# Lab 8: Operational Amplifiers

Lab report from the “Art of Electronics” student manual.

## 8-1 Open Loop Test Circuit

Introduction:

The purpose of this lab is to become acquainted with the normal output of an operational amplifier (op amp). An op amp is a class of amplifiers that are close to an ideal differential amplifier. Op amps consist of about 10-20 transistors, related resistors, capacitors and diodes. A differential amplifier wants to pick up the difference between two input signals, and so remove any unwanted signals.

Procedure:

To set up the op-amp circuit shown below, we begin by placing the op-amp into the breadboard so that it straddles between 2 rows. The op-amp has 8 pins with different functions; we will use 5 of them in this circuit. Apply a 15 V DC power supply to a 10k potentiometer (variable resistor) and allow it to lead into the non-inverting input (+) pin of the op amp. Connect the inverting input to ground. As usual, connect “pin 7” to a +15 V source and “pin 4” to a -15 V source. We will measure the output signal at the op amps “output” pin using the oscilloscope (5 V scale, . Once the power supplies are turned on we are to “twiddle the pots”, thus varying the resistance, and observe the output voltage as measured by the scope.

Data and Calculations:

As the resistor varies from high to low we observe only 2 different voltage outputs.

At a “low” resistance, Vout = -13 V At a “high” resistance, Vout = +14.5 V

Results:

We can get the output to ever be 0 V as it can only be either of 2 discrete values as recorded above. This is because of the large differential gain (Gdiff) that causes big changes in output voltage for very small changes in the resistance. This is consistent with the 411 specifications.

## 8-2 Inverting Amplifier

Introduction:

The purpose of this lab is to construct an inverting amplifier and observe the output of the circuit as well as other attributes such as impedance. Inverting amplifier just implies that the feedback loop is attached to the – pin of the op amp, causing the output signal to be a 180˚ phase shift (“inverted”) from the input signal.

Procedure:

To build the inverting amplifier, we must connect an AC signal (function generator) to a 1 k resistor that leads to the inverting input pin of the op-amp as well as to another resistor of 10k which then leads to the output pin of the op-amp. We will use channel 2 of the scope (5 V scale, 500 S timescale) to measure the output. As usual, we must also connect a +15 V and -15 V DC power supply to the “7” and “4” pins of the op-amp respectively. Channel 1 of the scope (1 V scale) will measure the input signal. The function generator will drive a 1k Hz sine wave. We will attempt to measure gain, maximum output swing, and impedance. We will also observe the output when with difference frequencies and a triangle wave.

Data and Calculations:

Ch.1pp = 2.60 V Vmean = 18 mV 0

Ch,2pp = 26.0 V VOmean= -200 mV 0

G = – (R2 / R1) = – (10/1) = -10. (Confirmed) Vout = -10(Vin)*

*The output is 180o out of phase

Results:

As seen, the output signal is inverted 180o out of phase and amplified by a factor of 10. The maximum output swing is observed to be around 26 V before the imperfections of the op-amp become apparent, we originally expected to reach a value of 27 V before such limit is reached.

To check the linearity of the circuit’s output, we drove it this time with a 1 kHz triangle wave with an amplitude of 4 V. The maximum output swing here was about 1.4 V. So linearity checks out.

Next we tried the inverting amplifier out on sine waves of different frequencies. We noticed that at low frequencies the circuit works well, but at high frequencies, the shape of the output distorts (around 3.5 kHz driving frequency). The output of a sine wave changes to a squarish wave and is no longer inverted.

Next we measured the input impedance of the amplifier circuit by adding a 1 kOhm resistor in series with the input. We drove the circuit with a 1 kHz sine wave and noticed that the output after the 1k Ohm is about 50% of the input. And using Thevenin logic, we know that the other resistor must be about 1k Ohm as well. Therefore the input impedance is about 1 kOhm.

The input impedance of the op amp is determined by R1. So if we want large amplification, we should make R1 (and thus the input impedance) small, or vice versa.

To measure the output impedance, we placed a 1k Ohm resistor in series with the output and tried to measure the impedance. It didn’t work which means it comes close to the ideal amplifier. The impedance is very low, and so the output and the impeded output are the same.

## 8-3 Non-Inverting Amplifier

Introduction:

The non-inverting amplifier works much like the circuit we constructed in the previous lab, except that the signal is not inverted. The voltage gain will also be slightly different.

