manual lab 2: operational amplifier

Carleton University: Faculty of Engineering: Electronics 1 Summer-2021 ELEC-2507 Lab Manual

Lab 2: Operational Amplifier January 10, 2021 2-1

1.0 Introduction

Lab 2: Operational Amplifier

Operational Amplifiers are circuits with an extremely high voltage gain (A), 104 or more. They are called

“operational” because they were originally used to perform certain mathematical operations such as

addition, subtraction, scaling, integration, and differentiation.

Operational amplifiers are widely used by engineers. One can design circuits using operational amplifiers

in a fraction of the time it takes with transistor circuits. Also, an integrated circuit “op amp” can be

obtained for about the price of three transistors. Unfortunately, they are not good for high-frequency,

high-power or low noise circuits. The output voltage of an operational amplifier is the gain A times the

difference between its two inputs vo = A (v+ - v-).

Since the voltage gain of the amplifier is of the order of thirty thousand, a (V+ - V-) of a few millivolts will

saturate it. If no feedback resistor is used the amplifier may saturate itself because of stray dc voltages

inside it. Even with a feedback resistor it is not hard to saturate the amplifier.

The six examples of OP-Amps in this lab are designed to work with both AC and DC signals. In some cases,

it is important to see only the AC component of a signal. In this case, a large capacitance in series with the

signal will create a DC open circuit and an AC short circuit. When viewing a signal on the oscilloscope,

DC COUPLING connects the signal directly so both DC and AC can be displayed. AC COUPLING inserts

a capacitor so that only the AC component of the signal will be displayed.

REFERENCE: Sedra & Smith, 7th Edition, 2014, Chapter 2, and the class notes.

Prior to doing the prelab, read the section 3 (experiment) which contains details relevant to prelab.

**PLEASE SUBMIT BOTH MULTISIM FILES IN .ZIP or .7Z FORMAT AND PDF DOCUMENT

OF REPORT, DUE ON CuLEARN ONE WEEK FROM THE EXPERIMENT DATE**

2.0 Pre Lab Calculations

1. For the inverting amplifier in Fig. 3, assume RF = 100k and R1 given in Resistors.pdf. What is the

voltage gain.

2. For the summing amplifier circuit in Fig. 4, assume RF=100k, R1 and R2 given in Resistors.pdf

Obtain an expression for Vo in terms of inputs V1 and V2. If V1 is represented by a 0.5 volt peak-to-

peak 1kHz sine wave and V2 by a 0.5 volt DC, sketch the output waveform.

3. For the differentiator circuit in Fig. 6, assume RF=10k, C1=0.1uF. Sketch the output waveform for

an input of 1kHz, 0.5V peak-to-peak sine-wave signal. Is there be a phase difference between input and output? If so, how much? Explain the reason for any phase shift using the expression for Vo.

4. Sketch the output waveform if the input is changed to a triangular waveform of 1kHz in exercise 3.

5. Design a high-pass filter (Fig. 7) with a 3-dB cut-off frequency of 3kHz and unity gain in the pass band. Choose C = 0.01f and calculate RF and RI taking the source impedance (50) into account.

6. Design an integrator (Fig. 8) to integrate a 2 kHz square wave with peak-to-peak amplitude of 0.5 volt.

Choose RF=150 K CI=10F, CF such RF>>1/ωCF, and RI such that RICF << 0.5 msec and 1/ωCI

<< RI. Comment on the phase shift.

7. Design a low-pass filter (Fig. 9) having a 3 dB cut-off frequency at 1kHz, and unity gain in the pass



band. Choose C = 0.01f and calculate RF and RI taking the source impedance into account.

8. What is the relationship between 20dB/decade and 6dB/octave fall in gain? Establish the relationship by deriving it (greater, equal, or less).



3.0 Experiment

While performing the online lab, you will use similar modules from the Multisim library.

**Follow the Lab2 video on CuLearn For Both HW and SW Portions** [ In a lab setting, you would be using the following physical components for the lab and follow the

guidelines below:

Equipment: Oscilloscope: Tektronix TDS3012, Oscillator: DG1022Z Function Generator

Multimeter: Wavetek DM15XL, DC Power Supply: DOE FG515

Parts: 741 Op-amp, Resistors and capacitors according to design

IMPORTANT NOTE: INTEGRATED CIRCUIT OPERATIONAL AMPLIFIERS WILL BURN OUT IF THE POWER SUPPLY DOES

NOT SUPPLY THE CORRECT VOLTAGE AND WITH THE CORRECT POLARITY.

