Theoretical and experimental analyses of piezoelectric stacks submitted to periodical electrical boundary conditions via electrodes are conducted. The presented structures exhibit Bragg band gaps that can be switched on or off by setting electrodes in short or open circuit. The band gap frequency width is determined by the electromechanical coupling coefficient. This property is used to design a Fabry-Perot cavity delimited by a periodic piezoelectric stack. An analytical model based on a transfer matrix formalism is used to model the wave propagation inside the structure. The cavity resonance tunability is obtained by varying the cavity length (i.e., by spatially shifting boundary conditions in the stack). 26% tuning of resonance and antiresonance frequencies with almost constant electromechanical coupling coefficient of 5% are theoretically predicted for an NCE41 resonator. To optimize the device, the influence of various parameters is theoretically investigated. The cavity length, phononic crystal (number and length of unit cells), and transducer position can be adapted to tune the frequency shift and the coupling coefficient. When the transducer is located at a nodal plane of the cavity, the value of the coupling coefficient is 30%. Experimental results are presented and discussed analyzing the effects of damping.