A modified macromodel of operational transconductance amplifier is proposed for application in design of high-frequency bandpass active filters based on film bulk acoustic resonators. The presented solution is an optimal tradeoff according to the criteria of completeness of simulated characteristics, its accuracy and calculation time. Nonlinear amplification behavior of the macromodel is modelled by minimax Chebyshev approximation which allows the use of highorder polynomials and solves the convergence challenge. At the same time, bias-dependent noise model accounts for JohnsonNyquist and flicker noise sources enabling the evaluation of active filter's signal-to-noise ratio, noise figure and output dynamic range. Finally, the differential active filter circuit was analyzed to validate the macromodel's capabilities, simulation ranges and filter characteristics.

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Film bulk acoustic resonators (FBARs) are becoming increasingly requested as an element of high-performance bandpass filters for modern microwave communication systems due to its inherent advantages at high frequencies. Active filter design using FBAR allows realizing of a wider range of characteristics. The FBAR active filter design process is related with the optimization of multiple parameters including filter architecture, biasing of active elements, impedance matching and also the topology and structure of resonators. Obtaining of filter's frequency characteristics with high selectivity and smooth phase response is only possible using high-precision models of resonators. The purpose of this work is to propose a three-dimensional finite element model (FEM) of a FBAR for further integration into the computer-aided filter design system. The simulation results of the proposed solution are compared with a frequently used modified Butterworth- Van-Dyke (mBVD) model to designate the significance of changes in the output filter characteristics arising from the application of 3D piezoelectric resonator model.

The application of active elements such as gyrator and negative capacitance simulator in conjunction with piezoelectric resonators allows to imitate simple LC circuits employed in bandpass, low-pass and high-pass filter design. In contrast to the circuits composed of distributed elements, active circuits with resonators provide minimal sensitivity to component variations and less parameter offsets during production. They also have smaller dimensions and can be integrated with digital signal processing on a single chip including the possibility electronic adjustment. The replacement principle of LC circuit prototypes by the active analogs is described in details. The active low-pass filter was designed and analyzed using the presented approach to review the special considerations about resonators application.