According to the invention, the cartridge includes a thermostatic element which is thermally activated by a mixture of a cold fluid and a hot fluid, which is mechanically connected to a regulator slide and which is moved by a single lever for controlling the flow rate and the temperature of said mixture. A first power supply line is connected to a positive terminal of a rechargeable battery, while a ground line is connected to a negative terminal of the rechargeable battery. The EHE system determines a separate EHE gain for each harmonic.