Microelectromechanical-systems (MEMS) electrostatic energy harvesters, converting vibration energy into electricity, is an active area of research and is envisioned to supply power to the myriad of sensors for Internet of Things applications. However, although a variety of approaches have been investigated to improve either power output or frequency range, a solution capable simultaneously addressing both is yet to emerge. This paper explores an energy harvesting system comprised of two parallel connected devices of different resonant frequencies, which is demonstrated to exhibit a broadened operating frequency range and enhanced power output as compared with an individual device. While it is straightforward that the frequency operating band is to be broadened due to the difference in natural frequencies, an increase in system power output is not guaranteed due to intrinsic phase shift exhibited by the two dissimilar devices undergoing oscillation. However, it is shown that the power output by the two parallel connected devices may be significantly enhanced above that of a single device, an effect referred to as power-combining or constructive interference, which appears under operating conditions that enable partial synchronization of the oscillatory motion of each device. Such an approach is especially promising since it is possible to employ multiple parallel connected devices to increase the output power to levels matching those seen in applications. However, this technique is not yet explored theoretically or experimentally, a task undertaken here, where a case study consisting of a system with two parallel coupled devices is presented. System dynamics is investigated theoretically and experimentally to understand conditions enabling power-combining. A modular theoretical model, which can be readily extended to any number of devices connected in parallel, is developed with co-dependent, simultaneous mechanical and electrical simulations carried out in VerilogA and Cadence Spectra .

Silicon-based kinetic energy converters employing variable capacitors, also known as electrostatic vibration energy harvesters, hold promise as power sources for Internet of Things devices. However, for most wireless applications, such as wearable technology or environmental and structural monitoring, the ambient vibration is often at relatively low frequencies (1–100 Hz). Since the power output of electrostatic harvesters is positively correlated to the frequency of capacitance oscillation, typical electrostatic energy harvesters, designed to match the natural frequency of ambient vibrations, do not produce sufficient power output. Moreover, energy conversion is limited to a narrow range of input frequencies. To address these shortcomings, an impacted-based electrostatic energy harvester is explored experimentally. The impact refers to electrode collision and it triggers frequency upconversion, namely a secondary high-frequency free oscillation of the electrodes overlapping with primary device oscillation tuned to input vibration frequency. The main purpose of high-frequency oscillation is to enable additional energy conversion cycles since this will increase the energy output. The devices investigated were fabricated using a commercial microfabrication foundry process and were experimentally studied. These devices exhibit non-uniform cross-section electrodes and a springless mass. The non-uniform width electrodes were used to prevent pull-in following electrode collision. Springless masses from different materials and sizes, such as 0.5 mm diameter Tungsten carbide, 0.8 mm diameter Tungsten carbide, zirconium dioxide, and silicon nitride, were added in an attempt to force collisions over a range of applied frequencies that would not otherwise result in collisions. The results show that the system operates over a relatively wide frequency range (up to 700 Hz frequency range), with the lower limit far below the natural frequency of the device. The addition of the springless mass successfully increased the device bandwidth. For example, at a low peak-to-peak vibration acceleration of 0.5 g (peak-to-peak), the addition of a zirconium dioxide ball doubled the device’s bandwidth. Testing with different balls indicates that the different sizes and material properties have different effects on the device’s performance, altering its mechanical and electrical damping.

This paper reports a predictive model for vibration-to-electrical energy harvesters based on an in-plane, gap-closing variable capacitor with frequency up-conversion triggered by the impact between the electrodes. Since the output power is proportional to the output frequency, rectifying low-frequency ambient vibrations (1–50 Hz) to high-frequency electrical signals (200–600 Hz) increases the power output. While such a device has been previously reported experimentally, this is the first time a model able to predict the experimental data has been described. The model is based on lumped approximation. The central area supporting the mobile electrodes, or the shuttle mass, is represented by a point mass suspended by springs and has its own equation of motion. The motion of the electrodes attached to the shuttle is described by a set of two equations, each associated with a distinct dynamic mode. In these equations, the electrodes are represented by an equivalent mass and spring constant. The first equation describes the separate motion of mobile and fixed electrodes. In this mode, the electrodes experience damped free vibration due to the electrostatic and air damping between them. The second equation describes the combined motion when the two set of electrodes move together. In this mode the air damping forces between the collided electrodes is eliminated and the electrostatic force is kept constant. The motion equations are solved simultaneously with Kirchhoff’s law to compute the voltage drop across a resistor in series with the variable capacitor and a DC bias voltage source. Predictions are shown to be consistent with the experimental results, and frequency up-conversion effects are observed with exponentially decaying voltage amplitude as seen in experiments. A parametric study is also carried out to identify main parameters that affect the up-conversion, laying the foundation for future design optimization to maximize the power output.

This paper reports on the modeling of a common structure employed in microelectromechanical systems (MEMS) that involves a suspended plate vibrating out-of-plane. A few examples of applications include pressure sensors, accelerometers, micro-mirrors and energy harvesters. In the design process of these devices, it is often required to predict the dynamic response of the structure to an applied force or base excitation, which is not a straightforward process, due to the multi-dimensional bending of the plate. To address this challenge, a simplified but effective approach is proposed here. Central to the proposed approach is modeling the beam-plate device as a sectionalized beam, consisting of the original suspension beam and a replacement beam representing the plate, with non-uniform properties and loading. The beam equation is then solved for the sectionalized beam to determine the static displacement. The results closely match those of finite element modeling. Finally, the effective mass and the effective spring constant are determined using the Rayleigh energy method and used to find the natural frequency of the system. The steady-state oscillatory response can thus be determined by employing classical theory for second order systems, on which the design parameters can be optimized.