Lab 1: LabView (1 Week)

• Work through Ch. 1-2 of Essick. Also make the "Do It Yourself" projects at the end of Ch. 1 and Ch. 2. Submit your work as described in the SmartSite Lab Assignment.

Lab 2: LabView (1 Week)

• Work through Chapters 3 and 5 of Essick. Also make the "Do It Yourself" (DIY) projects at the end of Ch. 3 and Ch. 5 (amplitude modulation is discussed in Sec. 10.6 of Bobrow).

Lab 3: LabView (1 Week)

• Work through Chapter 4 of Essick (this requires the lab computers with National Instruments data acquisition PCI cards). Do as many of the examples in Chapter 4 as possible in the time available. The "Do-It-Yourself " at the end of Ch. 4 is not assigned this time. Additional LabVIEW work during week: Essick, Chapter 6 plus "Do-It-Yourself" project at the end of Ch. 6. See SmartSite Assignments for deadlines.

Lab 4: Geiger Counter (~2Weeks)

• Start Geiger Counter and Counting Statistics Lab (details in SmartSite Assignments)

Lab 5: Muon Lifetime

• Start Muon Lifetime lab. See information in SmartSite Resources under Labs/Muon Lifetime. You will all follow the exercises at the end of the Muon Manual excluding varying the High Voltage. Groups will sign up for lab time outside of normal lab for ~2hr intervals and take data for 24hrs.

Lab 6: LabView (1 Week)

• do the exercises in Ch. 10 of Essick. You do not need to do the "do-it-yourself" at the end. Next week you will use a pre-built DAQ VI (based on techniques in Ch. 10 and 11) to collect data and do FFT spectral analysis of a Johnson noise source.

For further reading see below:

Horowitz and Hill References
Differential and instrumentation amplifiers: Ch. 7, 421-428
Amplifier noise: Ch. 7, 428-455
Interference, shielding and grounding: Ch. 7, 455-466
A/D conversion: Ch. 9, 613-641
Active filters: Ch. 5, 263-281
Coaxial cables: Ch. 13, 879-880.

Lab 7: Johnson Noise (~2 Weeks)

• Johnson Noise Lab: The goal of the lab is to make a plot of output noise power times BW vs. R. The slope will be used to determine Boltzmann's constant, k. We will also compare the results with the expected Johnson noise from the resistors and the amplifier.
  • Here is the writeup for the Physics 122 Johnson noise experiment. It gives an overview of the subject and theory. The LabVIEW version of the experiment is similar, but our circuit, VI and procedures are different. See below.
  • Reference for the procedure and circuit we will use:
    • Melissinos and Napolitano (M&N), Experiments in Modern Physics, 2nd. Ed., Sec. 3.6, "Measurements of Johnson Noise."
    • Links near the bottom of the page give leads to the history of Boltzmann's entropy formula and connections with statistical mechanics, information theory and cosmology.
  • Here is a checklist for the writeup for the experiment. A complete writeup in the form of a brief technical report is required.
  • Our circuit (available here with additional notes) uses a different low-noise op-amps from the ones indicated in the reference. We use the LT1793 op-amp for the first stage and the AD797 for the second stage. An LF411 is used to make a 2-pole Butterworth low-pass filter (see Horowitz and Hill, Secs. 5.06 and 5.07). Note that the LT1793 has low voltage noise and extremely low current noise specifications. This will allow us to use relatively large resistance values where the thermal noise from the resistor will greatly exceed the amplifier contribution.
  • The Johnson Noise Test Fixture (JNTF): for this experiment, you will use a pre-built circuit for the amplifier and filter for better performance and to save time wiring (the circuit diagram is here). It has +15 V, -15 V and ground connections (wires color-coded to match the binding posts on the circuit test boards), a BNC output jack and a threaded SMA input connector for the calibration signal or for an external resistor. A multiple positiion switch allows you to connect one of the following 0.5% metal film resistors to the input. Note the labels differ from the nominal (and actual) values in some cases! The nominal values are given below.

