Demand for CMOS compatible and smaller footprint devices in modern day wireless communication systems has forced a shift in focus from high Q off chip passives like Quartz resonators and SAW filters towards MEMS resonators. Crystal resonators were widely used due to its high Q and temperature stable properties. Piezoelectric-on-silicon resonators emerged as a favoured choice for low noise oscillators on account of its high coupling coefficient and low motional resistance compared to other MEMS resonators. Thin Piezoelectric on Silicon (TPoS) resonators which consists of a piezoelectric thin film sandwiched between top and bottom electrodes deposited on a high energy density material such as Silicon have low motional resistance and relatively higher Q. In this work, we analyse and model the anchor loss, which is one of the dominant loss mechanisms that brings down the total Q, in longitudinal TPoS resonators. A semi-analytical model is derived to calculate the anchor loss using data from Finite Element Method (FEM) simulations in COMSOL. The results are validated with experimental data. This provides valuable insights on the effect of number, position and dimensions of anchors on Q of these resonators. The optimum position and number of anchor pairs in order to deliver the highest Q are also discussed. Design and simulation of Phononic Crystals (PnCs) with a wide Acoustic Band Gap (ABG) is also presented. A new PnC unit cell topology is designed, which has a very wide ABG of 138 MHz with centre frequency around 1 GHz. ABG for 1D and 2D periodicity is simulated and geometrical dimensions to obtain similar ABG in both cases are compared.