Simulation and Optimization of Analog Circuits (NM 6016)

Lecturer Priv.-Doz. Dr.-Ing. Helmut Gräb
Amount 45 hours (2 weeks)
Cycle each spring


  • Fundamentals of numerical optimization processes and some aspects of statistics
  • Applying optimality conditions to formulate circuit design tasks like worst-case and yield analysis and optimization
  • Differentiated knowledge of circuit sizing tasks
  • To know what happens inside EDA tools for sizing as a designer, and to be prepared for developing such EDA tools.


  • Lectures and Tutorials. Lagrange function, optimality conditions (constrained, unconstrained); worst-case analysis, classic, realistic, general; multivariate statistical distribution, transformation of distribution functions, expectation values, estimation of expectation values; yield analysis, statistical, geometric, Monte-Carlo analysis; circuit sizing, yield optimization/design centering; structure of an optimization process, univariate optimization, line search, multivariate optimization, polytope method, coordinate search; Newton approach (Quasi-Newton, Levenberg-Marquardt, Least-Squares, Conjugate Gradient; Quadratic Programming (equality/inequality constraints), Sequential Quadratic Programming (SQP); structural analysis of analog circuits, analog sizing rules. Principles of circuit simulation: DC/AC/TR analysis.
  • Laboratory. Circuit analysis and optimization with WiCkeD(R); nominal design, sizing rules, circuit performance features; worst-case and yield analysis, deterministic and statistical; yield optimization.


The examination is in written form with open book policy.


A compendium, exercises and lab instructions will be provided at the start of the course, electronically and in printed form. Further material will be provided electronically during the course.


  • R. Fletcher, Practical Methods of Optimization, John Wiley & Sons, 2nd Edition, 2000.
  • H. Graeb, Analog Design Centering and Sizing, Springer, 2007.