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A model for tunable thin film bulk acoustic resonators (TFBARs) based on ferroelectric films is proposed. The model is based on electromechanical equations taking into account piezoelectric effect and electrostriction effect induced by the dc electric field. The dc field induced shift of the resonant frequency is explained by the high-order nonlinear effects in the ferroelectric material. The main contribution to the tunability of the resonant frequency under dc electric field can be attributed to electrostriction, which is nonlinear with respect to the mechanical deformation. It is shown that the upward or downward shift in the resonant frequency is given by the sign of the nonlinear component of the electrostriction tensor M. The model is verified by comparing the results with the measured microwave input impedance of BaTiO3 and Ba0.25Sr0.75TiO3 based TFBARs. For a positive sign of the nonlinear coefficient of electrostriction M, the model predicts an upward shift of the resonant frequencies (resonance and antiresonance) under dc biasing in case of the TFBAR based on BaTiO3, whereas a negative sign of the nonlinear coefficient of electrostriction M predicts downward shift of the resonant frequencies for TFBAR based on Ba0.25Sr0.75TiO3 films.

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An original structure of tiled transmitarray is presented, comprising a number of topologically similar unit cells arranged in arbitrary pattern within a planar array frame. Each unit cell represents a passive receiver-transmitter structure with integrated phase-shifter, fabricated in commercial 5-layer printed circuit board process, which can take either of two coding states corresponding to 0° or 180° phase shift imparted to the signal transmitting through the device. The unit cell design supports two orthogonal linear polarizations. An example of a 10x10 element 1-bit beam steering transmitarray operated in C-band is demonstrated by simulations and measurements. The proposed structure represents a cost-efficient solution for scalable transmitarrays and also for proof-of-concept experiments in research and education.