Efficient finite-difference method for quasi-periodic steady-state and small signal analyses

This paper discusses a finite-difference mixed frequency-time (MFT) method for the quasi-periodic steady-state analysis and introduces the quasi-periodic small signal analysis. A new approach for solving the huge nonlinear system the MFT finite difference method generates from practical circuits is given, which makes efficient frequency-sweeping quasi-periodic small-signal analysis possible. The new efficient solving technique works well with the Krylov-subspace recycling or reuse, which can not be achieved with existing techniques. In addition, this paper gives a way to calculate the quasi-periodic Fourier integration weights, necessary in the adjoint MFT small-signal analyses, and a way to calculate quasiperiodic large-signal Fourier spectrum that is more efficient than existing methods. Numerical examples also show that the finite-difference MFT method can be significantly more accurate than shooting-Newton MFT method and the new preconditioning technique is more efficient.