Procedure:

Drive the function generator through the non-inverting input pin. Connect the output to a 10k resistor and lead it to the inverting input pin and a 1k resistor that leads to ground. We will measure the gain by connecting the oscilloscope channel 2 (2 V scale, 500 Stimescale) to the output pin and also attempt to measure the input impedance. We expect the input impedance to be the same before we even run the experiment due to the similarity with the previous section. As usual, make sure to power the op-amp with the + and – 15 V DC supply. Channel 1 of the scope (1 V scale) will measure the input signal.

Data and Calculations:

Ch.1pp = 2.75 V Vmean = 20 mV 0

Ch.2pp = 5.50 V Vmean= 6 mV 0

G = 1 + (R2 / R1) = 11.*

No changes after applying a 1M Ohm resistor.

Results:

Why is my output twice as large in my measurements but the gain is calculated to be 11?

The signal was successfully amplified without inverting it.

We measured the input impedance by putting a 1M Ohm resistor in series with the circuit. There is about a 50% voltage drop across the resistor. From that, we know that the input impedance should also be about 1M Ohm.

This configuration still maintains the low output impedance measured with the inverting amplifier. Really the two circuits are the same, just with their polarity reversed.

## 8-4 Follower

Introduction:

The purpose of this lab is to test the effectiveness of a follower circuit and to measure the input and output impedances. This type of amplifier has a gain of 1, which means that the output signal exactly follows the input signal. Essentially, it is the non-inverting amplifier in the limit that R2 –> 0 and R2 –> infinity. It has a very high input impedance and a very low output impedance, but is unable to supply large currents.

Procedure:

This circuit is designed exactly like the non-inverting amplifier but with no resistors to produce a gain. Begin by connecting the function generator to the positive input pin and connect the negative input pin to the output. Drive the generator with a 1k Hz sine wave and observe the input and output as measured by the oscilloscope. Let channel 1(1 V scale, 500 S timescale) measure the input while channel 2 (1 V scale, 500 S timescale) measures the output.

Data and Calculations:

Vin = 2.75 V Vout = 2.75 V means 0

No changes after adding 1 M Ohm resistor at input.

Results:

The output matches the input exactly.

## 8-5 Current Source

Introduction:

The purpose of this lab is to create a precise and stable current source using an op amp. We will then adjust the circuit to correct issues pertaining to the “floating load” requirement and speed limitations.

Procedure:

Connect a +15 DC power supply to a 15k resistor and connect one lead to ground ground a 1k resistor and another lead going into the positive input pin of a 411 op-amp. Connect the output to a 10k potentiometer that leads into the negative input pin and ground after going through a 180 Ohm resistor. Measure the current of the wire out of the 10k pot using a DVM. We will then measure several currents after adjusting the load resistor. As usual, make sure to power the op-amp with the + and – 15 V DC supply.

Now we will reconfigure the circuit to solve some initial problems with the original circuit. Connect the +15 V DC power supply to a 2.7k resistor and a 470 Ohm resistor. Lead the 4.7k to the positive input pin of the op-amp and to ground through a 12k resistor. Lead the 470 Ohm resistor to the negative input pin of the op-amp and to the emitter of a 2N3906 transistor. The base of the emitter will connect to the op-amp’s output while the collector will lead to the 10k pot and into ground. Use the DVM to measure the current between the 10k pot and ground. Twiddle the pot and record the varying current. We can also use another DVM to measure the voltage across the transistor (VCE).

Data and Calculations:

Part 1: Current (I) = 1.38 mA @ max resistance and Iout = 5.32 mA @ min resistance

Part 2: Iout = 1.18 mA @ max resistance and Iout = 6.39 mA @ min resistance*

*At this point the current wasn’t completely stable until it reached 6.58 mA

Results:

Note that IR2 = IR1 = Vin / R1. Thus the current flowing through R2 (a variable resistor) is independent of the value of R2 over a wide range of resistances. And so we have an excellent current source. This only changes in the limit that R2 gets really large and affects the current.

We calculated that the current of the circuit output should be 5 mAmps. The current that we’re measuring with the initial R2 = 10 kOhm is ~ I = 1 mA. So doing some calculations, we realized that R2 should be at a value of 2k Ohms in order to supply the maximum 5 mA current. So changing the value of the variable resistor, we got an output current of 5.32 mA, which is good! Looking into it a bit further, we realized that increasing the resistance to even 2.1k Ohms causes the current to decrease.

## 8-6 Current to Voltage Converter

Introduction:

The purpose of this lab is to convert voltage to current using a phototransistor as a photodiode. When current flows through a light emitting diode, one photon of light is emitted

for every electron of current. The reverse process is also possible: when light is

absorbed by a diode, a “photo-current” is generated. In this way, a diode can serve as a light detector (and so a “photodiode”). The direction of the photo-current is in the direction opposite to the normal direction of current flow in a diode.

