## 3 Prototype and Controller Fabrication  
Two prototype actuators were fabricated to study the effect that electrode configuration has on the vibration intensity of the electrostatic resonant actuator module. Both actuators are proof-of-concept designs, made primarily to study the effect of adding an electrode above the mass. The dual-electrode ERA consists of five main parts: the lower electrode, the lower spacer, the inertial mass and spring, the upper spacer, and the upper electrode. Ten thin radial beam springs surround the center of the middle plate, creating a restoring force to the mass as it displaces away from its equilibrium position. This plate also has a protrusion that is used to wire the mass to electrical ground. A finite element method (FEM) simulation was performed to select the spring constant of the radial springs (see Figure 3a). A force of 2 N was applied to the mass, resulting in a maximum displacement of 0.1166 mm. Using the given size and mass constraints, the spring stiffness was selected to be 17.15 kN/m. In Figure 3b, each component of the actuator is separated, and its fabrication material is shown. The surface of each copper electrode closest to the mass is covered in a very thin layer of polyimide film to insulate them. The rest of the electrode is surrounded by a thicker layer of polyimide film to further insulate and support them. A stainless-steel spacer (thickness of 0.3 mm) is placed between each electrode and the mass at its equilibrium, creating an air gap, or rattle space, for the mass. The component containing the radial beam springs is a 0.5-mm-thick stainless steel plate. A stainless-steel cylinder was welded onto the center of the plate, providing significantly more mass, to increase vibration intensity. The complete assembled dual-electrode ERA is seen in the lower-left corner of Figure 3b. The single-electrode ERA was fabricated in the same manner but does not have a top electrode or spacer. The values of key parameters for fabricating the ERA module are summarized in Table 1. The fabricated ERA's overall dimensions are 52.5 mm \(\times\) 60.5 mm \(\times\) 3 mm. The small size makes it able to be installed on the backs of large touchscreen displays, providing effective vibrotactile haptic feedback. Moreover, multiple ERAs can be mounted over the large display surface to create various vibrotactile patterns and to enhance the overall intensity of vibrotactile feedback. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Notation** & **Unit** & **Value** \\ \hline Mass & \(m\) & g & 25 \\ Stiffness & \(k\) & kN/m & 17.15 \\ Bottom Surface Area of Moveable Mass & \(A\) & mm\({}^{2}\) & 2375.83 \\ Air Gap & \(d_{air}\) & mm & 0.30 \\ Thickness of Dielectric Film & \(t_{Didctictic}\) & mm & \(5.50\times 10^{-2}\) \\ Vacuum Permittivity & \(\varepsilon_{0}\) & F/mm & \(8.85\times 10^{-15}\) \\ Relative Permittivity of Air & \(\varepsilon_{r}\) & – & 1.00 \\ Relative Permittivity of Dielectric & \(K_{e}\) & – & 3.40 \\ Input Voltage Signal Amplitude & \(V\) & V & 2000 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters used for the proposed ERA module’s fabrication. Figure 3: \(Cont.\)To power the electrodes and control the oscillation frequency of the module, a custom controller with a high voltage amplifier was also fabricated. The controller is necessary to alternate the powering of the electrodes in the duel-electrode actuator. The timing between each electrode activation must be accurate and consistent, making the controller highly important for the proper function of the dual-electrode ERA. The high voltage amplifier is necessary to amplify control signal inputs, which are less than 5 volts, producing the high voltage inputs required to effectively power the electrodes and activate the actuator. Figure 4a shows the schematic structure of a circuit diagram for the controller and high voltage amplifier. These are used in combination to provide two alternating high voltage cosine signals of the same frequency to the ERA module.