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The Basic Inverting Amplifier

### Introduction

The fundamental component of any analog computer is the operational amplifier, or op amp. And the fundamental configuration in which it is used is as an inverting amplifier. The schematic diagram to the right shows the basic configuration for this circuit.

An input voltage, Vin is applied to the input resistor, Rin. The amplifier, represented by the triangle, amplifies the input voltage it receives and inverts its polarity, producing an output voltage, Vout. This same output voltage is also applied to a feedback resistor, Rf, which is connected to the amplifier input along with Rin.

The amplifier itself has a very high voltage gain. As a result, the junction of the two resistors, which is also the amplifier input, must be virtually at ground potential. A non-zero input voltage will be amplified so much that the output voltage would try to exceed its electronic limits. At the same time, the amplifier requires almost zero input current to operate. Therefore, the input current (Vin/Rin) must be the same as the feedback current (Vout/Rf). This in turn means that the effective gain of the circuit with feedback in place is simply the resistance ratio, Rf/Rin. This is the beauty and value of the operational amplifier: we can obtain precision results if we use precision resistors.

If Rf = Rin, Vout = -Vin. We will demonstrate this relationship in this experiment.

### Schematic Diagram

The schematic diagram above is often used to depict op amp circuits. However, it is incomplete. An operational amplifier is actually a high-gain differential amplifier, and as such has both an inverting and a non-inverting input. Both inputs must be connected in order for the circuit to work. The figure to the right shows the more complete schematic diagram.

The input and feedback connections are both made to the inverting (-) input. The non-inverting input (+) is grounded through a resistor. This is what forces the inverting input to be a virtual ground: the amplifier output voltage depends on the voltage difference between the two inputs, rather than the absolute voltage at either input.

Because the input transistors inside the op amp do actually require a very slight input current, there is a very slight corresponding voltage drop across the resistors connected to those inputs. However, if the resistor connected to the non-inverting input is approximately the same as the parallel combination of Rin and Rf, the resulting voltage drops will be the same and will tend to cancel each other out. If Rin and Rf are each 10K, then a standard 4.7K resistor to the non-inverting input will be satisfactory in this capacity. We could also use a 5.1K resistor here.

Because the ratio of Rf/Rin completely controls the effective gain of the amplifier, these resistors should be as precise as possible. Radio Shack sells a package of 50 ¼-watt metal film resistors, having a tolerance of 1%. You don't have to use them in these experiments, but your results will be more accurate if you do. All results discussed in these pages will be based on the use of 1% resistors in critical locations. We'll identify these in the assembly diagrams, and show the bodies of the 1% resistors in light blue rather than the more usual light brown color.

Vin is typically some sort of signal. Since we don't have such a signal right now, and want to measure voltages to verify the operation of this circuit anyway, we'll supply the input voltage from a 10K trimpot, like the one we used to set the ±15 volt power supplies.

### Precision Resistors

With 1% resistors, it becomes necessary to read the color codes a bit differently. The colors themselves have the same meanings for digits 0-9, but these precision resistors use three significant digits rather than two. Thus resistor values of 127K, 4.99K, or 2.15K are quite legitimate when we use this degree of precision.

1% resistors thus have three color bands to define significant digits, a fourth band for additional zeros, and a fifth tolerance identifier, which is brown for 1% tolerance. Be sure to keep this in mind, and to distinguish between resistors of different tolerances. Otherwise it becomes very easy to misread resistor color bands in such cases.

While it is possible to use 5% resistors and get reasonable results, by using 1% resistors, you can ensure that your results will be much more accurate. Radio Shack sells a package of 50 1% tolerance metal film resistors which will serve well in these projects. We will specify these in critical locations, and limit the values specified in these experiments to those included in the Radio Shack package.

### Parts List

To construct and demonstrate the inverting op amp circuit on your breadboard, you will need the following experimental parts:

• (1) 4.7K, ¼-watt 1% resistor (yellow-violet-black-brown).
• (2) 10K, ¼-watt 1% resistors (brown-black-black-red).
• (1) 10K, 15-turn trimmer potentiometer.
• (1) 741C operational amplifier IC.
• Orange hookup wire.
• Blue hookup wire.
• Your analog breadboarding system with ±15 volt power supplies in place.

