]Eout=12QmaxVmax=12CminVmax2,

[32]⇒Eideal=12CminVmax2−12Cmin2CmaxVmax2

Using eqs [14] and [32] to solve for the net energy harvested yields:

[33]Enet=η12CminVmax2−12ηCmin2CmaxVmax2.

Using eq. [15], the normalized net energy harvested is shown to be:

[34]NEnet=ηRc−1ηRc2.

A plot of eq. [36] is shown in Figure 6 to elucidate some of the trends. It can be shown that the highest ratio of harvested energy to available energy is when the power electronic efficiency is high and the capacitance ratio has a value of 2. In this case, the Constant Charge method harvests a quarter of the maximum available energy. As the capacitance ratio becomes large, the Constant Charge Method harvests very little energy relative to the available energy. In this case we see that NEnet does not fall below zero until very low efficiencies.

$Figure 6: The voltage-limited normalized energy harvested, NEnet${N_{Enet}}$, using the Constant Charge Method is plotted as a function of efficiency (η$\eta $) for various values of the capacitance ratio (Rc${R_c}$).$

Figure 6:

The voltage-limited normalized energy harvested, NEnet, using the Constant Charge Method is plotted as a function of efficiency (η) for various values of the capacitance ratio (Rc).

3.2.2 Charge-Limited

The net energy harvested using the Constant Charge Method on a charge-limited device is

[35]Enet=12Qmax2ηCmin−1ηCmax.

Using eq. [15], the normalized net energy harvested is shown to be

[36]NEnet=η−1ηRc.

Figure 7 illustrates the normalized net energy harvested as a function of power electronic efficiency. Several important trends for the Constant Charge Method are illuminated. First, for large capacitance ratios the normalized net energy is

[37]limRc→∞NEnet≈η.

$Figure 7: The charge-limited normalized net energy harvested, NEnet${N_{Enet}}$, using the Constant Charge Method is plotted as a function of efficiency (η$\eta $) for various values of capacitance ratio (Rc${R_c}$).$

Figure 7:

The charge-limited normalized net energy harvested, NEnet, using the Constant Charge Method is plotted as a function of efficiency (η) for various values of capacitance ratio (Rc).

For this case, the power electronic efficiency essentially only impacts the energy extracted from the system. Therefore, power electronic efficiency has a reduced importance on the harvesting performance of this method. Next, at high efficiencies and large capacitance ratios, this method can harvest up to 100 % of the available energy. Finally, for devices with smaller capacitance ratios, the Constant Charge method can still harvest an appreciable amount of power; however, as Rc is reduced, the impact of power electronic efficiency increases.

3.2.3 Threshold Efficiency

The Constant Charge Method can harvest energy over a very wide efficiency range. The threshold efficiency is

[38]ηthresh=EinEout=1Rc.

As the capacitance ratio becomes large, the threshold efficiency for the Constant Charge Method is

[39]limRc→∞ηthresh=0.

3.3 Charge Pump Method

The Charge Pump Method energy harvesting cycle starts at an initial voltage Vmin when the capacitance is at a maximum such that

[40]Qmax=CmaxVmin.

The device is then open-circuited, undergoing a constant-charge phase until the voltage on the device reaches Vmax. Once the voltage on the device has reached Vmax, it is held there such that the device undergoes a constant-voltage phase until the device’s capacitance reaches Cmin.

[41]Qmin=CminVmax

Once the device has reached Cmin, its voltage drops during another constant charge phase as the capacitance increases to Cmax. Charge is returned to the device during another constant voltage phase in order to get the device back to its original state (Yen and Lang 2006). The resulting voltage and charge variations on the device from this method are provided in Figure 8. The circuit shown in Figure 9 implements the desired behavior of the Charge Pump Method and is useful for gaining an intuitive understanding of the approach.

In order to harvest energy using the Charge Pump Method, Vmax and Vmin must be constrained such that

[42]Vmin<Vmax<RcVmin.

Figure 8:

Voltage versus charge plot for the Charge Pump Method.

Figure 9:

Diode-based Charge Pump Method energy harvesting circuit.

The conditions noted in eq. [42] are developed from fundamental circuit principles. First, Vmax must be larger than Vmin so that the diodes of Figure 9 do not continuously conduct, effectively shorting Vmax and Vmin. Secondly, if Vmax is larger than RcVmin, then the voltage across the device will never be large enough to forward bias the output diode, and so electrical power is never extracted.

