Parameter Space Exploration Algorithms for Nonlinear Dynamical Circuits
نویسندگان
چکیده
This paper describes methods of the behavioural analysis of nonlinear dynamic circuits and systems in electrical engineering. The investigation starts with the network analysis results in the set of state equations. The state equations undergo several numerical analysis algorithms described in this paper. The results of these analysis are qualitative and quantitative characterisations of the system behaviour. In the paper all the analysis steps are described. An implementation of a program system called TADS, which performs this analysis automatically, is presented. In order to illustrate the system analysis, the Colpitts Oscillator as a simple example circuit is used. A main task in electrical engineering is the investigation of the behaviour of circuits and systems. We consider the analysis of continuous time nonlinear dynamical systems such as generators for diierent waveforms. Nonlinear dynamical system exhibit a huge variety of qualitative asymptotic behaviour. The systems may have a stable xed point or may oscillate periodically or chaotically. The analysis task is to determine the qualitative asymptotic behaviour of the system for given parameters automatically. In order to perform this automatic behaviour analysis, certain characteristics of the system's solution have to be estimated. Our goal was to implement a program system that numerically solves (integrates) the system equations, nds the steady state of the solution and estimates the periodicity and the Lyapunov exponents of the steady state solution. These results should be used to qualify the asymptotic behaviour of the system automatically. Moreover, this analysis should be combined with a automatic scanning of the parameter space. As a result bifurcation diagrams which relate the system's behaviour to the system parameters is obtained. These diagrams can be used as design rules for desired behaviours of the analysed system. It is desired to maintain the favourable features of the program system INSITE 6] while adding the automatic parameter scan and the automatic behaviour characterisation. Moreover our tool is suitable for a wide range of dynamical systems. The rst step of the circuit investigation is the network analysis. In this step of the analysis, from the circuit together with the device models a network graph is obtained. This network graph is analysed by means of suitable methods based on Kirchhoo's Laws. A set of node and mesh equations is obtained. Introducing the v-i-Relations of the network branches results in the set of state equations. Prior further analysis these equations are normalised and rewritten in a form …
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