On Measuring Johnson (thermal) Noise Generated by Resistors (A list of References)
While designing our newest experiment for measuring the Johnson (thermal) noise generated by resistors, we came across many relevant and interesting references. Our sources for these references range from GoogleTM to the many electronics hobbyists and professionals who volunteered time and helpful comments during the development of the “JCan” experiment. Our approach is different from most experiments discussed below, yet the basic concepts, discussions, and other approaches are interesting. Please see our observations on Copyright with respect to these references below.
Our Johnson Noise Can "JCan" Project:
Joe Geller, “Build a JCan to Measure Resistor Noise”, July, 2007, JCan Article reprinted by permission of T&L Publications, Inc.
related: "Use resistor noise to characterize a low-noise amplifier", Measure gain or noise with an AC voltmeter, Joe Geller, edited by Martin Rowe and Fran Granville, EDN, June 23, 2011
Of particular pleasure is the new trend for universities to post lab experiments and excerpts of text books on the Internet for anyone to view. We list below several different representative approaches to measuring resistor noise used in university curriculum.
The University of Sheffield, Department of Physics and Astronomy, "Johnson Noise", "E17", March, 2006.
Johnson Noise and Shot Noise, MIT Department of Physics, September 6, 2006.
Field Effect Transistors and Noise, Physics 3330 Experiment #8, Experiment #8 8.1, University of Colorado, Boulder, Fall 2005 (the link is broken, just GoogleTM "Field Effect Transistors and Noise, Physics 3330").
EXPERIMENTAL PHYSICS, Notes for Course PHYS2350, Prof. Jim Napolitano, Department of Physics, Rensselaer Polytechnic Institute, Spring 1999, chapter 13 “Noise and Noise Reduction” page 227, chapter 14 “Experiment 7: Johnson Noise”, page 251.
“Thermal Johnson Noise Generated by a Resistor”, UCDavis.
Chapter 5 and Experiment, Georgia Tech ece6416, undated, a composite JFET / OpAmp input circuit similar to the one used the JCan experiment.
J.B. Johnson, “Thermal Agitation of Electricity in Conductors”, Physical Review, vol. 32, July, 1928, page 97.
L. Callegaro, et. al., “Very simple FET ampliﬁer with a voltage noise ﬂoor less than 1 nV/√Hz”, Istituto Nazionale di Ricerca Metrologica (INRIM), arXiv.org, Cornell Library, Nov. 18, 2008. This is very much like the JCan BF244/LT1028 composite front end amplifier. Instead of AC coupling the JFET drain to the OpAmp virtual common, the OpAmp is used to establish a DC feedback loop which sets the drain voltage to a reference voltage at the OpAmp non-inverting input. That is, the OpAmp supplies the JFET IDss constant current via the OpAmp feedback resistor, which here is also the drain resistor for the common source stage. The closed loop is only to establish the DC constant drain current (IDss), the composite front end AC circuit is open loop. The author does not discuss the battery voltage, it is not clear if Vds is being set by the natural Idss for Vgs of zero, or if they are somehow forcing the quiescent point by varying the output voltage via the OpAmp output. In any event, beyond the DC IDss servo, use of the OpAmp virtual common to reduce Miller effect is about the same as our JCan composite input circuit. The OpAmp "driven" virtual common (DC here, small signal by the 1 uF coupling capacitor in the JCan) is believed to be what supplies the cascode effect, the impedance conversion which reduces the Miller capacitance. For example, in the JCan composite input circuit, the small signal RL for the input common source BF244 stage is the 1k resistance in parallel with the 1 uf capacitor to virtual common, so the JFET stage alone has a gain of <1, serving as an ultra low noise, low capacitance impedance transformation. In this article, the JFET small signal RL is even lower, the boot strapped 1 k ohm R in parallel with direct connection to the virtual common of the OpAmp. The operative aspect of this approach appears to be a small signal JFET with the source connection coupled directly to small signal common and a very low small signal RL impedance. Since Miller capacitance is proportional to Av for the common source JFET circuit topology, Av<1 means little contribution of Cgd as additional Miller input capacitance. This group went on to use two of these input stages in a pseudo-differential configuration to do Johnson noise thermometry, “An absolute Johnson noise thermometer”.
