The focus of this work is on the steady-state analysis of RE circuits using a coupled device and circuit simulator. Efficient coupling algorithms for both the time-domain shooting method and the frequency-domain harmonic balance method have been developed. A modified Newton shooting method considerably improves the efficiency and reliability of the time-domain analysis. Three different implementation approaches of the harmonic balance method for coupled device and circuit simulation are investigated and implemented. These include the quasi-static, non-quasi-static, and modified-Volterra-series approaches. Comparisons of simulation and performance results identify the strengths and weakness of these approaches in terms of accuracy and efficiency