3.3.1 Voltage-Limited

The terms Ein, Eout, Eideal are derived from the shaded areas in Figure 8:

[43]Ein=Vmin(Qmax−Qmin)=Vmin(VminCmax−VmaxCmin),

[44]Eout=Vmax(Qmax−Qmin)=Vmax(VminCmax−VmaxCmin),

[45]⇒Eideal=(Vmax−Vmin)(VminCmax−VmaxCmin).

Including efficiency as a parameter as demonstrated in eq. [14], the net harvested energy is given by:

[46]Enet=ηVmax−Vminη(VminCmax−VmaxCmin).

The net energy equation for the Charge Pump Method is a function of two controllable design criteria: Vmax and Vmin. To maximize the energy harvested, Vmax should be limited to the maximum allowable device voltage. Given a limited Vmax, there exists an optimum Vmin that maximizes the energy harvested. The optimum Vmin, denoted as Vminopt, is derived by taking the derivative of the net energy equation with respect to Vmin and solving. The resulting optimal value of Vmin is:

[47]Vminopt=Vmaxη22+12Rc.

In eq. [47], it is shown that Vminopt is a strong function of power electronic efficiency. Assuming both a large capacitance ratio and high efficiencies the optimum maximum to minimum voltage ratio is two.

Using Vminopt, the normalized net energy harvested is derived as a function of efficiency and shown in Figure 10.

[48]NEnet=[Rcη2−1]22Rc2η

Figure 10:

The voltage-limited normalized net energy harvested using the Charge Pump Method is plotted as a function of efficiency, while V_max is limited and V_min is optimized. If the method constraint in eq. [42] is violated, the normalized net energy harvested is plotted as zero.

The normalized net energy equation is only valid when, for the given harvesting conditions, the equation for Vminopt does not violate the constraint in [42].

It is illustrated that, for large values of Rc and high-efficiency power electronics, at most half of the maximum available energy can be harvested. At lower power electronic efficiencies, the ratio of harvested energy to available energy is significantly impacted by the capacitance ratio. As the capacitance ratio declines, this method becomes less effective at harvesting the available energy.

3.3.2 Charge-Limited

The net energy harvested using the Charge-Pump Method on a charge-limited device is

[49]Enet=(Qmax−Qmin)(ηVmax−1ηVmin)=(Qmax−Qmin)ηQminCmin−QmaxηCmax.

The net energy equation can be maximized through careful selection of Qmin. To derive the optimal Qmin, denoted as Qminopt, the derivative of eq. [49] is taken with respect to Qmin, and set to zero. It can be shown that,

[50]Qminopt=Qmax2+Qmax2η2Rc

Combining Qminopt into the net energy equation, the normalized net energy harvested can be shown to be

[51]NEnet=η2−1ηRc+12η3Rc2.

Once again the normalized net energy equation is only valid when the selection of Qminopt does violate the constrain in eq. [42].

The normalized net energy harvested is plotted in Figure 11. At high efficiencies, the charge pump method used on charge-limited variable-capacitance devices with large capacitance ratios can harvest up to 50 % of the maximum energy.

$Figure 11: The charge-limited normalized net energy harvested, NEnet${N_{Enet}}$, using the Charge Pump Method is plotted as a function of efficiency (η$\eta $) for various values of capacitance ratio (Rc${R_c}$). If the method constraint in eq. [42] is violated, the normalized net energy harvested is plotted as zero.$

Figure 11:

The charge-limited normalized net energy harvested, NEnet, using the Charge Pump Method is plotted as a function of efficiency (η) for various values of capacitance ratio (Rc). If the method constraint in eq. [42] is violated, the normalized net energy harvested is plotted as zero.

3.3.3 Threshold Efficiency

Finally, to ensure a positive net energy harvested, the threshold efficiency is given by:

[52]ηthresh=EinEout=VminVmax=QmaxQminRc.

For this method the threshold efficiency is determined by Vmin and Vmax which are controllable variables. Therefore, with the Charge Pump Method the threshold efficiency can be manipulated to guarantee energy harvesting.

