A Fluctuation-Dissipation Model for Electrical Noise

Jose-Ignacio Izpura, Javier Malo

.

DOI: 10.4236/cs.2011.23017                

Abstract

This paper shows that today’s modelling of electrical noise as coming from noisy resistances is a non sense one contradicting their nature as systems bearing an electrical noise. We present a new model for electrical noise that including Johnson and Nyquist work also agrees with the Quantum Mechanical description of noisy systems done by Callen and Welton, where electrical energy fluctuates and is dissipated with time. By the two currents the Admittance function links in frequency domain with their common voltage, this new model shows the connection Cause-Effect that exists between Fluctuation and Dissipation of energy in time domain. In spite of its radical departure from today’s belief on electrical noise in resistors, this Complex model for electrical noise is obtained from Nyquist result by basic concepts of Circuit Theory and Thermo-dynamics that also apply to capacitors and inductors.

Keywords

Admittance-Based, Noise Model, Fluctuation, Susceptance, Dissipation, Resistance

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	L. Callegaro, “Unified Derivation of Johnson and Shot Noise Expressions,” American Journal of Physics, Vol. 74, No. 5, 2006, pp. 438-440. doi:10.1119/1.2174034
[2]	J. B. Johnson, “The Schottky Effect in Low Frequency Circuits,” Physical Review, Vol. 26, No. 1, 1925, pp. 71-85. doi:10.1103/PhysRev.26.71
[3]	G. Gomila, C. Pennetta, L. Reggiani, M. Sampietro, G. Ferrari and G. Bertuccio, “Shot Noise in Linear Macroscopic Resistors,” Physical Review Letters, Vol. 92, 2004, Article ID: 226601. doi:10.1103/PhysRevLett.92.226601
[4]	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
[5]	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
[6]	J. I. Izpura and J. Malo, “Noise Tunability in Planar Junction Diodes: Theory, Experiment and Additional Support by SPICE,” TAEE’2006 Conference, Madrid, July 2006. http://taee.euitt.upm.es/Congresosv2/2006/papers/2006S1F02.pdf
[7]	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
[8]	M. Sampietro, L. Fasoli and G. Ferrari, “Spectrum Analyzer with Noise Reduction by Cross-Correlation Technique on Two Channels,” Review of Scientific Instrumentation, Vol. 70, No. 5, 1999, pp. 2520-2525. doi:10.1063/1.1149785
[9]	J. B. Johnson, “Thermal Agitation of Electricity in Conductors,” Physical Review, Vol. 32, No. 1, 1928, pp. 97-109. doi:10.1103/PhysRev.32.97
[10]	H. Nyquist, “Thermal Agitation of Electric Charge in Conductor,” Physical Review, Vol. 32, No. 1, 1928, pp. 110-113. doi:10.1103/PhysRev.32.110
[11]	D. A. Johns and K. Martin, “Analog Integrated Cicuit Design,” John Wiley & Sons, New York, 1997.
[12]	“Dual Low Noise, Picoampere Bias Current, JFET Input Op Amp,” http://www.datasheetcatalog.org/datasheet/lineartechnology/1169fa.pdf
[13]	C. D. Motchenbacher and F. C. Fitchen, “Low Noise Electronic Design,” John Wiley & Sons, New York, 1973.
[14]	D. A. Bell, “Noise and the Solid State,” Pentech Press, London, 1985.
[15]	J. Malo and J. I. Izpura, “Feedback-Induced Phase Noise in Microcantilever-Based Oscillators,” Sensors and Actuators A: Physical, Vol. 155, No. 1, 2009, pp. 188-194. doi:10.1016/j.sna.2009.08.001
[16]	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
[17]	J. Malo, Ph.D. Thesis, Chapter III (in Spanish). Universidad Politecnica de Madrid, Madrid, pp. 70-145.