A robust periodic arnoldi shooting algorithm for efficient analysis of large-scale RF/MM ICs

The verification of large radio-frequency/millimeter-wave (RF/MM) integrated circuits (ICs) has regained attention for high-performance designs beyond 90nm and 60GHz. The traditional time-domain verification by standard Krylov-subspace based shooting method might not be able to deal with newly increased verification complexity. The numerical algorithms with small computational cost yet superior convergence are highly desired to extend designers´ creativity to probe those extremely challenging designs of RF/MM ICs. This paper presents a new shooting algorithm for periodic RF/MM-IC systems. Utilizing a periodic structure of the state matrix, a periodic Arnoldi shooting algorithm is developed to exploit the structured Krylov-subspace. This leads to an improved efficiency and convergence. Results from several industrial examples show that the proposed periodic Arnoldi shooting method, called PAS, is 1000 times faster than the direct-LU and the explicit GMRES methods. Moreover, when compared to the existing industrial standard, a matrix-free GMRES with non-structured Krylov-subspace, the new PAS method reduces iteration number and runtime by 3 times with the same accuracy.