3.4 Constant Charge with Parallel Capacitance (CCPC) Method

The Constant Charge with Parallel Capacitance Method, or CCPC Method, is very similar to that of the Constant Charge Method, with the exception that a capacitor is placed in parallel with the device. The parallel capacitor aids in energy harvesting because it allows the variable-capacitance device to undergo a change in both voltage and charge (Lee et al. 2009). For the CCPC Method, the device and the parallel capacitor are charged to Vinit when the device is at Cmax. Then the device and the parallel capacitor are open-circuited. As the capacitance changes from Cmax to Cmin, charge flows out of the device and into the parallel capacitance, simultaneously raising the voltage of both. The voltage across the device reaches Vmax when the device’s capacitance is at Cmin. At this point the energy is harvested from the device and the parallel capacitance (Meninger et al. 2001). The device varies from Cmin back to Cmax with no charge, allowing the cycle to restart. The variations of both the voltage and the charge on the harvesting device are portrayed in Figure 12. When Cp is zero, the cycle is identical to the Constant Charge cycle. However, as Cp gets arbitrarily large, the cycle becomes identical to a Constant Voltage cycle. As will be seen, this method provides a versatile energy harvesting technique which can be tuned by varying the capacitance Cp based on the circuit efficiency to maximize the energy being harvested.

Figure 12:

Voltage versus charge plot for the Constant Charge with Parallel Capacitance Method.

3.4.1 Voltage-Limited

The shaded enclosed areas in Figure 12 represent Ein, Eout, and Eideal are used to derive Enet as shown by:

[53]Ein=12(Cmax+Cp)Vinit2,

[54]Eout=12(Cp+Cmin)Vmax2,

where

[55]VmaxVinit=Cmax+CpCmin+Cp.

The ideal energy extracted is given by:

[56]Eideal=12(Cp+Cmin)Vmax2−12(Cmin+Cp)2Cmax+CpVmax2.

We assume that energy transfer between the two capacitors, when they are in the open-circuit configuration, is considered to occur without loss. Using eq. [14] an equation for Enet is derived:

[57]Enet=η2(Cp+Cmin)Vmax2−12η(Cmin+Cp)2Cmax+CpVmax2.

In Meninger et al. (2001) it was shown through simulation that there exists an optimal Cp; however, no analytical expression is presented. By including efficiency as a parameter, an analytical expression can be derived for the optimal Cp. The optimal Cp, denoted as Cpopt, is given by

[58]Cpopt=Cmax(1−η2)−(1−1Rc)(1−η2)η2−1

The relationship between Cpopt and power electronic efficiency is illustrated in Figure 13. A highly-efficient converter will have a large Cp, which will make the cycle look mostly like a constant voltage cycle; however, an inefficient converter’s ideal Cp will be small, so the cycle is similar to the constant charge cycle.

$Figure 13: Optimal Cp${C_p}$ for a given power electronic efficiency and capacitance ratio.$

Figure 13:

Optimal Cp for a given power electronic efficiency and capacitance ratio.

Using the optimal Cp, the normalized net energy harvested is derived as a function of efficiency and plotted in Figure 14.

[59]NEnet=η(Cp+Cmin)Cmax−(Cmin+Cp)2ηCmax(Cmax+Cp)

$Figure 14: The voltage-limited normalized net energy harvested plotted as a function of efficiency while using the optimal Cp${C_p}$ for the CCPC Method.$

Figure 14:

The voltage-limited normalized net energy harvested plotted as a function of efficiency while using the optimal Cp for the CCPC Method.

Given highly-efficient power electronics and a device with a large Rc the CCPC Method harvests the maximum available energy; however, the energy harvested declines rapidly as efficiency decreases.

3.4.2 Charge-Limited

The CCPC method is not an effective method of energy harvesting for a charge-limited device. The parallel capacitance increases the input energy into the device, and does not provide any benefit to the energy harvesting process.

3.4.3 Threshold Efficiency

The threshold efficiency for the CCPC Method is given by:

[60]ηthresh=EinEout=Cmin+CpCmax+Cp.

Similar to the Constant Charge Method, as the capacitance ratio becomes arbitrarily large,

[61]limRc→∞ηthresh=0.

3.5 Comparison of Methods

In the following comparison of energy harvesting methods, it is assumed that the maximum energy harvesting density of a charge-limited device and a voltage-limited device is the same, as suggested in Roundy, Wright, and Rabaey (2004). Although in practice there may be some difference, this assumption provides a grounds for comparison of the normalized net energy harvested. The normalized net energy harvested for the discussed methods on a device with a very large capacitance ratio is shown in Figure 15.

