## 3 Results and Discussion
### Comparison with Experiment
However, the simulated and experimentally observed \"jumps\" (cf. Section 3.1) of the bandwidth differ by approximately 0.2-0.5 Hz. The difference between the two simulated curves can be explained by diode losses. Figure 13 also demonstrates the involvement of several harvesters in bandwidth widening and enhancement of the output power. If \(\Delta f\)\(\rightarrow\) 3 Hz, a single PEC determines the frequency bandwidth (\(\approx\)1.2 Hz) and the guaranteed output power of the array (\(\approx\)0.65 mW) within the working frequency range. Even a cantilever working farther away from its resonance frequency brings its contribution to the frequency bandwidth and the output power. Figure 13a,c show that there are frequency detuning regions where the frequency bandwidth can be increased by more than two or three times, respectively. Figure 12: Dependence of the normalized electrical power on the load resistance. It is observed that in these frequency detuning regions, the total output power of the array can be significantly larger than the maximum guaranteed power of 0.65 mW from the single PEC. To illustrate the difference between the measurement and the simulation, Figure 14 depicts two individual measuring points for two cantilevers. The first measurement point is \(\Delta f\) = 1.5 Hz, where there is reasonable agreement between the simulation and the experiment. The second measuring point at \(\Delta f\) = 2 Hz is where the differences are easily noticeable. Figure 15 presents the differences for the case of three PECs. Figure 14: Comparison of the simulated and measured power with dependence upon frequency for the parallel connection of two PECs with individual rectifiers and \(\Delta f\) = 1.5 Hz (**left**) or \(\Delta f\) = 2 Hz (**right**). Figure 13: Comparison of the frequency dependency of the bandwidth (**a**,**c**) and the guaranteed electrical power (**b**,**d**) between simulation and measurement for arrays with two (**a**,**b**) and three (**c**,**d**) PECs. As explained in [19], the disadvantage of a PEC array design with frequency-detuned cantilevers based on the overall electrical rectification is the inevitable charge cancellation causing lower power output. In the present paper, we considered the respective electrical rectification of individual PEC outputs. In the considered experimental situation, such an approach seems to pay off with respect to the achieved frequency bandwidth and guaranteed output power. Obviously, the complexity of the electronic circuitry is somewhat increased in comparison to the overall electrical rectification due to the presence of additional rectifiers. The discrepancies between the simulation results and the experiments are obviously explained by the imperfection of the model. One reason for these differences is the non-linear behavior of cantilevers. The resonance curve is noticeably asymmetric with respect to the resonance frequency, which can be attributed to the softening behavior of the cantilever [28]. Although the bandwidth can be reproduced sufficiently well with the simplifying approach of Section 2, the course of frequency dependencies between the half-power-frequencies for measurements and simulations is different. Therefore, the nonlinearity of the cantilevers should be considered in the future simulations, in order to achieve better agreement. Furthermore, some differences can be seen in the voltage amplitudes of the individual PECs. We attribute these differences to the additional mechanical coupling the cantilevers through the base plate where they are fixed. The model should be extended to include the coupling through the base plate into the simulations in order to achieve a better accuracy. However, it is observed that even a simplified model such as that presented in this paper is useful since it provides reasonable agreement with experiments and allows one to understand the basic regularities of vibration energy harvesting with tip-mass tuned PECs.