Numerical method for analyzing transient and steady states of sine wave oscillator circuit with stiffness
| Autor: | Kohshi Okumura, Akira Kishima, Hisashi Yasuda |
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| Rok vydání: | 1987 |
| Předmět: | |
| Zdroj: | Electronics and Communications in Japan (Part I: Communications). 70:1-11 |
| ISSN: | 1520-6424 8756-6621 |
| DOI: | 10.1002/ecja.4410701001 |
| Popis: | This paper proposes a method for analyzing the transient and steady states of a sine wave oscillator circuit with reactive elements which have large differences in their values. These reactive elements can be divided broadly into three categories: elements for determining the frequency of the oscillation; very small elements such as stray capacitors in the transistor; and very large elements such as by-pass capacitors. The circuit equation is represented by an autonomous nonlinear differential equation with the values of these elements. There are remarkable differences in magnitude between the eigenvalues of the linear parts of the equation. In this paper, first, we describe the method for solving numerically the differential equation regardless of the stiffness by the asymptotic method developed by Krylov, Bogolyubov and Mitropolskiy. Second, we present the method for obtaining solutions of the differential equation with regard to the stiffness by combining the asymptotic method with numerical integration. Especially, when we obtain the transient solution, we demonstrate that the application of the interpolation method to the asymptotic method reduces the computing time considerably. As examples, we consider the CR sine wave oscillator circuit using the Ebers–Moll model of transistors. |
| Databáze: | OpenAIRE |
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