Lab 1: The Digital Multimeter - College of Engineering...

Department of Electrical and Computer EngineeringUniversity of Colorado at Colorado Springs

"Engineering for the Future"

ECE2205: Circuits and Systems I Lab 1–1

Lab 1: The Digital Multimeter

1.1 Objective

The objective of this lab is to gain proficiency using a digital multimeter to measure resistance, dc voltage, and dccurrent. You will also learn how a real multimeter behaves differently from an ideal multimeter.

1.2 Pre-Lab Preparation

Read the lab overview in section 1.3 and answer the questionsbelow. The instructor is to review your answers beforeyou begin the lab tasks.

1. What color code designates a 1Ä, 10% resistor?

2. What color code designates a 1kÄ, 5% resistor?

3. What color code designates a 10MÄ, 1% resistor?

4. What is the ideal resistance of a voltmeter?

5. What is the ideal resistance of an ammeter?

6. How do you measure a voltage between two points in a circuit? (draw a diagram)

7. How do you measure a current between two points in a circuit? (draw a diagram)

8. How do you measure the resistance of a circuit element?

Be sure to bring a graphite pencil to the lab!

1.3 Background

The dc power supply and the multimeter. This laboratory assignment will introduce you to two of the laboratoryworkhorses: the dc power supply, and the digital multimeter. Each workstation in the electronics lab possesses oneAgilent E3630A triple output dc power supply, drawn in Fig. 1.1, and one Agilent 34401A digital multimeter, drawnin Fig. 1.2. The multimeter can be used as a voltmeter, ammeter, or ohmmeter, depending on how it is configured.The workstations have other equipment, which will be investigated in more detail in later labs.

Please be careful with these (and all other) laboratory instruments. They cost thousands of dollars to replace.

A voltmeter is designed to measure the voltage between any two points in a circuit, when the circuit is energized.If the voltage to be measured isv12 = v1 − v2, then the black probe is placed on node 2 (corresponding tov2) andthe red probe is placed on node 1 (corresponding tov1). Since the voltmeter is placed in parallel with a part of thecircuit it potentially can disrupt circuit operation. Ideally, a voltmeter’s resistance is infinite—in which case therewould be no change in circuit operation.

An ammeter is designed to measure current at a point in an energized circuit. To take this reading, the circuit mustbe disconnected at the point of interest and the ammeter inserted in series with the circuit at that point. Again,

Lab reader prepared by & Copyright c© 2006, Dr. Gregory L. Plett, ECE Dept., CU Colorado Springs

ECE2205, Lab 1: The Digital Multimeter Lab 1–2

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Figure 1.1 The Agilent E3630A triple output dc power supply.

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Figure 1.2 The Agilent 34401A digital multimeter.

the ammeter can potentially disrupt circuit operation. Ideally, an ammeter’s resistance is zero—in which case therewould be no change in circuit operation.

An ohmmeter is designed to measure the resistance of a device. To do so, the device must be disconnected fromthe circuit (or else the resistance of the device in parallelwith the circuit is measured). Two-wire and four-wireresistance measurement techniques are possible, as discovered in the laboratory exercise.

Resistors. You will also be working with resistors. These are located inthe shelving units in the lab. Resistorvalues are designated using a color code: see Fig. 1.3. Most resistors have four colored bands. The first three bandsindicate the nominal value of the resistor and the fourth band indicates the manufacturing tolerance in value. Thefirst two bands form the mantissa, and the third the exponent of 10. Values corresponding to the colored bands aretabulated in Table 1.1. Many offensive mnemonics exist to help memorize the color bands, but if you want a G-ratedversion: “Black Beetles Running On Your Garden Bring Very Good Weather”.

First band: First digitSecond band: Second digitThird band: MultiplierFourth band: Tolerance

Figure 1.3 Resistor color code example.

Table 1.1 TABLE OF RESISTOR COLOR BAND VALUES.

Color First digit Second digit Multiplier ToleranceBlack 0 0 1 ±20%Brown 1 1 10 ±1%Red 2 2 100 ±2%Orange 3 3 1,000 ±3%Yellow 4 7 10,000 ±4%Green 5 5 100,000 NABlue 6 6 1,000,000 NAViolet 7 7 10,000,000 NAGray 8 8 100,000,000 NAWhite 9 9 1,000,000,000 NAGold NA NA 0.1 ±5%Silver NA NA 0.01 ±10%

The tolerance band is typically either gold or silver. A goldtolerance band indicates that the measured value willbe within 5% of the nominal value. A silver band indicates 10%tolerance. For example a resistor with color codebrown-black-red-silver indicates a nominal value of 1 kÄ. The first two bands (brown-black) produce the mantissa(10) and the third band (red) is the exponent of ten (102 = 100). So the value is 10× 100= 1, 000Ä or 1kÄ. Since



the tolerance band is silver, we can expect the measured value of the resistor to be between 900Ä and 1100Ä. Asanother example, a 47kÄ, 20% resistor has color code: yellow-violet-orange-black.

1.4 Lab Assignment

Task 1: Prelab Certification. Have the Lab Assistant/Instructor review your answers to the prelab assignmentquestions and sign the certifications page.

Task 2: Orientation. Visually examine the set of test instruments at your lab station. You should find the followinginstruments:

• Agilent E3630A triple output dc power supply;

• Agilent 33120A function generator;

• Agilent 34401A digital multimeter;

• Agilent 54624A digitizing oscilloscope.

In addition, you should also find a PC and a switch-box that connects the PC to the oscilloscope. You will be usingall of these instruments this semester.Locate the dc power supply. Examine the controls on its frontpanel. This is a relatively simple instrument to use.It is used to provide dc (constant) voltages and currents. Itis important to prevent the leads of the dc power supplyfrom touching each other. When the power supply leads touch,a short circuit is formed which can cause seriousdamage to the power supply. Consider what would happen if youshorted the wall socket, or a car battery! Shortcircuits can be dangerous, and special care should be taken to avoid them.Locate the digital multimeter. Examine the controls on its front panel. This instrument is used to measure voltage,current and resistance. When configured to measure voltage,its function is a voltmeter. Likewise, it may functionas an ammeter or as an ohmmeter.It will be extremely important that you become comfortable (and proficient!) with the use of all lab test instruments.

Task 3: Measuring Resistance (Two-Wire). The most common way to measure a resistance is to use a two-wireohmmeter. The meter places a small voltage across the deviceunder test, measures the current that flows, and usesOhm’s law to calculate the resistance.

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Figure 1.4 Two-wire resistance measurement setup. A “minigrabber” probe is shown to the right.

1. Select a (nominal) 1kÄ resistor. Record the complete color-code of the resistor you used (and particularly thetolerance of the resistance).

2. Use minigrabber probes to connect the multimeter to both terminals of the resistor, as shown in Fig. 1.4.

3. Set the multimeter to measure resistance. To do this, press the softkey labeled “Ä2W”. Determine the actualvalue of the resistor. The words “actual” and “measured” maybe used interchangeably.

4. Compute the percent difference between the actual (measured) value of the resistor and the nominal value of1kÄ as indicated by its color code. Record the actual and percentdifference values. Hang on to this particularresistor—you will use it again later.



Task 4: Measuring Resistance (Four-Wire). The two-wire resistance-measurement method works well in mostsituations. However, it introduces errors for measuring small resistances (e.g., values less than about 10Ä). Theproblem is that you are measuring the resistance ofboth the device under testand the probe wire leads. The scenariois illustrated in Fig. 1.5.

Deviceundertest

Test lead 2

Deviceundertest

Test lead 1

Test lead 2

Test lead 1

Test lead 3

Test lead 4

i(t)

i(t)

i(t)

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i(t) ≈ 0

i(t) ≈ 0

v(t) v(t)R R

R1R1

R2 R2

R3

R4

Figure 1.5 Two-wire (left) versus four-wire (right) methods for measuring resistance.

In the two-wire scheme, a voltage is imposed on the test leadsand the device under test by the multimeter. Currentflows through the circuit according to the total resistance.The current will be

i(t) =v(t)

R1 + R2 + R.

The current is measured and the resistance is estimated asR ≈ v(t)/ i(t) = R1 + R2 + R. If the resistance of theleads is significant compared to the resistance being measured, the two-wire scheme is not adequate.

In the four-wire scheme, a voltage is imposed on one pair of the test leads, again causing a current to flow. Whilethis current is measured, it is used differently in the calculation. A second pair of test leads connect to the terminalsof the device under test, and the voltage across that pair of test leads is measured. Current flowing through these testleads is approximately zero since the voltmeter has approximately infinite resistance. Therefore, the true resistanceof the device under test may be much better approximated asR = v(t)/ i(t).

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Figure 1.6 Four-wire resistance measurement setup.

1. Select a 1Ä resistor. Record all color bands of the resistor.

2. Repeat the steps from task 3 to measure the resistance using the two-wire method.

3. Now, the four-wire method: Use minigrabber probes to connect the multimeter to both terminals of the resistorusing two pairs of test leads, as shown in Fig. 1.6.



4. Set the multimeter to measure resistance. To do this, press the softkey labeled “shift” and then the softkeylabeled “Ä2W”. This selects the “Ä4W” function. Determine the actual value of the resistor.

5. Compute the percent difference between the actual (measured) value of the resistor and the nominal value of1Ä as indicated by its color code. Record the actual and percentdifference values. Compare results measuringthe 1Ä resistor using both methods.

Task 5: Graphite Resistor. You will now create a sequence of carbon resistors. Based on their measured values,you will draw conclusions about the relationship between their physical dimensions and resistance.

1. Using a pencil, draw a rectangle whose length (approximately 1") is twice its width on a sheet of paper. Fillin the rectangle with pencil mark. Measure and record the resistance over the length and then over the widthof the graphite resistor.

2. Using a pencil, draw a square whose side-length is approximately 1". Fill in the square with pencil mark.Measure and record the resistance over the width of the graphite resistor.

3. Based on your measurements, draw conclusions relating the physical dimensions and resistance. Draw resis-tors with other shapes, if necessary. Record your measurements and conclusions.

Task 6: Biologic Resistor.

1. Holding one probe between the thumb and forefinger of each hand, measure the resistance of your bodybetween your hands. Squeeze the probes tightly so that good contact is established. Record the value of yourbody’s resistance. You should probably use a standard probetip (cf. Fig. 1.7) to ensure good contact.

2. Considering that a current of 100–200 mA through your heart will almost certainly kill you, how much voltageacross your hands would be lethal?

Figure 1.7 Standard probe to be used to measure the biologic resistor.

Task 7: Measuring Current and Verifying Ohm’s Law.

1. Configure the multimeter to measure voltage by pressing the “DC V” softkey. Configure the meter on the dcpower supply to display the voltage on the +6V output by pressing the “+6V” softkey. Adjust the voltage ofthe power supply using the “+6V” knob until it reads 5V. Measure the exact voltage using the multimeter.

2. Assemble the circuit in Fig. 1.8. The figure shows the physical setup of the experiment, with the schematic ofthe circuit also shown in the inset. You will use the (nominal) 1kÄ resistor you measured previously.

3. Set the multimeter to measure dc current by pressing the shift softkey followed by the “DC V” softkey (forthe “DC I” function). Make sure that the leads are in the correct jacks in the front panel of the multimeter.

4. Measure the current flowing through the resistor. An ammeter measures the current flow from the red probeto the black probe within the meter. Does this value agree with Ohm’s Law?

5. Measure the current flowing through the resistor in the opposite direction. This is done by reversing the leadsof the ammeter. Does this value agree with Ohm’s Law?

Task 8: Ideal versus Practical Voltmeter An ideal voltmeter has infinite resistance: It is an open circuit. Al-though it is impossible to make a physical voltmeter with infinite resistance, a well designed voltmeter exhibits avery large internal input resistance. In some experiments,it is important to take into account the finite, non-ideal,internal resistance. To determine the internal resistanceof the voltmeter, set up the circuit shown in Fig. 1.9. Thevoltmeter reads the voltage across itself, which includes its internal resistance. Since the circuit has only a sin-gle branch, the current flowing through the resistor also flows through the voltmeter. The current is given by the



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Figure 1.8 Setup for verifying Ohm’s law.

equation:

I =Vs − Vm

R,

whereVs is the source voltage (nominally 5V in this experiment),Vm is the voltmeter-measured voltage, andR isthe value of the (nominal) 10MÄ resistor. From Ohm’s Law, if we know the current and the voltmeter-measuredvoltage, we can compute the voltmeter resistanceRm .

Rm =Vm

I=

VmVs−Vm

R

=RVm

Vs − Vm.

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Figure 1.9 Setup for determining the voltmeter’s internal resistance.

1. Select a (nominal) 10MÄ resistor. Record all color bands of the resistor.

2. Measure its value using the multimeter. Record this value.

3. Set the power supply to provide 5V (Remember, always measure the voltage provided by the power supplywith the voltmeter. Do not rely on the digital display on the front panel of the power supply.)

4. Assemble the circuit in Fig. 1.9.



5. Record the voltage measured by the voltmeter.

6. Compute the internal resistance of the voltmeter. Recordall values.

Task 9: Ideal versus Practical Ammeter An ideal ammeter has zero resistance so that the the circuit in which ithas been placed is not disturbed. An ideal ammeter is a short circuit. However, as with the voltmeter, no ammetercan ever be ideal, and therefore all ammeters have some (hopefully) small internal resistance. To determine theresistance of the ammeter, we will use the circuit in Fig. 1.8, although with a different value of resistance.

According to Ohm’s Law, the current in this circuit will beI = Vs/Rtot whereRtot = R + Rm . The discrete resistorR has value (nominally) 100Ä in this experiment. We can re-write this relationship as:I = Vs/(R + Rm). By usingthe known quantitiesI , Vs and R, we can solve for the unknown quantityRm . In the procedure that follows it isextremely important that you take precise and accurate measurements. Record each measurement as precisely as theinstrument will allow.

1. Select a (nominal) 100Ä resistor. Record all color bands. Measure and record its actual value.

2. Measure the voltage across the dc power supply. It should be set to a nominal value of 5V.

3. Assemble the circuit in Fig. 1.8, but substituting the 100Ä resistor for the 1kÄ resistor in the figure.

4. Set the multimeter to the ammeter mode for dc current measurement. Recall this means two things: Place thetest leads in the correct banana jacks on the front panel and press the proper sequence of softkeys.

5. Measure the value of the current using the ammeter and determine the value ofRm . Record all values.

Task 10: Lab report. Submit your results in the form of a typed report. While content is clearly the primary ob-jective, neatness and organization will be weighted significantly in the grading of your lab reports. Circuit diagramsmay be hand-drawn, but wires should be drawn using a straightedge. A good laboratory report is concise whileproviding enough detail such that another person could reproduce the results. Another person should be able to readyour lab reports and know what you did and how you did it. Your lab reports should not contain the degree of detailpresent in the lab manual. Try to keep your reports as conciseas possible without deleting essential information.Provide minimum procedure statements (e.g., “We obtained four 22 nF capacitors.”). You may assume thatthereader has knowledge and proficiency in the use of the lab instruments. Writing of lab reports is not intended to be“busy work” in which you simply rephrase what is stated in thelab manual. You should provide data, calculations,as well as comments, observations, and conclusions to indicate your understanding.

