CSE 245Circuit SimulationWinter 2013University of California, San Diego

## Instructor

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

- Lectures: 5:00-6:20PM, MW, Room CSE2154
## 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.
## Notes and Papers

- 1. Introduction
- 2. Problem Formulation

- Lecture 2: Formulation,
- Regularization article by Chen, Weng and Cheng,
- 2.1 Topology, 2.1.1 tree trunks and links, 2.1.2 incidence matrix, 2.2 Branch equations, 2.2.1 forward integration model, 2.2.2 backward integration model, 2.2.3 trapezoidal model, 2.3 Regularization
- 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. Matrix Solvers

- Matrix Solver I, Matrix Solver II, Matrix Solver III
- 4.1 Formulation, 4.2 Matrix condition and range of eignevalues, 4.3 Direct solvers, 4.4 Iterative solvers, 4.4.1 Stationary solvers, 4.4.2 Nonstationary solvers: gradient descent, conjugate gradient descent methods.
- 5. Integration of Linear Circuits

- Integration
- Dahlquist stability theory paper, and slides
- 5.1 Formulation, 5.2 Local truncation errors, 5.2.1 Exact errors, 5.2.2 Error from Taylor expansion, 5.2.3 Multistep integration derivation, 5.3 Stability, 5.3.1 Motivation, 5.3.2 Region of stability, 5.3.3 Dahlquist's theorem, 5.4 Convergence, 5.5. Adaptive time steps, 5.6 Stiffness of the system
- 6. Nonlinear Systems

- Nonlinear System Integration
- Newton-Raphson method, Nesterov methods, homotopy methods
- 7. Sensitivity Analysis

- Adjoint Network
- direct method, adjoint network approach
- 8. Various Simulation Approaches FDM, FEM, BEM, Monte Carlo, random walks, multipole method
- 9. Applications power distribution networks, IO circuits, full wave analysis, Boltzmann transport equations
## Exercises

- Exercise 1: (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. (2) Devise a simple but non-trivial circuit with one or more loops of capacitors. Express its state equation. (3) Devise a simple but non-trivial circuit with one or more cuts of inductors. Express its state equation. (4) Devise a method to formulate circuits with branch voltage sources using nodal analysis. Describe the conditions that the nodal analysis formulation is feasible.
- Exercise 2: For matrix computations using iterative methods, according to the formulations of minimal error in A norm and minimal residual, derive the procedure of a) Lanczos, b) conjugate gradient, c) GMRES, and d) conjugate residual. (1) Describe the algorithm of the procedure. (2) Use a 5x5 matrix to demonstrate your algorithm using Krylov space of dimension two, i.e. K(r,A,2). (3) Discuss the error in the example due to the limit of the dimension of Krylov space. (4) Discuss the error in the example due to the numerical error.
- Exercise 3: Use Tellegen's theorem to prove the reciprocal theorem in (1) frequency domain and (2) in time domain. State the conditions for nonlinear systems.
- Possible Project List.