Impact-Based Electrostatic Harvesters Considered as A Multi-Source Problem

Cuong Phu Le Department of Micro and Nano Systems Technology

Vestfold University College Raveien 197, 3184 Borre, Norway

Email: Cuong.Le@hive.no

Einar Halvorsen Department of Micro and Nano Systems Technology

Vestfold University College Raveien 197, 3184 Borre, Norway Email: Einar. Halvorsen@hive.no

Abstract—This paper presents a simulation study that compares two microscale impact-based electrostatic energy harvesters with multiple transducers contributing to power conversion as separate electrical sources. One harvester with rigid end-stops has two-sources and another with transducing end-stops has four sources. Each source is connected to a voltage-doubling rectifying circuit and the outputs of all rectifiers charge a common storage capacitor thus constituting a parallel passive circuit topology. The two devices are constrained to have the same total chip area and maximum displacement limit dmax=10µm. Generator performance is evaluated by considering the voltage reached on a storage capacitor C=100nF within 5s. Simulation results show that the impact device with the four-source scheme yields an output energy of 50.0nJ in the impact regime, while the reference device exhibits a saturated energy of 24.5nJ.

I. INTRODUCTION A great number of recently proposed energy harvesting

devices exploit impact nonlinearities to tailor the devices' operation to more realistic, and also more complicated, vibrations than a harmonic vibration with pre-determined frequency and amplitude [1-4]. We have previously implemented a microscale impact-device concept with end-stops functioning as additional transducers. The device concept has demonstrated power improvement even though maximum displacement limit is reached [5-7]. This overcomes a drawback of conventional harvesters which typically exhibit power saturation. For demonstration of the device concept, the power was evaluated by connecting transducer outputs to separate resistive loads. This use of a simple resistor as a model of the electrical load is the de-facto standard method to evaluate harvester performance, but most power conversion circuits are not well represented by such an equivalent. On the contrary, circuits ranging from standard rectifier bridges to sophisticated adaptive circuits are often the choice for power conversion [8-11]. In addition, it is clearly an objective to deliver the generated energy from multiple transducers of a single harvester into one common unit of energy storage [12-13].

In this contribution, a simulation study of nonlinear electrostatic MEMS harvesters under harmonic driving is presented. It focuses on our previous impact-harvesters with transducing end-stops [5-6]. A single harvester of this type presents multiple sources to the power conversion electronics and therefore additional challenges with respect to combining these constructively into a single electrical output. The device models are constructed by using parameters obtained from measurements on microfabricated devices. We then compare to a reference-device model of conventional type to assess if improvement of the harvested energy can still be obtained by the impact-device when combining its multiple outputs.

II. MEMS DEVICES WITH MULTI-SOURCE ARRANGEMENT FOR THE CONVERSION CIRCUIT

In this part, we describe the reference and impact devices and how their multiple transducer sources are connected. The devices have different end-stop configurations to limit their proof mass displacement.

Figure 1. A schematic drawing of the reference device with a two-source

scheme for electrostatic charging circuit.

Figure 1 illustrates a two-source scheme for the reference device. The device includes a comb-drive structure with

This work was supported by the Research Council of Norway underGrant no. 191282.

978-1-4673-5762-3/13/$31.00 ©2013 IEEE 2731

overlap-varying capacitors for two anti-phase transducers R1 and R2. In modeling, a parasitic capacitance Cp is taken into account for each variable capacitance C1/2(x) of the two transducers. The variable capacitance has a nominal overlap x0=10μm. Therefore, the maximum proof mass displacement is limited to this nominal capacitor overlap dmax=x0. This means that one of the transducers results in a zero overlap when the proof mass displacement reaches the maximum position. Its capacitance is then determined by the parasitic capacitance. Rigid end-stops confine the proof mass motion under high accelerations. The total active area of the reference device is 4×5mm2.

A voltage-doubling rectifier-circuit with two diodes is connected to each transducer. The low-leakage diode BAS416 is used in order to reduce leakage currents flowing back to the transducer circuit. The rectifier-circuits for the two transducers R1 and R2 are connected in parallel to a storage capacitor C with a chosen value of 100nF. An alternative would have been to use one full rectifier bridge between the two fixed electrodes while providing some low-conductivity path from the ports to ground in order to establish the bias.

