Parameter Selection of Oscillator Resonant Circuit Based on Stochastic Differential Equation

Authors

  • Yan Gang Feng College of Computer Science, Sichuan University
  • Huang Xian He School of Automation Engineering, University of Electronic Science and Technology of China
  • Xu Ning Jing School of Electronic Information Engineering, Chengdu University

DOI:

https://doi.org/10.5614/j.eng.technol.sci.2014.46.2.4

Abstract

Because the choice of oscillator resonant circuit parameters depends mostly on experience, we propose nonlinear differential equations to describe an oscillator based on an equivalent circuit of the oscillator and then to describe the internal electrical noise of the oscillator by introducing a stochastic term that establishes a nonlinear stochastic differential equation to analyse the oscillator's behavior. For optimization of the oscillator resonant circuit parameters, first, we used Advanced Design System (simulation software of the Agilent company) to verify the conclusion, and then, using a 10MHz Pierce crystal oscillator, provided experimental evidence.

Downloads

Download data is not yet available.

References

Yan, G.F. & Huang, X.H., Research on Phase Noise of Oscillators: A Survey, Journal of Astronautic Metrology and Measurement, 29(4), pp. 74-78, 2009.

Edson, W.A., Noise in Oscillators, Proc. of IRE, 48(8), pp. 1454-1466, 1960.

Mullen, J.A., Background Noise in Nonlinear Oscillators, Proc. of IRE. 48(8), pp. 1467-1473, 1960.

Leeson, D.B., Simple Model of Feedback Oscillator Noise Spectrum, Proceedings Letters, IEEE, pp. 329-330, 1966.

Sauvage, G., Phase Noise in Oscillators, A Mathematical Analysis of Leeson's Model, IEEE Transactions on Instrumentation and Measurement, 26(4), pp. 408-410, 1977.

Hajimiri, A. & Lee, T., A General Theory of Phase Noise in Electrical Oscillators, IEEE Solid State Circuits, 33 (2), pp. 179-194, 1998.

Kaertner, F.X., Determination of the Correlation Spectrum of Oscillators with Low Noise, IEEE Trans Microwave Theory Tech, 37(1), pp. 90-101, 1989.

Kaertner, F.X., Analysis of White and fa^ Noise in Oscillators, Int. J. Circuit Theory Appl., 18(5), pp. 485-519, 1990.

Demir, A., Mehrotra, A. & Roychowdhury, J., Phase Noise in Oscillators: A Unifying Theory and Numerical Methods for Characterization, IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications, 47(5), pp. 655-674, 2000.

Yan, G.F., Huang, X.H. & Tan, H., The Optimal Selection of Oscillator Resonant Circuit Parameters Based on Genetic Algorithm, ACTA Metrologica Sinica, 31(2), pp. 165-169, 2010.

Liu, M.L., Principle and Application of Oscillator, Higher Education Press, Beijing, pp. 41-43, 1984.

Yan, G.F. & Huang, X.H., Chaos on Phase Noise of Van Der Pol Oscillator, TELKOMNIKA, 8(3), pp. 301-308, 2010.

Agilent Technologies, Advanced Design System 2001 User's Guide, 2001.

Downloads

Published

2014-07-01

Issue

Section

Articles