Optimum Load

Due to the capacitance of the piezoelectric patches, the power output depends on the load resistance. To ensure maximum power delivery, the optimum load has been found to be 100 and 60 kΩ for the outer and inner beam, respectively (see Figure 8). The power in the load is proportional to the square of the excitation amplitude. Therefore, we performed the simulations at several excitation levels.

**Figure 8.** (**a**) Load matching to ensure maximum power output from the outer patches electrically connected in the series, (**b**) respectively the inner patch.

Voltage Regulation

Piezoelectric energy harvesters, which employ PZT as a piezoelectric material, easily generate voltage levels, which exceed the range compatible with electronic circuits and related components, such as microcontrollers or super capacitors. Voltage regulation is required for reliable operation. The voltage regulation is achieved, e.g., by using a buck converter, which includes a MOSFET, a capacitor, an inductor, and a diode as shown in Figure 9. The duty cycle of the MOSFET's state affects the voltage output in such a circuit. A controller alters the duty-cycle to maintain constant output voltage for varying loading situations.

**Figure 9.** Two independent buck converter circuits for voltage regulation.

Figure 10 shows the simulation results of the voltage regulation. Here, the voltage at the outer and inner beam have been regulated to 5 V within 10 s.

**Figure 10.** (**a**) Simulation results of the voltage regulation of the outer patches and (**b**) the inner one under 0.2 g base excitation.

#### 2.3.4. Energy Harvester Frequency Tuning

We also studied the effect of our frequency tuning mechanism on the voltage output in analogy to the procedure described in Section 2.3.1. The results of the system-level simulation are shown in Figure 11.

**Figure 11.** (**a**) The voltage amplitude variation of the piezoelectric energy harvester under bidirectional magnetic frequency tuning of first and (**b**) second resonance frequency at 0.2 g harmonic base excitation.

These results show the voltage amplitude variation as a result of the bidirectional frequency shift of the piezoelectric harvester. These simulations show bidirectional frequency tuning by up to 9% relative to the unaltered resonance frequencies. The reduced tuning range is due to the increased beam stiffness induced by the piezoelectric patches.
