Principles of circuit simulation: DC/AC/TR analysis. Basic analog optimisation tasks: worst-case analysis, yield analysis, nominal design and design centering. Basic principles of optimisation: optimality conditions, line search, Nelder-Mead method, Newton approach, Conjugate Gradient approach, Quadratic Programming, Sequential Quadratic Programming. Structural analysis of analog circuits.
Application of a commercial analog optimisation tool (WiCkeD) to an analog design example.
i) Circuit Simulation (5 hrs)
DC analysis; AC analysis, Newton-Raphson; TR analysis, numerical integration; modified nodal analysis, linearised and discretised circuit model.
ii) Worst-Case Analysis (10 hrs)
Lagrange function, optimality conditions (constrained, unconstrained); classical worst-case analysis, realistic worst-case analysis, general worst-case analysis.
iii) Yield Analysis (10 hrs)
Multivariate statistical distribution, transformation of distribution functions, expectation values, estimation of expectation values; statistical yield analysis, geometric yield analysis, Monte-Carlo analysis.
iv) Circuit Sizing (5hrs)
Design objectives and derivatives, nominal design, tolerance design; yield optimisation; design centering; structure of an optimisation process.
v) Basics of numerical optimisation (10 hrs)
Univariate optimisation, line search, multivariate optimisation, polytope method, coordinate search; Newton approach (Quasi-Newton, Levenberg-Marquardt, Least-Squares, Conjugate Gradient; Quadratic Programming (equality/inequality constraints), Sequential Quadratic Programming (SQP).
vi) Structural Analysis of Analog Circuits (5 hrs)
Hierarchical analog building block library, sizing rules.
Lecturers: Apl. Prof. Dr.-Ing. habil. Helmut Gräb / Hours: 45 / Semester: 2