This article presents the results of the theoretical and experimental study of the fractional Bennet's electricity doubler based on the Dickson charge-pump topology. This electrical network is used for the conditioning of capacitive transducers in kinetic energy harvesters. This study investigates the operation of the circuit in a purely electrical mode (no electromechanical coupling), addressing the transient processes and the influence of the parameters' values on the circuit behaviour. Several original results are obtained: (i) the existence of three different transient processes, (ii) a strong qualitative influence of the diode's threshold compared with the ideal behavior, and a stability criterion on one of the transient processes. These results provide useful insight into the operation of the circuit and are of practical interest for its application in electrostatic kinetic energy harvesters. The analysis is validated by Spice simulations and by measurements performed on a silicon MEMS (MicroElectroMechanical Systems) device.