The Department requires formal lab reports which must satisfy the following format rules:

1. Title page: This must include a title, name, course and section name and date of the lab assignment (not thedue date of the lab writeup).

2. Table of Contents (with page numbers).

3. Introduction: Explain the background and objective of the lab indicating requirements and desired results.

4. Discussion: Discuss the underlying applicable theory and concepts that support the measurements and/orsimulations. Indicate and discuss the measurement/simulation set-up and equipment used.

5. Measurement/Simulation Data and/or Results: Present measurement results in tabular, graphical or numericform. Present results from required lab exercises. Organize according to task.

6. Discussion of Measurements: Discuss measured data and results of simulation in context of comparison toexpectation, accuracy, difficulties, etc. Organize according to task.

7. Summary and Conclusions: Discuss findings, explain errors and unexpected results; to what extent were theobjectives achieved?; summarize and indicate conclusions. Organize according to task. Also answer specificquestions (below).

Further requirements on the lab report are:



1. Correct spelling, grammar and punctuation is required.

2. Report must be typed; figures, drawings and equations may be handwritten.

3. Format of references (if any) must conform to IEEE (transactions) standards.

In this lab report, please also address the following questions:

• Suppose you set the voltage of the dc power supply to 5V. You connect it to a circuit and the voltage providedby the power supply drops to 3V. What happened?

• What is the “resolution” of a digital display? Compare the resolution of the digital display on the front panelof the dc power supply to the display on the front panel of the multimeter. Why must you use the multimeterif you wish to set the dc supply to 0.755V?

• In task 6, you measured the dc resistance between your left and right hands. To make this measurement, theohmmeter applied a small (known) voltage and measured the resulting current. The ratio of applied voltage toresulting current is the resistance between the ohmmeter probes (in this case, the resistance between your leftand right hands). Based on the resistance you measured, you calculated the voltage range that would cause100–200 mA of electric current to flow through your body and termed this “the lethal voltage.” However,in “real life,” the lethal voltage would be far less than the value you calculated.Voltages above 50V areconsidered potentially lethal (really clever people have even been able to kill themselves with lower voltagesthan this). You are to explain in detail why the lethal voltage is in fact much less than the value you calculated.Your explanation should include the change in skin resistance that occurs when an electric shock occurs andother physiologic effects of electric shock that can be lethal (e.g., pulmonary failure).

• Comment on how close the digital multimeter is to ideal with respect to measuring voltage and current. Whenmight the meter not be accurate?





Lab 2: Kirchoff’s Laws

2.1 Objective

The objective of this lab is to continue developing proficiency in the use of the digital multimeter in the contextof verifying Kirchhoff’s Voltage and Current Laws (KVL and KCL). In the process you will investigate both thevoltage-divider and current-divider circuit, you will become familiar with the use of the breadboard, and you willlearn how to build light-sensor circuits.



1. Let the voltmeter in Fig. 2.3 be represented by a resistance Rm . Derive Eq. (2.2) for this circuit.

2. Recall that an ideal voltmeter has infinite resistance. Letting the value ofRm in Eq. (2.2) be infinite shouldresult in the familiar voltage-divider equation (2.1). Derive Eq. (2.1) from Eq. (2.2) by taking the limit asRm → ∞. L’Hôpital’s Rule may be helpful.

3. Suppose that you measure the full-light and full-dark resistances of two CdS cells and find:R1,low = 90Ä,R2,low = 100Ä, R1,high = 32kÄ, andR2,high = 37kÄ. Find resistancesR3 andR4 to match the characteristicsof these CdS cells. Which scenario is this?

4. Suppose that you measure the full-light and full-dark resistances of two CdS cells and find:R1,low = 90Ä,R2,low = 100Ä, R1,high = 37kÄ, andR2,high = 32kÄ. Find resistancesR3 andR4 to match the characteristicsof these CdS cells. Which scenario is this?

Be sure to bring your Matlab codeminfn1.m andminfn2.m to the lab. If you have a bright flashlight, bring thattoo.

2.3 Background

Prototyping a circuit using a breadboard. The solderless breadboard (sometimes called a protoboard)is the mostcommon type of prototyping circuit board. Prototyping a circuit is valuable for complete evaluation of its designand performance. This requires the circuit to be designed, built and tested in the laboratory. Theoretical calculationsand computer simulation are generally part of the design process. Once the circuit configuration is determined, thecircuit is built on a prototyping board. There are two main types of prototyping circuit boards:

1. Solderless breadboards,

2. Perfboard.


ECE2205, Lab 2: Kirchoff’s Laws Lab 2–2

Perfboard is a thin slab of either epoxy glass or phenolic with small holes punched through it at a 0.1" spacing. Acircuit built on perfboard requires either soldering or wire-wrapping the connections. A circuit built on a breadboardrequires neither soldering nor wire wrapping the connections.

Your laboratory instructor will assign to you a breadboard on which you will build your circuits throughout thesemester. This breadboard has a single (two-sided) terminal strip, two bus strips, and three binding posts as shownin Fig. 2.1. The terminal strips and bus strips have many holes (contact receptacles) with a 0.1" spacing where wiresor circuit-element terminals may be inserted. The real value of a breadboard is not as a pincushion, however, but asa wiring aid. The secret is in the hidden wiring inside the breadboard that helps you connect components together.

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Figure 2.1 R.S.R. Electronics MB-102-PLT solderless breadboard.

Each bus strip has two rows of contacts. Each of the two rows ofcontacts on the bus strips comprise a single node.That is, every contact along a row on a bus strip is connected together with wiring hidden inside the breadboard. Busstrips are used primarily for power supply connections but are also used for any node requiring a large number ofconnections. The terminal strip has 5 rows and 63 columns of contacts on each side of the center gap. Each columnof 5 contacts is a node. The internal connections of the breadboard are illustrated in the zoomed cutout view inFig. 2.2 as orange (grey) lines.

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Figure 2.2 Zoomed cutout view of breadboard, showing internal connections.

You will build your circuits on the terminal strips by inserting the leads of circuit components into the contactreceptacles and making connections with 22 AWG (American Wire Gauge) wire. There are wire cutter/strippers andspools of wire in the lab. You will be using the red and black binding posts for power supply connections. Hence, itis a good idea to wire them to a bus strip.

Using the multimeter as a voltmeter. A voltmeter is a device for measuring voltage. It measures and displays thevoltage (potential difference) of the positive (e.g., red) probe with respect to the negative (e.g., black) probes. The



voltmeter is placed in parallel with the circuit element whose voltage is to be measured. Recall that two elements arein parallel when they share the same pair of nodes and hence share the same voltage. Consider the voltage dividercircuit shown in Fig. 2.3 in which the voltage acrossR2 is to be measured. If the presence of the voltmeter does notaffect the voltage it is intending to measure, the meter mustdraw no current. That is, it must act as an open circuit.An open circuit may be thought of as an infinite resistance. Hence, an ideal voltmeter has an infinite resistance. Youmeasured the internal resistance of the voltmeter in Lab 1 and found the value to be on the order of 10MÄ, which islarge, but certainly not infinite.

Red probe

Black probe

Voltmeter

R1

R2vs

Figure 2.3 Voltage divider circuit, with voltage measured by real voltmeter.

First consider the circuit with the voltmeter not present. In this case the voltagev2 across the resistorR2 can beexpressed in terms of the source voltagevs and the resistorsR1 andR2 by

v2 = vsR2

R1 + R2. (2.1)

With the voltmeter present, its resistance alters the voltage division equation, which becomes

v2 = vsR2Rm

R2Rm + R1(R2 + Rm), (2.2)

where Rm is the resistance of the voltmeter. You will not be able to seehow this equation was obtained at firstexamination. Let the voltmeter in Fig. 2.3 be represented bya resistanceRm . Use resistance reduction and voltagedivision to obtain an expression forv2 in terms ofvs . Then, clear the fractions in the numerator and denominator.Be sure to show your derivation in your lab report. You will now build the voltage divider circuit using the dc powersupply as the voltage sourcevs in Fig. 2.3.

Using the Multimeter as an Ammeter An ammeter is a device for measuring current. It measures thecurrentflowing into the positive (e.g., red) probe and out of the negative (e.g., black) probes of the meter. The ammeteris placed in series with the circuit element whose current isto be measured. Recall that two elements are in serieswhen they share in the same branch and hence share the same current. The ideal ammeter will have zero rresistance,thus not alter the resistance or current of the branch whose current is being measured. Consider the current dividercircuit shown in Fig. 2.4. The currenti1 throughR1 may be expressed as a fraction of the currentis flowing out ofthe source in terms ofR1 andR2 using current division

i1 = is

1R1

1R1

+ 1R2

= isR2

R1 + R2. (2.3)

In this lab you will build the current divider circuit and make several measurements. Recall that your ammeter isnot ideal—in fact you measured its resistance in the first lab. The resistance of the ammeter will be an importantconsideration when measuring currents in the circuit shown. Record all measured values and present percent errorcalculations and tables as appropriate.

10kÄ

R1 R2vs

Figure 2.4 Current divider circuit.



Photoresistors (CdS Cells) Photoresistors are a special kind of resistor that change their value when exposed tolight. Some types increase resistance while others decrease resistance. One common photoresistive substance iscadmium-sulfide (CdS), out of which “CdS cell” photoresistors are made. Figure 2.5 shows both a picture of a CdScell and its schematic symbol (sometimes the schematic symbol is drawn with arrows pointing at the cell to indicateimpinging light).

Figure 2.5 CdS photoresistor pictorial representation (left) and schematic representation (right).

Photoresistors may be used in a voltage-divider circuit forthe purpose of sensing the intensity of light. Figure 2.6gives an example of how this sensor circuit may be designed. In the circuit,R1 is a known resistor andvs is a knownvoltage. By measuringvCdS, we can computeRCdS and from there infer the level of light. Here is how:

1. First, a table of CdS resistance versus light level is created.

2. By re-arranging the voltage-divider equation, we find that

RCdS =vCdS

vs − vCdSR1.

3. We measurevCdS, computeRCdS, and use the table to look up the light level.

R1

vCdS

vs

Figure 2.6 CdS-cell light sensor using voltage divider.

Balancing Two CdS Cells The above method for constructing a light sensor works well if you have a speciallycalibrated table of resistance versus light level for the CdS cell that you are using. A practical problem, however,is that all CdS cells require slightly different calibration tables. If your circuit is being used in some embeddedsystem, the software can be written to automatically calibrate the sensors (you have had some experience with thisin ECE1001: Introduction to Robotics).

If you want to match the performance of two CdS cells electronically, however, you must follow a different approach.In this lab, we will consider some circuit modifications so that the two CdS cells have identical resistances at twodifferent reference light settings. For example, if you were constructing a line-following robot, you might wantidentical readings over the dark part of the line and over thewhite part of the background. Here, we will calibrateidentical readings in maximum darkness and maximum brightness.

First, we measure the minimum resistances of both CdS cells (in maximum brightness). We denote the CdS cell withthe lower of these values “CdS cell 1” and the other as “CdS cell 2”. Then, we measure the maximum resistancesof both CdS cells (in maximum darkness). There are two possible scenarios: (1) CdS cell 1 has the lower maximumresistance as well; or (2) CdS cell 2 has the lower maximum resistance.

In the first scenario, we replace the CdS cells in the voltage-divider circuits with the circuit shown in the left frameof Fig. 2.7. R3 is a resistor in series with CdS cell 1 to increase its lower resistance value (a side effect that wemust consider is that its higher resistance value is also increased). R4 is a resistor in parallel with CdS cell 2 todecrease its higher resistance value (a side effect is that its lower resistance value is also decreased). If we match the



conductances of these two cells at both low and high ends, we must satisfy the following equations:

1

R1,low + R3=

1

R2,low+

1

R4

1

R1,high + R3=

1

R2,high+

1

R4.

Notice that these are two simultaneous equations in two unknowns (R3 and R4). Further, they are nonlinear! Wecan do some algebra to solve them, or we can ask Matlab to iteratively solve the equations using an optimizationtechnique. First, re-arrange the equations as

e1 =1

R1,low + R3−

1

R2,low−

1

R4

e2 =1

R1,high + R3−

1

R2,high−

1

R4.

The new “variables”e1 ande2 are “equation errors”. If these errors are zero, then both equations are unmodified.We will ask Matlab to pick values forR3 and R4 such thatJ = e2

1 + e22 is minimized, and ifJ is “small enough”

then we have solved the equations. Before we see how, let’s first consider the second scenario.

CdS Cell 1CdS Cell 1 Cds Cell 2 Cds Cell 2

R3 R3

R4 R4

Figure 2.7 Two scenarios for matching CdS-cell characteristics. “Scenario 1” is on the left; “Scenario 2” is on the right.

In the second scenario, we replace the CdS cells in the voltage-divider circuits with the circuit shown in the rightframe of Fig. 2.7.R3 is a resistor in series with CdS cell 1 to increase its lower resistance (a side effect that we mustconsider is that its higher resistance value is also increased). R4 is a resistor in parallel with CdS cell 1 to decreaseits higher resistance (a side effect that we must consider isthat its lower resistance value is also decreased). If wematch the resistances of these two cells at both low and high ends, we must satisfy the following equations:

R2,low = R3 +R1,low R4

R1,low + R4

R2,high = R3 +R1,highR4

R1,high + R4.

Again, we re-arrange these equations into an equation-error format:

e1 = R3 +R1,low R4

R1,low + R4− R2,low

e2 = R3 +R1,highR4

R1,high + R4− R2,high.

When J = e21 + e2

2, minimizing J is the same as solving forR3 andR4, providedJ is “small enough”.

The easy way to solve forR3 and R4 uses Matlab’s optimization toolbox (available in the lab, but not included aspart of the student version). Specifically, you will invoke aMatlab procedure that will minimizeJ = e2

1 + e22 where

e1 ande2 are defined for whichever scenario you encounter. A Matlab function for computing the costJ if youencounter the first scenario is:

% Minimization function to determine cost for case where% CdS cell 1 has lower minimum resistance and lower maximum



% resistance than CdS cell 2. Therefore, CdS cell 1 needs% a resistor R3 in series and CdS cell 2 needs a resistor R4 in% parallel.

% The input "theta" comprises [R3, R4]. The output is the% matching error-squared (goal = 0).

function cost = minfn1(theta)global R1low R1high R2low R2highlowerror = 1/(R1low + theta(1)) - 1/R2low - 1/theta(2);higherror = 1/(R1high + theta(1)) - 1/R2high - 1/theta(2);cost = lowerror^2 + higherror^2

end

Similarly, a Matlab function for computing the costJ if you encounter the second scenario is:

% Minimization function to determine cost for case where% CdS cell 1 has lower minimum resistance and higher maximum% resistance than CdS cell 2. Therefore, CdS cell 1 needs% a resistor R3 in series and a resistor R4 in parallel.

