Analysis of Reactance Oscillators Having Multi-Mode Oscillations

Yoshihiro YAMAGAMI  Yoshifumi NISHIO  Akio USHIDA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E89-A   No.3   pp.764-771
Publication Date: 2006/03/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e89-a.3.764
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Circuit Theory
Keyword: 
oscillator,  multiple oscillations,  harmonic balance method,  Newton homotopy method,  SPICE,  

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Summary: 
We consider oscillators consisting of a reactance circuit and a negative resistor. They may happen to have multi-mode oscillations around the anti-resonant frequencies of the reactance circuit. This kind of oscillators can be easily synthesized by setting the resonant and anti-resonant frequencies of the reactance circuits. However, it is not easy to analyze the oscillation phenomena, because they have multiple oscillations whose oscillations depend on the initial guesses. In this paper, we propose a Spice-oriented solution algorithm combining the harmonic balance method with Newton homotopy method that can find out the multiple solutions on the homotopy paths. In our analysis, the determining equations from the harmonic balance method are given by modified equivalent circuit models of "DC," "Cosine" and "Sine" circuits. The modified circuits can be solved by a simulator STC (solution curve tracing circuit), where the multiple oscillations are found by the transient analysis of Spice. Thus, we need not to derive the troublesome circuit equations, nor the mathematical transformations to get the determining equations. It makes the solution algorithms much simpler.