A filtering circuit includes a substrate; an acoustic mirror or a membrane destined to act as a mechanical support of acoustic resonators and to isolate these resonators from the substrate; a first section comprising an upper resonator and a lower resonator coupled to each other by at least one acoustic coupling layer; and a second section comprising an upper resonator and a lower resonator coupled to each other by at least one acoustic coupling layer. The filtering circuit also includes metallic vias implementing an inter stage connection between the lower resonator of a section and the upper resonator of the other section. Preferably, the upper resonators exhibit a piezoelectric layer having a thickness selected in order to achieve an optimal impedance matching between the said first and second sections.