Electrical fluctuations of a resistor in thermal equilibrium: measurement of Boltzmann’sconstant, and the Centigrade value of Absolute zero.

Lab manual version 0

Theory of Johnson, or Nyquist noise: Please refer to the chapter from Kittel, ElementaryStatistical Physics, which is posted online—especially to the transmission line derivation.

What you need to do this experiment:

1. The stuff in these two pictures. Please leave the lab looking like this when you are done.You won’t need the LN Dewar the first day.

OverviewIn this lab, you should spend a large fraction of the first day simply learning how to use the FFTspectrum analyzer, and understanding how to make your measurements. Section 1 will guideyou through this.

Section 2 will discuss measurements you will make of resistors at room temperature withdifferent values of resistance, which you can use to measure either the temperature (assumingyou know Boltzmann’s constant), or Boltzmann’s constant (assuming you know thetemperature). You will see that making quantitative measurements of the Johnson noise from aresistor requires care, as there are many other sources of noise which are not fundamental andwhich you will need to avoid.

Section 3 will discuss measurements of Johnson noise as a function of temperature. As of thiswriting, we have a set-up that works well to cool a resistor to liquid Nitrogen temperature, but noset-up to warm up resistors (it would be good to get them up to about 100 degrees C, but notmuch higher as then things will start to melt). You may want to think about making a set-up todo the warming experiments.

Section 1: Learn how to operate the SR760 FFT spectrumanalyzer.

Setting up the spectrum analyzer.

First, with NOTHING plugged in, turn on the spectrum analyzer.

Now we’ll go through essentially all of the relevant menus, so you can learn how this instrumentreally works and how to set it up to do what you want. This is a research grade instrument, thatyou will find in many labs. Please see section 5 of the manual for an explanation of all thebuttons and menus. This set of instructions may seem tedious, but please think about them asyou are going through them. You will need to make decisions about measurements later on inthe lab, and it will be from learning at this point that you will know how to set up the instrumentfor those measurements.

Frequency menu:

Press the button labeled “Freq”. Using “soft keys” (just to right of monitor), set the “Span” to100 kHz. Set the “Start” to 0 kHz. Note the Linewidth and the Acquisition time. What do thesemean? Please vary the Span, while keeping the Start at 0 kHz, and observe how the linewidthand Acquisition time vary. Please explain. (See section 3 of manual). Now, set the analyzerback to Span=100kHz, “Start=0 kHz).

Now, press “auto-range” button (this sets the pre-amplifier so it is amplifying as much as it canwithout overloading). Then press “auto-scale” button (this sets the scale to optimize viewing ofyour signal).

Input menu: Press button labeled Input. Using the soft menu keys,set the input source to Aset grounding to “ground” (you can see what difference it makes to float it. In ourmeasurements, since there will be no external ground, we will set the grounding to“ground.”)Set the coupling to DCThe input range was set by auto-range, so leave this alone. You can set it manually if youwish.Set the auto offset=on (read about what this does)

Measure menu: (this is a complicated on, which goes several levels deep)Press the Measure soft key (top one).

Now try each of the first three choices:SpectrumPSD (power spectral density—this is the one we want to stick with)Time recordExplain the difference between the Spectrum and PSD measurements.We will be using PSD almost exclusively in this lab.Press “return” to get back to the previous menu.

Press the Display soft key.Press Log Mag. What will you be measuring, in terms of the FFT?

Press the Meas soft keyPress Volts RMS. Given that we are eventually interested in white noise, whyis Volts RMS more useful than Volts Pk (peak)?

Press the Window soft keyPress BMH (Blackman-Harris window). What is “windowing” in a FFT? Whyis it important? (you might need to do a Google search or look in a book ondigital signal processing). This is not so important for this particularexperiment, but is a concept that will come up over and over with digitalsignal processing.

Display menu:Format=singleMarker=OnMarker width= normal (play with this. You may want to make it “wide” if you can)Marker seeks=mean.Grid div/screen=8 or 10 ( I like 10, it’s up to you)Graph style=line.

Average menu: You will be coming back to this one oftenAveraging=on (when you are changing things, it’s useful to turn this off so things“settle” more quickly, then turn it on when you are doing a measurement.”Number of averages=128 (you can play with this)

Average type=rmsAverage mode=exponential (when you are measuring, you will want to do repeated linearaverages. To start a linear average, you need to press the “start”button in the “controlbuttons at the top of the instrument panel) What is the difference between linear andexponential averaging?

The knob:The knob can change a numeric field in a menu (the one that is lit up). It can also movethe marker in frequency. The latter is more useful in general. To make the knob controlthe marker, press the “marker” button on the control section of the keypad.

Your first measurement

Whew!! You are now ready for your first measurement. We’ll begin by studying the SR760under the following conditions:

1. With nothing plugged into it.2. With the BNC-alligator cable plugged into input A, with alligator clips not connected to

each other or to anything else.3. With the BNC alligator clips shorted together.4. With the shorting cap attached directly to input A.

These seem like trivial conditions! But we will actually learn a lot about the instrument, as wellas about different sources of signal that will appear on the screen of the spectrum analyzer.

With nothing plugged into any inputs, and the instrument set up as above, Press the “Print”button under the System portion of the keypad to print out what you see on the screen. Makesure the printer is switched to “noise” and that there is paper in the printer. Paste this output intoyour lab notebook.