You will also need your longnose pliers, wire strippers, diagonal cutters, thin-bladed screwdriver, and voltmeter.

### Constructing the Circuit

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

### Circuit Assembly

#### Starting the Assembly

Make sure the right side of your breadboard socket is clear of all components. The left side should already have the power supplies installed, with jumpers to the bus strips on the right side. The upper bus strips shold be connected to +15 and +5 volts, while the lower bus strips should be connected to ground and -15 volts. Power should be turned off while you construct the experimental circuit.

If your power supplies are not in place yet, go back and install them in accordance with the instructions on these pages. With your power supplies in place, you are ready to construct this experimental circuit.

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" Orange Jumper

Prepare a 0.3" orange jumper as you have done in past projects, and install the jumper in the location shown in the assembly diagram to the right.

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

#### 0.5" Orange Jumper

In the same manner, prepare a 0.5" orange jumper and install it in the location indicated to the right.

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

#### 0.5" Orange Jumper

Prepare a second 0.5" orange jumper and install it in the location indicated to the right.

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

#### 0.5" Blue Jumper

Prepare a 0.5" blue jumper and install it in the location shown in the assembly diagram.

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

#### 0.1" Bare Jumper

Cut a 5/8" length of bare hookup wire, or locate a clipped component lead of similar length. Bend it in half as shown in the pictorial, and install it in the location shown to the right.

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

#### 741 IC

Locate a type 741 operational amplifier IC in an 8-pin mini-DIP package and install it on your breadboard socket across the center channel as shown to the right.

As you install this IC, make sure that all eight pins get inserted into their respective contact holes on the breadboard socket, and do not bend upwards under the3 body of the IC itself.

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

#### 4.7K, 1% Resistor

Locate a 4.7K, 1% resistor (color code yellow-violet-black-brown) and form its leads to a spacing of 0.4". Clip the formed leads to a length of ¼" and install this resistor in the location shown in the assembly diagram.

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

#### 10K, 1% Resistor

Locate a 10K, 1% resistor (brown-black-black-red) and form its leads to a spacing of 0.6". As before, clip the formed leads to a length of ¼" and install the resistor in the location shown to the right. The resistor will cover the bare jumper you installed earlier; this is perfectly all right.

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

#### 10K, 15-Turn Trimpot

Locate a 10K, 15-turn trimmer potentiometer of the same type you used in the ±15 volt power supply. Install this trimpot on your breadboard socket as shown in the assembly diagran, with the adjustment screw to the right near the end of the breadboard socket. Be sure the three contact wires from the trimpot are inserted into the breadboard contacts indicated by the gold squares.

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

#### 10K, 1% Resistor

Locate a second 10K, 1% resistor (brown-black-black-red) and form its leads to a spacing of 0.6". This time, however, leave the leads longer than usual (about 5/8") so you can install this resistor over the top of the 741 IC. Install the prepared resistor as shown to the right.

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. Then, proceed with the experiment on the next part of this page.

### Performing the Experiment

The two 10K, 1% resistors mark the input and output connections to the inverting amplifier. Their common connection at pin 2 of the IC is the summing junction, the input voltage is to the connection between one 10K resistor and the sliding connection of the trimpot, and the output voltage is taken from IC pin 6, which is the other end of the feedback resistor, Rf.

Turn on power to your experimental circuit and your voltmeter, and set your voltmeter to measure voltages in the ±20 volt range. Do not change ranges in the middle of this experiment. Adjust the trimpot for an input voltage to the circuit of 0.00 volts. Now measure the output voltage from the op amp and record this voltage in the top text box of the table to the right, in the column designated "Output for + Input."

