Download Advanced Model Order Reduction Techniques in VLSI Design by Sheldon Tan, Lei He PDF

By Sheldon Tan, Lei He

Version order relief (MOR) options decrease the complexity of VLSI designs, paving tips to larger working speeds and smaller function sizes. This ebook provides a scientific creation to, and remedy of, the major MOR equipment hired quite often linear circuits, utilizing real-world examples to demonstrate the benefits and downsides of every set of rules. Following a evaluation of conventional projection-based ideas, assurance progresses to complex 'state-of-the-art' MOR equipment for VLSI layout, together with HMOR, passive truncated balanced consciousness (TBR) equipment, effective inductance modeling through the VPEC version, and structure-preserving MOR options. the place attainable, numerical equipment are approached from the CAD engineer's point of view, warding off complicated arithmetic and permitting the reader to tackle genuine layout difficulties and improve better instruments. With functional examples and over a hundred illustrations, this e-book is appropriate for researchers and graduate scholars of electric and laptop engineering, in addition to practitioners operating within the VLSI layout undefined.

Show description

Read or Download Advanced Model Order Reduction Techniques in VLSI Design PDF

Best circuits books

CMOS Digital Integrated Circuits Analysis & Design

CMOS electronic built-in Circuits: research and layout is the main whole publication out there for CMOS circuits. acceptable for electric engineering and laptop technological know-how, this publication begins with CMOS processing, after which covers MOS transistor versions, simple CMOS gates, interconnect results, dynamic circuits, reminiscence circuits, BiCMOS circuits, I/O circuits, VLSI layout methodologies, low-power layout concepts, layout for manufacturability and layout for testability.

Activities Manual to accompany Programmable Logic Controllers

The actions handbook includes true/false, final touch, matching, and multiple-choice questions for each bankruptcy within the textual content. in order that scholars get a greater knowing of programmable common sense controllers, the handbook additionally encompasses a wide variety of programming assignments and extra perform workouts.

Materials for Rigid and Flexible Printed Wiring Boards (Electrical and Computer Engineering)

Complicated digital circuits and units are flooding functions in approximately each aspect of industrial and business job, from automatic apparatus to every kind of customer items. right choice of fabrics is essential to satisfy the end-use requisites of versatile and inflexible published wiring forums.

Mathematical Modelling and Simulation of Electrical Circuits and Semiconductor Devices: Proceedings of a Conference held at the Mathematisches Forschungsinstitut, Oberwolfach, October 30 – November 5, 1988

Numerical simulation and modelling of electrical circuits and semiconductor units are of primal curiosity in present day excessive know-how industries. on the Oberwolfach convention greater than 40 scientists from all over the world, in­ cluding utilized mathematicians and electric engineers from and universities, awarded new leads to this zone of becoming significance.

Additional resources for Advanced Model Order Reduction Techniques in VLSI Design

Sample text

49) where A ∈ Rn×n , B ∈ Rn×p , C ∈ Rp×n , y(t), and u(t) ∈ Rp . , C = B T . In this case, both Gramians are equal. As a result, we only need to look at the controllability Gramian, X, ∞ X= T eAt BB T eA t dt. 51) where superscript H denotes the Hermitian transpose. We now consider evaluating X by applying numerical quadrature to the above equation, given a quadrature scheme with nodes ωk and weights ωk , and defining zk = (jωk I − A)−1 B. 48) under impulse responses. For general POD methods, we can apply typical inputs to ˆ to X can then be the system and obtain the responses.

B, ˜ C; ˜ ˜ c ≥ 0, then terminate and return A, 3. 2. Truncated balanced realization algorithms are important from the theoretical point of view. For small systems (a few hundred states or so) they are superior in accuracy to the Krylov subspace methods and other parameter-matching techniques, and also provide computable bounds on the reduction errors. For large systems, direct application of the techniques used to balance and truncate the systems is computationally infeasible, since the computations required have O(n3 ) complexity when performed directly (n being the order of the system to be reduced).

As a result, we have the eigendecomposition of the response Gramian as X X T = U ΣΣT U T ≈ Uk Σk ΣTk UkT . 8) Let x(t) ≈ Uk η(t), η(t) ∈ Rk ; then we have the following reduced system in terms of η(t), η(t) ˙ = Uk T f (Uk η(t), u(t)), y(t) = h(Uk η(t), u(t)). 10) Thus the approximation of the state x(t) uses a low-dimensional space that is spanned by the k leading columns of U , which essentially are the dominant eigen vectors of the response Gramian X X T . This reduction process can be used directly for both linear and non-linear dynamic systems.

Download PDF sample

Rated 4.78 of 5 – based on 41 votes