Passivity Assessment and Model Order Reduction for Linear Time-Invariant Descriptor Systems in VLSI Circuit Simulation

of thesis entitled Passivity Assessment and Model Order Reduction for Linear Time-Invariant Descriptor Systems in VLSI Circuit Simulation Submitted by Zheng ZHANG for the degree of Master of Philosophy at the University of Hong Kong in June 2010 This thesis presents some theoretical and numerical results for linear time-invariant (LTI) descriptor systems (DSs), with emphasis on their corresponding passivity assessment and model order reduction (MOR). DSs are widely used in VLSI circuit modeling, including on-chip parasitics, RF passives, chip packagings, as well as linearized models of transistor networks. In the first part (Chapters 2 to 4), we focus on the passivity assessments of LTI DSs. In Chapter 2, a generalized Hamiltonian method (GHM) and its half-size version (HGHM) are developed. The most significant advantage of GHM/HGHM passivity test is that they are purely algebraic routines, thereby rendering the test results highly accurate. Not only can they tell a LTI DS is passive or not, but they also accurately locate the possible nonpassive regions, thereby providing a versatile tool for subsequent DS passivity enforcements. Chapter 3 presents a projector-based passivity test for large-size LTI DS models which can not be readily tackled by GHM. It is the first time that spectral projectors are used, which are based on our proposed fast canonical projector construction, to efficiently decompose a large DS model into its proper and improper subsystems. After the fast system decomposition, the proper part is tested by GHM, via a fast iterative numerical implementation. Chapter 4 presents the S-parameter generalized Hamiltonian method (S-GHM), and also its half-size algorithm (S-HGHM). Similar to GHM/HGHM, S-GHM and S-HGHM can locate all possible nonpassive regions with high numerical accuracy. A passivity test flow for admittance/impedance DSs is also proposed, based on S-GHM and S-HGHM after a Moebious transform of DS state-space equations. The second part (Chapters 5 & 6) solves two issues in DS MOR: passivity and improper part preservation, as well as efficient MOR for multi-port DS models. Chapter 5 focuses on the first issue. The improper part of a DS is preserved by fast spectral projector-based additive system decomposition. After that, the proper part is reduced via DS-format positive-real balanced truncation (DS-PRBT). Since the main bottleneck of DS-PRBT is in solving the dual generalized algebraic Riccati equations (GAREs), a generalized quadratic alternating direction implicit (GQADI) algorithm is developed to efficiently compute the positive-real Gramians. To further speed up the matrix solver, a low-rank version of GQADI (LR-GQADI) is also devised, which reduces the complexity from O(n) to O(n). Chapter 6 constructs “good” macromodels for multi-port LTI DSs, motivated by power grid simulation in modern VLSI design. Due to the large number of ports, existing MOR techniques are not efficient for power grids. To overcome this problem, we develop a MOR routine based on input matrix splitting, called BDSM (block-diagonal structured model order reduction). The BDSM ROM (reduced-order model) is as accurate as standard moment-matching MORs; its resultant ROMs are block-diagonal structured which permits high efficiency for subsequent simulations; the BDSM ROM size can be further scaled down for clock-gated power grid models; finally and most importantly, unlike many existing power grid MORs that need to generate different ROMs for different input waveforms, the resultant ROM from BDSM is reusable under various input wave patterns. Abstract word count: 504word count: 504 Passivity Assessment and Model Order Reduction for Linear Time-Invariant Descriptor Systems in VLSI Circuit Simulation