Application of the Acceleration Method to SolveSystems of Nonlinear Equationsin the Modeling of Analog Integrated Systems

Dhiabi, Fathi (2018) Application of the Acceleration Method to SolveSystems of Nonlinear Equationsin the Modeling of Analog Integrated Systems. Doctoral thesis, Université Mohamed Khider – Biskra.

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Abstract

All technologies used the electrical circuits with integrated components based on semiconductor devices such as Diodes, BJTs, MOSFETs…etc,it are nonlinear elements.Before construct any circuit, thesimulation method should be usedto verifying the function of circuit and eliminate of any problem. But there is a problem in the simulation of analog circuitsor complex circuits in particular case.The problem is finding the operating point;this problem dependson the method used by the simulatorto solve nonlinear equations. Thecontinuous method was frequently used in the last ten years; it is an algorithm which deals with the problem of convergence of nonlinear equations using the continuous (homotopy) parameter. It is consists of three stages: the first stage was converts the nonlinear equation to the homotopy equation; the second uses the prediction process to obtain a good approximation of the solution. The last stage based on the correction process which is related on the Newton Raphson method. In this work, we have proposed a new approach to accelerate the solving of nonlinear equations, which can beimprovethe continuous method by adding a new stage in the control of the step length of the continuous parameter. The main objectives of this work are: 1. The adding a new stage (four stage) to the continuous method forcontrolling the step length of the continuous parameter. 2. We have used the Newton order three in the correction process rather than the Newton order twoused inthe Newton-Raphson method. 3. We have introduced a new idea to converting the analog elements of the circuit of their dependent of voltage or current sources for applying the KCL and the KVL laws to obtain the equation of the complex circuit. 4. We have created new software called PyAMS (Python for Analog and Mixed Signals) based on the proposed method in thewindows system, which it is defined by the followingsoftware: • Modeling the analog element in the form of dependent source. • Create circuits by eitherthe textual or the schema method (CAD). • Analysis of circuits. The obtain results show that the using a new software based on the proposed method having a effectiveness in the our approach. Compared to other methods, this method is more efficient. Our new software is faster than the SPICE simulator in analyzing circuits, and offers the modeling of elements contrary to SPICE.

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