EE 240 Evaluation of Circuits Laboratory. Muhammad Khaliq Julio C. Mandojana

Transcription

1 EE 240 Evaluation of Circuits Laboratory Muhammad Khaliq Julio C. Mandojana August 31, 2004

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3 Contents 1 Laboratory Safety Electric Shock Safety Precautions Circuit Grounding Sources of Errors General Laboratory Operating Procedure Digital and Analog Multimeters Objectives Equipment Procedure Resistance Measurement DC Measurements Ohm s Law Protoboard Connections Voltmeter Internal Resistance Measurement Ammeter Internal Resistance Measurement Resistive Circuits and Power Objectives Equipment Procedure Parallel Resistance Circuit Series and Parallel Resistance Circuit Reference Ground Ohm s Law Plot Wheatstone Bridge Objectives Equipment Introduction Reading Assignment Procedure iii

4 iv CONTENTS 5 Divider Circuits and LEDs Objectives Equipment Reading Assignment Procedure Current Divider Circuit Light Emitting Diode (LED) Equivalent Circuits Objectives Equipment Reading Assignment Procedure Superposition and Maximum Power Transfer Objectives Equipment Reading Assignment Prelab Assignment Procedure Operational Amplifiers Objectives Equipment Reading Assignment Prelab Assignment Procedure Oscilloscopes and Function Generators Objectives Equipment Introduction Oscilloscope Function Generator Procedure Measuring Sine and Nonsinusoidal Waveform with Oscilloscope Measuring DC Voltage with Oscilloscope Evaluation of Equivalent Circuits via SPICE Objectives Equipment Prelab Assignment Introduction Procedure

5 CONTENTS 1 11 Measurement of Capacitance and Resistance Objectives Equipment Reading Assignment Prelab Assignment Procedure Measurement of Inductance and Resistance Objectives Equipment Reading Assignment Prelab Assignment Procedure Evaluation of RC and RL Circuits via SPICE Objectives Equipment PreLab Assignment Introduction Procedure A Laboratory Notebook 71 B Laboratory Reports 73

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7 Laboratory 1 Laboratory Safety The EE 240 Evaluation of Circuits Laboratory course require the students to build simple circuits, make measurements, verify the theory, compare the results with simulated values obtained from SPICE, and finally diasssemble the circuit. During the experiment, document your measurements, observations, any comments, circuit modification in the Note Book, and later on report you results in the Laboratory Report. Improve your Note Book entries and Laboratory Report writing skills by the feedback you will receive from the laboratory instructor. The laboratory sessions will be three hours duration, come prepared for the lab, read the theory related to the experiments, and plan the experiments to finish it in three hours session. The experiments are designed to be in synchronous with the topics taught in the course EE 230Circuit Analysis I. There may be some occasions, the lab experiment ahead of the topic covered in the course. The following topics will be covered in this section: Electric Shock Lab Safety Precautions Circuit Grounding Sources of Errors General Laboratory Operating Procedure 1.1 Electric Shock Electric shock is caused by an electric current through the human body. The severity depends on the current through body rather than voltage. The threshold of electric shock current is about 1mA, which produces unpleasant tingling feeling. At 10mA of electric current severe muscle pain occurs, and current of 100mA to 200mA causes ventricular fibrillation of heart, which is lethal. Voltage of 110V, which can cause 160mA on a wet skin, will be fatal. 3

8 4 LABORATORY 1. LABORATORY SAFETY 1.2 Safety Precautions Don t work alone while working on high voltage Never leave high voltage unattended Keep one hand in pocket while probing high voltage or discharging capacitor All high voltage terminal taped or insulated to prevent accidental contact After switching off power discharge capacitors Don t trust the capacitor is discharges Use shortening bar across capacitors to keep it discharged On electrolytic capacitor, don t put excessive voltage across, and don t connect them in reverse polarity Use insulated tools. In case of accidental contact the insulated tool will help to prevent electric shock Shut off power immediately, in case a person comes in contact with high voltage.do not attempt to remove the person in contact with high voltage, unless you are insulted. Check current carrying capacity of the wire before using for interconnections and connectors with insulated shrouds. Make sure the test leads are rated for the test voltage Make sure the lab instruments are connected to ground terminals Use instruments with three wire power cords. Always shut off power before touching wires or connectors. Always wear shoes and keep shoes dry. Do not stand on metal or wet floors. Never handle instruments when your hands are wet. Always make the connection to the point of high potential at the last step. Set the current limited (but enough to supply the circuit under test) on power supplies to prevent too large currents to flow. This will protect you, the circuit and instruments under test. Do not use a very long cable (short cables will reduce noise pick up as well) and never have cables lay on the ground to prevent tripping over it.