% The input "theta" comprises [R3, R4]. The output is the% matching error-squared (goal = 0).

function cost = minfn2(theta)global R1low R1high R2low R2highlowerror = theta(1) + R1low*theta(2)/(R1low + theta(2)) - R2low;higherror = theta(1) + R1high*theta(2)/(R1high + theta(2)) - R2high;cost = lowerror^2 + higherror^2

end

The actual work gets done in Matlab using the following code segment:

global R1low R1high R2low R2highR1low = <insert value>;R1high = <insert value>;R2low = <insert value>;R2high = <insert value>;g3 = <insert value>; % initial guess for value of R3g4 = <insert value>; % initial guess for value of R4fminsearch(’minfn1’,[g3 g4])

Useminfn2 instead ofminfn1 in the last line if you encounter the second scenario. Valuesof R3 andR4 will bereturned from thefminsearch procedure.

Variable Resistors In order to match your two CdS cells, you will need to be able toconstruct the resistance valuesreturned by Matlab’s optimization routine. Since fixed-value resistors are only manufactured with certain nominalvalues, it is necessary to use a variable resistor (perhaps in combination with a fixed-value resistor) to achieve thedesired resistance. A variable resistor is a three-terminal device, depicted schematically in the left frame of Fig. 2.8.

Figure 2.8 The variable resistor, or potentiometer (“pot”).



Two terminals are connected across the full resistance. Thethird terminal is connected to a sliding contact that cansweep across the resistive surface to achieve any value between zero resistance and the full resistance of the device.A common configuration for wiring a variable resistor is shown in the right frame of Fig. 2.8. The slider terminal ishard-wired to one of the end terminals. Now, the end-to-end resistance is variable.

There are different kinds of mechanisms for adjusting variable resistors. Some have linear sliders; others haverotational sliders. The kind we will use in this lab use a screwdriver to rotate a small rotational slider. If you arecareful, you should be able to adjust the resistance in increments of roughly 1% of the full-scale resistance of thedevice.

2.4 Lab Assignment

Task 1: Prelab Certification. Have the Lab Assistant/Instructor review your answers to the prelab assignmentquestions and sign the certifications page.

Task 2: Check out a Breadboard Check out an “R.S.R. Electronics MB-102-PLT” breadboard from your labinstructor. You will be using this board throughout the semester. Obtain a piece of masking tape and affix it to thetop of your board. Write your name on the tape. After you have checked out your breadboard, examine it closelyand compare with Figs. 2.1 and 2.2. Use the ohmmeter to verifythe hidden wiring of Fig. 2.2.

Task 3: Voltage Divider with Moderate-Valued Resistors.

1. Obtain two 1kÄ resistors from the parts bin. Designate one of the resistorsasR1 and the other asR2

2. Measure and record the resistor values using the multimeter as an ohmmeter. Be sure to keep track of whichresistor corresponds to which value measured!

3. Build the circuit in Fig. 2.3 on your breadboard using the 1kÄ resistors forR1 andR2.

4. Set the power supply to 5V. Use the voltmeter, not the frontpanel display of the power supply to ensure theproper setting.Important note: You built the circuit before you set the power supply voltageto 5V. If thecurrent limiter is set to a value lower than than the current demanded by the circuit, the constant current (cc)indicator will light up and the voltage control knob will no longer adjust the output voltage. If this happens,simply increase the current limiter until you are able to achieve 5V in the constant voltage (cv) mode.

5. Using the voltmeter, measure the voltage across resistorR1, and then across resistorR2. Record these values,as always, and verify Kirchhoff’s Voltage Law (KVL).

6. Comment on the accuracy of measurements made consideringthe internal resistance of the voltmeter.

7. Create a table presenting theoretical and measured voltages along with percent error. Consider whether yourtheoretical values for the voltages acrossR1 andR2 should include the effect ofRm . Important Note: Whenyou are calculating percent error, you should avoid cases inwhich the theoretical value is zero since the percenterror is meaningless. To calculate percent error between theoretical and experimental verification of KVL, usethe source voltage as the reference. For example, in the measurements made in this section, the theoreticalvalue (and measured value!) for the voltage across the supply is 5V. The measured value is the same as thetheoretical value because you used the voltmeter to set the power supply voltage to 5V. To obtain the KVLmeasured voltage, add the voltage acrossR1 to the voltage acrossR2. Compare with 5V.

Task 4: Voltage Divider with Large-Valued Resistors

1. Obtain two 10MÄ resistors from the parts bin. Designate one of the resistorsasR1 and the other asR2.

2. Measure the resistor values using the multimeter as an ohmmeter. Be sure to keep track of which resistorcorresponds to which value measured!

3. Build the circuit in Fig. 2.3 on your breadboard using the 10MÄ resistors forR1 andR2.



4. Set the power supply to 5V.

5. Using the voltmeter, measure the voltage across resistorR1, and then across resistorR2. Record these values,and verify Kirchhoff’s Voltage Law (KVL).

6. Comment on the accuracy of the voltage measurements made (consider the internal resistance of the volt-meter).

7. Create a table presenting theoretical and measured voltages along with percent error. Consider whether yourtheoretical values for the voltages acrossR1 andR2 should include the effect ofRm .

Task 5: Current Divider with Moderate-Valued Resistors

1. Obtain two 1kÄ resistors from the parts bin. Designate one of the resistorsas R1 and the other asR2. (Youmay use the same resistors that you used in Task 3 if you wish).Also, obtain one 10kÄ resistor. Designatethis resistor asR3.


3. Build the circuit in Fig. 2.4 on your breadboard using the 1kÄ resistors forR1 andR2.

4. Set the power supply to 10V. Don’t forget to set the voltageusing the voltmeter rather than depending onthe front panel display of the power supply.Important Note: You built the circuit before you set the powersupply voltage to 10V. If the current limiter is set to a valuelower than than the current demanded by thecircuit, the constant current (cc) indicator will light up and the voltage control knob will no longer adjust theoutput voltage. If this happens, simply increase the current limiter until you are able to achieve 10V in theconstant voltage (cv) mode.

5. Using the voltmeter, measure the voltage across the 10kÄ resistor followed by the parallel combination ofresistorsR1 andR2. Record these values, as always, and verify Kirchhoff’s Voltage Law (KVL).

6. Configure the multimeter to measure current. Remember that this requires two things: Remove the terminalof the red probe from the voltage/resistance measuring receptacle and insert it in the current measuring re-ceptacle on the front panel of the multimeter. Then press the“shift” and “DC I” buttons to select dc currentmeasurement.

7. Measure the current through the 10V source. Remember thatyou have to break the circuit and insert theammeter in series with the 10V source to allow the current to flow through the ammeter.

8. Measure the current throughR1 and then the current throughR2.

9. Verify Kirchhoff’s Current Law (KCL). Remember that a theoretical value of zero produces a meaninglesspercent error.

10. Comment on the accuracy of the voltage measurements made(consider the internal resistance of the volt-meter).

11. Comment on the accuracy of the current measurements made(consider the internal resistance of the ammeter).

Task 6: Current Divider with Small-Valued Resistors

1. Obtain two 10Ä resistors from the parts bin. Designate one of the resistorsasR1 and the other asR2.


3. Build the circuit in Fig. 2.4 using the 10Ä resistors forR1 andR2.

4. Set the power supply to 10V. Don’t forget to set the voltageusing the voltmeter rather than depending onthe front panel display of the power supply.Important Note: You built the circuit before you set the powersupply voltage to 10V. If the current limiter is set to a valuelower than than the current demanded by the



circuit, the constant current (cc) indicator will light up and the voltage control knob will no longer adjust theoutput voltage. If this happens, simply increase the current limiter until you are able to achieve 10V in theconstant voltage (cv) mode.

5. Using the voltmeter, measure the voltage across the 10kÄ resistor followed by the parallel combination ofresistorsR1 andR2. Record these values, as always, and verify Kirchhoff’s Voltage Law (KVL).

6. Configure the multimeter to measure current. Remember that this requires two things: Remove the terminalof the red probe from the voltage/resistance measuring receptacle and insert it in the current measuring re-ceptacle on the front panel of the multimeter. Then press the“shift” and “DC I” buttons to select dc currentmeasurement.

7. Measure the current through the 10V source. Remember thatyou have to break the circuit and insert theammeter in series with the 10V source to allow the current to flow through the ammeter.

8. Measure the current throughR1 and then the current throughR2.

9. Verify Kirchhoff’s Current Law (KCL). Remember that a theoretical value of zero produces a meaninglesspercent error.

10. Comment on the accuracy of the voltage measurements made(consider the internal resistance of the volt-meter).

11. Comment on the accuracy of the current measurements made(consider the internal resistance of the ammeter).

Task 7: Check out a parts box Check out a “parts box”. Initially, this will only contain the two CdS cellsrequired for this lab exercise, and two variable resistors.However, you will collect other parts over the duration ofthe semester that you will keep in this box. At the end of the semester you will return the box, and all the parts. Affixa piece of masking tape on the back of the box and write your name on the masking tape.

Task 8: Matching CdS cells

1. Determine a way to differentiate between your two CdS cells. Perhaps you could use masking tape on theleads of one, or perhaps you can keep track using a position onthe breadboard.

2. Measure the full-dark resistance of both CdS cells. Coverthe cell’s surface completely with your finger tomake sure that it “sees” no light. Record both values.

3. Measure the full-light resistance of both CdS cells. It helps if you use a bright flashlight shining directly intothe cells. Record both values.

4. Determine whether your cells fall within scenario 1 or scenario 2.

5. Compute the resistancesR3 andR4 required to match the CdS cells.

6. Using the variable resistors from your parts box and perhaps some fixed resistors from the parts bins in thelab, construct the circuit(s) required to match resistances of the CdS cells.

7. Repeat the full-dark and full-light resistance measurements to verify that your CdS cells are now matched.Record the values. Are the cells matched under ambient lightconditions?

Task 9: Lab report. Submit your results in the form of a typed report. Refer to Lab1 for instructions regardingproper format and content of an acceptable lab report. Please also address the following questions:

• The current division equation (Eq. (2.3)) does not include the resistance of the ammeter. Let the internalresistance of the ammeter beRm . Write the expression for the currenti1 throughR1, including the resistanceof the meter assuming that the ammeter is being used to measure the currenti1. Then take the limit of thisexpression as the ammeter internal resistance goes to zero,showing that the limit is given by Eq. (2.3).



• The voltage source and 10kÄ resistor in Fig. 2.4 form an approximate current source for small load resistances.If the voltage source and 10kÄ resistor formed an ideal current source, then the currentis would be constant,independent of the resistances ofR1 andR2, which is certainly not the case. Consider the parallel combinationof R1 andR2 as a single resistanceRL . If RL is small compared to 10kÄ, then the current is will be very nearly1mA (Recall thatvs = 10V) independent ofRL . Calculate the range of values ofRL such that the current iswill deviate from 1mA by no more than 5%.

• Consider the circuit shown in Fig. 2.9. Suppose you want to know the value of all voltages and currents in thecircuit. Assume that you know nothing at all about the resistor values. You want the results to be as accurate aspossible. You have a multimeter that you may use as either a voltmeter or an ammeter. Explain the sequenceof measurements that you make. Comment on your level of confidence that your results are accurate. Don’tforget that you have Ohm’s Law and Kirchhoff’s Laws that may be used. Try to find the minimum set ofmeasurements required to solve for all unknowns.

R1

R2 R3vs

Figure 2.9 Resistive network.





Lab 3: Oscilloscope Crash Course

3.1 Objective

The objectives of this lab are twofold. First, you will learnhow to use many of the common functions of anoscilloscope and function generator (including some limitations of the latter). Secondly, you will gain hands-onexperience with the ubiquitous resistor-capacitor (RC) circuit.



1. According to the discussion on Fig. 3.2, a function generator will provide the set output voltage only if theconnected circuit (the “load”) has a resistance of 50Ä. If a peak-to-peak output voltage of 1V has beenrequested, what is the actual peak-to-peak voltage of the “source” inside the function generator?

2. Using Matlab, plot the Lissajous figures of two sinusoids having the same frequency, different amplitudes,and phase differences of 0,π/3, π/2, andπ radians. Using the plots and the Lissajous method, demonstratethat you can recover the phase from the ellipses. Do the amplitudes of the sinusoids matter? Why?

3. Of the two RC filters shown in Fig. 3.5, one is a low-pass filter (passing low frequencies but attenuating highfrequencies) and the other is a high-pass filter (just the opposite). Which is which? (Try puttingω = 0 intothe frequency response and finding the magnitude response ofboth).

4. By hand, find the step responses of the two RC filters via the method of your choice (e.g., convolution). Sincea square-pulse waveform may be created asp(t) = u(t) − u(t − τ ), sketch the square-pulse response of thetwo RC filters (you need to have the right shape, but not perfect detail).

5. A low-pass RC filter has a step response that achieves its steady-state value in about five time constants, wherethe time constantτ is defined asτ = RC. For R = 390 kÄ andC = 0.01µF, what isτ and how long do youexpect the step response of that filter to take to converge to steady-state?

If you have one handy, bring a 3.5” floppy disk to the lab to practice saving scope data to disk. This is not arequirement, however.

3.3 Background

Function Generator A function generator is used to generate source voltages in acircuit that vary with time.The Agilent function generator available in the electronics lab is depicted in Fig. 3.1. It can produce four primarywaveforms: sine, square, triangular and ramp, as well as other kinds of waveforms under computer control. Thereare three parameters that can be varied for each of the primary waveform types:


ECE2205, Lab 3: Oscilloscope Crash Course Lab 3–2

1. Peak-to-peak signal amplitude (0–10V);

2. Frequency (0–15MHz);

3. DC offset.

To set any of these features, press the button labeled with the feature you wish to modify (i.e., “Ampl”, “Freq”, or“Offset”). The present setting of this feature will appear.Notice that one of the digits is blinking—turning the dialwill affect this digit. You may change which digit is flashingby pressing the left or right arrow keys. It is alsopossible to enter a number directly by first pressing the button marked “Enter Number” and then typing the valueusing the keypad. Pressing “Enter” immediately following will alter the setting to the new value.

On

Power

Off Shift

Enter

MENUOn / Off

MHz

kHz

HzdBm

Back SpaceRecall Menu

ArbNoise

RecallSingleOffsetAmplFreqNumberEnter

42VMax

SYNC

OUTPUT

TRIG STATEMODIFY LOCAL

3 4 5 ±

6 7 8 9 0

2 1

.

