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Ver. AR
EE 210 Laboratory 08 Fall Semester
The purpose of this laboratory session is to study the transient response of RC networks and to
study the response of op amp integrator and differentiator circuits.
Pre-Lab Activities

1. Read the remainder of this handout.
2. Consider the RC circuit in Figure 1. Determine analytically the time constant if
   R = 2.7 kΩ and C = 0.22 μF. Repeat this time constant calculation for the
   parallel/series capacitor combinations given in steps 6 and 7 of experiment 1.
   You will compare actual time constants to these calculated time constants
   throughout the lab.
3. Upload your work to Canvas before the beginning of the lab.
   In-Lab Activities
   Required Items:
4. myDAQ
5. Parts Kit
6. Breadboard and wires
   Ver. AR
   Experiment 1: RC Network – Transient Response
   In this experiment, the transient response of an RC network will be studied. More
   specifically, a capacitor will be charged to a specified voltage and then discharged
   through a resistor. The charging/discharging will be accomplished by driving the RC
   circuit with a square wave that varies from 0 V to 5 V. The transient response of the
   capacitor voltage as it charges and discharges will be measured, so that the time
   constant associated with the network can be determined.
   Procedure:
7. Construct the network shown in Figure 1 on a prototyping board:
   a. Set up the myDAQ function generator to serve as a square wave
   input, vin, that varies from 0V to 5V with a frequency of 100 Hz.
   b. Select R = 2.7 kΩ and C = 0.22 μF.
   c. Connect channel 0 and channel 1 of the myDAQ oscilloscope to
   observe vin and vout, respectively.
8. Turn on the function generator. On channel 1, you should see a series of
   rising and falling exponentials (between 0 V and 5 V) in response to the
   square wave input.
9. Adjust the myDAQ oscilloscope to measure the transient response:
   a. Adjust the vertical position and the scale for channel 0 and channel 1
   and the timebase so that the waveform covers most of the screen
   vertically and that 2-3 periods of transient responses occupy the
   screen horizontally.
   b. Select the trigger for an edge-triggered rising slope on channel 1.
   c. Adjust the trigger level to just above the initial voltage (e.g.,
   approximately 0.1 V).
10. Measure the time constant of both the charging (driven) transient response
    and discharging (undriven) transient response using the cursor
    measurement feature of the myDAQ oscilloscope.
    a. Make sure the “Cursors On” box is checked, and make sure that both
    C1 and C2 are set for Channel 1. The cursors appear on the left side of
    the screen; click and drag to place them accordingly.
    Figure 1. RC network.
    vin vout
    +
    −
    R
    C
    +
    −
    Ver. AR
    b. To measure the time constant associated with the discharging
    waveform, move the first cursor bar (Cur1) to a point where the
    response begins its decay. Move the second cursor bar (Cur2) to the
    point where the voltage is 36.8% of its maximum value. The voltages
    for each cursor, along with the dT value (distance between the 2
    cursor bars) appear below the screen. Record this dT measurement
    on the lab worksheet – it is the time constant of this circuit. Also
    record the expected time constant from the prelab.
    c. To measure the time constant associated with the charging
    waveform, move the first cursor bar (C1) to a point where the
    response begins its rise. Move the second cursor bar (C2) to the point
    where the voltage is 63.2% of its maximum value. Record this time
    constant, as well.
11. Save a screen capture image of your oscilloscope display and upload it into
    the lab worksheet.
12. Repeat Steps 1-4, with the single 0.22 µF capacitor in Figure 1 replaced by
    two 0.22 µF capacitors in parallel. Record the expected and measured time
    constants on your worksheet.
13. Repeat Steps 1-4, with the single 0.22 µF capacitor in Figure 1 replaced by
    two 0.22 µF capacitors in series. Once again, record the expected and
    measured time constants on your worksheet.
    Q1 (answer on the lab worksheet): For each of the cases, compare your
    measured time constants (both charging and discharging) with the expected
    time constants (from prelab). Do your expected and measured values match
    each other (within 10%)? If not, why do you suspect they don’t match?
14. Going back to the single capacitor circuit, gradually increase the frequency
    of the square wave and observe what happens to the amplitude and shape
    of the output waveform at high frequencies.
    Q2 (answer on the lab worksheet): Explain (in terms of the time constant) what
    is happening as the square wave frequency increases. At what input signal
    frequency does the output no longer cover the entire 0V to 5 V range? Does this
    make sense mathematically?
    Ver. AR
    Experiment 2: Op amp Integrator and Differentiator
    In this experiment you will use a capacitor in the feedback path of an inverting amplifier
    to create an integrating amplifier. The output of an integrating amplifier is the integral
    of the input signal. You will then modify this circuit to create a differentiator.
    Procedure:
15. Before constructing the circuit, it is important that you first make sure your
    0.22 F capacitor is discharged (this will make sense shortly). To do this,
    construct a simple undriven parallel RC circuit using the 0.22 F capacitor
    and a 330 Ω resistor. Simply connect these two components in parallel, then
    wait a few seconds to allow the capacitor to discharge fully through the
    resistor. Then, remove the capacitor for use in the circuit shown in figure 2.
16. Construct the circuit shown in Figure 2 with C1 = 0.22 F and R1 = 1 kΩ. Do
    not connect the function generator yet.
17. Connect the oscilloscope to monitor both vin and vout.
18. Before connecting the function generator (vin) to the circuit, set it to a 200
    Hz, 2 Vpp, square wave with a zero volt DC offset and click “Run”. Then, as
    the final step, connect the function generator to the circuit.
19. Measure the amplitude and mean of both vin and vout and record both on
    the lab worksheet.
    Note: If the waveform is not stable on the display, you may stop the
    oscilloscope to freeze the display before taking measurements.
20. Save a screen capture image of your oscilloscope display and upload it into
    the lab worksheet.
21. Now, manually remove the function generator connection from the circuit
    (without turning it off), then reconnect it again. Repeat this a few times. Take
    note of how the oscilloscope display changes.
    Figure 2. Integrating amplifier.
    R1
    C
    1
    vout
    vin
    −
    +
    +
    −
    +
    −
    
    Ver. AR
    Q3 (answer on the lab worksheet): Consider the process outlined in step 1, as
    well as the results observed in step 7. Explain what gives rise to the behavior
    observed in step 7. What aspect of the procedure in step 1 prevents the results
    observed in step 7?
22. Try other waveforms as input signals to the amplifier. For example, set vin to
    be a sine wave, triangle wave, etc. Also, change the frequency of the input
    signal and observe what happens. Note: You may want to repeat the
    procedure outlined in step 1 before trying this.
    Q4 (answer on the lab worksheet): If the input is a sine wave, what is the shape
    of the output signal and what happens to the amplitude of the output signal as
    the frequency of the input signal increases?
23. Exchange the positions of the capacitor and resistor in Figure 2. This turns
    the circuit into a differentiator circuit. Since differentiator circuits tend to
    amplify noise, a modification to the circuit is needed to control this. A
    simple fix is to add a 68 Ω resistor in series with the capacitor. Why this
    works is beyond the scope of this course.
24. Set vin to be a triangle wave with amplitude 2Vpp and frequency 1 kHz.
    Display the input and output on the oscilloscope.
25. Save a screen capture image of your oscilloscope display and upload it into
    the lab worksheet.
    Q5 (answer on the lab worksheet): What would happen to the amplitude of the
    output as the frequency of the input signal increases? Explain why this is.

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