9 1.3. CIRCUIT GROUNDING Circuit Grounding Circuit grounding reduces the noise interference in the signal, which could produce false measurements. Earth in considered electrically neutral, because of its large and equal number of positive and negative charges. Therefore earth can be considered as reference voltage to measure the test voltage. A reference of zero volt is technically attributed to a well in which either a rod having a length of at least 8 feet is in contact with the soil directly or a suitable wire is being connected to the Earth through a plate of a conducting material surrounded by Carbon layers. In the schematic diagram the ground terminal in the reference terminal or earth is physical connected. The most common noise problem encountered in the complicated electronic systems originates from a lack of good grounding practice. If more than a few points are used for ground connections, differences in potential between the reference points can cause ground loops phenomenon, which will cause errors in voltage readings, (i.e., the reference points would not be in the same level of zero voltage any more) which often exist in the ground plane to which the circuits are connected. A good sign of the existence of a ground loop or missing a wellgrounded circuit is the presence of a 60 Hz noise component in the output signal. The ground loop voltage can be eliminated by connecting all ground points in the circuit to only one point which is connected to the earth ground. Another good practice is to use short cables, which carry small signals and keep them fixed. In addition, analog and digital grounds should be generally kept separated and connected together only at one single point. The potentially floating circuits can cause serious danger for the people who are working with them. Connecting the reference point of the circuit to the Earth would eliminate the shock hazards. 1.4 Sources of Errors The laboratory experience is usually a pleasant and insightful experience. This is tool that strengthens concepts learned in lectures. However, sometimes it is frustrating if the circuit does not work, results are unexpected, and trouble shooting of the circuit experience is not enough to solve the problem. Best way to prevent this time consuming experience is to follow good lab practices, and prepare yourself before doing lab experiment. The common sources of errors in the lab that lead to errors in results are: Improper grounding. Improper organization of connections on the protoboard. Use short and straight wires of different color. The layout of the protobaord should follow close the circuit. Lack of understanding of the equipment being used for measurements. Insufficient understanding of the instructions or the schematics. Rushing through the experiment.

10 6 LABORATORY 1. LABORATORY SAFETY Never connect a power supply to the output of a function generator. This will damage the function generator. When doing current or resistance measurements with the multimeter, do not put a voltage over the current or resistance input terminal of the multimeter. Best of all, read instruction carefully, understand the operation of equipment used in the experiment, understand the theory behind the experiment, and do the calculations before starting the experiment. Come prepared with a plan to manage the time properly, so that experiment can be finished within the lab session. 1.5 General Laboratory Operating Procedure Following is the list of operating procedures that you are expected to follow: Read the experiment directions carefully prior to each lab session. Treat every instrument carefully, as they are very expensive. Prepare the lab before coming to the lab session, and make list of data to be taken during experiment. Put all data in the lab notebook, and follow the instructions for laboratory notebook. Do not work in a group of more than two students per bench, unless authorized by lab instructor for a group of three students. Collaborate and discuss your results with your group members. Observing safety precautions is important while working in the lab Do not bring food, drink or beverages in the lab. Learn the instrument being using for each experiment. Make sure every aspect of the experiment is clear for you by reading the instructions carefully. Do grounding in your circuit properly according to what has been mentioned in the circuit grounding section. Keep the breadboard circuitry well organized and with the same lay out as mentioned in the lab note for each experiment. Never connect a power supply to the output of a function generator. This will damage the function generator. Manage your lab time properly divided between the experiments. Return all components, wires, and protoboard back to their original location.

11 1.5. GENERAL LABORATORY OPERATING PROCEDURE 7 If an instrument is malfunctioning, report to the lab instructor Before leaving lab, place the stools under the lab bench. Before the lab, turn off power to all equipment on the bench. Before leaving lab, turn off the main power to the bench. Leave your workplace at least as clean and tidy as you found it. Put everything back in its proper place.

