ELEC 101
Prof. Rich Kozick
February 12, 1998

## Laboratory 4 Operational Amplifier Applications

In this lab, will experiment with useful circuits that use the operational amplifier. In particular, we will look at the inverting amplifier, a summing amplifier, and we will begin to study a digital-to-analog (D/A) conversion circuit. The D/A converter will be completed next week for lab.

The goals in this lab are to gain a better understanding of how op amp circuits work, as well as to wire and test the circuits. Some parts of this lab assignment ask you to analyze a circuit. Please include that analysis in your lab notebook, and briefly discuss your analysis with the lab instructor or lab assistant.

## 1. Electronic Lessons on Op Amps

Execute the three electronic lessons on op amps that are contained in the Exploring Electrical Engineering program. The lessons are located under the menu Elements, submenu Amplifiers, with names Introduction, Op Amps - General, and Op Amp Inverter. You do not have to perform the quizzes at this time. However, if you find these lessons helpful, feel free to run through these lessons at your own pace at any time.

## 2. Inverting Amplifier

Consider the inverting amplifier circuit shown in Figure 2.15 on page 75 of the Bobrow text.
1. Repeat the analysis that leads to the result that the output voltage vo is related to the input voltage vs according to vo = -(R2 / R1) vs.

2. Suppose you want to design an inverting amplifier with gain = -(R2 / R1) = -10. Ideally, any resistor values that satisfy R2 = 10 R1 will work. However, with real op amp circuits, the resistor values need to be chosen with some care. What would be different in the circuit if R1 = 1 ohm, R2 = 10 ohm versus R1 = 1 k ohm, R2 = 10 k ohm?

Look at the data sheet for the National Semiconductor LM 741 Op Amp, which is available on the Web at http://www.national.com/pf/LM/LM741.html
What is the maximum current that the 741 op amp can provide into and out of its output terminal? In order to satisfy this limitation, what size resistors should be chosen for R1 and R2?

Important: Record your result clearly in your lab notebook, and keep this in mind whenever you are choosing resistor values in an op amp circuit.

3. Using the 741 op amp integrated circuit (IC) in your lab kit, design and set up inverting amplifiers with "gains" vo / vs = -1, -2, and -10. For each case, measure the output voltage vo for several positive and negative input voltages vs. Are there any limitations to these circuits? In other words, are there circumstances under which the desired gain is not achieved?

4. Suppose you want to design an inverting amplifier with a variable gain using a potentiometer (pot) whose resistance varies from 100 ohms to 10 k ohms as a dial is turned. (This might be used for a volume control in a radio.) Should the pot be placed at R1 or R2? A microphone, speaker, and pot will be supplied so that you can demonstrate an amplifier with a variable gain.
Record your circuit designs, measured results, and explanations in your lab notebook.

## 3. A Summing Amplifier

Many applications require that two or more signals be added while also being amplified. This need arises frequently in audio systems. For example, in a music performance, we might have several microphones, each connected to a different singer or instrument. A "mixing panel" is usually available that allows each microphone signal to be amplified separately before being added and sent to the speakers.

An op amp circuit that amplifies and adds signals is shown in Figure 2.17 on page 77 of the text. Let us generalize the circuit slightly by replacing the resistors R1 by different resistors Ra and Rb connected to the input sources va and vb, respectively.

1. Show that vo = -(R2 / Ra) va -(R2 / Rb) vb. Does this circuit amplify and add two voltages?

2. Design an inverting, summing amplifier whose output voltage is the negative average of the two input voltages. Record your design in your notebook, and demonstrate the circuit operation to the lab instructor. Are there any limitations on the size of the input signals so that the circuit correctly outputs the negative average?

3. Explain how two potentiometers can be used to provide an "audio mixer" for two microphones with variable gains. Demonstrate the mixer circuit.

## 4. Digital-to-Analog Conversion

A digital-to-analog (D/A) conversion circuit is needed in any system that produces an analog output signal (voltage) based on inputs that are digital (0's and 1's or binary). An example that all of us are familiar with is the audio compact disk (CD). The music is digitally encoded on the CD, but your CD player converts the 0's and 1's into an analog music signal that is played through your speakers.

Let us consider a 3-bit D/A converter. A binary (base 2) number with 3 bits b2b1b0 is equivalent to the decimal (base 10) number 22 b2 + 21 b1 + 20 b0 = 4 b2 + 2 b1 + b0. For example, the binary number 110 is equivalent to the decimal number 6.

Use the summing amplifier studied in the previous section to design a 3-bit D/A conversion circuit. Assume that a binary '0' is represented by a 0 volt source, while a binary '1' is represented by a +5 volt source. Pages 891-893 in the text discuss D/A conversion. The circuit in Figure 13.37 will be useful, if you take the output after the first op amp at v1. With reference to Figure 13.37, your D/A converter should operate as follows.

```    A2    A1    A0      Output voltage v1
--    --    --      -----------------

0V    0V    0V       0 V
0V    0V   +5V      -1 V
0V   +5V    0V      -2 V
0V   +5V   +5V      -3 V
+5V    0V    0V      -4 V
+5V    0V   +5V      -5 V
+5V   +5V    0V      -6 V
+5V   +5V   +5V      -7 V
```
1. Design the D/A converter, specifying all resistor values and explaining your reasoning.

2. Build the circuit and demonstrate that it operates properly.

3. The D/A converter in a CD player must convert 16-bit binary numbers to analog voltage values. If you were to extend your design to 16 bits with the output voltage level between 0 V and -10 V, which resistor values would be needed in your circuit?

4. The D/A converter in Figure 13.38 of the text uses an R-2R ladder. Why is this design better than your previous design?

5. We will discuss the operation of the R-2R ladder D/A converter in class on Friday. Include a discussion of the operation in your lab notebook.

6. Each student should individually design and construct a 3-bit D/A converter using an R-2R ladder, as in Figure 13.38. Specify the resistor values in your lab notebook, with an explanation of your reasoning. Your circuit should operate according to the following table.
```    A2    A1    A0      Output voltage v2
--    --    --      -----------------

0V    0V    0V       0 V
0V    0V   +5V      +1 V
0V   +5V    0V      +2 V
0V   +5V   +5V      +3 V
+5V    0V    0V      +4 V
+5V    0V   +5V      +5 V
+5V   +5V    0V      +6 V
+5V   +5V   +5V      +7 V
```

7. On Thursday, February 19, each student will individually demonstrate his/her circuit to the lab assistant. Proper operation of this circuit will be counted as a "lab quiz" grade for each student. The lab assistant can help you to debug your circuit, if necessary. The purpose of having each student do this individually is to make sure that all of you are progressing in your EE lab skills. Also on February 19, please hand in your lab notebook so that Labs 1-4 can be graded.