An efficient reciprocity and passivity preserving balanced truncation for RLC networks is presented in this paper. Reciprocity and passivity are fundamental principles of linear passive networks. Hence, reduction with preservation of reciprocity and passivity is necessary to simulate behavior of the circuits including the RLC networks accurately and stably. Moreover, the proposed method is more efficient than the previous balanced truncation methods, because sparsity patterns of the coefficient matrices for the circuit equations of the RLC networks are fully available. In the illustrative examples, we will show that the proposed method is compatible with PRIMA, which is known as a general reduction method of RLC networks, in efficiency and used memory, and is more accurate at high frequencies than PRIMA.

An efficient balanced truncation for RC and RLC networks is presented in this paper. To accelerate the balanced truncation, sparse structures of original networks are considered. As a result, Lyapunov equations, the solutions of which are necessary for making the transformation matrices, are efficiently solved, and the reduced order models are efficiently obtained. It is proven that reciprocity of original networks is preserved while applying the proposed method. Passivity of the reduced RC networks is also guaranteed. In the illustrative examples, we will show that the proposed method is compatible with PRIMA in efficiency and is more accurate than PRIMA.

The alternating direction implicit (ADI) method is proposed for low-rank solution of projected generalized continuous-time algebraic Lyapunov equations. The low-rank solution is expressed by Cholesky factor that is similar to that of Cholesky factorization for linear system of equations. The Cholesky factor is represented in a real form so that it is useful for balanced truncation of sparsely connected RLC networks. Moreover, we show how to determine the shift parameters which are required for the ADI iterations, where Krylov subspace method is used for finding the shift parameters that reduce the residual error quickly. In the illustrative examples, we confirm that the real Cholesky factor certainly provides low-rank solution of projected generalized continuous-time algebraic Lyapunov equations. Effectiveness of the shift parameters determined by Krylov subspace method is also demonstrated.

As we scale toward nanometer technologies, the increase in interconnect parameter variations will bring significant performance variability. New design methodologies will emerge to facilitate construction of reliable systems from unreliable nanometer scale components. Such methodologies require new performance models which accurately capture the manufacturing realities. In this paper, we present a Linear Fractional Transform (LFT) based model for interconnect parametric uncertainty. The new model formulates the interconnect parametric uncertainty as a repeated scalar uncertainty structure. With the help of generalized Balanced Truncation Realization (BTR) and Linear Matrix Inequalities (LMI's), the porposed model reduces the order of the original interconnect network while preserves the stability. The LFT based new model even guarantees passivity if the BTR reduction is based on solutions to a pair of Linear Matrix Inequalities (LMI's) generated from Lur'e equations. In case of large number of uncertain parameters, the new model may be applied successively: the uncertain parameters are partitioned into groups, and with regard to each group, LFT based model is applied in turns.