    Label

    Short

    300

    1K

    3K

    6K

    10K

    30K

    60K

    100K

    500K

    1M

    Ext

    Resistor Nominal Value

    0 Ohms

    301

    1.00 K

    3.16 K

    6.03 K

    10.0 K

    24.3 K

    60.4 K

    100. K

    499 K

    1.00 M

    SMA Input

  • Accurately measured values of resistance are given in a chart linked here.
  • Key points for measurement (see our circuit diagram):
    • Measure and plot g(f), the gain of the amplifier as a function of frequency, using the function generator, voltage divider and accurate wide-band digital multimeter (DMM). It is sufficient to check for midband flatness plus a few points near the corner frequency and beyond rather than to do a detailed measurement of the entire function. Be sure the high frequency corner frequency is as expected (16 kHz), the low frequency is still flat in the range 100 Hz to 1 kHz and that the gain is down by an order of magnitude by the Nyquist critical frequency (100 kHz). Use the provided approx. 1000:1 voltage divider (in a shielded box) between the signal generator output and the JNTF external input. Use shielded cables for connections to prevent pickup of interference. Measure the voltage divider voltage ratio and note the accuracy of your measurement. Check that the midband gain G agrees with the stated value for your JNTF in the chart available in the lab.
    • Connect the circuit output to the NI ADC using a nonreferenced single-ended (NRSE) input with voltage range from -0.5 V to 0.5 V (use analog input 0)..
    • The power spectrum will be measured using the VI on SmartSite (Scope_Spect_mod_nw_mod.vi). It also displays a histogram and waveform plots of the sampled noise waveform. The number of points should be 8192 and the sampling frequency should be 200000. The spectrum should extend from 0-100 kHz in bins 0-4096
    • Start with the100 kilohm 0.5% metal film resistor as the noise source. The spectrum should have the same shape as your amplifier gain vs. frequency curve if the signal is dominated by Johnson noise (either from the amplifier or the resistor). There may be some additional pickup of signals from 60 Hz AC (and harmonics). These should show up as peaks at the low end. But there should be a region which is fairly flat within the amplifier bandwidth (perhaps from approx. 1 kHz to 8 kHz – calculate which channels correspond to this frequency interval). If there is excessive pickup, check the wiring.
      • The sum of the squares of the amplitudes of the FFT components within these limits (f₁ to f₂) will correspond to a measurement of <V²>, the mean squared output voltage in that bandwidth. For an explanation, refer to these notes.
      • For each resistor value, you will need to sum the channels of interest for a single measurement. Repeat at least N=10 times to get a more accurate mean value for <V²> and an estimate of its standard deviation, sigma. The error in the mean value of <V²> will be sigma/(square root of N). You should automate this procedure in your VI. The VI is set up to make multiple measurements of <V²> but you will need to modify it to calculate the desired statistics and write an output file of the measurements if desired.
      • Repeat for other resistor values available in the JNTF.
      • Find and plot <V²> vs. R with errors and fit to a straight line (two parameter fit). (See example in SmartSite wiki on linear least squares fit with errors.)
        • This linear fit corresponds to the function <V²> = (e_A² + 4kTR)G²(f₂-f₁), where
          • e_A² represents the noise contribution from the amplifier (amplifier current noise component should be negligible with LT1793)
          • G² is the average of the square of the gain of the amplifier g(f) over the frequency range used. If you use the range 1 kHz - 8 kHz, this should be reasonably constant.
          • If g(f) is not sufficiently constant over your interval, you would have to find the integral from f₁ to f₂ of g²(f) df. This should not be necessary if the system is functioning properly.
          • Be sure to record the ambient temperature T from the thermometer in the lab.
          • The parameters e_A² and Boltzmann's constant k can be found from the fitted parameters. Find the errors in these quantities from the fit covariance matrix (using propagation of errors as appropriate).
          • Compare with the accepted value of Boltzmann's constant.
          • Compare e_A with what you expect from the op-amp specifications in a non-inverting amplifier configuration (see Horowitz and Hill, p. 447).
  • Reference for the procedure and circuit: Melissinos and Napolitano (M&N), Experiments in Modern Physics, 2nd. Ed., Sec. 3.6, "Measurements of Johnson Noise."
    

