The electrical supply of portable electronic devices is a crucial problem, which may be solved by harvesting a part of the mechanical energy dissipated in our environment. For the last ten years, many prototype piezoelectric generators have been proposed in research literature, offering different technological choices, but always working according to the same schematics: three different conversion stages. The first one, named mechanical application device (MAD), transforms the initial mechanical stress into a higher level or higher frequency stress. This stress is applied to the second stage, the piezoelectric device (PD). The last stage, an electronic circuit named harvesting system (HS), is essential to maximise the electrical energy delivered to the targeted electronic device. In this paper, we present an experimental test bench that can replace any association of MAD and PD. Then we describe our HS, and demonstrate its performances for our application, where the applied mechanical stress is exponential and varies with a low frequency. Thanks to this HS, the conversion from mechanical energy to electrical energy is improved, and this phenomenon can be explained by simulation, using an equivalent circuit. At last, some experimental results are commented, leading to the perspectives of this research project.