互连线高效时域梯形差分模型降阶算法

为了进一步提高现有互连电路模型降阶方法的精度和效率,提出一种基于时域梯形法差分的互连线模型降阶方法.首先将互连电路的时域方程用梯形法差分离散后获得一种关于状态变量的递推关系,形成了一个非齐次Krylov子空间;然后利用非齐次Arnoldi算法求得非齐次Krylov子空间的正交基,再通过正交基对原始系统进行投影得到降阶系统.该算法可以保证时域差分后降阶系统和原始系统的状态变量在离散时间点的匹配,保证时域降阶精度,同时也保证了降阶过程的数值稳定性及降阶系统的无源性.与现有的时域模型降阶方法相比,文中算法可降低计算复杂度;与频域降阶方法相比,由于避免了时频域转换误差,其在时域具有更高的精度.

An Efficient Time-Domain Trapezoidal Difference Based Model Order Reduction Method for Interconnect Circuits

An efficient time-domain trapezoidal difference based model order reduction(MOR) method is proposed to further improve the efficiency and accuracy of the existing methods for interconnect circuits.A recursive relation is derived from the trapezoidal difference formulation of the time-domain equation of interconnect circuits.The recursive relation formulates a non-homogenous Krylov subspace.A non-homogeneous Arnoldi method is employed to construct the orthonormal basis of this non-homogenous Krylov subspace.The orthonormal basis is then used to project the original interconnect circuits to reduced-order models.The proposed method can guarantee the value matching of the state vector after time-domain trapezoidal difference for the original interconnect circuits and the reduced-order models.The accuracy of the reduced-order models can thus be guaranteed.The MOR procedure is numerically stable and the reduced-order models also preserve the passivity.In comparison with the existing time-domain methods,the computational cost of the proposed method is significantly reduced.Compared with the existing frequency-domain methods,the proposed method can achieve higher accuracy.