1. Check the voltages appearing at the +15, GND and -15 terminals on the power supply using the Digital

Voltmeter (DVM). There should be +15 volts +− 10% between the +15 and there should be -15 volts +−10%

between the -15 and the GND terminals. If the voltages are both correct, you may start, if not talk to a TA.

Obtain a 741 operational amplifier integrated circuit (IC). Connect the power supply to +VSS and -VSS as

indicated in Fig. 1. With the two inputs and one output, you will use only 5 of the eight pins as shown. The

supply connections will remain unchanged for the rest of the lab, but you will be making various connections

to the two inputs and the output.

FIG. 1. A 741 OpAmp Pin Out, Common Connections and Interpretations

Most operational amplifiers use equal positive and negative power supply voltages, +VSS and -VSS. The

neutral or ground connection to the power supply is not connected to the op amp but is used as the com-

mon return lead for vo, v+ and v-.



2. SHORTING THE OUTPUT OF AN OPERATIONAL AMPLIFIER TO GROUND CAN RUIN IT. Most such

shorts occur because one inadvertently connects the oscilloscope ground clip, or the ground for some

other instrument, in the wrong place. To avoid this, connect all oscilloscope, signal-generator, and

power-supply ground leads to the bus at the bottom of your circuit board and leave them there.

When connected directly between the +IN and -IN terminals, 5 volts will BREAK DOWN THE AMPLIFIER

INPUT. Since the laboratory signal generators can deliver much more than that, never connect them directly

between the two inputs.

Operational Amplifiers contain directly coupled transistor circuitry. The output voltage can never be more

positive than the supply voltage +VSS or more negative than -VSS. When Vo is maximum (approximately

+VSS) or minimum (approximately -VSS), the amplifier is said to be saturated.

Notes with Regards to measurements and drawing of figures/graphs

a) How to Read a Capacitor value => Read the # on the Cap: eg. 103 = 10 ×103 ×10-12 F = 10 nF

b) Always use: Vpk-pk for Input & output; the Oscilloscope for gain measurement; "Average"

to clean signal

c) All plots need to show both Input & Output waveforms

d) All plots need to be annotated Completely & Clearly (axis, legends, labels, units etc.) ]



3.1 Inverting Amplifier

To use an op-amp with normal input voltages, and still avoid saturation, a feedback resistor RF is used as

shown in Fig. 3. The output voltage feeds back to cancel the input voltage and lowers the gain of the total

system. To understand the derivation of the formula, note that there is a high impedance between +IN and

- IN so that negligible current flows into the amplifier, thus.

Note that to a first approximation, the amplifier voltage gain is determined by the two external elements

RI and RF and is independent of the op-amp.

If capacitors or inductors are used with the amplifier, the resistances are replaced by impedances, and the

gain of the circuit can then be expressed as

vo

-vi (ZF/ZI). This more general formula is used to construct differentiators, integrators, and filters.

1. Use circuit 3.1 in Multisim file shown in Fig. 3. The power supply connections to the amplifier were

made as in Fig. 2 and are not shown again in the circuit diagrams. Use RF = 100k and R1 resistance

given by your lab station number in Resistors.pdf. Calculate the expected gain using the tolerances on the resistors.

2. Connect the oscilloscope ground to the supply ground. Using the supply ground and a meter check that

DC levels of +/- 15V supplies and record the values.

3. Using the signal generator and the oscilloscope apply a 1kHz, 0.5V peak-to-peak sinusoidal signal at

the circuit input. Use the second channel on the scope to observe the output voltage. What is the gain

of the circuit? Compare it to the expected value.

4. Increase the size of the input signal until you observe clipping in the output waveform indicating that

the output stage of the amplifier is saturating. You may have to connect the Wavetek generator signal

to the high setting. What is the peak-to-peak voltage of the clipped output waveform?

Tips: a) Don't short the output to ground (that is where you take the measurement).

b) Make sure to connect all GNDs (Power Supply + Signal Input + Oscilloscope) together.



3.2 Summing Amplifier

1. Use circuit 3.2 shown in Fig. 4 using RF = 100k, R1 and R2 resistor given by your lab station

number in Resistors.pdf.

