## 3 Results and Discussion
### Comparison with Experiment  
The experiments were performed with nominally identical PECs as described above and shown in Figure 3. The resonance frequency was changed by fine adjustment of the tip mass. The parameters of the corresponding equivalent circuit are given in the Table 1, where only the effective mass and the amplitude of the excitation voltage must be modified accordingly. It is known that the effective mass of the cantilever beam can be calculated as \(\mathrm{m1}=m_{\mathrm{tip}}+(33/140)m_{\mathrm{b}}\), where \(m_{\mathrm{b}}\) is the beam mass [27]. In all experiments, the cantilever with the lowest resonance frequency of 40 Hz (PEC 1) is maintained constant. In Sections 3.1, 3.2.1 and 3.2.2, all theoretical considerations were investigated for the case when each PEC is loaded by the experimentally obtained optimum resistance \(R_{\mathrm{L}}=275\) k\(\Omega\). However, the replication of this optimum power in the experiment represents a challenge, when only the single load resistance is present. Many of the previous works investigated different approaches to connect individual cantilevers like parallel connection, series connection, connection with the full wave bridge rectifier, and SSHI or commercial LTC 3588 circuits. Most of the earlier works were based on the limitation that the cantilevers have the same resonance frequency and thus equal output voltage amplitude and phase. In the present work, the characteristics and limits of mass tuning are investigated from the perspective of the bandwidth enhancement. A striking feature of mass tuning is dependence of the voltage amplitude and phase on the adjustment mass. By usage of a single load, different voltage amplitudes have an impact on the previously investigated circuits. Figure 10 compares the series and \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Number of cantilevers** & **Cantilever 1** & **Cantilever 2** & **Cantilever 3** & **Cantilever 4** \\ \hline
2 & 40 Hz & 42.4 Hz & - & - \\
3 & 40 Hz & 42.4 Hz & 44.64 Hz & - \\
4 & 40 Hz & 42.4 Hz & 44.7 Hz & 46.7 Hz \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The best theoretical arrangement to achieve the maximum theoretical bandwidth. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{3}{c}{**Non-Equidistant Gaps**} \\ \hline
**Number of Cantilevers** & \multicolumn{2}{c}{_Frequency Gaps_} & \multicolumn{2}{c}{_Maximum Bandwidth_} \\ \hline
2 & 2.32 Hz & - & - & 3.7 Hz \\
3 & 2.40 Hz & 2.24 Hz & - & 5.92 Hz \\
4 & 2.40 Hz & 2.3 Hz & 2.0 Hz & 7.85 Hz \\ \hline \hline \multicolumn{3}{c}{**Equidistant Gaps**} \\ \hline
**Number of Cantilevers** & \multicolumn{2}{c}{_Frequency Gaps_} & \multicolumn{2}{c}{_Maximum Bandwidth_} \\ \hline
2 & 2.32 Hz & - & - & 3.7 Hz \\
3 & 2.25 Hz & 2.25 Hz & - & 5.7 Hz \\
4 & 2.1 Hz & 2.1 Hz & 2.1 Hz & 7.4 Hz \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison between the theoretical maximum bandwidth with non-equidistant and equidistant gaps between the resonant frequencies. parallel connection of two cantilevers (PEC 1 and PEC 2 without rectifiers) with \(\Delta f\) of 1 Hz at the optimum resistance \(R_{\mathrm{LP}}=R_{\mathrm{L}}/2=137.5\) k\(\Omega\) for parallel connection and \(R_{\mathrm{LS}}=2R_{\mathrm{L}}=550\) k\(\Omega\) for series connection with the optimum output power. The curves \"PEC 1\" and \"PEC 2\" show experimental dependences of both PECs loaded by the optimum resistance \(R_{\mathrm{L}}\) without any rectifiers. The curve \"PEC 1 + PEC 2\" is the sum of dependences \"PEC 1\" and \"PEC 2\". It gives the experimentally obtained power limit (optimum power), which can be scavenged from these two energy harvesters.