Fixed electrode

Fixed electrodePrimary mass

Impact area

Secondary massSecondary mass

Rigid end-stop

C

+_ Vb

Fixed electrode

Fixed electrode

P1

P2

S2

S1

Figure 2. A schematic drawing of the impact device with a four-source

arrangement for electrostatic charging circuit.

The impact device consists of two structure types: a primary structure and two secondary structures. See figure 2. The primary structure is identical to the reference structure in design, except for having a smaller nominal capacitance and a smaller proof mass. This is because the impact device was designed with the same area 4×5mm2 as the reference device. A small area is sacrificed to give space for the secondary structures which are two transducing end-stops replacing the rigid end-stops in the reference device. They therefore confine the primary mass motion while providing extra power. The secondary structures use gap-closing transducers. In both the reference and impact devices, the maximum displacement is constrained to the same value dmax=10μm. In the impact device, the primary proof mass starts to hit the secondary structures when their relative displacement is larger than d1=6μm and the maximum displacement of the secondary structure is limited to d2=dmax-d1=4μm.

The two additional secondary transducers give two additional sources that must charge the same storage capacitor. This means that the impact device has a total of four sources that need to be combined: two primary sources P1 and P2, and two secondary sources S1 and S2. These are

coupled in parallel and connected to a single storage capacitor C with the same value as for the reference device. The same bias voltage Vb is used as shown in figure 2.

Figure 3. MEMS devices compared in this study. a) Reference device [7] b)

Impact device [6]

TABLE I. MODEL PARAMETERS

Parameters Impact device

Reference device Primary structure

Secondary structure

Proof mass 1.1mg 0.05mg 1.2mg Spring stiffness 18.2N/m 21.0N/m 21.1N/m

Damping coefficient 2.1×10-5Ns/m 1.0×10-5Ns/m 2.5×10-5Ns/m

Impact force

ksp=1.62MN/m: between primary and secondary masses

kss=8.08MN/m: between secondary mass and rigid end-stops

ks=3.36MN/m: between reference proof mass and rigid end-stops

Nominal capacitance 1.08pF 1.3pF 1.3pF

Capacitor gap 2µm 5µm 2µm

Capacitor overlap 10µm 55 µm 10µm

Parasitic capacitance 7.5pF 4.0pF 7.5pF

Active area 4×5mm2 Maximum displacement dmax=10µm

Charging capacitance C=100nF

Figure 4. Model of the impact force when the proof mass displacement reaches the end-stops

The outputs of the two devices are compared under the same conditions, i.e. acceleration, bias voltage and charging time, for observation of differences in the charging of the storage capacitor while operating in the impact regime. The LTspice IV circuit simulator is used for evaluating the performance of the two topologies. The voltage on the storage capacitor C=100nF is simulated for 5s of charging. The dynamic interplay between the proof mass and the end-

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stops is represented by a simple spring force model with the spring stiffness ks.. The constant value ks is estimated as in [7]. All parameters of the two models are listed in Table 1. Figure 3 shows device pictures of the reference and impact designs. Further details of the designs are given in our own previously published work [5-7]. Both circuits are of the parallel passive circuit topologies in the terminology of [12].

III. SIMULATION RESULTS Figure 5 shows a comparison of open circuit voltages for

the reference and impact devices in the linear regime at an acceleration A=0.05g and a bias voltage Vb=10V. The low acceleration causes the reference and primary masses to move within the displacement limit, giving linear frequency responses and no extra output from the secondary transducers. We kept the resonant frequencies in the models at the previously measured values of fr=675.0Hz and fi=651.3Hz for respectively the reference and impact devices. At the resonant frequency, the maximum open circuit voltage of the reference device VR=0.49V is slightly higher than that of the impact device VI=0.46V. At the same acceleration, the higher nominal capacitance and the larger proof mass in the reference structures cause this higher output voltage.

600 650 700 7500

0.1

0.2

0.3

0.4

0.5

Frequency [Hz]

Ope

n C

ircui

t Vol

tage

[V]

Reference deviceImpact device

Figure 5. Comparison between the reference and impact devices of open-

circuit voltage responses for a single port, an acceleration A=0.05g and a bias voltage Vb=10V.

0 0.2 0.4 0.6 0.8 1 1.20

0.2

0.4

0.6

0.8

1

Acceleration [g]

Vol

atge

[V]

Vb=8V

Vb=10V

Vb=12V

Figure 6. Storage-capacitor voltage of the reference device v. acceleration

for different bias voltages Vb when driven at the resonant frequency.