2. Use the signal generator to supply a 0.5 volt peak-to-peak 1kHz sine wave as V1 and connect this to

channel 1 on the scope. Use the DC supply to make V2 a 0.5 volt DC level

3. Make sure the scope channels are DC COUPLED. Screenshot the output waveform in your book.

Note the location of the peaks relative to ground (what difference does DC/AC coupling make on

the scope?)

4. Increase V2 until the output just starts to clip (saturation). Note the value for V2 where saturation

occurs and screenshot the output waveform. Note the location of the peaks relative to ground.

3.3 Differentiator

The circuit shown in Fig. 6 acts as a differentiator and the gain of the circuit can be described using the

general equation as

V O = –RF dVi

CIdt such that the input and output waveforms are as shown in Fig. 5.

1. Build the circuit for Circuit 3.3 found below in Fig. 6. Use CI=0.1uF and RF= 10K.

2. Using the signal generator set Vi to a 1kHz 0.5V peak-to-peak sine wave. Using both scope channels

screenshot Vi and Vo as they appear together. Center the traces so their ground level is at the same point.

Record the peak-peak levels. Explain the difference between the two signals.

3. Increase the frequency of the input signal to 2kHz. Screenshot the input and output signals and record



the peak-to-peak levels. Explain the difference in the two signals.

4. Compare the phase-difference with the calculated values of pre-lab, in exercise 3 of pre-lab.

5. Return the input to a 1kHz signal and switch to a triangular waveform. Describe and explain the

behavior of the output signal.

3.4 High Pass Filter

A circuit like the differentiator may be used as a high-pass filter as shown in Fig. 7.

The behavior of the circuit is described by the following:

𝑣𝑜

𝑣𝑖=

−𝑅𝐹

𝑅𝐼⁄

1−𝑗(𝜔𝑜

𝜔⁄ ) where 𝜔𝑜 =

1

𝑅𝐼𝐶𝐼 is the 3dB cut-off frequency defined as (

𝑣𝑜

𝑣𝑖) |𝜔=𝜔𝑜

= −3𝑑𝐵



For o, the voltage gain (in dB) decreases with decreasing frequency at a rate of 20dB/decade.

Refer to your pre-lab calculations for a value for RI to construct a high-pass filter (Fig. 7)

1. Construct the circuit for 3.4 as found in Fig. 7 below. Change resistor values to the calculated values

of RI and RF in step 5 of prelab. What is the expected passband gain and 3-dB frequency based on the

measured values of resistors tolerances (5%), include the 50 Ohm source resistance in the calculations.

2. Construct an 8-line table in your lab book. Measure magnitude Vo and the phase difference at

frequencies of 300Hz, 600Hz, 1.2KHz, 2.5Khz, 5KHz, 10KHz, 20KHz, and 40Khz, put the values

in the table. Describe how the relative phase of the output and input signals change with frequency.

3. Note the gain of the filter as (Vo/Vi) dB and add it to the table using Bode Plotter. Screen shot the

bode plot of the circuit verses frequency. Use equally spaced points (1,2,3,4,5...) for the frequency

axis and label them with the frequency points, this approximates a log scale for the frequency axis.

Attach both a plot and table of data points.

4. Calculate the slope of (Vo/Vi) dB in the stop band and compare it to the 20dB/decade theoretical

value. Would incorrect component values change this slope?

3.5 Integrator

The operational amplifier can be used to integrate an input signal as shown in Fig. 8. The capacitor CF

has an infinite impedance at = 0, consequently the integrator has an infinite dc gain. This means that a

small dc component at the input of the amplifier will saturate it after some time. Therefore, in the case of integrating a periodic signal the source must be ac coupled to the integrator. Further reduction of the dc

gain can be achieved by connecting a large resistor RF in parallel with CF.

Refer to your pre-lab calculations for component values for an integrator (Fig. 8).

1. See 3.5 in your Multisim file, make sure everything is connected, and that all the components have the

correct values as calculated in prelab section 6.

2. Connect a 2 kHz square wave to the input of your integrator and screenshot the input and output

waveforms.



3.6 Low-Pass Filter (Modified Integrator Circuit)

A circuit similar to the integrator may be used as low-pass filter as shown in Fig. 9

For o, the voltage gain decreases at a rate 20dB/decade. o is the 3-dB cut-off frequency.

1. See 3.6 in your Multisim file, make sure everything is connected, and that all the components have the

correct values as specified in prelab section 7.