Figure 15:

A comparison of the normalized net energy harvested is shown as a function of power electronic efficiency for the more promising method and device architecture combinations. The normalized net energy is plotted using an infinite capacitance ratio, to show the best harvesting scenario for each method.

The Constant Voltage method on a voltage-limited device, and the Constant Charge method on a charge-limited device, both have a maximum normalized net energy that approaches 1 at high efficiencies. Given the physical constraints of the device, both methods utilize the entire constraint boundary for energy harvesting (0→Vmax or 0→Qmax) when the device is at Cmax and Cmin, therefore they can harvest up to the maximum energy. This suggests that the Constant Voltage Method used on a voltage-limited device can harvest the same amount of energy as the Constant Charge Method on a charge-limited device. However, at practical power electronic efficiencies the harvested energy using the Constant Voltage Method on a voltage-limited device decreases significantly more rapidly. The energy harvested by the Constant Charge Method is less impacted by power electronic efficiency.

The Constant Voltage method on a charge-limited device, and the Constant Charge method on a voltage-limited device, both have a normalized net energy that is small even at high efficiencies. This is because these combinations of harvesting methods and device constraints limit the utilized constraint boundary when the device is at Cmax and Cmin.

The Charge Pump method has a maximum normalized net energy of 0.5, which illuminates an important upper bound on the capabilities of this method. The energy harvesting capabilities of the Charge Pump Method are limited by the fact that it is a passive cycle. The voltage and charge are not driven to zero when the device capacitance is at Cmin, so only a faction of the maximum energy can be harvested. The energy harvested using this method is impacted by power electronic efficiency differently depending on the constraint applied to the method. As the efficiency declines, the normalized energy harvested using a charge-limited device is significantly higher than that of a voltage-limited device. For example, if the efficiency of the power electronics is 85 %, the charge-limited device can harvest 1.37 times more energy. Using the optimal output voltage and input voltage, the Charge Pump Method is the only harvesting method that cannot lose energy regardless of efficiency.

The CCPC Method on a voltage-limited device has a normalized net energy harvested that approaches 1. Once again, this method utilizes the entire constraint boundary (0→Vmax) at Cmax and Cmin, so the method can harvest up to the maximum possible energy. However, at practical power electronic efficiencies, the CCPC Method harvests less energy than the Constant Voltage Method without providing any inherent advantages.

Figure 15 illustrates important conclusions about the various energy harvesting methods. This plot shows that:

At 100 % efficiency the charge-limited Constant Charge Method, the voltage-limited Constant Voltage Method, and the CCPC Method can all harvest 100 % of the available power.
At 100 % efficiency the Charge Pump method harvests up to 50 % of the available power for both voltage and charge limited devices.
The Constant Charge method is less impacted by efficiency than the Constant Voltage method.

Charge constrained portions of energy harvesting cycles are less impacted by circuit efficiency. During the constant charge portion of the energy harvesting cycle, the device is in an open-circuit configuration, and therefore is not impacted by the efficiency of the electronics as there is no power flow. Conversely, voltage constrained portions of energy harvesting methods have power flow. The constrained voltage is generated using power electronics, and therefore the harvested energy is more impacted by the efficiency of the power electronics.

3.6 Voltage and Charge Constrained (VCC) Method

The Constant Charge Method on a charge-limited device harvests the most energy of any method at practical power electronic efficiencies; however, energy harvesting systems that utilize this device architecture and harvesting method typically produce large voltages. For example, in Mitcheson et al. (2004) a gap-closing device is used with the Constant Charge method. The experimental results show device voltages in excess of 350 volts. In such a system, the maximum charge should be limited to limit the pull-in effect, but also the maximum voltage may need to be limited to accommodate the silicon process that creates the device, or the power electronic circuitry which implements the energy harvesting method. In order to meet both constraints, a new energy harvesting method is proposed, the Voltage and Charge Constrained (VCC) Method.

The VCC Method charges the gap-closing device to Qmax when the device capacitance is at a maximum. Therefore the input electrical energy into the system is

[62]Ein=Qmax22Cmax.

The device is then open-circuited and, as the device capacitance declines, the voltage on the device increases. Once the voltage on the device reaches the maximum allowable voltage Vmax, the device is clamped to Vmax until the device capacitance reaches Cmin. When the device reaches Cmin, energy is extracted from the system. The energy taken out of the device is

[63]Eout=Vmax2Cmin2+(Qmax−Qmin)Vmax.

The resulting voltage-versus-charge plot for the VCC Method is illustrated in Figure 16.

