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A Non-Inverting Amplifier

### Introduction

Although the standard op amp configuration is as an inverting amplifier, there are some applications where such inversion is not wanted. Since the op amp itself is actually a differential amplifier, there is no reason why it cannot be configured to operate in a non-inverting mode.

However, we can't just switch the inverting and non-inverting inputs to the amplifier itself. We'll still need negative feedback to control the working gain of the circuit. Therefore, we will need to leave the resistor structure around the op amp intact, and swap the input and ground connections to the overall circuit.

Of course, in doing so, we will change the characteristics of the overall circuit, so that its behavior will necessarily be different in some way. In this experiment, we will construct and test such a circuit, and determine experimentally just how this modified circuit behaves.

### Schematic Diagram

The circuit shown to the right is the basic inverting op amp circuit. The non-inverting input is grounded through a resistor, and the input signal and feedback are applied to the inverting input. As we have seen in an earlier experiment, the gain of this circuit configuration is set entirely by the ratio of Rf/Rin.

The reason for this is that the output must assume whatever voltage will hold the inverting input at ground potential, which is where the non-inverting input is held directly. But what if we turn this circuit over and swap the input and ground connections? How will the resulting circuit behave?

The circuit to the right shows the implementation of this concept. The series resistor, Rs, still affects only the input offset voltage, so we can ignore it for our calculations of circuit gain. Therefore, we must look at the voltage divider formed by Rf and Rin. Vout must be such that the output of the voltage divider is the same as Vin. Thus:

 Vin = Vout Rin Rf + Rin Vin = Rin Vout Rf + Rin Vout = Rf + Rin Vin Rin Vout = Rf + 1 Vin Rin

From these calculations, we can see that the effective voltage gain of the non-inverting amplifier is still set by the resistance ratio Rf/Rin, but is one greater than this ratio. Thus, if the two resistors are of equal value, the non-inverting gain will be 2, rather than 1. To get a non-inverting gain of 1, we can simply eliminate both Rf and Rin, and connect the output directly to the (-) input. We would eliminate Rs at the same time, or else use equal resistances in series with the two inputs.

In this experiment, you will construct and demonstrate a non-inverting amplifier circuit using a type 741 op amp IC.

### Parts List

To construct and test the non-inverting amplifier circuit on your breadboard, you will need the following experimental parts:

• (1) 5.6K, ¼-watt resistor (green-blue-red).
• (2) 10K, ¼-watt, 1% resistors (brown-black-black-red).
• (2) 15K, ¼-watt, 1% resistors (brown-green-black-red).
• (1) 10K, 15-turn trimpot.
• (1) 741 op amp IC.
• Black hookup wire.
• Orange hookup wire.
• Yellow hookup wire.
• Blue hookup wire.

### Constructing the Circuit

Select an area on your breadboard socket that is clear of other circuits. You'll need two adjacent sets of five bus contacts for this project. Then refer to the image and text below and install the parts as shown.

### Circuit Assembly

#### Starting the Assembly

You can assemble this circuit on any open space on your breadboard socket. Our assembly example is on the right end of the breadboard.

Click on the `Start' button below to begin. If at any time you wish to start this procedure over again from the beginning, click the `Restart' button that will replace the `Start' button.

#### 0.3" Black Jumper

Locate or prepare a 0.3" black jumper, using the same methods you have employed in past experiments. Install this jumper in the location indicated in the assembly diagram to the right.

Click on the image of the jumper you just installed to continue.

#### 0.5" Blue Jumper

Locate or prepare a 0.5" blue jumper, and install it in the location shown in the assembly diagram.

Again, click on the image of the jumper you just installed to continue.

#### 0.5" Orange Jumper

Locate or prepare a 0.5" orange jumper, and install it in the location indicated to the right.

As before, click on the image of the jumper you just installed to continue.

#### 0.2" Bare Jumper

Locate or prepare a 0.2" bare jumper, and install it in the location shown in the assembly diagram.

Once more, click on the image of the jumper you just installed to continue.

#### 5.6K, ¼-Watt Resistor

Locate a 5.6K, ¼-watt resistor and form its leads to a spacing of 0.5". Clip the formed ends to a length of ¼" and install this resistor in the location indicated to the right.

Click on the image of the resistor you just installed to continue.