2. Set Vi = 1 volt peak-to-peak. Note the magnitude of Vo/Vin at frequencies of 300Hz, 600Hz, 1.2KHz,

2.5Khz, 5KHz, 10KHz, 20KHz, and 40KHz using the bode plotter. Screen shot a Plot of the gain of

the circuit v/s frequency. Use equally spaced points (1,2,3,4,5...) for the frequency axis and label

them with the frequency points, as you did in (3.4). Attach both a plot and table of data points.

3. Note the slope of (Vo/Vi) dB in the stop band using two points on the bode plotter. Compare

this value to the 20dB/decade theoretical value.

4. Input a square wave of frequency equal to 1kHz to the low pass filter and screenshot the output

waveform.



4.0 High and Low Pass Filter Bode Plots

For this lab, each station is connected to a summing amplifier. The DG1022Z waveform generator creates

two signals which are fed into V1 and V2 while the resistors R1 and R2 are replaced with a digital

potentiometer. Using the amplification, inversion, and summation, you must create several arbitrary

waveforms using the waveform generator and the summing amplifier. Access your assigned lab computer

using LabStats and the Remote Desktop Application like you had done in lab 1 and complete part 3 of this

lab. There three applications which are used for this lab, the Oscilloscope Remote Front Panel, Rigol DG1022

(Rigol) function generator application, and Carleton University ELEC2507 GUI (Digital Potentiometer)

application. See each of their desktop shortcuts below:

FIG. 10. Example Applications from Left to Right: Waveform Generator, DigiPOT, Oscilloscope

Physical Station Setup

The setup for each lab station is as follows:

FIG. 11. Lab Station Connections

The voltage V1 and V2 are controlled by the Rigol DG1022 app, the probes CH1 and CH2 are measured by

the R&S Scope 01, and the DigiPOT is controlled by the Carleton University elec2507 GUI.

Rigol DG1022 (Rigol)

If the signal generator is on, then you will find the application appear like this:

https://remoteaccess.labstats.com/Carleton-University-Electronics-Engineering-elec2507



FIG. 12. Rigol Function Generator (DG1022_UI)

The VISA code should not be changed when open, otherwise the instructions cannot be sent. There are

five options which can be changed for each of the outputs, along with six different waveforms, the four

central buttons control and send the output commands. The highlighted channel (CH) selects which channel

is to be sent, channel 1 (CH1) controls V1 and channel 2 (CH2) controls V2, and while the channel is selected,

hitting the Send button will change the properties of the waveform of the corresponding output. Enabling or

disabling Output1 or Output2 using these buttons will turn the voltage signals on or off. Be creative when

using these two channels.

Carleton University DigiPOT GUI

FIG. 13. Digital Potentiometer Controls

There are three connectors to the Digital Potentiometer: high, low, and wiper. The wiper is connected to the

first channel of the oscilloscope, while the high and low are connected to V1 and V2. Varying the Resistors,

A and B allow for changes in influences from each of the input signals. The only especially important issue

which comes up when dealing with the digital potentiometer is the limited current. Please make sure to keep

the current through each of the resistors less than 4mA. To start hit the SET_MID button.



Rhode & Schwarz Oscilloscope Portal

This oscilloscope uses Channel 1 and Channel 2 for the inputs 1 and 2 of the summing amplifier CH4 is the

summation of these signals. Using the camera on the desktop, we can see the circuit it is probing. If one

opens the scope shortcut on the desktop as seen in FIG. 10, they will need to access the Remote Front Panel,

and set the scope horizontal and vertical scalars to see the following:

FIG. 14. Oscilloscope Screen



4.1 Arbitrary Waveform Building

Using two signals V1 and V2 we can build some interesting waveforms using the summing amplifier. Try using each

of the tools described in this section to build some arbitrary waveforms. Build the following waveforms for the output

of the summing amplifier (Ch4):

FIG. 15. Waveform A “The Broken Heart”

FIG. 16. Waveform B “Crags and Crests”

FIG. 17. Waveform C “Modified Stair Wave”

FIG. 18. Waveform D “Broken Mountain Pass”

Please include a screenshot of your built waveform, the digital potentiometer settings, and the settings from the

waveform generator that were used to build the same. Vary the phase, frequency, magnitude, offset, duty cycle, and

waveform shape to achieve your desired results.

manual lab 2: operational amplifier

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