DFG Research Cluster
Discrete Algorithms

Computer Algebra and Design of Analog Circuits

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Circuit Design
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Singular

### Summary of the Project

The goal of this project is to develop and implement Computer Algebra based algorithms for analysis and design of analog electronic circuits.

Due to the growth of digital electronic, the design of analog electronic circuits has played a minor role during the last two decades. Presently, however, analog circuit design is rapidly becoming an important factor again, particularly in the area of mixed-signal design.

Symbolic analysis and design strategies provide the basis for a modern, systematic approach to circuit design. They constitute an efficient supplement to the toolbox of a circuit designer when used in combination with conventional numerical simulators for the analysis, sizing, and optimization of small-scale analog building blocks.

To gain insight into the function of a circuit structure a designer needs to calculate circuit characteristics such as transfer functions analytically in terms of the circuit's design parameters (transistor dimensions, resistor values, etc). This task may be very time-consuming and error-prone and often it is even impossible if done by hand. To support designers in this phase of their work, a symbolic circuit analyzer toolbox Analog Insydes has been developed and implemented as framework for our further research, which focuses on the development of symbolic computation techniques for knowledge acquisition and sizing of analog circuits.

Needed symbolic computations are mainly simplifications and solving large systems of equations which may contain linear as well as nonlinear polynomial or transcendental parts. The development of advanced Computer Algebra systems and the implementation of more and more specialized powerful Computer Algebra algorithms as this is done in Singular, make it nowadays feasible to symbolically solve or preprocess systems of symbolic equations needed for sizing analog circuits.

### Concrete Goals of the Project

• Design and implementation in Singular of algorithms especially suited for the requirements of symbolic sizing of analog circuits.

• Development of highly specialized and efficient stand-alone libraries (SYNCRO) for hybrid (symbolic/numerical) computation of key components of the design cycle of analog circuits.

• Integration of the various special-purpose components into a convenient and user-friendly framework providing tools for designing analog circuits. The integration is accomplished by means of the Multi Protocol (MP), a protocol for the exchange of scientific data; the development framework is based on general-purpose CAS like Mathematica, Macsyma or Maple.

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