| Title | Efficient Model Reduction of Interconnects Via Double Gramians Approximation |
| Author | Boyuan Yan, *Sheldon Tan (UC Riverside, U.S.A.), Gengsheng Chen (Fudan University, China), Yici Cai (Tsinghua University, China) |
| Page | pp. 25 - 30 |
| Keyword | model order reduction, interconnect, SVD, simulation |
| Abstract | The gramian approximation methods have been proposed recently to
overcome the high computing costs of classical balanced truncation
based reduction methods. But those methods typically gain
efficiency by projecting the original system only onto one
dominant subspace of the approximate system gramian (for instance
using only controllability gramian). This single gramian reduction
method can lead to large errors as the subspaces of
controllability and observability can be quite different for
general interconnects with unsymmetric system matrices. In this
paper, we propose a fast balanced truncation method where the
system is balanced in terms of two approximate gramians as
achieved in the classical balanced truncation method. The novelty
of the new method is that we can keep the similar computing costs
of the single gramian method. The proposed algorithm is based on a
generalized SVD-based balancing scheme such that the dominant
subspace of the approximate gramian product can be obtained in a
very efficient way without explicitly forming the gramians.
Experimental results on a number of published benchmarks show that
the proposed method is much more accurate than the single gramian
method with similar computing costs. |
| Title | Wideband Reduced Modeling of Interconnect Circuits by Adaptive Complex-Valued Sampling Method |
| Author | Hai Wang, *Sheldon Tan (UC Riverside, U.S.A.), Gengsheng Chen (Fudan University, China) |
| Page | pp. 31 - 36 |
| Keyword | interconnect, simulation, model order reduction |
| Abstract | In this paper, we propose a new wideband model order reduction
method for interconnect circuits by using a novel adaptive
sampling and error estimation scheme. We try to address the
outstanding error control problems in the existing sampling-based
reduction framework. In the new method, called WBMOR, we
explicitly compute the exact residual errors to guide the sampling
process. We show that by sampling along the imaginary axis and
performing a new complex-valued reduction, the reduced model will
match exactly with the original model at the sample points. We
show theoretically that the proposed method can achieve the error
bound over a given frequency range. Practically the new algorithm
can help designers choose the best order of the reduced model for
the given frequency range and error bound via adaptive sampling
scheme. As a result, it can perform wideband accurate reductions
of interconnect circuits for analog and RF applications. We
compare several sampling schemes such as linear, logarithmical,
and recently proposed re-sampling methods. Experimental results on
a number of RLC circuits show that WBMOR is much more
accurate than all the other simple sampling methods and the
recently proposed re-sampling scheme with the same reduction
orders. Compared with the real-valued sampling methods, the
complex-valued sampling method is more accurate for the same
computational costs. |
| Title | VISA: Versatile Impulse Structure Approximation for Time-Domain Linear Macromodeling |
| Author | *Chi-Un Lei, Ngai Wong (The University of Hong Kong, Hong Kong) |
| Page | pp. 37 - 42 |
| Keyword | Linear Macromodeling, Interpolations, Walsh theorem, Rational function, Time domain |
| Abstract | We develop a rational function macromodeling algorithm named VISA (Versatile Impulse Structure Approximation) for macromodeling of system responses with (discrete) time-sampled data. The ideas of Walsh theorem and complementary signal are introduced to convert the macromodeling problem into a non-pole-based Steiglitz-McBride (SM) iteration (a class of first- and second-order interpolations) without initial guess and eigenvalue computation. We demonstrate the fast convergence and the versatile macromodeling requirement adoption through a P-norm approximation expansion, using examples from practical measured data. |
| Slides |
| Title | An Extension of the Generalized Hamiltonian Method to S-parameter Descriptor Systems |
| Author | *Zheng Zhang, Ngai Wong (Department of Electrical and Electronic Engineering, The University of Hong Kong, Hong Kong) |
| Page | pp. 43 - 47 |
| Keyword | Passivity, Descriptor system, Bounded Realness, Scattering parameter |
| Abstract | A generalized Hamiltonian method (GHM) was recently proposed for the passivity test of hybrid descriptor systems [1]. This paper extends the GHM theory to its S-parameter counterpart. Based on the S-parameter GHM, a passivity test flow is proposed, which is capable of detecting nonpassive regions of descriptor-form physical models. The proposed method is applicable to S-parameter and hybrid systems either in the standard state-space or descriptor forms. Experimental results confirm the effectiveness and accuracy of the proposed method. |