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13 Laboratory 2 Digital and Analog Multimeters In this lab we present the basics of digital and analog multimeters for measuring resistance, voltage, and current. 2.1 Objectives The purpose of this lab is to learn the operation of equipment on the workbench workbench, and some methods for measuring physical quantities with digital and analog multimeter. You will learn: The principles of measuring resistance Resistance color code, and power rating Measure voltage (v), and current (I) Understand common sources of errors in measuring resistance (R), voltage (V), and current (I) Connections on protoboard, and find its contact vertically, horizontally, IC connections, ground terminal, variable power supply connection 2.2 Equipment The following equipment is required for this lab: 1. Digital multimeter 2. Analog multimeter 3. DC Power Supply 4. Resistors 9

14 10 LABORATORY 2. DIGITAL AND ANALOG MULTIMETERS 5. Protoboard 6. Connecting cables and connecting wires 2.3 Procedure Resistance Measurement 1. Get resistances from the box in the lab: 500 Ohm, 1kOhm, 500Kohm 2. Measure the resistance with digital multimeter (DMM) shown in Fig. 2.1, and analog multimeter (AMM) shown in Fig 2.2 Record the measured values. Figure 2.1: Digital multimeter (Fluke 867B)

15 2.3. PROCEDURE 11 Figure 2.2: Analog multimeter (Simpson) 3. Find resistance values (nominal) using color code. Calculate the difference between nominal and measured value. Calculate the percentage difference. Is the difference within the specified tolerance value? Use the format of Table Connect the following circuits shown in Fig. 2.3 on the protoboard and measure the resistance between the points indicated in the circuit. Do the measured values agree with calculated values? 5. Measure resistance of your body by holding probes tightly between thumb and forefinger. Record the value of body resistance. Considering a current 100mA through the body quiet dangerous. How much voltage across your hands would be lethal? Resistance Nominal Value ( ) Measured Value ( ) Difference (%) Tolerance (%) Table 2.1: Experimental and nominal values of resistance

16 12 LABORATORY 2. DIGITAL AND ANALOG MULTIMETERS 1 kω 330 Ω DMM A B A 1 kω B C 1.5 kω 10 kω 15 kω 12 kω DMM D Figure 2.3: Series and parallel resistors DC Measurements The power supply generates either constant voltage or a constant current. The voltage on the power supply is controlled by a knob labeled as voltage, and the current is controlled by another knob labeled as current. There is a current limiting circuit in the power supply that will not generate more current than the limiting value. 1. Set the DC power supply shown in Fig. 2.4 to provide 5V using the meter on the front panel of power supply. Adjust the multimeter to measure DC voltage, and connect the leads for voltage measurement. Figure 2.4: Power supply 2. Measure the voltage using DMM and AMM 3. Make measurements between positive (+) and negative () terminals, and from positive (+) to common and from negative () to common Ohm s Law 1. Set up the circuit shown in Fig. 2.5

17 2.3. PROCEDURE 13 I 2 V 2.2 kω Figure 2.5: Ohm s law 2. Adjust DMM for DC current, and the leads set for current measurement 3. Measure the current flowing through the resistor, and verify the measured value agree with Ohm s Law, i.e. 4. Reverse the DMM leads, and measure the current. The value measured agree with Ohm s Law or not? Protoboard Connections 1. Use continuity setting on DMM, and determine the connections of pins on the protoboard shown in Fig Note that pins are connected, horizontally, ground connections, IC chip connector pin, rows of pin with no electrical connection. 2. Make a sketch of the protoboard showing the pins connections determined by DMM. 3. Repeat the above measurement with AMM Voltmeter Internal Resistance Measurement Ideally a voltmeter has an infinite resistance, which is not physically possible. In practice, a voltmeter has a high resistance, which can be measured by the circuit shown in Fig. 2.7 The current through the circuit is given by: If represents the internal resistance of the voltmeter, we can write 1. Measure resistance value with DMM 2. Connect the circuit shown in Fig. 2.7 (2.1) (2.2)

