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Thermodynamical Phase Noise in Oscillators Based on L-C Resonators

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DOI: 10.4236/cs.2012.31009    5,231 Downloads   7,876 Views   Citations

ABSTRACT

Using a new Admittance-based model for electrical noise able to handle Fluctuations and Dissipations of electrical energy, we explain the phase noise of oscillators that use feedback around L-C resonators. We show that Fluctuations produce the Line Broadening of their output spectrum around its mean frequency f0 and that the Pedestal of phase noise far from f0 comes from Dissipations modified by the feedback electronics. The charge noise power 4FkT/R C2/s that disturbs the otherwise periodic fluctuation of charge these oscillators aim to sustain in their L-C-R resonator, is what creates their phase noise proportional to Leeson’s noise figure F and to the charge noise power 4kT/R C2/s of their capacitance C that today’s modelling would consider as the current noise density in A2/Hz of their resistance R. Linked with this (A2/Hz?C2/s) equivalence, R becomes a random series in time of discrete chances to Dissipate energy in Thermal Equilibrium (TE) giving a similar series of discrete Conversions of electrical energy into heat when the resonator is out of TE due to the Signal power it handles. Therefore, phase noise reflects the way oscillators sense thermal exchanges of energy with their environment.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

J. Malo and J. Izpura, "Thermodynamical Phase Noise in Oscillators Based on L-C Resonators," Circuits and Systems, Vol. 3 No. 1, 2012, pp. 61-71. doi: 10.4236/cs.2012.31009.

References

[1] J. I. Izpura and J. Malo, “Thermodynamical Phase Noise in Oscillators Based on L-C Resonators (Foundations),” Circuits and Systems, 2011, Article in Press.
[2] J. I. Izpura and J. Malo, “A Fluctuation-Dissipation Model for Electrical Noise,” Circuits and Systems, Vol. 2, No. 3, 2011, pp. 112-120. doi:10.4236/cs.2011.23017
[3] D. B. Leeson, “A Simple Model of Feedback Oscillator Noise Spectrum,” Proceedings of IEEE, Vol. 54, 1966, pp. 329-330. doi:10.1109/PROC.1966.4682
[4] D. Ham and A. Hajimiri, “Virtual Damping and Einstein Relation in Oscillators,” IEEE Journal of Solid-State Circuits, Vol. 38, No. 3, 2003, pp. 407-418. doi:10.1109/JSSC.2002.808283
[5] H. B. Callen and T. A. Welton, “Irreversibility and Generalized Noise,” Physical Review, Vol. 83, No. 1, 1951, pp. 34-40. doi:10.1103/PhysRev.83.34
[6] J. Malo and J. I. Izpura, “Feedback-Induced Phase Noise in Microcantilever-Based Oscillators,” Sensors and Actuators A, Vol. 155, No. 1, 2009, pp. 188-194. doi:10.1016/j.sna.2009.08.001
[7] T. H. Lee and A. Hajimiri, “Oscillator Phase Noise: A Tutorial,” IEEE Journal of Solid-State Circuits, Vol. 35, No. 3, 2000, pp. 326-336. doi:10.1109/4.826814
[8] A. Hajimiri and T. H. Lee, “A General Theory of Phase Noise in Electrical Oscillators,” IEEE Journal of Solid- State Circuits, Vol. 33, No. 2, 1998, pp. 179-194. doi:10.1109/4.658619
[9] E. Hegazi, J. Rael and A. Abidi, “The Design Guide to High Purity Oscillators,” Kluwer Academic, New York, 2005.
[10] J. I. Izpura, “1/f Electrical Noise in Planar Resistors: The Joint Effect of a Backgating Noise and an Instrumental Disturbance,” IEEE Transactions on Instrumentation and Measurement, Vol. 57, No. 3, 2008, pp. 509-517. doi:10.1109/TIM.2007.911642
[11] J. I. Izpura, “On the Electrical Origin of Flicker Noise in Vacuum Devices,” IEEE Transactions on Instrumentation and Measurement, Vol. 58, No. 10, 2009, pp. 3592- 3601. doi:10.1109/TIM.2009.2018692
[12] J. Malo, “Contribución al dise?o de lazos de realimentación Electrónica para sistemas electromecánicos (MEMS) resonantes: ruido de fase generado en lazos osciladores por sus realimentaciones,” PhD. Thesis, Chapter III (in Spanish) Universidad Politécnica de Madrid, Madrid, Article in Press, 2012, pp. 70-145.

  
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