Freq Level % Duty Internal Store CancelAM/FM

FUNCTION / MODULATION

Agilent 33120A15 MHz Function / Arbitrary Waveform Generator

Vppm

m Vrms

Arb ListAM FM FSK Burst Sweep

50 Ω

Figure 3.1 Function generator.

The function generator has an internal resistance of 50Ä and “expects” to be connected to a 50Ä load resistance,as shown in Fig. 3.2. When you select a signal amplitude on thefront panel, it will configure its internal sourceto provide that amplitude at the output terminals only if theload is in fact 50Ä. If the load that you connect hasa different resistance, then you will need to measure the function-generator output to ensure that it has the desiredamplitude. The voltage-divider equation can also be used tounderstand how the internal source voltage relates tothe voltage at the function generator’s terminals.

SourceCircuitLoad

InternalResistance

Figure 3.2 Assumed configuration for function generator. Both the internal resistance and the assumed load resistance are 50Ä.

Oscilloscope An oscilloscope (scope) is used to view one or more voltage waveforms on a built-in display. Thescopes in the lab also have the capability of uploading waveform data to a PC for further analysis and for inclusion inreports. Most often, the waveform is displayed as a functionof time; however, it is possible to show one waveformas a function of another waveform in a parametric plot. The Agilent oscilloscope available in the electronics lab isdepicted in Fig. 3.3.

This scope has four channels, each of which may have an input waveform to be displayed. Each channel has avertical placement knob that moves the waveform for that channel up and down. Each channel also has a knob thatselects the vertical scale of the waveform in terms of volts per division. Divisions are the visible grid lines on theoscilloscope screen. The knobs that set horizontal placement and horizontal scale in time per division control allchannels simultaneously.

The oscilloscope operates by sampling the input waveform(s) very quickly and plotting the sampled data on thescreen. Since only a short segment of time can be shown, the scope most naturally works with periodic waveforms—one or more periods are shown, and the rest of the waveform canbe inferred. However, it is also possible to causethe scope to sample a single “trace” of data starting with a triggering event and ending when the scope’s data bufferis full. We will explore both of these operating modes in thislab.



! !

1mV 1mV

Agilent

Probe Comp

500

5V5V5V5V 1mV 1mV

Meas

QuickPrint

MainDelayed

54624A 100 MHzOSCILLOSCOPE 200MSa/s

oomZMEGA

2 4Math

MorePattern

Edge

PulseWidth

Aquire

Utility

Display

SaveRecall

Auto−Scale

ModeCoupling

Level

1 432

~ 14 pF300 V Max

CAT I

~ 14 pF300 V Max

CAT I

1M Ω1M Ω

5ns50s

POWER

0 1

INTENSITY

Run

Stop

31

YX

Horizontal Run Control

TriggerMeasure Waveform

File

Vertical

Single

Cursors Quick

mv RUN

1

1 1.00 sm

/0.00s 1

Figure 3.3 Oscilloscope.

The scope face has knobs and buttons to control the more common operations of the device. Directly under thescope display are five other buttons called “softkeys” that change their function according to the present mode of thescope. Labels on the display directly above the softkeys identify the key functions at the present time.

Oscilloscopes have a bewildering number of possible settings, so that it is easy to get confused about the presentconfiguration. If you wish to reset the scope to the factory default configuration, simply press the “Save/Recall”button, and then the “Default Setup” softkey.

Saving Oscilloscope Data Oscilloscopes are often used to debug and understand circuit operation. They may alsobe used to help document circuit behavior. This can be done byuploading the measured information to a PC or bysaving the data to a floppy disk (remember what that is?). The saved information can then be included in a report.

The lab scopes are connected to the PC at their workstation using a serial RS-232 link. You will notice a switchbox on this cable that may be set either to “Oscilloscope” or “Open line”. Make sure that the switch is in the“Oscilloscope” position. Then, on the PC, first log in to yourUFP account. Run the “Intuilink Data CaptureApplication”. In the instrument menu select “54620/40 - Series” and click on the “Get Data” Icon. Two windowswill open after the upload is complete. One has a bitmap imageof the scope’s screen; the other contains a vectordrawing of the actual data that the scope is displaying. Whenthe image window is selected, you may save it to a“.bmp” file for inclusion in a report. When the plot window is selected, you may also save its data as a text file. Besure to select the “x-axis” button so that both time and value information is saved. An example of the text file is:

x-axis ch1-1.00000000E-03 -2.500E-04-9.80000000E-04 -2.500E-04-9.60000000E-04 -3.150E-02-9.40000000E-04 -3.005E-02-9.20000000E-04 -2.150E-02(etc)

If your text file does not have the “x-axis” column, you forgot to select the “x-axis” button. If you were displayingmore than one channel, there will be more than two columns.

The information in this file cannot be directly read into Matlab for plotting because of the first line, which containstext instead of data. Roger Perkins has written the following simple Matlab program that will read and plot the datain the file by first opening the file, discarding the first line, and then reading the rest of the data. If you know how todo file input/output in “C”, then the following will make sense.

% Template for plotting scope data data saved with x axisclc; clear;fid = fopen(’Waveform_test_all_data.txt’,’r’);



% First, read the line of text dataline1 = fscanf(fid,’%s’,2); % change ’2’ if there are more columns

data = fscanf(fid,’%e’); % get data now

time = data(1:2:end); % extract time columnvolt = data(2:2:end); % get voltage datafclose(’all’); % close data fileplot(time,volt);

grid on; title(’Scope Data’);xlabel(’Time (seconds)’); ylabel(’Voltage’);

Alternately, you can edit the text file with “Notepad”, delete the first line, and read the data file with the Matlabstatementload -ascii Waveform_test_all_data.txt.

The scope also has the ability to save data to a file on a floppy disk. To do so, press the “Save/Recall” key, then the“Save” softkey, and the “New File” softkey. The name of the file may be entered one character at time using theknob to the left of the “Cursors” key to select the present character, and then pressing the “Enter” softkey to acceptthat character. As practice, try saving the scope data to a disk using the filename “ROCK_ON”.

Determining Phase Difference—Lissajous Figures As we progress through this course, we will more-and-more-often be working with circuits containing capacitor and inductors—components that havev-i relationships that aredifferential equations. We will find that it is easiest to analyze these types of circuits in the frequency domain ratherthan the time domain.

Recall from ECE2610 that the frequency response of a linear-time-invariant (LTI) system predicts how the system’soutput compares to its input when the input signal is a sinusoid. The frequency response comprises both a magnituderesponse and a phase response. The magnitude response predicts how the amplitude of the output sinusoid is scaledfrom the amplitude of the input sinusoid. This is easy to measure on an oscilloscope: Simply measure how manyvolts peak-to-peak are displayed for a sinusoid, and divideby two to get its amplitude.

The phase difference between the input and output is a littletrickier to measure. One method is to display bothsignals simultaneously on the scope, measure the time difference between the zero crossings (tm) and compute thephase asφ = −ωotm = −2π fotm . Since phase is a signed quantity, it is important to measuretm from the inputwaveform to the output waveform.

A second method is to use “Lissajous (pronounced LEE-suh-zhoo) figures” named after their discoverer Jules An-toine Lissajous. The oscilloscope is configured to display two signals inx-y mode: the input signal is applied tothe horizontal axis of an oscilloscope, and the output signal is applied to the vertical axis. The resulting pattern is afunction of the ratio of the two frequencies and the phase shift between the signals. Since LTI systems do not changea signal’s frequency, the output pattern may be used to determine phase shift.

A sample Lissajous figure is displayed in Fig. 3.4. Two out-of-phase sinusoids displayed on anx-y plot produce anellipse. The phase difference between the sinusoids may be computed as either

sin(φ) = y2/y1, or sin(φ) = x2/x1.

Note that the origin must be at the center of the scope for thismethod to work. The scope cursors may be used tomeasurey1, y2, x1, and/orx2.

To gain some experience with Lissajous figures, the following Matlab script will create one for you:

% Create two out-of-phase sinusoids and plot the Lissajous% figure for them. amp1 and amp2 are the amplitudes of the two% sinusoids, freq is the frequency of the sinusoids, phase is



y

y1

y2

xx1 x2

Figure 3.4 Sample Lissajous figure.

% the phase shift between the sinusoids. Experiment to see% that the amplitudes and frequency do not change the basic% Lissajous pattern.function lissajous(amp1, amp2, freq, phase)clf;inc = 1/(freq*200); % plot 200 points in the ellipset = 0:inc:1/freq;x = amp1*sin(2*pi*freq.*t+phase);y = amp2*sin(2*pi*freq.*t);plot(x, y, ’k-’);

end

RC Filters The simple combination of a resistor and capacitor can create a circuit with interesting applications.There are two ways this can be done, as shown in Fig. 3.5. Both circuits result in frequency-selective filters.

vin vinvout vout

Scenario 1 Scenario 2

Figure 3.5 Two kinds of RC filter.

If the resistor has valueR and the capacitor has valueC, then the left circuit has differential equation (assumingnegligible load):

RCd

dtvout(t) + vout(t) = vin(t).

By using the differentiation property of the Fourier transform, we can find the Fourier transform of this differentialequation term-by-term:

RC jωVout( jω) + Vout( jω) = Vin( jω)

H ( jω) =Vout( jω)

Vin( jω)=

1

1 + jωRC.

The impulse response of this circuit may be found via inverseFourier transform of the frequency responseH ( jω)

and is

h(t) =1

RCe− t

RC u(t),

whereu(t) is the unit-step function.

The right circuit has differential equation



RCd

dtvout(t) + vout(t) = RC

d

dtvin(t).

We can similarly find its frequency response to be

H ( jω) =jωRC

1 + jωRC,

and its impulse response to be

h(t) = δ(t) −1

RCe− t

RC u(t).

3.4 Lab Assignment

Task 1: Prelab certification. Have the Lab Assistant/Instructor review your answers to the prelab assignmentquestions and sign the certifications page.

Task 2: The function generator assumed load impedance.In this section, we will be using the function gener-ator to provide a time-varying voltage which will then be measured using the oscilloscope.

Important: DO NOT let the leads from the function generator touch each other! If the function generator leads toucheach other, either the internal fuse will blow or serious damage to the instrument can occur. It is very important thatyou keep this in mind at all times.

Important: The function generator has an internal resistance of 50Ä. The voltage displayed on its front panel isthe voltage that would appear at its terminals if it were connected to a 50Ä load. Under open circuit conditions, thevoltage across the terminals of the function generator is twice as large as the value indicated on its front panel. Thisis an important concept and often misunderstood.

1. Set the function generator to produce a 10 kHz sine wave with 1V peak-to-peak.

2. Connect the oscilloscope channel directly to the output of the function generator.

3. Locate the “Vertical” section on the front panel of the oscilloscope. It is the section that includes the connec-tions of the scope probes to the scope.

4. Press the key labeled “1”. Adjust the signal’s vertical position to be centered on the screen using the up/downknob; adjust the volts/division so that the signal nearly fills the screen; adjust the time scale using thetime/division knob in the “Horizontal” section on the frontof the scope. Your lab TA may rap your knuckleswith a solid object if you even think about touching the “Auto-Scale” button, so beware!

5. Press the “Cursors” key and adjust the scope’s displayed measurement value to determine manually the peak-to-peak voltage of the input signal. Then, press the “Quick Meas” key to double-check your result. In general,the “Quick Meas” is less accurate since it does not average out noise as you can do visually, and hence over-predicts peak-to-peak amplitude. Observe that the measured peak-to-peak voltage is approximately twice thepeak-to-peak voltage shown on the front panel of the function generator.

6. Using the automatic measure features (“Quick Meas”) of the oscilloscope, determine the frequency, and theperiod of the sinusoidal voltage.

7. Measure the peak-to-peak voltage by hand,i.e., count the vertical divisions from the minimum to the maximumand multiply by the number of volts per division. The volts per division setting is shown in the upper left cornerof the scope screen.

8. Using the same screen, measure the period of the sine wave,i.e., count the number of horizontal divisions inone period of the sine wave. The time per division setting is shown at the top-right-center of the scope screen.

9. Using the formula, frequency = 1/period, determine the frequency of the sine wave.



10. Connect the function generator across a (nominal) 51Ä resistor. Leave the settings on the function generatorunchanged.

11. Connect the oscilloscope channel 1 probe across the resistor (and function generator).

12. Repeat the measurement of peak-to-peak voltage. Observe that the measured peak-to-peak voltage is approx-imately the same as the peak-to-peak voltage shown on the front panel of the function generator. Hence, thevoltage at the terminals of the function generator is load dependent. Whenever you use the function generatorto provide a voltage waveform and desire a specific amplitude, you must use either the multimeter or the scopeto set the desired voltage because the value shown on the front panel of the function generator is valid only fora 50Ä load.

Task 3: Upload waveforms to a PC. In this section, you will experiment with shifting and scaling waveformsmanually on the scope display, and uploading these waveforms to the PC.

1. Set the function generator to produce a 100 Hz square wave.When displayed on the scope screen, theamplitude should be 2 V peak-to-peak.

2. Configure the scope to display as close to exactly one period of this wave as possible (filling the screen).

3. Upload the scope display to the PC; save the display as a “.bmp” file (include in your report); also, save thedisplay data as a “.txt” file to be plotted in Matlab and included in your report. Be sure to select the option tosave thex-axis information as well!

4. Repeat steps 2–3 except show two periods of the wave, and have the bottom of the wave align with the middleof the display, and the top of the wave align with the top of thedisplay.

5. Repeat steps 1–3 with a 1 kHz sine-wave source.

6. Repeat steps 1–3 with a 100 kHz triangle-wave source.

7. Optionally, save data to a floppy disk.

Task 4: RC low-pass filter, integrator In the prelab exercise you determined which circuit in Fig. 3.5 was thelow-pass filter. We will investigate that circuit here (no hints—you figure it out!).

1. Construct the RC low-pass filter usingR = 390 kÄ andC = 0.01 µF. Use an square-wave input to thiscircuit with frequency 100 Hz.

2. Connect channel 1 of the scope to the input and channel 2 to the output (press the “2” button on the scope todisplay channel 2 as well).

3. Adjust the function generator so that the input waveform is 2 V peak-to-peak. Include this figure in yourreport.

4. Estimate the time constant of the circuit from the scope waveform. If necessary, adjust the frequency of thesquare wave to make this possible. The most reliable way of determining the time constant is to measure thetime it takes the output signal to climb from 0% to 63% of its final value. Is this the same as the time taken tofall from 100% to 37%? (If not, something is amiss in your way of taking these readings!)

5. Now, drive the circuit using a 1 kHz triangle wave, 10 V peak-to-peak; what is the output waveform called?(Doesn’t this circuit seem clever? An inanimate object performing calculus!). Include this figure in yourreport.

6. Does the integrator work for all frequency inputs? Can youfind frequencies for which it works well, andothers for which it does not?

7. Drive the circuit using a 1 kHz, 10 V peak-to-peak sine wave. What should the magnitude response be at thisfrequency? What should the phase shift be?