#### 741 Op Amp IC

Locate a type 741 op amp IC and make sure that all eight pins are straight and parallel with each other. Place this IC gently on the location indicated in the assembly diagram with the notch indicating pin 1 oriented to the left as shown. Make sure that all pins are aligned with their respective contact holes; then gently press the IC into place.

Click on the image of the IC you just installed to continue.

#### 10K, 15-Turn Trimpot

Locate a 10K, 15-turn trimpot. Install this trimpot on your breadboard socket so that the three connection pins line up with the contact holes indicated by the gold squares in the assembly diagram, and then press the trimpot firmly down into place.

Click on the image of the trimpot you just installed to continue.

#### 6" Yellow Jumper

Locate a 6" yellow jumper, or else cut a 6" lengtrh of yellow hookup wire and remove ¼" of insulation from each end. Connect one end to the location shown to the right. Connect the other end to your regulated +10 volt reference source.

Click on the image of the jumper you just installed to continue.

#### 10K, 1% Precision Resistor

Locate a 10K, 1% precision resistor (brown-black-black-red) and form its leads to a spacing of 0.4". You need not clip the leads of this resistor, but if you do, leave them ½" long so you can easily remove and re-install this resistor.

This is resistor Rin for this experiment.

Click on the image of the resistor you just installed to continue.

#### 10K, 1% Precision Resistor

Locate another 10K, 1% precision resistor (brown-black-black-red) and form its leads to a spacing of 0.5". As with the previous resistor, you need not clip the leads at all, but if you do so, leave them ½" long for easier handling of this resistor.

This is resistor Rf for this experiment.

Once more, click on the image of the resistor you just installed to continue.

#### Assembly Complete

This completes the construction of your experimental circuit. Check your assembly carefully against the figure to the right, and correct any errors you might find.

In addition to the parts you have already installed, you will need two (2) 15K, 1% precision resistors (brown-green-black-red) during the course of the experiment.

The labels on the assembly diagram show the points at which you can measure the input voltage (Vin) and output voltage (Vout) throughout this experiment.

### Performing the Experiment

Step 1. Before turning on power to your experimental circuit, calculate the expected gain of this circuit for resistance values of 10K for both Rf and Rin. Use the formula:

 Vout = Rf + 1 Vin Rin

Enter your calculated results for this pair of resistors in the first text box in the row labelled "Gain" in the table to the right, in the column labelled Steps 1 - 6.

Step 2. Now, turn on power to your experimental circuit, and adjust the trimpot to produce a Vin of 0.00 volts. Measure the output voltage, Vout, at pin 6 of the 741 IC. Enter this value in the appropriate text box in the table to the right.

Step 3. Adjust the trimpot to produce a Vin of 1.00 volts. Measure the resulting value of Vout, and record this value in the corresponding text box in the table to the right, just under your entry for Step 2.

Step 4. Disconnect the yellow jumper from your +10 volt reference, and connect it to your -10 volt reference instead. Verify that Vin is now -1.00 volts and adjust your trimpot if necessary. Then, measure Vout and record this result in the table to the right, under your previous entries.

Step 5. Adjust your trimpot to produce a Vin of -2.00 volts, and record the resulting Vout in the appropriate space in the table to the right. Continue this process, setting Vin to each positive and negative voltage listed in the table, and recording the resulting value of Vout to the right of the corresponding Vin in the table. This will fill in the first column of text boxes.

Step 6. Pause in your measurements and look over your results. Allowing for the inevitable errors that you have experienced, does the gain of this circuit closely match the gain you calculated for it in Step 1? If not, how do you account for the discrepancy?

Step 7. Turn power off, and remove Rf, which is the 10K precision resistor placed across the top of the 741 IC (from pin 6 to pin 2). Replace this resistor with a 15K, 1% precision resistor (brown-green-black-red). This will change the ratio of Rf/Rin, and will therefore change the voltage gain of this circuit. Calculate the new voltage gain, using the same formula as in Step 1, and record this value in the Gain row of the table to the right, under the column labelled for Steps 7 and 8.

Step 8. Turn power back on and repeat all of the voltage tests and measurements you made in Steps 2 through 5. Record your results in the second column of text boxes in the table to the right.

Step 9. Review your results for this set of measurements, and verify that the actual gain of this circuit matches your calculated gain, to within the appropriate margin of error.

