Advanced CMOS Circuit Design
Design a low-power operational amplifier (op-amp) using CMOS technology. Your design should minimize power consumption while maintaining a high gain and bandwidth. Discuss trade-offs in your design, such as between power, speed, and noise. Provide a detailed schematic, explain your design choices, and simulate the circuit to verify its performance under different process corners.

Quantum Effects in Nanoscale Transistors
As transistor dimensions continue to shrink, quantum mechanical effects become significant. Analyze the impact of quantum tunneling and subthreshold slope degradation on the performance of nanoscale transistors. Develop a model that includes these effects and compare it with classical models. Discuss how these quantum effects influence device scaling and suggest possible techniques to mitigate them.

RF Circuit Design: Mixer Design
Design a high-linearity, low-noise mixer for a 5G RF front-end operating at 28 GHz. Consider the requirements for gain, noise figure, and linearity (IP3). Explain the design process, including the choice of topology, and use simulation to optimize the performance parameters. Discuss how parasitic elements and substrate effects at high frequencies affect your design.

Digital Signal Processing: Adaptive Filtering
Develop an adaptive filtering algorithm using the least mean squares (LMS) method to remove noise from a signal received in a communication system. Derive the convergence conditions for the algorithm and analyze the impact of step size on the convergence speed and stability. Implement the algorithm in MATLAB or Python and compare its performance with other adaptive filtering techniques, such as the Recursive Least Squares (RLS) algorithm.

VLSI: Thermal Management in Integrated Circuits
As power densities increase in VLSI circuits, thermal management becomes a critical challenge. Analyze the heat dissipation mechanisms in a multi-core processor designed at the 5 nm technology node. Propose a thermal-aware floorplanning strategy to minimize hot spots and optimize the thermal profile across the chip. Use finite element analysis (FEA) tools to simulate the thermal distribution and validate your design.