Procedure:

Using a phototransistor, connect the base to ground and the emitter to the negative input pin of a 411 op-amp. Note that this transistor does not have a collector. Attach a 1Meg Ohm resistor from the negative input pin to the output. Connect the positive input pin to ground. As usual, make sure to power the op-amp with the + and – 15 V DC supply. Shine a bright light on the phototransistor to power the circuit. Measure the input with channel 1 (1 V scale, 5 mS timescale) with the scope and measure the output with channel 2 (1 V scale, 5 mS timescale).

Data and Calculations:

T= 8.4 mS Vpp = 1.2 V Vtop = 2.36 V Vbot = 1.16 V Vrms = 1.7 V

The percent “modulation” is about 1.6%, which is very low.

The average DC output level for the photodiode circuit is about -350 mV with < 10 Hz.

Results:

The output was a very noisy sine wave (viewing AC coupling on the oscilloscope). The voltage level changes in altitude above or below the ground line when we block the light. When we use the DC coupling, there is a negative voltage with the light on, and it just goes to ground with the light off.

At the “summing junction” of the circuit, the current we see should be zero. This is because of the Golden Rule of Op Amps, which states that the current at V- equilibrates to that at V+ and vise versa. And since pin 3 is going to ground, the current at the summing junction must also be zero.

## 8-7 Summing Amplifier

Introduction:

Op amps can be configured to perform various mathematical operations. One of them is summing. If an op amp circuit is constructed in the way below, the currents through the input resistor will add up at the summing junction and flow through the feedback resistor.

A circuit can also be designed using two op amps that subtracts two voltages. This can be achieved by adding another inverting amplifier circuit so that it’s Vout is attached to one of the Vins in the circuit above. This will subtract the two input currents at the summing junction.

Procedure:

Connect the function generator (1k Hz sine wave) to a 10k Ohm resistor and into the negative input pin of the 411 op-amp. Run a + 15 DC power supply into a 10k potentiometer and into a -15 V DC supply. Run the 10k pot to the negative input pin of the op-amp. Connect a 10k Ohm resistor between the negative input pin and output of the op-amp. Connect the positive input pin to ground. Use the scope’s channel 1 (5 V scale, 500 S timescale) to measure the function generators input and channel 2 (5 V scale, 500 S timescale) to measure the output. As usual, make sure to power the op-amp with the + and – 15 V DC supply.

Data and Calculations:

Ch.1 Vrms = 90 mV Vpp = 12.4 V

Ch.2 (max R) Vrms = 9.86 V Vpp = 10.4 V (clipped)

Ch.2 (min R) Vrms = -9.14 V Vpp = 9.80 V

Ch.2 (max R) Vrms = 2.16 V Vpp = 12.60 V

Results:

The currents added up appropriately for the summing ampifier.

## 8-8 Push Pull Buffer

Introduction:

In this lab we will be driving a speaker with a push-pull op-amp circuit. A push–pull output is a type of electronic circuit that uses a pair of active devices that alternately supply current to, or absorb current from, a connected load.

Procedure:

To build this circuit, begin by connecting the function generator to a 10k resistor leading into the positive input pin of a 411 op-amp. Connect the negative input pin to ground and connect a 100k resistor from the positive input pin to the output pin of the op-amp. From the output, lead a 390 Ohm resistor to the bases of two transistors, one being a 2N3904 and another one being a 2N3906. Connect a +15 V DC power supply to the collector of the 2N3904 transistor and a -15 V DC power supply to the collector of the 2N3906 transistor. Connect both emitters to a 1k resistor leading in to ground. The output will be measure before the last resistor with channel 2 of the scope (20 V scale, 1 mS timescale). Let channel 1 (2 V scale) measure the input of the AC signal, the generator will drive a 250 Hz sine wave. Make sure there is no DC offset. We will then attach a speaker at the output (not the push-pull circuit) and listen to the pitch that is makes. The pitch is determined by the frequency of the signal while the volume is determined by the amplitude. After we record the results, we will attach the speaker to the output of the push-pull circuit.

Adjustment: The speaker was added in parallel with a 100 Ohm resistor that has replaced the 1k resistor.

Data and Calculations:

Part 1: Op-amp output Ch.1 = Vpp = 2 V Ch.2 = Vpp = 20 V

Part 2: Push-pull output Ch.1 = Vpp = 230 mV Ch.2 = Vpp = 300 mV

(100 mV scale, 2 mS timescale)

Results:

Finally, the last result. I was able to control pitch and volume using different levels of input frequency and amplitude. Alas, a real world application of the knowledge I’ve accumulated throughout the semester (just kidding).

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