Bulk Acoustic Wave (BAW) resonators are essential components in modern RF communication systems due to their high selectivity and quality factor. However, spurious resonances caused by Lamb wave mode propagation along the in-plane directions degrade the filter performance. Traditional Finite Element Method (FEM) simulations provide accurate modeling but are computationally expensive, especially for arbitrarily shaped resonators and solidly mounted resonators (SMRs), whose stack of materials is composed of many thin layers of different materials. To address this, we extend a previously published model (named the Quasi-3D model), which employs the Transmission Line Matrix (TLM) method, enabling efficient simulations of complex geometries with more precise meshing. The new approach allows us to simulate different geometries, and we will show several apodized geometries with the aim of minimizing the lateral modes. In addition, the proposed approach significantly reduces the computational cost while maintaining high accuracy, as validated by FEM comparisons and experimental measurements.

The Bluetooth Mesh Protocol (BMP) has become an excellent solution for sensor networks and Internet of Things (IoT) deployments due to its low power consumption, selforganizing capabilities, and security mechanisms. In this paper, we focus on analyzing reliability in Bluetooth Low Energy (BLE) mesh networks. Our investigation reveals an anomaly inherent to the standard, where the addition of extra relays may lead to a reliability degradation instead of improvement due to new packet collisions, particularly in scenarios with low error probabilities. This anomaly may appear undesirably even in small networks. This work demonstrates the influence of the number of relays in a two-hop section and how the Packet Error Ratio (PER) may be degraded by more than two orders of magnitude. The paper also provides a mathematical model validated through simulations and real measurements using a hardware network emulator based on nRF52840 development kits. We discuss the network reliability under standard parameters and offer insights into optimal relay configurations, proposing adjustments to mitigate this anomaly.

This work introduces a Quasi-3D modeling framework for the analysis of Film Bulk Acoustic Resonators (FBARs) and Solidly Mounted Resonators (SMRs) with Border Ring (BR), The method captures thickness-dependent behavior through precomputed dispersion curves, while discretizing the in-plane directions to account for lateral vibrations. Validation against Finite Element Method (FEM) simulations shows close agreement for FBARs and good accuracy for SMRs, despite the added complexity of the Bragg reflector and the presence of additional modes with lower cutoff frequencies. The model is further validated with measurements and applied to optimize SMR with BR designs, including apodized configurations, demonstrating its capability to suppress lateral modes in geometries that are computationally prohibitive for full 3D FEM. A computational analysis confirms that the Quasi-3D approach reduces simulation time and degrees of freedom by orders of magnitude compared to FEM. [2025-0203]