Thermodynamical Phase Noise in Oscillators Based on *L-C* Resonators (Foundations)

ABSTRACT

By a Quantum-compliant model for electrical noise based on Fluctuations and Dissipations of electrical energy in a Complex Admittance, we will explain the phase noise of oscillators that use feedback around L-C resonators. Under this new model that departs markedly from current one based on energy dissipation in Thermal Equilibrium (TE), this dissipation comes from a random series of discrete Dissipations of previous Fluctuations of electrical energy, each linked with a charge noise of one electron in the Capacitance of the resonator. When the resonator out of TE has a voltage between terminals, a discrete Conversion of electrical energy into heat accompanies each Fluctuation to account for Joule effect. This paper shows these Foundations on electrical noise linked with basic skills of electronic Feedback to be used in a subsequent paper where the aforesaid phase noise is explained by the new Admittance-based model for electrical noise.

By a Quantum-compliant model for electrical noise based on Fluctuations and Dissipations of electrical energy in a Complex Admittance, we will explain the phase noise of oscillators that use feedback around L-C resonators. Under this new model that departs markedly from current one based on energy dissipation in Thermal Equilibrium (TE), this dissipation comes from a random series of discrete Dissipations of previous Fluctuations of electrical energy, each linked with a charge noise of one electron in the Capacitance of the resonator. When the resonator out of TE has a voltage between terminals, a discrete Conversion of electrical energy into heat accompanies each Fluctuation to account for Joule effect. This paper shows these Foundations on electrical noise linked with basic skills of electronic Feedback to be used in a subsequent paper where the aforesaid phase noise is explained by the new Admittance-based model for electrical noise.

KEYWORDS

Admittance-Based; Noise Model; Energy Dissipation; Energy Conversion into Heat; Phase Noise

Admittance-Based; Noise Model; Energy Dissipation; Energy Conversion into Heat; Phase Noise

Cite this paper

J. Izpura and J. Malo, "Thermodynamical Phase Noise in Oscillators Based on*L-C* Resonators (Foundations)," *Circuits and Systems*, Vol. 3 No. 1, 2012, pp. 48-60. doi: 10.4236/cs.2012.31008.

J. Izpura and J. Malo, "Thermodynamical Phase Noise in Oscillators Based on

References

[1] 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

[2] 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

[3] H. Nyquist, “Thermal Agitation of Electric Charge in Conductors,” Physical Review, Vol. 32, 1928, pp. 110-113. doi:10.1103/PhysRev.32.110

[4] J. I. Izpura, 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

[5] 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

[6] J. Malo and J. I. Izpura, “Feedback-Induced Phase Noise in Resonator-Based Oscillators,” Proceedings of DCIS’09 Conference, Zaragoza, November 2009, pp. 231-236. http://www.linkpdf.com/ebook-viewer.php?url=http://dcis2009.unizar.es/FILES/CR2/p5.pdf

[7] 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

[8] D. Ham, 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

[9] A. Hajimiri, 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

[10] T. H. Lee, 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

[11] http://www.ti.com/lit/an/slod006b/slod006b.pdf

[12] 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

[1] 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

[2] 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

[3] H. Nyquist, “Thermal Agitation of Electric Charge in Conductors,” Physical Review, Vol. 32, 1928, pp. 110-113. doi:10.1103/PhysRev.32.110

[4] J. I. Izpura, 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

[5] 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

[6] J. Malo and J. I. Izpura, “Feedback-Induced Phase Noise in Resonator-Based Oscillators,” Proceedings of DCIS’09 Conference, Zaragoza, November 2009, pp. 231-236. http://www.linkpdf.com/ebook-viewer.php?url=http://dcis2009.unizar.es/FILES/CR2/p5.pdf

[7] 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

[8] D. Ham, 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

[9] A. Hajimiri, 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

[10] T. H. Lee, 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

[11] http://www.ti.com/lit/an/slod006b/slod006b.pdf

[12] 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