Now, move the meter probe back to the input connection at the trimpot and adjust the trimpot to produce an input voltage of exactly +1.00 volt. Then move the voltmeter probe back to the op amp output and measure the output voltage. Record this value in the text box directly under the one where you recorded the output voltage for a 0.00-volt input.

Using the same procedure as before, set the input trimpot to produce an input of +2.00 volts. Measure the output voltage as before, and record the output voltage in the approprate text box in the table to the right. Continue down the column, recording the output voltage for each input voltage up to +15.00 volts.

Next, reset the input trimpot for an input voltage of -1.00 volt, and measure the op amp output voltage once again. Record this output voltage in the text box to the right of the "±1.00" input label, under the heading "Output for - Input."

Continue in the same manner as before, setting the input to each exact negative input voltage and recording the resulting output voltage in turn. When you have recorded your measured output voltages for each input voltage in the table to the right, turn off your power supply and your voltmeter, and look over your results.

At this point, there are several questions you should ask yourself, based on your recorded measurements:

1. Is the voltage gain of this circuit exactly -1.0000?
2. Is the voltage gain the same for positive and negative inputs?
3. Is the voltage gain the same for input voltages over the entire input range from +15.00 volts to -15.00 volts?
4. How do you account for any discrepancies from the ideal behavior for this circuit?

Try to answer all of the above questions for yourself, before you continue on to the discussion below.

Output for
+ Input
Input
Voltage
Output for
- Input
0.00 (N/A)
±1.00
±2.00
±3.00
±4.00
±5.00
±6.00
±7.00
±8.00
±9.00
±10.00
±11.00
±12.00
±13.00
±14.00
±15.00

### Discussion

When you performed this experiment, you almost certainly observed three different types of errors that appeared in your results. By understanding these errors and the reasons for them, you will understand the capabilities and the limitations of op-amp based circuit design and operation.

Within these limitations, the operational amplifier offers accurate, predictable, repeatable behavior and is quite suitable in a wide range of applications. Outside of these limitations, however, you are better off seeking other ways to accomplish your purpose.

The three basic errors that caused the discrepancies in your results are:

Resistor Tolerance.

A resistor of tolerance 1% is accurate, but still not perfect. Thus, a 10K, 1% resistor may have an actual resistance value anywhere in the range 9900 ohms through 10,100 ohms (10,000 ± 100). Using these extremes for Rin and Rf, we find that our op amp inverter can have any voltage gain from 0.9802 to 1.0202. To narrow down this range, we must go to resistors of even closer tolerances. But we will always see a range of possible ampliier gains; not a guaranteed precise voltage gain.

For example, by switching to 0.1% resistors, we can have a gain in the range of 0.998 to 1.002. Or, with 0.01% resistors, the gain range becomes 0.9998 to 1.0002. This is much better, of course, but such resistors are quite expensive. Your circuit design will thus involve a trade-off between accuracy and cost.

Input Offset.

No op amp is perfectly ideal. The two inputs cannot have exactly matching characteristics except by blind luck. There are slight differences between input voltage requirements and input current requirements. These are known as input offset voltage and input offset current. These offsets are amplified like any other input signal and introduce an error into your results.

The basic 741 op amp includes a means of balancing out these offsets so as to minimize their effects. We'll see how this works in the next experiment in this series.

Output Saturation.

Another thing to remember about op amps in general is that their output voltage can never quite reach the power supply voltages. Their internal circuitry requires some of the power supply range for itself. When the output voltage tries to exceed its limits, the op amp is said to be saturated or in saturation. Since this condition causes incorrect op amp behavior, saturaion is to be avoided at all times. This is why the output voltage range in a modern analog computer is kept in the ±10 volt range, and why we will do the same in all future experiments.

Once you realize the basic limits within which all op amps must work, you can use that knowledge to design and build circuits that will function accurately to the edges of those limits. You will also know when and why to stop using op amps and seek other methods, under conditions where op amps cannot perform satisfactorily.

When you have completed this experiment, make sure power to your experimental circuit and voltmeter is turned off. Remove your experimental components from your breadboard socket and put them carefully aside for use in later experiments.

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