Electrical fluctuations of a resistor in thermal equilibrium: measurement of Boltzmann’s
constant, and the Centigrade value of Absolute zero.
Lab manual version 0
Theory of Johnson, or Nyquist noise: Please refer to the chapter from Kittel, Elementary
Statistical 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.
Overview
In this lab, you should spend a large fraction of the first day simply learning how to use the FFT
spectrum analyzer, and understanding how to make your measurements. Section 1 will guide
you through this.
Section 2 will discuss measurements you will make of resistors at room temperature with
different values of resistance, which you can use to measure either the temperature (assuming
you know Boltzmann’s constant), or Boltzmann’s constant (assuming you know the
temperature). You will see that making quantitative measurements of the Johnson noise from a
resistor requires care, as there are many other sources of noise which are not fundamental and
which you will need to avoid.
Section 3 will discuss measurements of Johnson noise as a function of temperature. As of this
writing, we have a set-up that works well to cool a resistor to liquid Nitrogen temperature, but no
set-up to warm up resistors (it would be good to get them up to about 100 degrees C, but not
much higher as then things will start to melt). You may want to think about making a set-up to
do the warming experiments.
Section 1: Learn how to operate the SR760 FFT spectrum
analyzer.
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 instrument
really works and how to set it up to do what you want. This is a research grade instrument, that
you will find in many labs. Please see section 5 of the manual for an explanation of all the
buttons and menus. This set of instructions may seem tedious, but please think about them as
you are going through them. You will need to make decisions about measurements later on in
the lab, and it will be from learning at this point that you will know how to set up the instrument
for those measurements.
Frequency menu:
Press the button labeled “Freq”. Using “soft keys” (just to right of monitor), set the “Span” to
100 kHz. Set the “Start” to 0 kHz. Note the Linewidth and the Acquisition time. What do these
mean? Please vary the Span, while keeping the Start at 0 kHz, and observe how the linewidth
and Acquisition time vary. Please explain. (See section 3 of manual). Now, set the analyzer
back to Span=100kHz, “Start=0 kHz).
Now, press “auto-range” button (this sets the pre-amplifier so it is amplifying as much as it can
without overloading). Then press “auto-scale” button (this sets the scale to optimize viewing of
your signal).
Input menu: Press button labeled Input. Using the soft menu keys,
set the input source to A
set grounding to “ground” (you can see what difference it makes to float it. In our
measurements, since there will be no external ground, we will set the grounding to
“ground.”)
Set the coupling to DC
The input range was set by auto-range, so leave this alone. You can set it manually if you
wish.
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:
Spectrum
PSD (power spectral density—this is the one we want to stick with)
Time record
Explain 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 key
Press Volts RMS. Given that we are eventually interested in white noise, why
is Volts RMS more useful than Volts Pk (peak)?
Press the Window soft key
Press BMH (Blackman-Harris window). What is “windowing” in a FFT? Why
is it important? (you might need to do a Google search or look in a book on
digital signal processing). This is not so important for this particular
experiment, but is a concept that will come up over and over with digital
signal processing.
Display menu:
Format=single
Marker=On
Marker 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 often
Averaging=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=rms
Average mode=exponential (when you are measuring, you will want to do repeated linear
averages. To start a linear average, you need to press the “start”button in the “control
buttons at the top of the instrument panel) What is the difference between linear and
exponential averaging?
The knob:
The knob can change a numeric field in a menu (the one that is lit up). It can also move
the marker in frequency. The latter is more useful in general. To make the knob control
the 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 SR760
under 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 well
as 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. Make
sure the printer is switched to “noise” and that there is paper in the printer. Paste this output into
your lab notebook.