8. Measure the magnitude of the signal at the input and the output. What is the ratio of these magnitudes? Whatshould the ratio be?

9. Measure the phase shift between the input and output usingthree methods:

(a) Automatic method 1: Press the “Quick Meas” key, then the “Select” softkey (select “phase”), then the“Measure Phase” softkey.

(b) Automatic method 2: In the same menu as above, press the “Select” softkey (select “delay”), then the“Measure Delay” softkey.

(c) Lissajous figure: Press the “Main/Delayed” key on the “Horizontal” section of the scope panel. Pressthe “XY” softkey. Make sure you adjust the “0” position on both axes, then use the Lissajous method tocompute phase. Upload the Lissajous figure to the PC for inclusion in your report.Note: Due to the low frequency input, you will need to also press the “Display” key in the waveformmenu, then the “∞ persist” softkey. This allows the entire Lissajous figure tobe displayed on the scopeand uploaded to the PC.

Task 5: RC highpass filter, differentiator In the prelab exercise you determined which circuit in Fig. 3.5 was thehighpass filter. We will investigate that circuit here (again, no hints—you figure it out!).

1. Construct the RC highpass filter usingR = 390 kÄ andC = 0.01 µF. Use an square-wave input to thiscircuit with frequency 100 Hz.

2. Connect channel 1 of the scope to the input and channel 2 to the output (press the “2” button on the scope todisplay channel 2 as well).

3. Adjust the function generator so that the input waveform is 2 V peak-to-peak. Include this figure in yourreport.

4. Now, drive the circuit using a 10 Hz triangle wave, 10 V peak-to-peak; what is the output waveform called?(Doesn’t this circuit seem clever? Pretty speedy doing calculus, huh?). Include this figure in your report.

5. Does the differentiator work for all frequency inputs? Can you find frequencies for which it works well, andothers for which it does not?

6. Drive the circuit using a 10 Hz, 10 V peak-to-peak sine wave. What should the magnitude response be at thisfrequency? What should the phase shift be?

7. Measure the magnitude of the signal at the input and the output. What is the ratio of these magnitudes? Whatshould the ratio be?

8. Measure the phase shift between the input and output usingthree methods:

(a) Automatic method 1: Press the “Quick Meas” key, then the “Select” softkey (select “phase”), then the“Measure Phase” softkey.

(b) Automatic method 2: In the same menu as above, press the “Select” softkey (select “delay”), then the“Measure Delay” softkey.

(c) Lissajous figure: Press the “Main/Delayed” key on the “Horizontal” section of the scope panel. Pressthe “XY” softkey. Make sure you adjust the “0” position on both axes, then use the Lissajous method tocompute phase. Upload the Lissajous figure to the PC for inclusion in your report.

Task 6: Bouncy switch. Sometimes even simple circuits produce mystifying results. One of these is the pushbut-ton switch circuit shown in Fig. 3.6. This kind of circuit might be connected to a micro-controller chip. The programin the micro-controller would continuously look at the output voltagevout(t). If the switch is not pressed, we expectthat the output voltage is zero (connected to ground throughthe “pull-down” resistor). If the switch is pressed, weexpect that the output voltage is near the input voltage (especially if the resistor has a large value).



vin vout

Figure 3.6 A circuit with a pushbutton switch.

However, strange things can occur. For a single press of the pushbutton, the output can very quickly turn “off” and“on” several times before settling at its final value. This isdue to arcing at the switch contacts, mechanical vibration,and other effects. Since the switch output is not a periodic waveform, it is not possible to see this effect using thestandard scope techniques.

The scope has another mode, where it displays a single sweep or frame of data. The data collection can be started(“triggered”) by some external event. We will explore this method here.

1. Obtain a pushbutton switch from your lab instructor. Notethat the switch will most likely have four wirescoming out of it. Use your multimeter to determine the internal connections.

2. Construct the circuit in Fig. 3.6. UseR = 1 MÄ. Connect the inputvin = 5 V using the dc power supply.Connect the output to channel 1 of the scope.

3. In the “Trigger” section of the front panel, press the “Edge” key and then the “1” softkey.

4. Press the “Mode/Coupling” key. The left softkey will havea “Mode” menu—select “normal”.

5. Use the “Level” knob from the same section of the front panel to adjust the trigger voltage to 2.5 V.

6. Press the “Single” key on the “Run Control” section of the front panel. The display should go blank.

7. Press your pushbutton. This should trigger the scope and display the output voltage. Adjust the time/divisionknob to be able to see detail in your trace. Be sure to show thiswaveform in your report.

As a comment, the switches you will be using provide a relatively clean signal. Some switches, especially toggleswitches, are absolutely terrible.

Task 7: De-bouncing the switch with an RC filter, Design an RC-filter circuit to put in series with the pushbuttonswitch to eliminate the bounce of the switch as much as possible. You will need to select values forR andC (I suggestthat you keep the 0.01 µF capacitor since resistors in different values are much more common, and you can use yourvariable resistors from Lab 2 to tune your design if necessary). Your circuit should turn on quickly when the buttonis pressed, but should smooth the bounce as much as possible.You might take a time-constant approach to design,or a frequency-response approach by estimating the frequency of bounce ripple and attenuating that frequency.

Construct this circuit and measure the voltage at the switchoutput (using the scope, of course) when the button ispressed. Include this figure in your report, as well as all your calculations and your final circuit design.

Task 8: Lab report. Submit your results in the form of a typed report. Refer to Lab1 for instructions regardingproper format and content of an acceptable lab report. Please also address the following questions:

• Suppose you set the function generator such that it producesa 1 kHz sinusoidal voltage with 5V peak-to-peak across a 25Ä load. What will be the peak-to-peak voltage displayed on thefront panel of the functiongenerator?

• Consider an arbitrary circuit with source voltage providedby a function generator and monitored by an os-cilloscope. Compare the values for the peak-to-peak voltage and frequency that would be 1) specified by thefunction generator, 2) measured by the oscilloscope and 3) determined manually from measurements carefullytaken from the scope screen. Assuming no calculation error on your part, do the measurements made manu-ally differ from those made by the oscilloscope? Which of thethree methods do you think are more accurate?Justify your answer.



• We saw that the high-pass filter was able to differentiate itsinput signal. Is the ideal differentiator a specialcase of the high-pass filter, or is the high-pass filter a special case of the differentiator? Why?

• We saw that the low-pass filter was able to integrate its inputsignal. Is the ideal integrator a special case ofthe low-pass filter, or is the low-pass filter a special case ofthe integrator? Why?

Also be sure to include scope display data wherever requiredin the Lab Assignment section. Use actual uploadeddata (either the bitmap or Matlab output, as requested, or ifnot specified, as your preference). Do not sketch byhand.





Lab 4: Basic Op-Amp Circuits

4.1 Objective

The objectives of this lab are gain familiarity with operational amplifiers, read and understand terms related to theparameters of operational amplifiers from its data-sheets,and learn to measure and understand limiting factors toop-amp operation.



1. Download the LM741 specifications from the course web site. For the LM741C, tabulate the typical andmaximum (if given) input offset voltage, input offset current, input bias current, input resistance, and slewrate. Include units in your table!

2. Label all op-amp diagrams in this lab writeup with correctpin numbers on all input/output and power supplysignals.

Come prepared to work efficiently. There are a lot of circuitsto build. Also, if you have one handy, bring a largemongoose. You never know. . .

4.3 Background

Operational Amplifiers Operational amplifiers, or op-amps for short, got their namefrom the modules used inanalog computers to perform “operations” such as adding, multiplying and so forth. Now they are integrated circuitsfor application as general feedback amplifiers. They seem easy to use, but the many types available and the greatvariety of ratings hint that their use requires considerable knowledge and skill, which is true. In this lab and thenext, we will examine a dozen or so circuits that will give a good understanding of how to use op-amps in variousapplications.

The power supply for an op-amp is normally bipolar, with voltages above and below ground, calledV+ and V−.Most common op-amps can stand up to 36 V, or±18 V. It is convenient for our experiments to use±15 V, but±12 V and even±9 V will also work, (the latter are usually available from multi-output power supplies). You canalways arrange a bipolar supply from two ordinary supplies.Ground in this case is merely a voltage between thesupply “rails”, as they are called, of no special significance. Op-amps have no ground terminal, since this referenceis unnecessary. If you have trouble remembering polarity, have lots of op-amps around, since they are instantlydestroyed by any mistake. (Just kidding. Sort of. Don’t be burning up my op-amps!)

The pinouts of several common op-amps are shown in Fig. 4.1. They are packaged in standard “dual-inline-packages” (DIP) with 0.1” spacing between pins and 0.4” spacing between one row of pins and the other. Youcan identify which is pin 1 by the indent on the top of the actual IC, which corresponds to the indent drawn in the


ECE2205, Lab 4: Basic Op-Amp Circuits Lab 4–2

figure. The figure shows the op-amp from the top, with pins numbered from upper left, down one side and up theother to upper right, according to standard convention. The411 uses JFET-type transistors in its input stage, and isquite suitable for our purposes. The 741 uses bipolar-type transistors, long a standard. These two op-amps can beused interchangeably in most circuits. The dual 411 is the 412, and the dual 741 is the 1458. The 351 is anotherpopular JFET-input op-amp. The actual part numbers of a 741 op-amp, for example, are often preceded with letterslike “LM” and followed by other letters, like “CN”. These distinguish one flavor of the 741 op-amp from another,each having slightly different specifications, but overallthe same pinout and design. We will simply refer to thebasic type of op-amp by its number.

Top View

Offset N1

IN−

IN+

NC

OUT

411, 741, 351

Offset N2

Top View

412, 358, 1458

OUT1

IN1−

IN1+

OUT2

IN2−

IN2+V−

V+

V+

V−

2

1

3

4

8

6

5

7 2

1

3

4

8

6

5

7

Figure 4.1 Op-amp pinouts.

The connections marked+ and− are the inputs to the op-amp, and the connection from the point of the triangle isthe output. The output can go from a value nearV+ to a value nearV− . When the output is near one of these limitsand can go no farther, it is said to be saturated. You can short-circuit an output if you want, since it is internallyprotected against too much current. On the other hand, the output will handle only up to about 20mA at best. Op-amps are not for power applications, but can drive a power amplifier (usually transistors) if power is needed. Theoutput is proportional to the difference in voltagev+ − v− between the two inputs, wherev+ is the voltage at the+or non-inverting input, andv− the voltage at the− or inverting input. The voltage gain of the amplifier is perhaps100,000 or 100 dB at low frequencies for open-circuit operation (no feedback).

With such a gain, the voltage difference between the inputs must be very small if the output voltage is not to be atsaturation. This amounts to a rule: the voltages at the inputs are equal when a circuit is working properly. In orderto make the voltages at the inputs equal to each other, it is necessary to arrange this by feedback. (Essentially) allop-amp circuits use feedback, and the properties of the circuit are determined by the feedback, not by the propertiesof the op-amp.

Thecommon-mode input signal is the average of the potentials of the two input connections. Since they are usuallyat the same voltage, this voltage is the common-mode input voltage. The op-amp ignores the common-mode input,and determines its output only by the difference signal. Nevertheless, it is important to look at the common-modeinput voltage and see that it does not leave its permissible range. The common-mode range of an op-amp is almostalways less than fromV+ to V−, and the op-amp usually does something unpleasant when the range is exceeded (the411, for example, goes from a large negative output suddenlyto a large positive output when this happens).

That the inputs are usually at the same voltage does not mean that they can be connected to each other. If you dothis, the output usually saturates. The voltages must be held equal by the active participation of the output, actingthrough the feedback network. The inputs also carry a small dc bias or leakage current that must have a route tothe power supply. With bipolar op-amps, this current is actually the base bias current for the input transistors, andsometimes has to be considered in the circuit design. JFET’s, on the other hand, have a much smaller input currentthat is largely leakage, and does not affect the circuit much—except that it has to have a route to ground. In ordinarycircuit analysis, the bias currents can be neglected, and itcan be assumed that the inputs carry no current. Don’tforget that this is only approximate!

The most important factor hidden from the casual user of op-amps is the question of stability. Stability is alwaysimportant with high-gain amplifiers, and when feedback is applied. The feedback loop can become the route fora signal to be fed back to the input in the proper phase to causeoscillation, called instability. Without some care,



feedback always results in instability, which is always fatal. The oscillation can occur either at a higher or a lowerfrequency than that for which the circuit is designed, usually higher (like the feedback with a microphone andspeaker). With ordinary op-amps (e.g., 741), stability is guaranteed by making the gain fall off at20 dB per decadeof frequency, beginning at about 10 Hz, so that the gain of theamplifier falls to unity at around 1 MHz. Unlessyou have capacitors in unfortunate places, this guaranteesthat the circuits you put together will be stable, no matterwhat you do. What you pay for this is a severe restriction on the bandwidth of op-amp circuits, and overcoming it isadvanced work.

Op-Amp Specifications: Reading the data sheet. When you download the “data sheet” for an op-amp (a tech-nical publication describing a device’s function, ratings, and limitations), you will see quite a number of parametersof the device described. You should understand how to read a data sheet and discover the information that you need.

Absolute Maximum Ratings tabulate factors that the op-amp can safely tolerate without the possibility (likelihood?)of destroying it. However, it is generally recommended thatyou operate a device at 75% or less of its maximumratings.

• Supply Voltage (±VS): The maximum positive and negative voltages that can be used to power the op-amp.

• Power Dissipation (Pd ): The maximum power the op-amp is able to dissipate, at ambient temperature.

• Differential Input Voltage (Vid ): This is the maximum voltage that can be applied across the+ and− inputs.

• Input Voltage (Vicm ): The maximum input voltage that can be simultaneously applied between either inputand ground (also referred to as the common-mode voltage).

• Output Short Circuit Duration: How long a short circuit (output to ground or to either supply voltage) can besustained without damaging the device.

• Operating Temperature Range (Ta): This is the ambient temperature range for which the op-ampwill operatewithin the manufacturer’s specifications. Note that the military grade versions have a wider temperature rangethan the commercial, or hobbyist, grade version.

Electrical Characteristics tabulate factors that describe how the input and output parameters of the op-amp differfrom an ideal op-amp model.

• Input Offset Voltage (Voi ): This is the voltage that must be applied to one of the input pins to give a zerooutput voltage. Remember, for an ideal op-amp, input offsetvoltage is zero!

• Input Bias Current (Ib): This is the average of the currents flowing into both inputs. Op-amps are designed sothat the two input bias currents are nearly equal and nearly zero.

• Input Offset Current (Ios): This is the difference of the two input bias currents when the output voltage is zero.

• Input Voltage Range (Vcm): The range of the common-mode input voltage (i.e., the voltage common to bothinputs and ground).

• Input Resistance (Zi ): The resistance “looking-in” at either input with the remaining input grounded.

• Output Resistance (Zoi ): The resistance seen “looking into” the op-amp’s output.

