Instructions: * Complete Part 1 of Lab 3. Once you have completed Lab 3-Part 1, complete the Lab Report. * Answer the questions and transcribe/transfer test results recorded in the lab’s tables to the tables provided. * Complete Part 2 of Lab 3. Once you have completed Lab 3-Part 2, complete the Lab Report. * Answer the questions and transcribe/transfer test results recorded in the lab’s tables to the tables provided. * Complete Part 3 of Lab 3. Once you have completed Lab 3-Part 3, complete the Lab Report. * Answer the questions and transcribe/transfer test results recorded in the lab’s tables to the tables provided.

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Part 1- Comparators and the Schmitt Trigger
Theory:
1. What is the purpose of a comparator?
A comparator is a switching device that provides a high or low output depending on which of the inputs is bigger.

2. What type of circuit uses hysteresis to avoid rapid switching due to noise?
Schmitt Trigger

Preparation: 3. Describe the transfer curve of a basic comparator circuit.
The horizontal axis represents the input and the vertical axis represents the output

Test Procedure: 4. Transcribe the comparator waveforms from Plot 22-1 to the Plot below.

Plot 22-1: Comparator waveform 5. Describe how the threshold voltage changes the comparator output.
As V+ increases, the output pulse width decreases. When V- decreases, the output pulse width increases. Varying the potentiometer changes the duty cycle of the output from 0 to 100%.

6. Transcribe the comparator transfer curve from Plot 22-2 to the Plot below.

Plot 22-2: Comparator transfer curve 7. Describe how the threshold voltage changes the transfer curve for a comparator.
The threshold voltage is a dc quantity that adds to or subtracts from the input plotted along the x-axis of the transfer curve. Varying the threshold shifts the vertical line along the x-axis.

8. Assume the circuit in Figure 22-2 had VREF set to zero volts. How would you expect the output to be affected by varying the dc offset control on the generator?
As V+ increases, the output pulse width decreases. When V- decreases, the output pulse width increases. The threshold voltage is a dc quantity that adds to or subtracts from the input plotted along the x-axis of the transfer curve. Varying the threshold shifts the vertical line along the x-axis.The offset control on the generator does not affect the threshold for the circuit but it adds a dc component to the input voltage. As a result, the duty cycle of the output waveform can be changed by the offset control. (Note: it is useful to show this with the transfer curve – it varies only the endpoints of the transfer curve, not the vertical line).

9. Transcribe the comparator transfer curve from Plot 22-3 to the Plot below.

Plot 22-3: Comparator transfer curve, leads reversed 10. Would a sinusoidal input to the comparators produce the same transfer curve as a triangle waveform? Explain.
The transfer curve is a characteristic that is independent of the input, however, the plot of the transfer curve on an oscilloscope will have various intensities that depend on the input because the waveform determines the time the beam spends in graphing any given point on the curve.

11. Transcribe the Schmitt trigger waveform from Plot 22-4 to the Plot below.

Plot 22-4: Schmitt trigger waveform

12. Transcribe the Schmitt trigger transfer curve from Plot 22-5 to the Plot below.

Plot 22-5: Schmitt trigger transfer curve

13. Summarize the important differences between a comparator and a Schmitt trigger.
A comparator has the same threshold for rising or falling signals; a Schmitt trigger has a different threshold for each.

14. Assume the input signal in Figure 22-4 could have as much as 100 mVpp noise. In order to avoid multiple tripping due to noise, you need to set the trip points at least 100 mV apart. What is the minimum value of resistance that the potentiometer can be set? Assume the output saturates at 13 V.
Setting up a voltage divider:
RxRx+100kΩx26V=100mV
Rx=383Ω

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Part 2- Summing Amplifiers
Theory:
15. How is the output of a summing amplifier calculated?
Vout=V1RfR1+V2RfR2+…+VnRfRn

16. List four common applications of summing amplifiers. * Summing different sources * Band reject filter * Precision rectifier * DAC generator

17. What is the major advantage of using summing amplifiers to connect different sources?
Combining multiple circuits while maintaining isolation.

Preparation: 18. What is the purpose of the 7493 IC used in the first summing circuit?
It is used to create a 0 to 7 binary input that will provide a varying input to the weighted DAQ summing amplifier.

Test Procedure:
Summing Amplifier: DAC and Step Generator 19. Transcribe the Weighted DAC Summing Amplifier waveform from Plot 23-1 to the Plot below.

