Lab-in-a-Box
Experiment 17: An Integrator Circuit
Name: ______
Pledge: ______
ID: ______
Date: ______
Procedure
Analysis:
1. Derive the input-to-output relationship of the amplifier circuit shown in Figure 1 as given in Eq (1). Which trim pot is required to have a unity gain over the desired operating frequency of 500 Hz to 3000 Hz? Note that the output of the circuit is negative. If a positive sawtooth is desired, you may use a unity gain op amp inverter circuit following the output of the integrator.
Figure 1: An ideal integrating op amp circuit.2. Select the values of the components required such that the integrator circuit of Figure 2 will have a gain of unity at 1500 Hz. Determine the values of R1, R2, and R4 based on the information provided in the Background. R1 should be a trim pot, or a combination of a trim pot and a fixed resistor with sufficient range to allow the frequency of the output pulse train be varied from 500 Hz to 3000 Hz and still maintain unity gain at the operating frequency.[†] Use a 0.1 μF capacitor for C1. Round your remaining component values to the nearest components available in your kit (see Appendix A).
Figure 2: A practical op amp integrator circuit.
Modeling:
3. Using the component values determined in step 1, model the circuit of Figure 1 in PSpice. Use a bipolar ±1.0 V amplitude pulse train as the input signal with frequencies (f) varying from 500 to 3000 Hz in steps of 500 Hz. For each frequency, adjust the value of R1 to obtain an output signal of amplitude -1.0 V. Tabulate the values of R1 for each frequency. Hint: instructions for sweeping a trim pot in PSpice may be found on the book WWW site at http://www.wiley.com/college/Hendricks.
4. Using your choice of a scientific graphing program (e.g., Excel or MATLAB), plot a graph (in log-log space) of the value of R1 versus f. Do not plot data points, but only plot a line joining the data points. Save your graph for use in step 17.
5. Do your results agree with the condition? Hint: rearrange this expression and plot it on the graph created in step 4.
6. Repeat steps 3 through 5 for the circuit in Figure 2 using the component values computed in step 2. Save your graph for use in step 27.
7. What effect, if any, do R2 and R3 have on the performance of the circuit as compared to the circuit of Figure 1 in the frequency range Hz? Hint: to model the circuit of figure 1 using the circuit of Figure 2, let R2=100G and R4=0.001. Explain the drift of the sawtooth output versus time in the circuit of Figure 2.
Measurements (Ideal Integrator):
8. Construct the integrator amplifier circuit shown in Figure 1. Notes: (a) Use the - 9 V and + 9 V supplies of the ANDY board to power the op amp. See Figure 28 in Section 2.12 for the pinouts of the LF356 op amp. (b) Use the ANDY board function generator with the shape set to SQ and the OFFSET set to zero for the input signal. (c) Be careful to use the center terminal and one end terminal of the trim pot. Following the “good practice” notes in Section 2.11, tie the unused terminal of the trim pot to the wiper of the pot. (d) Use a shorting wire from the inverting input of the op amp to the output to discharge the feedback capacitor before measuring the output waveform. Remove the wire to start making measurements. [See figure (2).]
9. Connect the output of the function generator to the ´10 attenuator of Channel 1 (green) to the oscilloscope and the output of the op amp to the ´10 attenuator of Channel 2 (red).
10. Adjust the frequency of the function generator (green trace) to produce a 500 Hz square wave. You may observe the signal frequency in the oscilloscope mode or you may change the view by pressing the “Frequency Analysis” tab at the top of the oscilloscope screen. In the latter view, you should see a single peak at the frequency of the source. You can determine the frequency by reading the “main frequency” just below the frequency distribution.
11. Adjust the amplitude of the function generator to ± 1.0 V. Be very careful to adjust the voltages to be as symmetric as possible. Remember that you are using the ´10 attenuator, so you should read 0.1 V amplitude on the oscilloscope screen and interpret it as 1.0 V.
12. Observe the output of the op amp on the oscilloscope (red trace). It should be a triangular wave of the same frequency as the function generator. Verify the frequency in either the “Oscilloscope” or the “Spectrum” mode of the oscilloscope. Record a screen shot of your output.
13. Adjust the trim pot R1 to produce an output signal of amplitude 1.0V.
14. Record your observations of the ease/difficulty with which you are able to construct and operate this circuit. Do you observe the result predicted by Eq (3)?
15. Remove the trim pot from the circuit and use your DMM to measure the resistance between the same two terminals as were wired in the experiment. Be sure to turn off the ANDY board before removing the pot. Be careful notto change the setting of the trim pot. Record the frequency and the value of the trim pot in a table.
16. Repeat steps 10 though 15 for frequencies of 1000 Hz to 3000 Hz in steps of 500 Hz.
17. Plot the data obtained in steps 15 on the graph created in step 4. Plot only the data points.
18. Do your experimental observations agree with your PSpice models and with the derivation presented in the Background? Comment and/or explain.
Measurements (Practical Integrator):
19. Turn off the ANDY board and add the components R2 and R4 to create the circuit shown in Figure 2. Use a wire to simulate the switch. Connect the wire to short the capacitor before starting each measurement.
20. Adjust the frequency of the function generator (green trace) to produce a 500 Hz square wave.
21. Adjust the amplitude of the function generator to ± 1.0 V.
22. Observe the output of the op amp on the oscilloscope (red trace). It should be a triangular wave of the same frequency as the function generator. Verify the frequency in either the “Oscilloscope” or the “Spectrum” mode of the oscilloscope. Record a screen shot of your output.
23. Adjust the trim pot R1 to produce an output signal of amplitude 1.0V.
24. Record your observations of the ease/difficulty with which you are able to construct and operate this circuit in comparison with the circuit of Figure (1).
25. Remove the trim pot from the circuit and use your DMM to measure the resistance between the same two terminals as were wired in the experiment. Be sure to turn off the ANDY board before removing the pot. Be careful to not change the setting of the trim pot. Record the frequency and the value of the trim pot in a table.
26. Repeat steps 20 though 25 for frequencies of 1000 Hz to 3000 Hz in steps of 500 Hz.
27. Plot the data obtained in steps 24 and 25 on the graph created in step 6. Plot only the data points.
28. Do your experimental observations agree with your PSpice models and with the derivation presented in the Background? Comment and/or explain.
29. Comment on the effect of the addition of R2 and R4 on the performance of the circuit. Do you observe the result predicted by Eq (3)?
Measurements (Improved Design):
30. Modify the circuit shown in Figure 2 by adding a summing amplifier in which a variable offset voltage is added to the output of the integrator. The offset should be variable between -9 V and +9 V. This offset can be used to compensate for any integrated dc bias that is introduced from the input signal. Remove the load resistor R3 from output of the op amp in the circuit shown in Figure (2) and put it on the output of the summing amplifier. The gain of each input to the summing amplifier should be 1.0. Hint: the variable input can be made with a 10 kΩ trim pot. Show a circuit diagram for your proposed solution.
31. Construct the circuit proposed in step 30. Adjust the offset so that the output of the summer is as predicted by Eq (3). Using your DMM, measure the offset voltage. Explain your result.
Last Revision: 4.0: 11/25/2006
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[†] See footnote on page 145 of the text.