• Output Voltage Swing (Vomax): Depending on what the load resistance is, this is the maximum “peak” outputvoltage that the op-amp can supply without saturation or clipping.

• Output Short-Circuit Current (Iosc): This is the maximum output current that the op-amp can deliver to a load.

• Slew Rate (SR): The time rate of change of the output voltage with the op-amp circuit having a voltage gainof unity (1.0).



• Common-Mode Rejection Ratio (CMRR): A measure of the ability of the op-amp to reject signals that aresimultaneously present at both inputs. It is the ratio of thecommon-mode input voltage to the generatedoutput voltage, usually expressed in decibels (dB).

Push-Pull Transistor Amplifier. Most op-amps cannot provide very large output currents. This means that theycannot directly drive low-impedance loads, such as speakers for audio application, and motors for robotic appli-cation. In these situations, the designer has two options: (1) purchase an expensive op-amp that is designed forhigh-current output, or (2) build a separate current-amplifier circuit. The second scenario is frequently chosen be-cause it is often less expensive.

The current amplifier we will build is a simple “push-pull” circuit. It consists of two power transistors: one to“push” current through the load, and one to “pull” current through the load, allowing us to apply bi-directionalvoltages across the load. This is important for audio applications, otherwise we would clip half the signal, and formotor applications, otherwise we could only run the motor inone direction. (If we only wished to run the motor inone direction, a single transistor would suffice.)

The push-pull amplifier that we will use is incorporated in the circuit drawn in Fig. 4.17. The push-pull sectionitself is the portion of the circuit to the right of the 390Ä resistor and to the left of the 1 kÄ resistor (not includingthe resistors). The three-terminal component on the top (connected to the+15 V supply, the 390Ä resistor and theoutput) is called an NPN transistor (you can tell because thearrow is Not Pointing iN). The three terminals are calledthe base (B), collector (C), and emitter (E). This transistor allows current to flow from its collector to emitter (“turnson”) if the base voltage is (sufficiently—approximately 0.7 V) higher than its emitter voltage. The three-terminalcomponent on the bottom is called a PNP transistor (you can tell because the arrow is Pointing iN Perpetually). Thistransistor allows current to flow from its emitter to collector (“turns on”) if its base voltage is (sufficiently) lowerthan its emitter voltage.

Thorough discussion of transistor function is beyond the scope of this course. Even so, we can easily understand themacroscopic operation of this circuit. For sufficiently positive values of the input voltage, the NPN transistor willturn on, and the output voltage (at its emitter) will be about0.7 V lower than the input voltage (at its base). Currentflows from the+15 V supply through the load to ground. For sufficiently negative values of the input voltage, thePNP transistor will turn on, and the output voltage will be about 0.7 V higher than the input voltage. Current flowsfrom ground through the load to the−15 V supply. Notice that both transistors will never be simultaneously “on”.

This is a very simple amplifier. It has some undesirable properties, such as a deadband when the input voltage isaround 0 V (|vin| . 0.7 V). We could do better by incorporating feedback around thepush-pull circuit. Also, it maybe a good idea to protect the amplifier using additional “flyback” diodes if driving an inductive load such as a motor.The latter will be done in Lab 5. For now, this simple circuit will serve the purpose.

As a practical note, the NPN transistor we will be using is a TIP31C, and the PNP transistor we will be using isa TIP32C. Both have an industry-standard package termed a “TO-220” three-terminal case. This is also drawn inFig. 4.17, with the base, collector, and emitter pins labeled. The three terminals need to be twisted 90 using needle-nose pliers in order to properly fit in your breadboard. Also,you will need to attach heatsinks to both parts to helpdissipate heat.

4.4 Lab Assignment


Task 2: Open-loop test circuit. Before you to build your first op-amp circuit we make three practical points:

1. First, how the integrated circuit (“IC”) package goes into the breadboard. It straddles the trench, as shown inFig. 4.2. A white dot sometimes identifies pin 1, and a divot onthe top is also generally used to identify thetop (and hence pin 1 is to the left of the divot).



F

G

H

50 55 60

B

A

C

D

E

411

Figure 4.2 Op-amp on a breadboard.

+15 V

−15 VFigure 4.3 Decoupling the op-amp from the power supplyusing ceramic capacitors.

2. Second, a point that may seem to go without saying, but sometimes needs a mention: the op-amp alwaysneeds power, applied at two pins; nearly always that means±15V in this course. We remind you of thisbecause circuit diagrams ordinarily omit the power connections. On the other hand, many op-amp circuitsmakeno direct connection between the chip andground. Don’t let that worry you; the circuit always includesa ground—in the important sense: common reference called zero volts. Whatever color convention you usefor your wires, you should use the green binding post of the breadboard for ground, the black for−15 V andthe red for+15 V.

3. “Decouple” the power supplies with a small ceramiccapacitor (0.01µF to 0.1µF) if you begin to see fuzzon your circuit outputs. Op-amp circuits, using feedback inall cases, are peculiarly vulnerable to “parasiticoscillations.” The decoupling method is shown in Fig. 4.3. Place the capacitors physically as close to the op-amp as possible. The capacitors act as high-pass filters thatlet high frequencies escape to the power supply.

4. Construct the open-loop test circuit in Fig. 4.4 using a 411 op-amp. Pin 8 is not connected. (Honest, it’sonly there so that the amplifier can fit in a standard 8-pin package.) Pins 1 and 5 are used to eliminate offsetvoltage—we won’t be using this feature right away, so don’t connect anything to these pins either.

5. With the power supply not yet connected, set the meter selector on the power supply to the+20 V setting.Adjust the voltage until the meter reads+15 V. Turn off the supply, and connect it to the binding posts,asdirected above.

6. Watch the output voltage as you slowly adjust the pot, trying to apply 0 volts tov+. Is the behavior consis-tent with the 411 specification that claims “Gain (typical) =200V/mV”? Don’t spend too long on this step,however; this is a most abnormal way to use an op-amp. Hurry onto the useful circuits!

+15 V+15 V

−15 V−15 V

41110 kÄ

Figure 4.4 Open-loop op-amp configuration.

vinvout411

10 kÄ1 kÄ

Figure 4.5 Non-inverting amplifier.



Warning: Do not try to unplug the op-amp with your thumb and forefinger.It’s a good way to end up with theop-amp plugged into your fingertip. Use an IC puller (in your toolboxes), or carefully use a small screwdriver to prythe op-amp off of the breadboard.

Caution: The components we’ve used so far have been simple (only two terminals) and fairly rugged (connectinga resistor or most capacitors “backward” won’t harm them). The op-amp has four times as many pins, so it’s easierto make a mistake in wiring it. Unfortunately, it’s also considerably more delicate, so connecting it incorrectly candestroy it (often without so much as a puff of smoke to let you know that it has become aninoperational amplifier).The moral—always wire your circuit with the power turned offand check your wiring carefully before turning thepower on.

Task 3: Non-inverting amplifier. The first feedback circuit we analyze is a non-inverting amplifier.

1. Wire up the non-inverting amplifier shown in Fig. 4.5. Measure and record the actual resistance values used.What is the theoretical gain of this amplifier? Measure and record the actual gain.

2. What is the maximum output swing? How about linearity (trya triangle wave)?

3. Try sine waves of different frequencies. Note that at somefairly high frequency the amplifier ceases to workwell: sinusoidal input does not produce sinusoida output. What is the approximate range of frequencies thatproduce sinusoidal output? (We will postpone until later measuring the slew rate that imposes this limit; weare still on our honeymoon with the op-amp: it is still ideal.).

Task 4: Inverting amplifier. Now, we construct a simple inverting amplifier.

1. Construct the inverting amplifier drawn in Fig. 4.6. If youhave been paying attention, you will notice that youdon’t need to start fresh: you can use the non-inverting amplifier, simply redefining which terminal is input,which is grounded.

2. Drive the amplifier with a 1 kHz sine wave. What is the theoretical gain? What is the measured gain? Is it thesame as for the non-inverting amp you built a few minutes ago?

3. Now drive the circuit with a sine wave at 1 kHz again. Measure the input impedance of this amplifier circuitby adding 1 kÄ in series with the signal source (simulating a signal sourcewith crummyRout). If you supposethat the 1 kÄ in series with your signal source representsRout for your source, then use the voltage-dividerequation to find the amplifier’s input resistance.

4. Using a second 411, build a voltage-follower circuit to place between the source with crummyRout and theinput to this inverting amplifier. This should solve the poorRsourceproblem we have created for you. With thefollower’s help, your circuit’s overall gain should jump back up to its original value. Does it?

vinvout411

10 kÄ

1 kÄ

Figure 4.6 Inverting amplifier.

vinvout411

−15 V +15 V

10 kÄ

1 kÄ

15 kÄ

10 kÄ“Offset”

Figure 4.7 Summing amplifier.

Task 5: Summing amplifier. Modify the inverting amplifier slightly, to form the circuitshown in Fig. 4.7.

1. This circuit sums a dc level with the input signal, lettingyou add a dc offset to a signal. What is the maximumpositive dc level added to the output voltage? What is the maximum negative dc level added to the outputvoltage?



Task 6: Integrator. Now, we construct an (approximate) integrating circuit.

1. Build the circuit shown in Fig. 4.8.

2. Try driving your integrator with a 1 kHz square wave. This circuit is sensitive to small dc offsets of the inputwaveform (its gain at dc is 100); if the output appears to go into saturation near±15 V, you may have to adjustthe function generator’s dc-offset control.

3. From the component values, predict the peak-to-peak triangle wave amplitude at the output that should resultfrom a 2 V peak-to-peak, 500 Hz square wave input. Then try it.

4. This is not an “ideal” integrator circuit, in part due to the addition of the 10 MÄ resistor. What is the functionof that resistor? What would happen if you were to remove it? Try it. Now have some fun playing aroundwith the function generator’s dc offset—the circuit will help you gain a real gut feeling for the meaning of anintegral!

5. Don’t take this circuit apart. You will need it in the next task.

vinvout411

10 MÄ

100 kÄ

0.01 µF

Figure 4.8 Integrator.

vinvout411

100 kÄ

1 kÄ

100 pf

0.01 µF

Figure 4.9 Differentiator.

Task 7: Differentiator.

1. Now, build the differentiator circuit in Fig. 4.9. Leave your integrator circuit intact, and use a second op-ampto build this circuit. Try driving it with a 1 kHz triangle wave.

2. A note on stability: Here we are obliged to mention the difficult topic of stability. A simple differentiatornecessarily lives at the edge of instability for reasons beyond the scope of our discussion here. To circumventthis problem, it is traditional to include a series resistorat the input, and a parallel capacitor across the feedbackresistor, converting the (low-frequency) differentiatorto an integrator above some cutoff frequency. You candetermine this crossover frequency by monitoring the inputand output of the differentiator when the input is asinusoid. When there is no phase shift, the circuit is crossing from one type to the other. For this circuit, whatis that crossing point? Incidentally, a faster op-amp wouldperform better: the switch-over to integrator mustbe made, but the faster op-amp allows one to set that switchover point at a higher frequency.

3. Integrate the Derivative—A more intriguing way to see theimperfection of the differentiator is to feed itsoutput to the integrator you built earlier, then compare original against output waveforms. Ideally, they wouldbe identical—at least in phase (that is, apart from gain artifacts). Are they? Does the answer depend on inputfrequency?

Task 8: Voltage follower—slew rate. We now introduce you to the sordid truth about op-amps: they’re not asgood as we’ve been saying! Sorry.

We begin by measuring slew rate and its effects, with the voltage-follower circuit in Fig. 4.10. Slew rate is themaximum rate at which the output of an op-amp can change. Ideally, the circuit has an output voltage that tracks theinput voltage exactly, but in practice the slew rate will introduce a delay and a ramping shape. Explore slew rate intwo phases:



vin

vout41110 kÄ

Figure 4.10 Voltage follower.

vin

vout4111 MÄ

Figure 4.11 Input impedance measure-ment.

vin

41110 kÄ1 kÄ

1 kÄ

Figure 4.12 Output impedance measurement.

1. Build the voltage follower circuit. (The 10 kÄ resistor prevents damage if the input is driven beyond thesupply voltages.)

2. Square wave input: Drive the input with a square wave, in the neighborhood of 1 kHz, amplitude of 1 V, andlook at the output with a scope. Measure the slew rate by observing the slope of the transitions.

3. Sine input: Switch to a sine wave, same amplitude, and measure the frequency at which the output waveformbegins to distort (this is roughly the frequency at which amplitude begins to drop, as well). That is, slowlyincrease frequency on the function generator. Adjust the scope to observe the zero-crossing of the output ofthe amplifier. Is this result consistent with the slew rate that you measured in part 1), just above?

4. Now go back and make the same pair of measurements (slew rate, and sine at which its effect appears) withan older op-amp: a 741. The 741 claims a “typical” slew rate of0.5V/µs; the 411 claims 15V/µs. How dothese values compare with your measurements?

Task 9: Voltage follower—input and output impedance. Ideally, an amplifier circuit has infinite input impedanceand zero output impedance. Here, we will estimate the impedances of the voltage-follower circuit based on the 411op-amp.

1. Replace the 741 op-amp with the 411 op-amp in the voltage-follower circuit you already built. Also, replacethe input resistor with a 1 MÄ resistor, as shown in Fig. 4.11. As always, measure and record the value of theresistor used.

2. Set the input voltage to 5 V. Carefully measure the output of the voltage source and the input voltage to theop-amp. Using the voltage-divider equation, compute the amplifier’s input impedance. Beware the finding“10 MÄ” (instrument limitation!). Does the resistance of the voltmeter interfere with your estimate? How so?How would you make a more precise measurement?

3. Now, construct the circuit in Fig. 4.12. The feedback pathshould use the solid line in this step.

4. We measure output impedance via voltage divider again. Measure the voltage at the output of the amplifier,and then between the two 1 kÄ resistors. (Use an input voltage that produces an output voltage in the linearrange). Compute the output impedance. It had better be 1 kÄ! Note: This measurement is not the amplifier’soutput impedance, but the output impedance plus the impedance of the resistor you added. From this step,what do you conclude the output impedance of the amplifier is?

5. Now, move the feedback path to use the dashed line instead.Insert a third 1 kÄ resistor after the feedback pathand before the 1 kÄ resistor to ground. Use these final two resistors as a voltagedivider to measure outputimpedance. What do you find it to be now? Is this a surprising result? Does the actual output impedance ofthe amplifier matter, with the effect of feedback operating on the circuit?

Task 10: Op-amp offset voltage. In this task we will measure the offset voltage of an op-amp. Note: use a 741,not a 411, for tasks 10 and 11. The 411 is too good for this exercise: its bias current is so tiny that you would not seeappreciable errors attributable toIb. (You might reasonably infer that you can forget aboutIb, simply by choosinga good op-amp. Often you can. This exercise means to prepare you for the unusual case in whichIb does producetroublesome errors.)



vinvout741

100 kÄ100Ä

10 kÄ

Figure 4.13 Offset-voltage measurement.