Plot 23-1: Weighted DAC Summing Amplifier 20. The step generator in Figure 23-4 forms negative falling steps starting at zero volts and going to a negative voltage (approximately –4.4 V). Explain why.
To approximate the column values in the binary system (1, 2, 4, etc.), the three inputs are amplified in proportion to the column values they represent. (This is in effect a three-bit D/A converter).
How could you modify the circuit to produce positive, rising steps at the output?
Add an inverting amplifier to the output.

21. Assume that all three inputs to the summing amplifier (QA, QB, and QC) in Figure 23-4 are 4.5V. Compute the output voltage from the summing amplifier.
Gains are -0.195, -0.39, and -0.76. The output is 4.5 V x (-0.195 -0.39 -0.76) = -6.05 V

Precision Non-inverting Half-wave Rectifier 22. Describe the waveform of the Precision Non-inverting Half-wave Rectifier.
The output waveform is the positive portion of the input waveform with no offset. The small jump on the output is due to slew rate limitation as the output moves from negative saturation.

Precision Inverting Half-wave Rectifier 23. Describe the waveform of the Precision Inverting Half-wave Rectifier. What happens when D1 is removed?
The output is a negative half-wave rectified signal. With D1 removed, the output appears to be a full-wave rectified signal with overshoot on the back side of every other pulse. This overshoot is frequency dependent, and disappears at a few hundred hertz.

Precision Full-wave Rectifier 24. Transcribe the Precision Full-wave Rectifier waveform from Plot 23-3 to the Plot below.

Plot 23-3: Precision Full-wave Rectifier Waveforms

25. Assume you have a function generator that does not have a dc offset control. Show how you could use a summing amplifier to add or subtract a DC offset from the output.
One of the inputs to the summing amplifier would be a variable dc as shown:

26. The gain for the summing amplifier in the full-wave rectifier circuit, Figure 23-6 is not the same for both inputs. Explain why.
The inverted half-wave rectified signal is amplified twice as much as the sine wave input in order to cancel the negative excursion of the sine-wave and add a positive going signal to it.

27. The word operational amplifier originated from mathematical operations that could be performed with it. Assume you wanted to produce a circuit for which the output voltage was given by the expression Vout = –3A – 2B (A and B are variable input voltages). Show how this operation could be accomplished with a summing amplifier by drawing the circuit. Show values for resistors.
The resistors shown are representative and can have other values; the ratios are important.

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Part 3- The Integrator and the Differentiator
Theory:
28. What is the purpose of an integrator, what is it used for?
An integrator produces an output voltage that is proportional to the integral (sum) of the input voltage waveform over time. 29. What is the purpose of a differentiator, what is it used for?
A differentiator circuit produces an output that is proportional to the derivative or rate of change of the input voltage over time.

Test Procedure: 30. Transcribe the voltages from Table 24-1 to the table below. VOUT | VREF | Red ON | Green ON | Threshold | ~+2V | ~-2V | ~0V |
Table 24-1 31. Compute the minimum and maximum VREF for the comparator in Figure 24-2.
VREF(MIN) = -.714V
VREF(MAX) = +.714V 32. The comparator output did not go near the power supply voltages. Explain why not.
The LEDs drop a maximum of about 2.0 V at the op-amp's current limit.

33. Transcribe the Comparator compared to Integrator waveforms from Plot 24-1 to the Plot below.

Plot 24-1: Comparator compared to Integrator 34. Describe the effect of varying R3 has on the output of the comparator and integrator.
Duty cycle changes as R3 is varied. Output B slope changes to follow

35. Transcribe the symptoms induced the circuit from Table 24-2 in the table below. Trouble | Symptoms | No negative power supply | Red LED on; B goes to positive saturation | Red LED open | A = -2 V to + sat; B = - sat w/small deviation | C1 open | B goes to a square wave (+ and - saturation) | R5 open | No change in A; B goes toward - saturation. |
Table 24-2 36. For the integrator circuit in Figure 24-3, what is the purpose of R5? What happened when it was removed?
R4 establishes a virtual ground at the inverting input through negative feedback and stabilizes the operating point. Without it, the output will saturate.
The output went to negative saturation. 37. What effect would you expect on the output of the integrator in Figure 24-3 if the frequency used had been 100 Hz instead of 1 kHz?
Higher amplitude due to longer charging of the capacitor until clipping occurs on both the positive and negative peaks.

38. Transcribe the Differentiator Waveform from Integrator from Plot 24-2 to the Plot below.

Plot 24-2: Differentiator Waveform from Integrator

39. Transcribe the Differentiator Waveform from Comparator from Plot 24-3 to the Plot below.

Plot 24-3: Differentiator Waveform from Comparator 40. What type of circuit will produce leading-edge and trailing-edge triggers from a square wave input?
Differentiator circuit