Figure 16:

The voltage versus charge plot is shown for the Voltage and Charge Constrained method of energy harvesting.

A new factor, K, is introduced to simplify the net energy and normalized net energy equations. K is the ratio of the unconstrained maximum voltage Vmax∗ in the system to the constrained maximum voltage Vmax.

[64]K=Vmax∗Vmax=QmaxCminVmax=QmaxRcCmaxVmax

The constrained maximum voltage Vmax is therefore

[65]Vmax=QmaxRcCmaxK.

The net energy equation is then derived in terms of K, Qmax, Cmax, Cmin, and η:

[66]Enet=ηQmax2RcCmaxK−Qmax2Rc2Cmin2K2Cmax2−Qmax22ηCmax.

The net energy equation is normalized by the maximum possible energy in the electrical system when K is equal to 1, which is

[67]Qmax22Cmin.

The normalized net energy harvested is therefore

[68]NEnet=η2K−1K2−1ηRc.

The impact of constraining the maximum voltage is elucidated by plotting the normalized net energy harvested as a function power electronic efficiency and K. This is shown for devices with a large capacitance ratio in Figure 17. This figure illustrates the impact of both power electronic efficiency and voltage constraints on the normalized net energy harvested. When the voltage is unconstrained (K=1), the resulting normalized net energy and impact of power electronic efficiency is the same as the Constant Charge method. As the voltage constraint becomes stricter (K gets larger), the normalized harvested power declines.

The VCC Method seeks to mitigate the maximum voltage in the system while still providing the energy harvesting benefits of the Constant Charge Method on a charge-limited device. For example consider a device with a very large capacitance ratio. At its best (K→1) the VCC Method approaches the same performance as the Constant Charge Method on a charge-limited device. As the voltage constraint increases (1<K<3.5) the VCC Method still harvests more power than the Constant Voltage Method on a voltage-limited device at practical efficiencies (85 %). For large values of K (3.5<K) the VCC Method is no longer the best method. Instead an area-overlap device should using the Constant Voltage Method should be considered as it outperforms the VCC Method at practical efficiencies.

$Figure 17: The normalized net energy harvested using the VCC Method is plotted as a function of both power electronic efficiency and K for a variable-capacitance device with a large capacitance ratio (Rc→∞${R_c} \to \infty $).$

Figure 17:

The normalized net energy harvested using the VCC Method is plotted as a function of both power electronic efficiency and K for a variable-capacitance device with a large capacitance ratio (Rc→∞).

The threshold efficiency for the VCC Method is

[69]ηthresh=1Rc[2K−1K2]

A possible implementation of the VCC Method can be created through modification of the circuit topology presented for the Constant Charge Method in Meninger et al. (2001). A diode connects a large capacitor, which is charged to Vmax, to the variable capacitance device. When the voltage on the variable-capacitance device reaches Vmax, the diode begins to conduct and the device voltage is clamped. A hysteresis controller connected to a DC-DC converter is used to maintain the voltage at Vmax. This circuit topology is depicted in Figure 18.

Figure 18:

Proposed circuit topology that implements the Voltage and Charge Constrained Method.

4 Case Study

In this section a case study is presented to demonstrate an application of the fundamental principles presented in this manuscript. The goal of this case study is to maximize the harvested power for a micro-sized energy harvesting system. To achieve this goal, the energy harvesting device is designed such that it can be integrated with both the power electronics and the wireless sensor node made using a CMOS process. This integration poses two challenges:

the power electronic circuit should be designed such that it can be implemented entirely in silicon
the maximum voltage in the system is limited by the CMOS process.

Due to these restriction an area-overlap device architecture is chosen, so that the voltage constraint can be accommodated. The device parameters are based on the device used in Meninger et al. (2001), and are shown in Table 2.

Table 2:

Area-overlap device parameters used in case study

Parameter	Value
Allowable Vmax	8 V
C _max	260 pF
C _min	2 pF
Frequency	2,520 Hz

The device is a comb-type variable-capacitance device that is excited at a frequency of 2,520 Hz, meaning the device varies from Cmax to Cmin at a frequency of 5,040 Hz. In order to harvest energy, a battery must be used to both supply energy to the harvesting cycle and provide energy storage for the harvested energy. The nominal voltage of the battery is referred to as Vbat, and is assumed to be 4 Volts.