Lab 8: PID Temperature Controller Lab (~2 Weeks)

• The upcoming labs (weeks 9 and 10) concern measuring temperature using a thermistor (Essick, "Do It Yourself" at the end of Ch. 9) and manipulating the temperature of an aluminum block with a PID temperature controller (Ch. 12 and Appendix I). Our version of the device in Appendix I has already been constructed. It includes the TE device driver (Fig. A.9) but you will have to provide the op-amp and and 470 Ohm resistor shown in Fig. A.7. Only general guidelines are given in Essick for the VI for PID control.
• The overall procedure (including temperature measurement) is outlined in Sec. 12.3 of Essick.
  • Read the above material in Essick.
  • Keep up your individual lab notebook for this project. This lab (PID temperature controller) will require a brief writeup when you are finished.
    • Here is a file (text file, tab-delimited with title and column header lines) of resistance vs. temperature data for the thermistor we will use. Use this instead of the R vs. T data in the text.
    • To save you time, we have already fitted the transformed R-T data with a third order polynomial in x (see Essick, pp. 321, 329). Note that this is not the Steinhart-Hart Equation since we have kept the second order term. Since we did not need to a fit with errors here, we just used a spreadsheet to do the fit. You should use this function to calculate T from a given voltage reading. The fitted function was y(x) where y = 1/T and x = lnR (with T in K and R in ohms). A plot of the data and the function (with the resulting equation) are here.
  • Information about thermoelectric devices from Tellurex
  • Begin by getting the temperature measurement going (aim to have this running during Week 9).
    • Wire the constant current driver circuit for the thermistor. Set the negative op-amp voltage to -12 V rather than -15 V to be compatible with the fan voltage for the heatsink fan of the temperature controller.
    • Measure and record the current going to the thermistor (don't rely on calculations).
    • Make the Digital Thermometer VI. This is even more of a do-it-yourself project than indicated in Ch. 9. You need to read the resistor voltage and convert to temperature using the parameters from the third order fit rather than using the Steinhart-Hart parameters and the Express VI temperature measurement (should not be very hard to do). Use the thermistor in the temperature control setup.
    • Check the thermistor temperature reading at room temperature using a thermometer provided. You can insert the end of it in the open end of the hole containing the thermistor (be careful not to dislodge the thermistor).
  • Develop the PID algorithm. This can be done outside of class.
  • Put together the circuit for the controller. Start on this during Week 9 if possible.
  • Be sure to use the large variable supplies (one per voltage) for +8 V and -8 V. The outputs of these supplies are floating. If you hook the + input to ground, the - input will be negative the indicated voltage. The supplies do not have their own ground points (other than the safety ground on the power plug). Connect the + input of one supply to the - input of the other. This common connection should then be connected to the breadboard ground banana plug. The remaining connections become the + and - supply voltages. Also hook the the ground lead from the thermoelectric device (black banana plug) to this common ground using a heavy banana plug lead since this is a high current return path.
  • Once you have your controller working, you should investigate the PID controller performance.
    • If you haven't done so already, add a "waveform chart" display of the temperature as a function of time. Then investivate the effect of the parameters on the waveform. Here are suggestions on tuning the parameters. Further information on the PID algorithm as applied to oven control (heater only) is also available from the site.
    • If possible, add the possibility of inhibiting the integral term until you are close to equilibrium. Otherwise, it takes a long time to overcome the accumulated error when changing the set point.
  • For your (brief) writeup, include an overview of the PID algorithm, your circuit and VI diagrams, a discussion of the performance of the system and a plot of temperature vs. time showing behavior after changing the set point (see checklist below). Turn in the report at the end of the lab on Wednesday, June 2.
    • Here is a checklist of points to address in your lab writeup (version modified for 2011: only the due date is changed).
• More information on temperature measurement and thermistors:
  • Horowitz and Hill (H&H), Ch. 15 has a good overview of many measurement transducers and techniques. There is a discussion of thermistor and thermocouple accuracy in H&H, Sec. 15.01. They state that thermistors are available with "tight conformity (0.1–0.2° C) to standard curves." This is better than what they claim for thermocouples (0.5 to 2° C). Here is a quick guide from the web which compares thermocouples, thermistors and a third device, the resistance temperature detector (RTD).
  • Here is the datasheet on BC Components negative temperature coefficient (NTC) thermistors covering the device we use (2232 640 5 5103). It contains data needed to estimate temperature measurement accuracy (see the the next reference).
  • Here is a thermistor selection guide discussing the Steinhart-Hart equation and thermistor accuracy from Vishnay, a corporation which acquired BC Components in 2002.