In this, the first of two papers, we present the working principle and the implementation of laterally acoustically coupled thickness-mode thin-film piezoelectric-on-substrate (TPoS) filters. This type of filter offers low insertion loss and small bandwidth in a broad frequency range--from a few hundred megahertz up to a few gigahertz--and occupy a small chip area. In this paper, we discuss several design concerns, including the choice of materials for TPoS filters. We demonstrate a design for an air-suspended AlN-on-Si filter, which offers a low insertion loss of 2.4 dB at 2.877 GHz. The bandwidth of this filter is 12 MHz with a return loss of better than 30 dB. In Part II of this paper, we present a comprehensive analysis of the effect of physical layout parameters on the frequency response of TPoS filters.