18 14 LABORATORY 2. DIGITAL AND ANALOG MULTIMETERS Figure 2.6: Protoboard 3. Adjust power supply to 10V, and measure the voltage with DMM. Don t rely on the meter on front panel of the supply. Why? 4. Compute the internal resistance of the voltmeter using above equation Ammeter Internal Resistance Measurement Ideally the internal resistance of an ammeter is zero, but in practice the ammeter has a small resistance.from the circuit shown in Fig. 2.8, the current in the circuit is given by Ohm s Law: Then (2.3)! " 1. Select a small resistance (100 # ) and measure its value with a DMM. 2. Set the power supply to 5V and measure the voltage with a DMM. (2.4) 3. Connect the circuit shown in Fig. 2.8, and set the DMM to measure DC current. 4. Measure the current using a DMM as an ammeter. 5. Calculate using Eq. (2.4).

19 2.3. PROCEDURE 15 1 MΩ 10 V V Figure 2.7: Measurement of a voltmeter s internal resistance 100 Ω 5 V A Figure 2.8: Measurement of an ammeter s internal resistance

20 16 LABORATORY 2. DIGITAL AND ANALOG MULTIMETERS

21 Laboratory 3 Resistive Circuits and Power This lab deals with the evaluation of circuits with parallel resistance, seriesparallel resistance, and term ground reference. Calculations of power rating, and total power of the circuit will also be performed. 3.1 Objectives Evaluate operation of parallel resistance, and seriesparallel resistance circuit. Measure current and voltages in parallel resistance, and seriesparallel resistance circuit. Measure total current is the sum of branch currents in parallel resistance circuit. Confirm branch voltages are equal in parallel resistance circuit. Analysis of seriesparallel circuit mathematically and through experiment. Measure voltage with respect to reference ground. Compute voltage drop across resistance. Ohm s Law plot, and Voltage vs. Power plot. 3.2 Equipment Digital Multimeter Analog Multimeter DC Power Supply Resistors Protoboard 17

22 18 LABORATORY 3. RESISTIVE CIRCUITS AND POWER Connecting cables and connecting wires 3.3 Procedure Parallel Resistance Circuit 1. Measure and record actual values of resistances in the Table 3.1. Connect the circuit, without the power supply. Component Value Measurement Voltage Current $&% $(' $) $*,+ / Table 3.1: Data table 2. Measure and record total resistance 54 of the circuit in Fig. 3.1 R 1 R 2 R 3 12 V 1 kω 1 kω 1 kω Figure 3.1: Parallel resistors 3. Set the power supply output to 12V, and connect to the circuit in Fig Measure and record voltage across each resistance, including the source voltage. 5. Set the DMM to current function, and measure the current in each branch. You have to remove wires and insert the ammeter in each branch to measure current. 6. Measure and record current in each branch in the circuit. 7. Using the measured resistances and voltages, calculate the branch currents. 8. Calculate the total resistance seen by the source by using measured values. 9. Calculate the total resistance using the measured value of and Compare the calculated and measured values.

23 8 < 3.3. PROCEDURE Series and Parallel Resistance Circuit 1. Measure and record actual values of resistance in Figs. 3.2 and 3.3. R 1 12 V kω R 2 R kω 6.2 kω R 4 10 kω Figure 3.2: Series and parallel resisitors R : Ω R 1 12 V ; + 1 kω R : Ω < 0 0 R : Ω Figure 3.3: Series and parallel resisitors 2. Calculate all unknown values listed in Table 3.2 for circuits in Fig. 3.2 and Fig. 3.3 using Ohm s Law. Calculated Measured =BA 6=BC Table 3.2: Application of Ohm s law 3. Apply power to the circuits in Fig. 3.2 and Fig. 3.3, measure and record all unknown listed in Table When measuring voltage use proper polarity, and break the circuit to measure current. 5. Determine total power, and the power dissipated in the resistances.

