CSE 245Circuit SimulationWinter 2015University of California, San Diego

## Instructor

- CK Cheng, CSE2130, ckcheng+245@ucsd.edu, tel: 858 534-6184
## Schedule

- Lectures: 5:00-6:20PM, TTH, Room CSE2217
## References

- 1. Electronic Circuit and System Simulation Methods, T.L. Pillage, R.A. Rohrer, C. Visweswariah, McGraw-Hill, 1998
- 2. Interconnect Analysis and Synthesis, CK Cheng, J. Lillis, S.Lin and N. Chang, John Wiley, 2000
- 3. Computer-Aided Analysis of Electronic Circuits, L.O. Chua and P.M. Lin, Prentice Hall, 1975
- 4. A Friendly Introduction to Numerical Analysis, B. Bradie, Pearson/Prentice Hall, 2005, http://www.pcs.cnu.edu/~bbradie/textbookanswers.html
- 5. Numerical Recipes: The Art of Scientific Computing, Third Edition, W.H. Press, S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery, Cambridge University Press, 2007.
- 6. Numerical Algorithms, Justin Solomon, pdf from http://web.stanford.edu/~justso1/share/book/numerical_book.pdf
## Notes and Papers

- 1. Introduction

- Lecture 1: Introduction,
- Lecture 1.1: Motivation. Figures are extracted from Modeling and Simulation at the Exascale for Energy and the Environment, H. Simon, T. Zacharia, and R. Stevens, 2007.
- 2. Problem Formulations: circuit topology, network regularization

- Lecture 2: State Equations,
- 2.1 Basic elements, 2.1.1 forward integration model, 2.1.2 backward integration model, 2.1.3 trapezoidal integration model, 2.2 Topology, 2.2.1 tree trunks and links, 2.2.2 incidence matrix.
- 3. Analytical Solutions

- 3.1 Time domain solutions, 3.1.1 Exponential functions, 3.1.2 Differential functions of inputs, 3.2 Frequency domain solutions, 3.2.1 Laplace transform, 3.2.2 Expansion when s->inf, 3.2.3 Expansion when s->0, 3.2.4 Moments, 3.2.5 Elmore delay model.
- 4. Linear Circuits: matrix solvers, explicit and implicit integrations, matrix exponential methods, convergence

- Lecture 3: Direct Matrix Solver, notes from Li,
- Lecture 3: Iterative Matrix Solver I , Lecture 3: Iterative Matrix Solver II , Lecture 3: Iterative Matrix Solver II (updated .pptm) ,
- Lecture 4: Numerical Integration , Lecture 4.1: Matrix Exponential Operators, Matrix Exponential by S.H. Weng .
- 5. Nonlinear Systems: Newton-Raphson method, Nesterov methods, homotopy methods
- 6. Sensitivity Analysis: direct method, adjoint network approach
- 7. Various Simulation Approaches: FDM, FEM, BEM, multipole methods, Monte Carlo, random walks
- 8. Multiple Dimensional Anlaysis:
- 9. Applications: power distribution networks, IO circuits, full wave analysis.
## Homeworks

Group discussion for homeworks is highly recommended. However, use different circuits (when needed) to demonstrate your cases.

- HW1:(1). Devise simple but non-trivial circuits to show at least five different ways to formulate state equations. Try to use similar circuits for the five different formulations. What is the implication of the formulation in the choice of the hardware platform? (2). Use the interconnect example in page 24 of lecture 2 to illustrate that inductances do not have any effect on the average delay (moment 1 of the output voltage). Derive a case that the inductances do have an effect. (3). Go through the exercise in page 27 of lecture 2. Could we use this approach for general circuit simulation? Explain your answer.
- HW2: Problems from Numerical Algorithms, by J. Solomon, (1)0.13/p24, (2)0.15/p25, (3)2.13/p64, (4)2.14/p64, (5)3.7/p89, (6)3.9/p89, (7)10.6/p228, (8)10.8/p229 (exercise/page#).
- HW 3 in pdf file.
## Projects