This document summarizes a study on stable haptic rendering methods using an FPGA. It discusses haptic interfaces and stability analysis, reviews the time domain passivity approach, and proposes new methods including a memory-based method and multi-rate TDPA method. Experimental results showed the multi-rate TDPA method achieved the best performance with the highest maximum virtual environment stiffness and least noise behavior, while the memory-based method had better performance than the conventional TDPA approach. Future work includes applying the methods to moving and time-varying virtual environments.