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Improved performance thin-film plate acoustic wave resonators (FPAR) using the lowest order symmetric Lamb wave (S0) propagating in highly textured AlN membranes have been previously demonstrated for the first time. In this work, an experimental study of the resonators' performance vs. a variety of design parameters is performed. Devices operating in the vicinity of the stopband center exhibiting a Q-value of up to 3000 at a frequency of around 875 MHz are demonstrated. Further, low-loss high-Q micromachined 2-port longitudinally coupled thin-film resonators using the S0 mode are demonstrated for the first time. For the analysis of the proposed structures, the coupling-of-modes (COM) approach is successfully employed. Initially, the COM model is used for the extraction of physical parameters from one-port FPAR measurements. Subsequently, using the COM model, a satisfactory agreement with the proposed experimental frequency characteristics of S0 2-port FPARs has been achieved, and possibilities for further improvements in the performance discussed. Finally, the frequency spectrum of the one-port devices has been studied and the excited plate modes at different frequencies identified and presented with their Q-factors and temperature coefficients of frequency (TCF).