Lab manual version 0

Transcription

1 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.

2 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).

3 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)

4 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.

5

6

7

8

9