0.435 0.44 0.445 0.45-10

-5

0

5

10

15

Dis

plac

emen

t [ μm

]

0.435 0.44 0.445 0.45-4

-2

0

2

4

Sec

onda

ry d

ispl

acem

ent [ μ

m]

Reference Primary

Figure 7. Displacement of the reference and impact devices for an

acceleration A=1g and a bias voltage Vb=10V.

0 1 2 3 4 50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Time [s]

Vol

tage

[V]

Reference deviceImpact device

Figure 8. Storage-capacitor voltages between the reference and impact

devices for an acceleration A=1g and a bias volatge Vb=10V.

The two-source scheme for the reference design in figure 1 was simulated for 5s with different bias voltages Vb and acceleration amplitudes. The resulting storage-capacitor voltages are shown in figure 6. For A<0.3g, the voltage rises monotonically with the acceleration amplitude. For A≥0.3g, the primary mass can reach the displacement limit and impact the rigid end-stops. In this impact regime of operation, the results show the typical saturation of the outputs. For example, the saturated storage capacitor voltage is VR=0.7V for Vb=10V.

Figure 7 shows the dynamic performance of the two devices in the impact regime at an acceleration amplitude A=1g. The high acceleration guarantees that the displacements of all proof masses can reach their limits. The reference proof mass displaces periodically at the resonant frequency and hit the end-stops at dmax=10µm as shown in the top subfigure. The displacements of the primary and secondary proof masses of the impact device are rather irregular and we do not observe any approach to periodic steady-state behavior. While the primary mass has a slowly fluctuating amplitude, the secondary proof masses move without a clearly discernible pattern except for their frequent traversals of the full distance within the limits -4µm≤xs≤4µm

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as shown in the bottom subfigure. Since the secondary structures function as end-stops to the primary structures, the primary displacement varies depending on the positions of the secondary proof masses. Therefore, the primary displacement is aperiodic and tends to peak at less than dmax.

Figure 8 shows a comparison of the voltages versus time for the reference and impact devices for an acceleration A=1g. When the impacts become strong enough to drive the secondary structures, the two extra sources contribute to the charging of the storage capacitor. As a result, the impact device gives a higher voltage than the reference device does. For example, after 5s the voltages are 0.79V and 0.70V respectively.

0 0.5 1 1.5 2 2.5 30

0.2

0.4

0.6

0.8

1

Acceleration [g]

Vol

atge

[V]

Reference deviceImpact device

Figure 9. Comparison of storage-capacitor voltages v. acceleration between

the reference and impact devices for a bias Vb=10V.

The difference between the two topologies is further exposed in figure 9 which compares the outputs under increasing acceleration amplitude for a bias voltage Vb=10V. In the four-source topology, the primary mass begins to hit the secondary masses at an acceleration A=0.09g, while A=0.3g is necessary to drive the proof mass to the end-stop positions in the two-source topology. That the four-source topology initially (A<0.2g) gives higher voltages than the two-source topology is an artifact of the devices being driven at the open-circuit resonant frequency which is slightly less optimal for the reference device. The output voltage of the impact device is the smallest of the two for 0.2g≤A≤0.8g because the end-stop transducers are ineffective at small displacements, but still limit motion. For A>0.8g, the voltage of the reference saturates at 0.7V, while the voltage of the impact device continously increases. At such a high acceleration, the impacts are strong enough to actuate the end-stop transducers significantly and the secondary output is beneficial. The impact device has an approximately saturated voltage of 1.0V at A=3.0g corresponding to an extracted energy of 50nJ, about twice that of the reference device. The advantage of the impact-device over the more traditional design therefore prevails with this more desirable interface, even though the performance gain is now about a factor two in terms of energy while the output power was about four times larger in experiments with resistive loads [6].

IV. CONLCUSION A parallel passive circuit topology was considered as a

means to deal with the multi-source nature of an impact-based electrostatic energy harvester. Models of two previously made energy harvester devices were used for the simulation study. The reference device had two anti-phase sources while the impact device had two additional transducing end-stops resulting in a four-source scheme. The latter topology yielded a higher voltage in the impact regime due to the extra secondary structures while the two-source topology exhibited saturation at a lower voltage with the same acceleration. At the acceleration A=3g, the estimated output power of the impact device is twice that of the reference device. Comparison with previous results on resistive loads suggests that there is still some room for improvement.

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