## 5 Conclusions  
This article sets out to provide an increased understanding of piezo- and magneto-electric energy harvesting systems and their combination, and to develop a tool to aid the development of harvester prototypes. Figure 15: Sensitivity of \(k\) to \(\xi_{E}\) as a function of dimensionless power, i.e., the ratio of \(k\) to \(\xi_{E}\) when tracing a specific power value. This relationship only holds for \(k>1\). We achieve this objective by deriving general expressions for PEH/EMEH power output, using the full set of relevant dimensionless parameters, \(\gamma\), \(Q\), \(\xi_{E}\), \(\xi_{C}\) and \(\eta\). While the model does not account in a direct way for nonlinear effects, it conveys an understanding of the behavior throughout the parameter space. Once the region of interest has been identified, one can apply refined nonlinear models. In this sense, the model helps in the choice of a suitable transduction method for a specific application as well as for the design of energy harvesters. To shed new light on previously well-established VEH systems, we perform a detailed analysis with regard to the resistive loss coefficient, which is lacking in the previous literature. We find that this parameter plays a significant role in differentiating inertially loaded PEH/EMEH systems, especially in the context of resonant and anti-resonant operation. We find that at resonance, both systems have similar potential power performance, with the EMEH being favored due to a potentially larger load voltage. At anti-resonance, the PEH is favored both in regard to power output and voltage. Our results show a larger input to output power efficiency at anti-resonance compared to resonance. It can thus be beneficial to run the VEH with a larger load resistance in cases where the source power is small, assuming the source vibration spectrum is similar around the energy harvester's resonance and anti-resonance frequencies. Considering typical parameter values for applied EMEH/PEH systems, we can conclude that they are generally designed to operate at resonance. Under these assumptions, we can still draw some important conclusions. Compared with a PEH, an EMEH will be practically limited in achieving a power output closer to the theoretical maximum, less sensitive to resistive loss with regard to critical \(Q\) factor and have an optimal load highly sensitive to the quality factor. Our investigation of the model under prescribed displacement, which is also lacking in the previous literature, shows that the expression for efficiency is equal to that of the model under inertial load, which is a reasonable result assuming efficiency is a purely intrinsic property (independent of external excitation). We also find that the expressions for optimal load differ between the two types of excitations only by the term naturally arising from electrical damping, supporting the argument that impedance matching is not the correct approach to load optimization of inertially loaded systems. From a practical viewpoint, our results indicate that under resonant excitation frequencies, a higher dimensionless power can generally be achieved if the proof mass oscillations can be forced. At anti-resonant frequencies, this is only holds for sufficiently small \(k\) and \(\xi_{E}\). Thanks to the detailed investigation of the resistive loss coefficient and the case of prescribed displacement, our investigation essentially widens the range of potential methods that may be used to find high-performance VEH designs and thus increases the possibility of VEHs being useful in an increasing number of applications. The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/app12199815/s1](https://www.mdpi.com/article/10.3390/app12199815/s1)]([https://www.mdpi.com/article/10.3390/app12199815/s1](https://www.mdpi.com/article/10.3390/app12199815/s1)). Conceptualization, J.B., F.O., C.R. and C.J. ; Formal analysis, J.B.; Funding acquisition, C.R. ; Investigation, J.B.; Methodology, J.B., F.O. and C.J.