Step 10. Turn power off again, and replace the 10K, 1% resistor Rin (connected from IC pin 2 to ground) with a 15K, 1% resistor (brown-green-black-red). Use the new ratio of Rf/Rin to recalculate the gain of the resulting circuit. Enter this value in the third text box in the "Gain" row of the table to the right, under the column head marking Steps 10-12.

Step 11. Turn power back on, and as before, measure Vout for each value of Vin listed in the table. Record your results as you did before.

Step 12. Review your results again. Do your recorded values correctly reflect your calculated circuit gain? Also, compare your results with your first set of results, from Steps 1-6. Within the appropriate margin of error, do you get the same results from a ratio of 15K/15K that you obtained from a ratio of 10K/10K? Would you expect them to be the same?

Step 13. Turn power off again, and remove the 15K resistor Rf, which you installed in Step 7 (across the top of the 741 IC, from pin 6 to pin 2). Install the original 10K, 1% resistor in this location. Now, Rf < Rin. Recalculate the gain of this circuit and record your result in the remaining column of the table to the right.

Step 14. Once more, turn power on and repeat your measurements of Vout for each listed value of Vin. Record your results in the table as you did before.

Step 15. Review your results for this set of measurements. Do they accurately reflect you calculated value of circuit gain, to within expected limits of error? Can you explain any discrepancy?

When you have complete all of your measurements, turn off the power to your experimental circuit and compare your results with the discussion below.

Steps 1 - 6 7 - 9 10 - 12 13 - 15
Rf 10K 15K 15K 10K
Rin 10K 10K 15K 15K
Gain
Vin Measured Vout
0.00
1.00
-1.00
2.00
-2.00
3.00
-3.00
4.00
-4.00
5.00
-5.00

### Discussion

In Step 1, you calculated the gain of the non-inverting amplifier, with both Rf and Rin equal to 10K. Since they're equal in value, their ratio is 1, and the total gain of the circuit is 1 + 1 = 2.

Your results for Steps 2 through 5 should have reflected this gain, and you should have seen it clearly in Step 6. Of course, with an input of 0.00 volts, the output should also be 0.00. You may have seen a very small offset voltage at the output, but not much. Then, with +1.00 volt input, vout measured +2.00 volts (between +1.96 and 2.04 volts) at the output. You should have obtained similar results for each value of Vin, obtaining a Vout that was just double the input voltage.

A key point here is that the output voltage polarity is the same as the input polarity. Thus, this amplifier circuit is indeed non-inverting. It is still bipolar, in that a negative input voltage produces a negative output voltage at twice the voltage. But the output polarity is always the same as the input polarity.

In Step 7, you changed Rf from 10K to 15K. The ratio of Rf/Rin is now 1.5, and the voltage gain of the circuit is now 2.5.

Then, in Steps 8 and 9, you recorded and reviewed the output voltages produced by the modified amplifier, for each of the listed input voltages. This gave you an output voltage of +12.5 for a +5 volt input. This is pushing the limits of saturation a bit. It was probably correct if your power supplies were set to ±15 volts. If they were set to ±12 volts, the output voltage couldn't exceed ±10 volts or so, and possibly not even that high.

In Steps 10 through 12, you repeated your measurements with both resistors set to a value of 15K. Here, your results were the same as with two 10K resistors. This is because the gain of the stage depends on the ratio of the two resistors, and not on the specific value of either one. Thus, the gain of the circuit in this configuration was 2.

Finally, in Steps 13 through 15, you tried the same measurement sequence with Rf = 10K and Rin = 15K. This gives us a resistance ratio of 10K/15K = 0.666667, for a stage gain of 1.666667. Your measured voltages should reflect this value of voltage gain.

One key point here is that, unlike the standard inverting amplifier configuration, the non-inverting amplifier configuration using op amps cannot produce a voltage gain less than 1.0. This doesn't make this configuration less useful than the inverting op amp configuration, but you need to be aware of this characteristic whenever you design or modify such a circuit.

You can reduce the gain by using a voltage divider at the non-inverting input. This reduces the input voltage applied to the op amp, and hence reduces the effective gain of the overall circuit. This approach leads to a true difference amplifier.

When you have completed this experiment, make sure power to your experimental circuit is turned off. Then, remove all of your experimental components from your breadboard socket and put them away for use in later experiments.