4.1 Selecting a Harvesting Method for a Micro-Sized Energy Harvester

In order to select the best harvesting method, a number of factors must be considered: power harvested, practicality of implementation, and ease of integration into a micro-sized energy harvester. As the device is voltage-limited only, charge-limited energy harvesting methods are not considered (including the VCC Method). Figure 19 highlights the Constant Voltage Method, the CCPC Method, and the Charge Pump method because they each harvest a significant amount of power over a wide efficiency range. However, the Constant Voltage Method and CCPC Method are practically difficult to implement. These methods require the device to be charged and discharged when the oscillating mass of the device is at a certain position. This requires the controller to have knowledge of the position of the energy harvester. Such a control strategy was developed by Meninger et al. (2001); however, 34 % of their harvested power was dedicated to their controller implementation. Even if a highly-efficient control circuit and power electronic converter was developed for these methods, the varying nature of the voltage on the device as energy is transferred back to the battery would require a magnetic-component-based power electronic circuit. This can be difficult to implement in a microsystem, as it requires a micro-sized magnetic core that is difficult to manufacture on a chip. In (Meninger et al. 2001) an estimated 5.6 μW could be harvested from the area-overlap device using the CCPC Method. If the Charge Pump Method was used in combination with the optimal minimum voltage shown in eq. [47], then based on eq. [46] we expect to harvest 10.8 μW from the same device given an assumed efficiency estimate of 80 % (η = 0.80).

$Figure 19: Comparison of power harvested for each harvesting methods using the area-overlap (voltage-limited) device presented in Table 2 assuming optimized conditions for the Charge Pump and CCPC methods. The Constant Charge Method harvests 0.32 μW at η=1$\eta = 1$ and 0.19 μW at η=0.6$\eta = 0.6$.$

Figure 19:

Comparison of power harvested for each harvesting methods using the area-overlap (voltage-limited) device presented in Table 2 assuming optimized conditions for the Charge Pump and CCPC methods. The Constant Charge Method harvests 0.32 μW at η=1 and 0.19 μW at η=0.6.

The Charge Pump Method has many advantages: it can be easily implemented on an integrated circuit, does not require active control, and it harvests significant energy over a wide efficiency range. The optimum ratio of Vmax to Vmin for the Charge Pump Method is fixed for a given efficiency, so transferring energy between these sources corresponds to a fixed voltage conversion ratio. This allows for the design of highly-efficient power electronic circuitry. Switched-capacitor converter topologies can accomplish a fixed voltage gain without a magnetic component (i. e. inductor or transformer). The control of the Charge Pump Method does not require knowledge of the state of the variable-capacitance device, which simplifies the design and saves energy. The theoretical energy harvested using this method is shown in Figure 19. The Charge Pump Method harvests a comparable amount of energy as the CCPC Method and the Constant Voltage Method over typical power electronic efficiency ranges, but was chosen because of the other advantages highlighted in this paragraph.

4.2 Design of a Voltage-Limited Energy Harvesting System

In order to maximize the power harvested, it is important that the design of the energy harvesting system is closely tied to the optimal harvesting conditions derived in eq. [47]. Assuming 100 % efficiency and a Vmax of 8 Volts, the optimum Vmin is 4.03 Volts, so if the converter is efficient then a 2:1 switched-capacitor circuit can be used to transfer energy from Vmax back to Vmin, and the ratio of these voltages will be very close to optimal. Figure 20 depicts the discrepancy between using Vminopt and the 2:1 converter as a function of efficiency. Using a 2:1 switched-capacitor converter is effective as long as the overall circuit efficiency is high (i. e., >85 %). The proposed circuit topology is shown in Figure 21.

$Figure 20: Comparison of power harvested using the Vmax${V_{\rm max}}$-limited Charge Pump Method when Vmin is optimal versus 12Vmax${1 \over 2}{V_{\rm max}}$.$

Figure 20:

Comparison of power harvested using the Vmax-limited Charge Pump Method when V_min is optimal versus 12Vmax.

As the device capacitance oscillates between Cmax and Cmin, energy is harvested and stored in the output capacitor, which causes Vmax to rise. A hysteresis controller dictates when the switched-capacitor converter is enabled. The switched-capacitor converter operates by turning “on” S1 and S3 for the first half of the switching period, and S2 and S4 for the second half of the switching period. The switching frequency of the switched-capacitor converter is much higher than the excitation frequency of the device, and thus is able to transfer energy back to Vmin on a faster time scale than it is harvested. In order to minimize switching losses, a hysteresis controller, implemented by a single comparator, only turns the switched-capacitor converter on for short bursts and allows a tiny voltage swing across Vmax. The hysteresis band is set to keep Vmax between 8.012 Volts and 8.004 Volts. By keeping the ratio of Vmin to Vmax greater than but close to 2:1, the efficiency of this topology can be high.

