| Titre : | Application of the Acceleration Method to Solve Systems of Nonlinear Equations in the Modeling of Analog Integrated Systems |
| Auteurs : | Fathi Dhiabi, Auteur ; Mohamed Boumehraz, Directeur de thèse |
| Type de document : | Monographie imprimée |
| Editeur : | Biskra [Algerie] : Université Mohamed Kheider, 2018 |
| Langues: | Anglais |
| Mots-clés: | Nonlinear equations ; Newton Raphson ; Homotopy,Newton order three ; NewtonKarylov,Analog Circuits,SPICE ; PyAMS. |
| Résumé : |
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, the simulation method should be used to verifying the function of circuit and eliminate of any problem. But there is a problem in the simulation of analog circuits or complex circuits in particular case. The problem is finding the operating point; this problem depends on the method used by the simulator to solve nonlinear equations. The continuous 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 be improve the 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 for controlling the step length of the continuous parameter. 2. We have used the Newton order three in the correction process rather than the Newton order two used in the 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 the windows system, which it is defined by the following software: Modeling the analog element in the form of dependent source. Create circuits by either the 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. |
| Sommaire : |
Contents
Introduction………………………………………………………………………... 1 Chapter I: The Application of Newton Raphson by SPICE for Analyses Circuit. I.1. Introduction………………………………………………………………….. 6 I.2. History of SPICE…………………………………………………………….. 7 I.3. Newton-Raphson Method…………………………………………………… 8 I.4. The circuit equation………………………………………………………….. 10 I.5. The application of NR by SPICE……………………………………………. 11 I.5.1. Diode…………………………………………………………………... 11 I.5.2. MOSFET………………………………………………………………. 12 I.5.3. Bipolar Junction Transistor……………………………………………. 14 I.5.4. Element of storage of energie……………………………….…………. 16 I.5.5. Example of circuit……………………………………………………… 17 I.6. Modified Nodal Analysis…………………………………………………….. 19 I.7. The structure of NR algorithm in algorithm of analyses circuits…………… 20 I.7.1. DC simulation…………………………………………………………. 22 I.7.2. Transient simulation…………………………………………………... 22 I.7.3. AC simulation…………………………………………………………. 23 I.8. Convergence Problem-Aiding Techniques………………………………….. 24 I.8.1. Limiting method………………………………………………………. 25 I.8.2. Model Damping……………………………………………………….. 26 I.8.3. Source Stepping……………………………………………………….. 26 I.8.4. Voltage Limiting………………………………………………………. 27 I.8.5. Diode damping………………………………………………………… 27 I.8.6. Continuation methods……………………………………………….… 28 I.9. Various Continuation (Homotopy) methods………………………………… 28 I.10. Homotopy Function………………………………………………………….. 29 I.10.1. Newton Homotopy……………………………………………………. 29 I.10.2. Fixed Point Homotopy…………………………………………………... 30 I.10.3. Newton Fixed Point Homotopy…………………………………………. 30 I.10.4. Nonlinear Homotopy……………………………………………………. 30 I.10.5. Variable Gain Homotopy……………………………………………….. 31 I.10.6. Variable Gain Newton Homotopy………………………………………. 31 I.11. Solvers by Continous method…………………………………………………. 32 I.11.1. Predictor corrector………………………………………………………. 32 I.11.2. Pseudo-arclength………………………………………………………… 33 I.11.3. ODE-based method……………………………………………………… 34 I.12. Conclusion……………………………………………………………………… 37 Chapter II: Accelerate the Solving of Nonlinear Equations using the Homotopy Method. II.1. Introduction …………………………………………………………………… 39 II.2. Continues method……………………………………………………………... 39 II.3. Homotopy function……………………………………………………………. 40 II.4. Solving the homotopy equation ………………………………………………. 42 II.4.1. Prediction……………………………………………………………… 43 II.4.2. Correction……………………………………………………………… 44 II.5. New method to control the step size………………………………………….. 45 II.6. Modeling of analog elements using the continuous parameter……………….. 46 II.6.1. Convert any element in the circuit to its equivalent ………………….. 47 II.6.2. Create the global equation of the circuit ……………………………… 49 II.6.3. Transform the global equation to the homotopy equation…………….. 51 II.7. Simulation results……………………………………………………………… 52 II.8. Conclusion…………………………………………………………………….. 55 Chapter III: Application of Third-Order Convergence to Find Operating Point and Analyses Systems of Analog Circuits. III.1. Introduction………………………………………………………………….. 56 III.2. Globally convergent algorithm of NR……………………………………….. 56 III.3. New iterative method and convergence analysis………………………….... 58 III.3.1. New family based by MA……………………………………………... 58 III.3.2. New family based by MW and MA………………………………….... 60 III.4. Globally convergent algorithm of NM………………………………………. 62 III.5. Application…………………………………………………………………... 62 III.5.1. Error of convergence………………………………………………… 63 III.5.2. Comparison NM with Newton-Krylov……………………………… 66 III.6. Conclusions…………………………………………………………………... 68 Chapter IV: New Software for Modeling and Analysis of Analog Circuits Based on the Continuous Method. IV.1. Introduction………………………………………………………………… 69 IV.2. What difference between SPICE and PyAMS………………………………. 69 IV.3. Theoretical background……………………………………………………… 71 IV.3.1. The structure of analog element in PyAMS…………………………… 71 IV.3.2. The equation of the circuit in PyAMS ………………………………... 72 IV.3.3. Method of finding operating point……………………………………. 73 IV.3.4. The algorithms of Analyses of circuit by PyAMS…………………….. 75 IV.4 The modeling of analog elements and simulation circuit by PyAMS……….. 79 IV.4.1. Modeling of analog element by PyAMS………………………………. 79 IV.4.2. Examples of models by PyAMS………………………………………. 81 IV.4.2.1. Resistor………………………………………………………… 81 IV.4.2.2. Capacitor………………………………………………………. 82 IV.4.2.3. Diode………………………………………………………….. 83 IV.4.2.4. Bipolar junction transistor…………………………………….. 84 IV.4.2.5. Complete model of BJT ………………………………………. 86 IV.4.2.6. MOSFET………………………………………………………. 88 IV.4.2.7. Voltage source……………………………………………….… 89 IV.4.2.8. Logic gates…………………………………………………….. 90 IV.4.3. The functions used by PyAMS language……………………………… 90 IV.4.4. Create circuit by PyAMS………………………………………...……. 92 IV.4.4.1. Create circuit by method of textual……………………………. 93 IV.4.4.2. Create circuit by method of schema…………………..……….. 95 IV.4.4.3. Method of analyzing and interface using………………….…… 96 IV.5 Example of analysis circuits ………………………………………………… 97 IV.5.1 Simple RC circuit…………………………………………...…………. 98 IV.5.2 MOS Oscillator………………………………………………………... 98 IV.5.3 Chua’s circuit……………………………………………..…………… 100 IV.5.4 Modeling a nonlinear transformer ……………………………………. 102 IV.6 Circuit analysis by PyAMS…………………………………………….….... 106 IV.7 Conclusion…………………………………………………………….….…. 109 Conclusion………………………………………………………………………….. 111 Reference…………………………………………………………………………… 117 |
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| Cote | Support | Localisation | Statut | Emplacement | |
|---|---|---|---|---|---|
| TH/0887 | Thèse de doctorat | BIB.FAC.ST. | Empruntable |
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