Jefferts, Steven R.; Walls,“A very low-noise FET input amplifier”, F. L., Review of Scientific Instruments (ISSN 0034-6748), vol. 60, June 1989, p. 1194-1196. I came across this article in 2012, an interesting design approach with detailed analysis. Compare with the front end JFET circuit of the hp 400GL PDF, where the original 400GL pre-amp used several feedback paths (see manual), note the addition of the new cascode JFET.
Horowitz and Hill, “The Art of Electronics”, Cambridge University Press, 1986, Section 7.10, “Origins and kinds of noise”, pages 288-290; 3. Section 7.20, “Bandwidth limiting and rms voltage measurement, page 306. (There is a newer 2nd edition, possibly a 3rd in the works?).
Profs. Jacob Millman and Christos Halkias, “Integrated Electronics: Analog and Digital Circuits and Systems”, Columbia University, 1977, pages 401-405.
Prof. Lloyd P. Hunter, “Handbook of Semiconductor Electronics”, Department of Electrical Engineering, University of Rochester, 1962, Chapter 11. (This reference was given to me by Gray Berry, K2SJN).
Manuals: hp 400 manuals, notes on the hp 3400A thermal true RMS AC voltmeter.
Don Tuite, Understanding Noise Terms In Electronic Circuits, March 02, 2012
, Noise 101, EDN, January 8, 2004.
New 1/f Noise Discovery Promises To Improve Semiconductor-Based Sensor, May 10, 2007.
Rarely Asked Questions... Resistor Noise can be Deafening, and Hard to Reduce, September 24, 2007, Design News and EDN, sponsored by Analog Devices.
Linear Technology, DN15 Noise Calculations in Op Amp Circuits.
Linear Technology, Application Note 83 , Jim Williams and Todd Owen, Performance Verification of Low Noise, Low Dropout Regulators, March 2000, see another noise measuring device in a cookie tin and notes on AC Voltmeters in Appendix C. Note that with "self calibration" to the Johnson curve, the meter errors discussed in AN-83 are less of a concern for the JCan. On the other hand, if you are shopping for a bench AC milliVoltmeter, you might consider a thermal based RMS measurement. Thanks to Jack Walton of Tech-DIY LLC for bringing this tech. note to the list (8/12/07).
National Semiconductor, “Noise Specs Confusing?”, National Semiconductor, Application Note 104, May 1974.
TI Application Note: Noise Analysis In Operational Amplifier Circuits (Rev. B), May 2007.
Agilent, “Fundamentals of RF and Microwave Noise Figure Measurements”, Application Note 57-1.
Agilent, “Noise Figure Measurement Accuracy-The Y-Factor Method”, Application Note 57-2.
Agilent, “10 Hints for Making Successful Noise Figure Measurements”, Application Note 57-3.
Manuals: hp 400 manuals, notes on the hp 3400A thermal true RMS meter.
B. Klein, N. Albaugh, “Amplifier Noise: Types, Origins, Magnitude Predictions and Reduction Techniques”, March, 2005.
Terry Ritter, Measuring Junction Noise, Random Electrical Noise: A Literature Survey, February 13, 2006.
Thermal Noise Calculator
A Bibliography on 1/f Noise
Jim Lesurf , Sources of Noise, University of St. Andrews, Scotland.
Notes on Noise and OpAmp circuits, Electronics Design Lab, Kansas State University.
Copyright Notice: We post here links to many materials that we found publicly available on the Internet. It is likely that some of these posts might not have been intended for public use, or might have been posted by one or more individuals in violation of the rights of the holder(s) of the copyright. It is also likely that some of these materials might be removed from public access; please let us know if any of the links fail. Also, and perhaps most important, if you see an excerpt from a textbook that looks generally interesting to you, we urge you to purchase the book where practical. Finally, we urge caution in copying any of these references further or any use of these references other than for personal use while learning more about noise measurements. The prudent thing to do would be to contact the author(s) and/or publishers before using these materials beyond personal use. Where there is no URL, we used an original paper copy and are unaware of copies on the net.
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