741

10 kÄ

−15 V

Figure 4.14 Offset trimming network.

1. Construct the non-inverting amplifier shown in Fig. 4.13.Measure and record the values of all resistors used.What is the gain of this op-amp circuit?

Note: Apply no input signal: we are interested in dc errors ofa non-ideal op-amp. In the remainder of thissection, you will use the amplifier itself to amplify input errors to measurable levels. Knowing the circuit gain,you will be able to infer the value ofVoi and Ib. The only challenge will be to peel these two effects apart, soas to be able to assign a value to each error.

2. Since the input voltage is zero, the output voltage is simply an amplified version ofVoi . Measure the outputvoltage and computeVoi . Compare your measured (or “inferred”) offset voltage against specs:Voi = 2 mV(typical), 6 mV (maximum). Don’t be shocked if yourVoi is well under 2 mV. They just don’t make 741’s theway they used to! (But the manufacturer can’t change the datasheet to announce the improvement, becausethen the part would not be a 741; it would have to be called something like 741a.)

3. Minimize the effects ofVoi : Trim the offset voltage to zero, using the recommended network shown inFig. 4.14. Note, the pot is connected between pins 1 and 5 on the op-amp. Adjust the pot until the outputvoltage is as close to zero as you can get it. Leave the op-amp in this configuration for the remaining tasks.

Task 11: Op-amp bias current/offset current. We now measure the bias current for the 741.

1. Construct the circuit shown in Fig. 4.15. Pick a value ofR to produce an output voltage in the linear range(non-saturated output). Make sure that your offset voltagehas been zeroed as much as possible in the stepabove.

2. ComputeIb for the non-inverting input as the op-amp’s output voltage divided by the value ofR that youfound. The bias current is positive if it is entering the op-amp; it is negative if it is leaving the op-amp.

3. Now, construct the circuit shown in Fig. 4.16. Again, picka value ofR to produce an output voltage in thelinear range.

4. ComputeIb for the inverting input as the op-amp’s output voltage divided by the value ofR that you found.

5. Compute the input offset current. How do the bias currentsand the offset current compare to spec?

vout741R

Figure 4.15 MeasuringIb for the non-inverting input.

vout741

R

Figure 4.16 MeasuringIb for the inverting input.

Task 12: Push-pull buffer. Finally, build the push-pull buffer circuit, shown in Fig. 4.17. You should attachheatsinks to the transistors. Be careful not to get heat-sink grease on your clothing—it is impossible to remove.



1. The transistor on top is NPN (TIP31C) and the transistor onthe bottom is PNP (TIP32C). At this point,vout

should only be connected to the 1 kÄ resistor.

2. Drive the circuit with a sine wave of 100 Hz–500 Hz. Look at the output of the op-amp, and then at the outputof the push-pull stage (make sure you have at least a few voltsof output, and that the function generator is setfor no dc offset). You should see classic crossover distortion. Describe the distortion you see.

3. Now, attach an “8Ä” speaker tovout (Note: the speaker is rated by its frequency-dependent impedance to asine wave at 1 kHz, which is 8Ä). Listen to this waveform on the speaker. Your ears (and those of people nearyou) should protect you from overdriving the speaker. But itwould be prudent, before driving the speaker, todetermine the maximum safe amplitude, given the speaker’s modest power rating. The transistors are toughguys, but you can check whether you need to lower the power-supply levels on your breadboard, to keep thetransistors cool, given the following power ratings:

• Transistors: 75W if very well heat-sunk, so that case remains at 25 degrees C. Much less if no heat-sinkis used, as is likely in your setup.

• Speaker: 250 mW rms.

4. Now, disconnect the right side of the 100 kÄ feedback resistor and reconnect it to the right side of the push-pull section (where the transistor emitters join), and onceagain look at the push-pull output. The crossoverdistortion should be eliminated now. If that is so, what should the signal at the output of the op-amp look like?Take a look. (Ain’t that op-amp clever!)

5. Listen to this improved waveform: does it sound smoother (more flute-like) than the earlier wave-form? Whydid the crossover distortion sound buzzy—like a higher frequency mixed with the sine? If you increase signalfrequency, you will discover the limitations of this remedy, as of all op-amp techniques: you will find a glitchbeginning to reappear at the circuit output.

vinvout411

B C E

B

BC

E

E

C

TIP31C

TIP32C

−15 V

+15 V100 kÄ

10 kÄ390Ä

1 kÄ

TO-220

Twist each leg 90

Figure 4.17 Push-pull amplifier. The transistors both have a “TO-220” case, with pinout shown to the right.

Task 13: Lab report. Submit your results in the form of a typed report. Refer to Lab1 for instructions regardingproper format and content of an acceptable lab report. Please also address the following question:

• Explain how moving the feedback path in the push-pull amplifier improves our previous push-pull amplifierby eliminating the crossover deadband and by increasing thecurrent gain (i.e., increasing the input impedanceof the amplifier and load).





Lab 5: Advanced Op-Amp Circuits

5.1 Objective

The objective of this lab is to explore some more advanced op-amp circuits including comparators, Schmitt triggers,oscillators, power amplifiers, and motor-driver circuits.



1. Label all op-amp/comparator diagrams in this lab reader with correct pin numbers on all input/output andpower supply signals.

2. Assuming that the pot in Fig. 5.5, is adjusted so that the wiper has resistance 1 kÄ to ground, compute thehysteresis levelsv2 andv

′

2. Note that when you compare this circuit with Fig. 5.1, the effective R2 = ∞ as novref connection is identified.

3. For the square-wave oscillator circuit in Fig. 5.6, compute the frequency of oscillation.

4. For the variable-duty-cycle oscillator in Fig. 5.7, in which direction must the potentiometer wiper be moved toincrease the duty cycle (more time spent with the output saturated atV+ and less time spent saturated atV−)?

5. Consider a 50Ä “power resistor” constructed by connecting five 10Ä resistors, each rated at 1/4 W, inseries. Show that this composite resistor will dissipate 1.25 W without exceeding the power rating of any ofthe individual resistances.

5.3 Background

Positive feedback. Until now, all of our op-amp circuits have used negative feedback to result in stable circuits.We have treated positive feedback as evil—or as a mistake: it’s what you get when you get confused about whichop-amp terminal you’re feeding. In this lab, you will qualify this view: you will find that positive feedback can beuseful: it can improve the performance of a comparator; or itcan be combined with negative feedback to make anoscillator (“relaxation oscillator”) where positive feedback dominates. However, it is still wise to be wary of positivefeedback. It can be a real pain in the neck when it sneaks up on you.

Comparators. Comparators are op-amp like circuits that compare their twoinputs. They saturate their outputvoltage at the positive rail if the non-inverting input is greater than the inverting input; they saturate their outputvoltage at the negative rail if the non-inverting input is less than the inverting input. Special-purpose comparatorchips like the 311 have separate power supplies for the op-amp circuit and for its output. This way, the op-amp canuse a standard±15 V supply, but the output can use a 0–5 V supply to be compatible with digital logic chips.

When the two inputs are nearly equal, the comparator will often go into oscillations as small noise on the inputor power supply can produce a quickly-changing decision. ASchmidt trigger is a comparator circuit with positivefeedback to produce hysteresis in the decision-making logic. This positive feedback will eliminate those harmfuloscillations. It works in the following way:


ECE2205, Lab 5: Advanced Op-Amp Circuits Lab 5–2

• Generally, ifv+ − v− > 0 then the comparator output will be positive. Ifv+ − v− < 0 then the comparatoroutput will be negative.

• With hysteresis, if the output voltage is presently negative, it will stay negative unlessv+ − v− > ε, whereε

is some positive value set with external resistors.

• Also, if the output voltage is presently positive, it will stay positive unlessv+ − v− < −ε.

The effect of hysteresis is to produce a deadband aroundv+ − v− ≈ 0 where no change in decision is made.Therefore, small input noise cannot switch the decision.

R3

R2

R1

v2

A

vref

vinvout

Figure 5.1 Positive feedback provides hysteresis.

R

C R2

R1

v1

v2vout

Figure 5.2 RC relaxation oscillator.

Fig. 5.1 shows a comparator wired with positive feedback. The positive input is biased, so that the decision pointdoes not need to be at zero volts. The output switches positive whenvin > v2 and switches negative whenvin < v

′

2.The hysteresis voltage levelsv2 may be determined by applying KCL to node A:

vref − v2

R2+

vout − v2

R3=

v2

R1

v2 =R123

R2vref +

R123

R3vout,

whereR123 = R1 ‖ R2 ‖ R3. This dependence on the output voltage gives the dual threshold, which are:

v2 =R123

R2vref +

R123

R3V+

v′

2 =R123

R2vref −

R123

R3V+.

Note that ifR2 is omitted, the decision points are at±R13V+/R3.

Square-wave oscillator. The Schmidt-trigger circuit can be modified to build a circuit that can generate a square-wave output. In this case, we are using both positive and negative feedback. The positive feedback produces ahysteresis level to stabilize the operation of the oscillator, and the negative feedback is used to alternately charge anddischarge a capacitor to produce a moving waveform that causes the switch in output polarity.

The square-wave generator circuit is shown in Fig. 5.2. We can analyze its operation as follows. First, considerthe positive-feedback path. From analogy to the Schmidt trigger circuit, the input to the non-inverting terminalof the comparator has voltagev+ = R1

R1+R2vout which means that the comparator hysteresis decision pointsare at

± R1R1+R2

V+.

The negative-feedback path is an RC low-pass filter. Whenvout = V+, the capacitor will charge up toward this value;whenvout = V−, the capacitor will discharge down toward this value. However, we know that the capacitor voltagewill never approach±V+ since the output voltage will switch sense when the capacitor voltage passes a hysteresisdecision point.

To analyze this more carefully, letλ = R1R1+R2

. Whenv− reachesλV+ then the switch to−V+ at the output occurs.The capacitor has charged toq = λCV+ and now begins to discharge. The general charging equation for a capacitor



which already has an original charge is

q = CV(

1 − e− tRC

)

+ qoe− tRC .

For this case,V = −V+ andqo = λCV+ so the charging equation is

q = −CV+

(

1 − e− tRC

)

+ λCV+e− tRC .

Now whenv− gets to−λV+ another switch will occur. This time is half the period of thesquare wave, so it will berepresented byT/2. At this time

−λCV+ = −CV+

(

1 − e− tRC

)

+ λCV+e− tRC

which, when solved forT , gives (and the frequency is, of course,f = 1/T )

T = 2RC ln

(

1 + λ

1 − λ

)

= 2RC ln

(

1 + 2R1

R2

)

.

5.4 Lab Assignment


Task 2: Open-loop comparators. Comparators work best with positive feedback. But before weshow you thesegood circuits, we will look at two poor comparator circuits:one using an op amp, the other using a special-purposecomparator chip. These circuits will perform poorly; they will help you to see what’s good about the improvedcomparator that does use positive feedback.

1. First, build the op-amp “comparator” circuit in Fig. 5.3.You will recognize this circuit as the very first opamp circuit you wired, where the point was just to show you the“astounding” high gain of the device. In thatfirst glimpse of the op amp, that excessive gain probably looked useless. Here, when we view the circuit as acomparator, the very high gain and the “pinned” output are what we want.

2. Drive the circuit inputvin(t) with a sine wave at around 100 KHz, making sure that there is nodc offset in thesource waveform. Notice that the output “square wave” is notas square as one would hope. Why not?

3. Secondly, substitute a 311 comparator for the 411, as shown in Fig. 5.4. (The pinouts arenot the same—youwill need to rewire the circuit.) While the output of the 311 can produce different voltages than the±15 Vsupply, in the circuits here, you will keep the±15 V swing. So arranged, the 311 output will remind you ofop-amp behavior.The 311 output stage is not a push-pull stage like the 411 op-amp’s is (recall the discrete push-pull sectionfrom Lab 4). Instead, it uses a single NPN transistor whose collector is connected to the output pin 7, whoseemitter is connected to output pin 1, and whose base is internally controlled. This is the feature that allowsusing different voltages at the comparator output than at the input. Note that in all subsequent 311 op-ampexperiments in this lab, pin 1 will be connected to−15 V and pin 7 will be connected through a 4.7 kÄ“pull-up” resistor to+15 V to provide the power supply for this output stage to allowa ±15 V swing. Thepin connection at pin 1 will not be drawn—you must recognize how it is to be connected.

4. Repeat step 2. Does the 311 perform better than the 411?

5. A side-effect of the 311’s fast response is its readiness to oscillate when given a “close call”—a small voltagedifference between its inputs. Try to tease your 311 into oscillating, by feeding a sine wave with a gentleslope. With some tinkering you can evoke strange and lovely waveforms. See if you can capture one of theseimages on the scope and upload to your PC for your report.



6. You can sometimes stabilize a comparator without the remedy of hysteresis, which we are about to promote.Let’s see how far these efforts can carry us. First, to get some insight into why the 311 is confusing itself, keepone scope probe on the oscillating output and put the other onthe +15V power supply line, close to the 311.AC-couple this second probe, and see if the junk that’s on theoutput appears on the supply as well. Chancesare, it does. Keep those ugly 311 oscillations on the scope screen, and try the following remedies:

(a) Put ceramic decoupling capacitors on positive and negative power supplies. If the oscillations stop, ticklethem into action again, by dropping the slope of the input sine.

(b) Short pins 5 and 6 together: these adjustment pins often pick up noise, making things worse. Again teasethe oscillations back on, if this remedy temporarily stops them.

+15 V

−15 V

411

10 kÄvin(t)

vout(t)

Figure 5.3 411 op-amp as simple comparator.

+15 V+15 V

−15 V

311

10 kÄvin(t)

vout(t)

4.7 kÄ8

71

42

3

Figure 5.4 311 comparator without feedback.

Task 3: Closed-loop comparator—the Schmidt trigger. Here, we use positive feedback to create a Schmidttrigger.

1. Wire the circuit in Fig. 5.5. Notice that this circuit looks exactly like a positive-gain amplifier circuit, exceptthat the “+” and “−” terminals of the op-amp are interchanged. This particularcircuit violates the third ruleof simple op-amp analysis: “Assume that the op-amp is configured such that the other two rules apply” (Theother two rules being that there is no difference betweenv+ andv− and thati+ = i− = 0. In this case, therewill be a difference betweenv+ andv−).

2. As inputvin(t), use a small sine wave (≈ 200 mV) around 1 kHz, and adjust the pot that sets hysteresis untilyou find the border between stability and instability of the output signalvout(t).

3. Then watch the waveform at thenon-inverting input. Here, you should see a small square wave (probablyfuzzy, too, with meaningless very-high frequency fuzz not generated by your circuit; perhaps radio, visiblenow that you have the gain cranked way up). This small square wave indicates the two thresholds the 311 isusing, and thus (by definition) just how much hysteresis you are using.

