This paper presents an analysis of a new type of feedthrough recursive surface acoustic wave (SAW) device. The device combines a conventional SAW structure with positive feedback in a way that allows use of selective properties of the SAW structure, control of the central frequency and bandwidth, achieving significantly higher quality factors for given dimensions of the structure, and reduction of the sidelobe level. Several possible implementations are discussed from a simple one that uses external circuitry to the most advanced that includes digital supervisory control. Equations are presented that relate the central frequency, bandwidth, and sidelobe level to the parameters of the SAW structure and feedback loop. The simulation results were found to be in good agreement with experimental data. These data show the control of the central frequency within 1%, a 10-fold increase in the quality factor compared to the original SAW structure, and a reduction of the side-lobe level by 20 dB irrespective of the influence of second order effects and random manufacturing fluctuations.