Mathematical Methods of Circuit Design

Module Number: EI74042

Duration: 1 Semester

Occurence: Winter Semester and Summer Semester

Language: English

Number of ECTS: 5


Professor in charge: Helmut Gräb

Amount of work

Contact hours: 90

Self-study hours: 60

Total: 150

Description of achievement and assessment methods

The examination is in written form with open book policy and allows a non-programmable calculator, but no other electronic devices. The duration of the examination is 60 minutes. The exmination consists of questions covering the knowledge of the course contents and hand calculations covering the ability to solve problems.

Recommended requirements

It is recommended, but not mandatory to take a module on numerical methods in electrical engineering before the course. It is recommended to take a module in the area of analog circuit design in addition to the course.

Intended Learning Outcomes

After the course, the student is proficient in
* fundamental methods and algorithms of numerical optimizations,
* basic methods of multivariate statistics,
* fundamental tasks and constraints of optimization of circuit sizing.
He/she is capable of
* applying and evaluating these methods as a circuit designer on the one hand and of
* developing and programming these methods as an EDA engineer on the other hand.


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.

Teaching and learning methods

Lecture and tutorial are designed as interactive ex-cathedra teaching. By chalk and talk, the algorithms are developed step by step and under the participation of the students. Examples of the algorithms are exercised with hand calculations in the tutorial. The participants prepare for the lecture by studying the course material, and repeat the subject matters after the presence lectures independently and by self-study. Self-study includes literature research.

Media formats

- chalk and talk
- slide presentations
- written compendium
- text books
- exercises with solutions
- teaching material as download from web page


  • Fletcher, Practical Methods of Optimization, John Wiley & Sons, 1987/2002
  • Graeb, Analog Design Centering, Springer, 2007.