4. Record the hysteresis thresholds and the values of all resistances used. Compare the measured hysteresisthreshold with those computed theoretically.

5. Finally, crank the hysteresis up to about 3× that borderline value (for a safety margin). If your square wavecollapses into dc, then increase the input-signal voltage.If you describe your circuit as a “zero-crossingdetector,” how late does it detect the crossings? Could you invent a way to diminish that lateness? Leave thiscircuit set up, for the next experiment.



+15 V +15 V

−15 V

311

10 kÄ

10 kÄ

100 kÄ

4.7 kÄ8

71

42

3vin(t)

vout(t)

Figure 5.5 Schmitt trigger—comparator with positive feed-back and hysteresis.

+15 V

311

10 kÄ

100 kÄ

100 kÄ

0.01 µF

vout(t)

4.7 kÄ

Figure 5.6 RC relaxation oscillator.

Task 4: Relaxation oscillator (square-wave generator).

1. Modify your circuit slightly to make an oscillator, as shown in Fig. 5.6. Note that pin connections for powerhave been omitted from the diagram for clarity—wire these asbefore. The hysteresis has been increased byreplacing the potentiometer of the preceding circuit with a10 kÄ resistor (which can also be done by adjustingthe pot to its maximum value, of course).

2. Then, connect an RC network from the output to the comparator’s inverting input. This feedback signalreplaces any external signal source; the circuit has no input. Here, incidentally, you are for the first timeproviding both negative and positive feedback.

3. Predict the frequency of oscillation, and then compare your prediction with what you observe. Upload anoscilloscope screen shot to a PC for inclusion in your report.

Task 5: Variable duty-cycle oscillator. The oscillator built in the previous task has a symmetric 50%duty cycle.Sometimes it is desirable to produce an asymmetric variable-duty-cycle waveform. This can be easily accomplishedby using the diode scheme in Fig. 5.7 to effectively produce adifferent RC time constant for charge and discharge.

1. Modify your circuit to include the variable-duty-cycle capability. Here we use special diodes called “Schottky”diodes that have very low voltage drop and fast turn on-time (instead of a pn-junction, they use a metal-siliconjunction, which has different properties). The picture to the top of the Schottky diodes shows how to know“which end is which”. The gray line on the black case denotes the same thing as the “bar” in the schematicdiagram.

2. A light-emitting-diode (LED) operates just like a standard diode, but emits light when it is conducting. Itis basically an on-off device—you cannot produce significantly different levels of light by using differentvoltages. When you adjust the duty cycle of your oscillator,you should perceive a change in LED intensity,however. How do you explain this phenomenon? (Note that the resistor is present in the LED portion of thecircuit to limit the current through the diode. Otherwise, “poof”). Does the direction in which you insert theLED matter? Why?

3. Record the minimum and maximum frequencies of oscillation for this circuit. Record the minimum andmaximum duty cycles for this circuit (duty cycle is measuredas the percent of time the signal is at its maximumoutput).

Task 6: Audio amplifier: Speaker-to-speaker. The example below illustrates using an op-amp as an audioamplifier for a simple intercom. A small 8Ä speaker is used as a microphone which is ac coupled to the op-ampinput through a 0.01 µF capacitor. The op-amp voltage gain is determined by the ratio of the feedback resistor tothe series input resistor which is around one thousand in this case. The non-inverting input to the op-amp is biased



+15 V

311

10 kÄ

100 kÄ

100 kÄ4.7 kÄ

820Ä

4.7 kÄ

0.01 µF

Figure 5.7 Variable duty cycle oscillator.

+9 V +9 V

741

1 MÄ

33 Ä

1 kÄ

1 kÄ

1 kÄ0.01 µF

TIP31C

Figure 5.8 Audio intercom design.

at 50% of the supply voltage (4.5 volts) by 1 kÄ resistors connected across the supply. Since both inputs will beequal when the op-amp is operating within it’s linear range,the voltage at the non-inverting input and the emitter ofthe buffer transistor TIP31C will also be 4.5 volts. The voltage change at the emitter of the transistor will be around±2 V for a 2 mV change at the input (junction of 0.01 µF capacitor and 1 kÄ resistor) which produces a currentchange of about 2/33 = 60 mA through the 33Ä emitter resistor and the speaker output. The peak output speakerpower is aboutI 2R = 0.062 × 8 = 28 mW.

1. Build the circuit in Fig. 5.8. Note that the power supply here is not the±15 V supply that we have previouslyused, and that we are now using the 741 op-amp again.

2. Place the “microphone” speaker several feet away from theoutput speaker. Have someone talk into themicrophone and listen to the output. How does it sound? If youhave a small radio or equivalent, use that asyour sound source.

3. The speaker is sensitive to low frequencies and the small value capacitor serves to attenuate the lower tonesand produce a better overall response. Experiment with different value capacitors to improve the response forvarious speakers.

Task 7: DC motor amplifier. Now we’re really getting to some fun stuff! You will build a dcmotor driver withpush-pull transistors and diode protection. You will also build in dead-zone reduction.

1. Using the multimeter, measure the armature resistance ofthe dc motor. Because of the commutator, this willvary with the shaft angle, so rotate the shaft and take the average of several consistent readings. Remark: Tosimplify testing we will use a resistor as the load for our sequence of circuits until the final step. What valueof resistor should be used? How might you make this resistance value using standard 1/4 W resistors, but stillbe able to dissipate more than 1 W?

2. Construct the circuit in Fig. 5.9. The supply voltage is set to ±9 V to avoid damage to the motor. The 1N4148diodes are identified by (very small) printing on the case. These are not the same as the Schottky or LEDdiodes you used earlier in the lab. Be sure to get the correct diodes.The diodes are a bit of magic to preventvoltage transients caused by the motor’s inductance from destroying the transistors. Be sure to insert thediodes in the correct way; otherwise, “poof”.

3. Set the function generator output to 3 V peak-to-peak sinusoid. Connect the function generator input tovin

and a load resistor capable of more than 1 W and similar resistance to your motor to the output.

4. Sketch the output waveform. Increase the function generator amplitude control to its maximum value. Is thereany clipping?



5. Dead Zone Reduction: Move the feedback from around the op-amp to around the combination of the op-ampand the emitter follower buffer, as you did last week (cf. Fig5.10). Also add the capacitor as shown. This isanother bit of magic, this time to try to control oscillations.

6. Connect to the function generator and the load resistor, as in the previous part. With a 3 V peak-to-peaktriangle wave, sketch the output.

7. Increase the function generator amplitude control to itsmaximum value. Is there any observable distortion inthe output?

8. Driving the Motor: Now for the moment of truth: Can we use this circuit to drive the motor? Disconnect theload resistor. Wire the motor in its place. Set the input voltage to an adjustable dc level. What happens whenthe dc level is greater than zero? What happens when the levelis less than zero? Do not exceed±9 V acrossthe motor.

+9 V

−9 V

741

1N4148TIP31C

TIP32Cvin

vout

Load

Figure 5.9 Motor driver circuit.

+9 V

−9 V

741

TIP31C

TIP32Cvin

vout

Load

1 µF

Figure 5.10 Improved motor driver circuit.

Task 8: Servo-motor control. A servo-motor controller is used to control the angular position of a motor, asopposed to its speed. They are often used in radio-controlled car steering mechanisms, and in robotic applications.We can control angle by measuring the angular position and feeding it back to a control system that drives the motorone way if the position error is positive, and drives it the other way if the position error is negative. In this lab, weuse a simple motor-potentiometer pair. The potentiometer is used to measure the shaft angular position.

The potentiometer is dual 10 kÄ, so one potentiometer can be used for feedback of the position, while the othermight serve as an output. What we are going to do here is to makea remote-controlled potentiometer that repeats thesetting of the control potentiometer. This is a typical feedback system, but since it involves a mechanical element,it is called a servomechanism, or servo, for short. The output could be the shaft position, as well as the electricaloutput of the controlled potentiometer. In fact, the outputof most servos is mechanical. The motor pot consistsof a small dc motor, gearing that drives the sliders, the support for the potentiometer resistances, and a shaft. Theconnections are shown in Fig. 5.12. We are looking at the motor end; the shaft is at the other end. A clockwiserotation of the shaft, looking from the shaft end, increasesthe resistance between the common end and the sliders. Avoltage applied to the motor terminals with the marked polarity turns the shaft counterclockwise, bringing the sliderstoward the common ends.

The motor requires a little more than 2 V to begin turning, so that 5 V is a reasonable maximum. The motor drawsabout 30 mA or a bit more. There are two connection pins (not shown) on the shaft side of the potentiometerconnections that light a red LED that shines through the holein the shaft. As you face the shaft, the anode is at theright. Pins 1 and 8 appear to be connected to nothing.

An elementary servo circuit is shown at the left. The usual op-amp, here an 411, cannot drive the motor by itself, andmust be helped by transistors. The complementary TIP31C andTIP32C do the job nicely. The 411 op-amp is usedas a comparator here, which is allowed by its common-mode range. The output saturates one direction or the otherto drive the motor. With a±5 V supply, the motor voltage will be between 3.5 and 4 V, so no further arrangementsare necessary. In this simple circuit, the motor is driven one way or the other at full voltage. A more complicatedcircuit could provide more sophisticated control.



+5 V

+5 V +5 V

−5 V

−5 V−5 V

411

TIP31C

TIP32C

10 kÄ10 kÄ

10 kÄ1 kÄ

5

6

4Figure 5.11 Servo motor driver circuit.

11 22334455 66

6 77

7 88

10 kÄ

3 4

2 5CW

Figure 5.12 Connections to servo motor.

This circuit finds the proper position rapidly, following the control potentiometer. It then oscillates on either side ofthe correct position at a frequency of about 5 Hz.

1. Build the servo-motor control circuit in Fig. 5.11. You may carefully bend the two pins in front of the 8-pinconnector down flat. We will not need these connections for this lab.

2. Observe the output voltage of the op-amp with the oscilloscope on the slowest speed sweep. If the feedbackhas the wrong sign when you test the circuit, simply exchangethe connections to the op-amp inputs.

The elimination of the position oscillation is a more challenging problem than would appear at first sight. If thevoltage applied to the motor is decreased as the equilibriumposition is approached (proportional control), the motorwill stop short at some point. If this is satisfactory, then the problem is solved, but there will be a little annoyinghysteresis because of the finite voltage required for movement. If the error signal is integrated (integral control), itwill cause the motor to approach a more correct position until the error is zero. These refinements are not (at thistime) within the scope of this exercise, which is to illustrate basic servo control, but are discussed at length in anytext on control systems.

Task 9: Lab report. Submit your results in the form of a typed report. Refer to Lab1 for instructions regardingproper format and content of an acceptable lab report.




ECE2205: Circuits and Systems I Inventory–1

Inventory

These labs were designed to minimize the number of differentparts required. However, there are still quite a few.Here is the list:

Lab 1: Resistors: 1Ä, 1 kÄ, 10 MÄ.

Lab 2: Breadboard (and for all subsequent labs as well).At least two CdS cells per person.Resistors: 10Ä, 1 kÄ, 10 kÄ, 10 MÄ.Pots: 100Ä and 100 kÄ.

Lab 3: Resistors: 51Ä, 390 kÄ, 1 MÄ.Capacitors: 0.01 µF.Bouncy SPST momentary pushbutton switch.

Lab 4: At least two LF411 op-amps per student, at least one LM741 op-amp per student.Pots: 10 kÄ.Resistors: 100Ä, 390Ä, 1 kÄ, 10 kÄ, 15 kÄ, 100 kÄ, 1 MÄ, 10 MÄ.Capacitors: 100 pF, 0.01 µF plus ceramic 0.01 µF for op-amp stabilization.Transistors: TIP31C and TIP32C.Speaker: One 8Ä speaker.

Lab 5: At least one LF411 op-amp, one LM311 comparator, and one LM741 per student.Diodes: Two Shottky diodes, one red LED, two signal (e.g., 1N4148).Resistors: 33Ä, 820Ä, 1 kÄ, 4.7 kÄ, 10 kÄ, 100 kÄ, 1 MÄ.Pots: 10 kÄ, 100 kÄ.Capacitors: 0.01 µF, 1µF.Transistors: TIP31C and TIP32C.Motors: One dc motor, and one dc servo motor.Speaker: Two 8Ä speakers.


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ECE2205: Circuits and Systems I Lab Reader Credits–1

Lab Reader Credits

This lab reader was assembled by scouring the Internet for lab experiments that were proven by time, suited to theeducational objectives of this course, and (hopefully) interesting as well. To a greater or lesser extent, all labs inthis course have been copied from these sources, with some modifications to suit the lab equipment at UCCS, and toreduce the required inventory of parts. It is highly likely that some of the original sources have been forgotten, buthere are the ones that I remember.

• The bulk of Lab 1 came from the Duke University “ECE-61L Electronic Circuits Laboratory” lab manual,“Lab 2—Operation of the Digital Instruments and Basic Measurements” fromhttp://www.ee.duke.edu/~gary/HP/ECE61labmanual.pdf.

• The bulk of Lab 2 came from the Duke University “ECE-61L Electronic Circuits Laboratory” lab manual,“Lab 3–Kirchoff’s Laws and Basic Instrumentation” fromhttp://www.ee.duke.edu/~gary/HP/ECE61labmanual.pdf.

• The bulk of Lab 3, especially the RC-circuit sections, were from “Lab 2: Capacitors” fromhttp://www.people.fas.harvard.edu/~thayes/phys123/lb2_feb06.pdf.

• The bulk of Lab 4 was from “Lab 8: Op Amps I” fromhttp://www.people.fas.harvard.edu/~thayes/phys123/lb8_oc05.pdf and from “Lab 9: Op Amps II” fromhttp://www.people.fas.harvard.edu/~thayes/phys123/lb9_oc05.pdf.

• The bulk of Lab 5 was from “Op Amps III: Positive Feedback, Part I: Benign (useful oscillators)” fromhttp://www.people.fas.harvard.edu/~thayes/phys123/lb10a_205.pdf.

• The intercom circuit from Lab 5 was from “Electronical basiccircuits” from http://www.qsl.net/yo5ofh/hobby%20circuits/electronical_basic_circuits.htm.

• The pulse-width-modulator circuit in Lab 5 was from “Opamp oscillator circuits” fromhttp://www.ibiblio.org/obp/books/socratic/output/opamp10.pdf.

• The dc-motor control system in Lab 5 was from “Experiment 4.3: Motor Amplifier” from http://www-ece.rice.edu/~jdw/242_lab4/exp4.3.html.

• The servo-control system in Lab 5 was from “Servo System” from http://www.du.edu/~etuttle/electron/elect32.htm.

• Additionally, the Internet sitehttp://hyperphysics.phy-astr.gsu.edu provided the theoreticaldescription for the Schmitt trigger and relaxation oscillator in Lab 5.


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