4.3 Simulation Results

The energy harvesting system portrayed in Figure 21 was simulated in LTSPICE. The simulation included many realistic loss mechanisms in order to provide an accurate estimate of power harvested. An appropriate loss model was created based on loss mechanisms associated with implementing this design on an integrated circuit. The switches required in this design are bi-directional switches which must be able to hold 10 Volts and carry 20 mA. In order to withstand the required voltage range a 12 Volts process was used for the design. Using models of this process, parameter values for the transistors were extracted. These transistors have an on-resistance of 257 mΩ (when Vgs is 3.3 Volts), a leakage current of 1 μA, a drain-to-source capacitance of 0.16 pF, and a gate to source capacitance of 1.6 pF. The absolute maximum ratings for drain to source voltage (12 Volts) and current (6 A) are not exceeded in the simulation. The gating losses are calculated by assuming the energy sourced to the gate capacitance is lost during each switching cycle. The diode characteristics are modeled based on the Fairchild Semiconductor BAX16 diode. This diode has a voltage drop of 0.65 Volts and a leakage current of 25 nA. Finally, an ESR of 1 mΩ is used for the capacitors. The control losses are derived from the operating power of a comparator. An Intersel-ISL7819 comparator’s losses (1.65 μW) are used to represent control losses.

Figure 21:

Charge Pump Method energy harvesting circuit topology with switched-capacitor energy return.

The results of this simulation are summarized in Table 3 and Figure 22, which shows the output voltage rising as energy is harvested from the device. Once the voltage reaches the top of the hysteresis band, the switched-capacitor converter is enabled and energy is returned to the source.

Table 3:

LTSPICE simulation results for the area-overlap device, using the Charge Pump Method with a switched-capacitor topology.

Simulation results
Switched-capacitor efficiency	86.9 %
Energy harvested	12.09 μW

$Figure 22: V m a x ${V_{\rm max}}$ voltage variations from the LTSPICE simulation of the Charge Pump energy harvesting system.$

Figure 22:

V m a x voltage variations from the LTSPICE simulation of the Charge Pump energy harvesting system.

Using the theory developed in this paper, an energy harvesting system that could be used for a micro-sized energy harvester was developed that harvests 12.09 μW, more than twice the amount of energy as predicted in Meninger et al. (2001) while using the same device properties.

5 Summary and Conclusion

Electret-free variable-capacitance energy harvesting devices are proposed as a solution for charging wireless sensor nodes from ambient vibrations because they can be made in silicon, are easily integrated with CMOS electronics in a micro-sized harvesting system, and do not have a limited lifetime; however, the small available power from these devices has limited their use. This work seeks to increase the viability of electret-free variable-capacitance energy harvesters by maximizing the power harvested from these devices. This was accomplished by incorporating power electronic efficiency into the existing analysis of the harvesting methods. Including power electronic efficiency as a parameter leads to: the derivation of a threshold efficiency for each of the energy harvesting methods, a comparison of the net energy harvested using different harvesting methods over a wide efficiency range, and analytical solutions for the optimal harvesting conditions for applicable methods.

The new theoretical background developed in this paper motivates the design of an energy harvesting system using a voltage-limited device with the Charge Pump Method. Analytical solutions for optimal energy harvesting conditions inspired the use of a 2:1 switched capacitor converter topology as the basis of the voltage-limited harvesting system. An LTSPICE simulation verified the advantages of the proposed Charge Pump Method harvesting system by revealing that 12.09 μW could be harvested from this system, which is more than twice the power previously asserted for the same device.

Ultimately, an in-depth understanding of the power electronic efficiency is key to maximizing the energy harvested from these devices. Future research in this area will focus on incorporating mechanical dynamics into this efficiency-based analysis of the energy harvesting methods.

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Published Online: 2016-08-04

Published in Print: 2016-08-01

Articles in the same Issue

https://doi.org/10.1515/ehs-2015-0020

Keywords for this article

vibration energy harvesting; power electronic efficeincy; electrostatic devices; energy harvesting methods