For an AlN thin film bulk acoustic resonator (FBAR), a passive piezoelectric layer and external electrical impedance are introduced into the thin film resonator structure for tuning the frequency characteristics of the resonator. The input electric impedance formula for the thin film resonator, after taking into account the passive piezoelectric layer and external impedance, is derived to describe the electromechanical behavior of the device. The frequency characteristics and effective electromechanical coupling coefficient k2eff of the thin film resonator are evaluated based on the calculated impedance frequency spectra. The effect of the external electric impedance, including electric resistance, inductance and capacitance, on the impedance frequency spectra of thin film resonator is investigated, and the calculation results reveal that the use of external electric impedance can substantially change the resonance frequency and has a significant effect on k2eff of the resonator.