24 20 LABORATORY 3. RESISTIVE CIRCUITS AND POWER 6. Given the power rating of the resistances used in the circuit shown in Figs 3.2 and 3.3, calculate the maximum voltage that can be applied without exceeding the power rating of these resistances Reference Ground 1. Measure the values of resistances used in the circuit shown in Fig. 3.4, and record the values. 2. Set up the circuits in Fig. 3.4, note the different reference nodes in the two circuits. I A K VA=? I A K VA=? 12 V G+ R 1 R 2 B F 330 Ω 1 kω H 0 12 V G+ R 1 R 2 F 330 Ω 1 kω B V B =? J C K VC=? H 0 Figure 3.4: Different reference nodes 3. Calculate the voltages across the resistance, and record voltage difference across each resistance. Unknown value Calculated Value Measured Value Voltage Difference N N (reference) 0 0 N O P Unknown value Calculated Value Measured Value Voltage Difference L L N N P (reference) 0 0 P QO 4. Set the power supply to 12V, and measure the voltage across each resistance with respect to ground terminals. Record the measured values. 5. Compare measured and calculated values.

25 3.3. PROCEDURE Does the circuit s reference point have any effect on the voltage difference across any of the resistances? Explain your answer Ohm s Law Plot 1. Using the circuit shown in Fig. 3.5, measure current as a function of power supply voltage from the calculated value 12V to +12V. A + V 1 kω V Figure 3.5: Ohm s law plot 2. Plot current vs voltage, and verify plot fits the definition of Ohm s Law. 3. For each setting of power supply voltage, calculate the power dissipated or converted to heat by resistors. 4. Plot voltage vs power. For this part of the experiment use a 100 # resistance. Consider the results in terms of Ohm s Law, does the plot fit the definition?

26 22 LABORATORY 3. RESISTIVE CIRCUITS AND POWER

27 Laboratory 4 Wheatstone Bridge In this lab, we analyze the Wheatstone Bridge Circuit, and use it to measure small changes in resistance accurately. 4.1 Objectives To understand theory of operation of resistive bridges. To calculate unknown values of resistances and voltage within a bridge circuit. To measure voltages and currents in bridge circuits. 4.2 Equipment Digital Multimeter. DC Power Supply. Resistors: 10 #, 2.2 k#, 2.7 k#, 3.3 k#, 6.2 k#, and six (6) 1 k#. 10 k# potentiometer. Protoboard. Connecting cables and connecting wires. 4.3 Introduction The system to be analyzed is the Wheatstone Bridge circuit which has been used for nearly a century in the measurement of very small changes, or differences, in the value of resistors. This in effect has made resistance variation a very powerful tool for use in the measurement of environmental properties. Resistors can be made to change their 23

28 24 LABORATORY 4. WHEATSTONE BRIDGE value, or vary, in proportion to a wide variety of physical properties in the environment surrounding them. A large fraction of all measurements made in mechanical engineering utilize Wheatstone bridges and resistive sensors. Strain gauges for mechanical stress, pressure sensors, torque sensors, airflow sensors and mechanical motion and position sensors all use resistive transducers. What is very important here is that the resistance change is usually very small compared to the absolute value of the resistance? 4.4 Reading Assignment Chapter3, pages 7079 of the textbook (Electric Circuits by Nillsson). 4.5 Procedure 1. Calculate the value of R in Figs. 4.1 and 4.2, when 5S UTVOWOXO# and when S TYOZTYO&#. 10 V \ + R 1 1 kω A R x [ Vo B Figure 4.1: Voltage divider 2. Compare the results for the Wheatstone bridge with the voltage divider. Which circuit gives the largest percentage change in R for 10 # change in resistance? Calculate the percentage change. Which circuit you will prefer to measure the change in resistance? Record values in Table 4.1, and Table Calculated Measured L N LBN Table 4.1: Voltage divider data 1 By convention, the first subscript denotes the plus terminal, while the second subscript denotes the minus terminal. When the voltage is referred to the reference or ground terminal, we omit the second subscript.

29 4.5. PROCEDURE V _ + R 1 R 2 1 kω 1 kω ^ A ] Vo B R 3 R x 1 kω Figure 4.2: Bridge circuit 3. Hook up the circuit shown Fig. 4.1, and measure actual resistance values using a DMM, and record them in your notebook. 4. Switch on the power supply to 10 V, and measure voltage R for `S atyoxoxò #. Repeat for `Sb ctvoztyod# 5. By how much does the voltage R change when the 1000 # resistor changes to 1010 #. 6. Built circuit shown in Fig. 4.2, and measure actual resistance values using a DMM, and record them in your notebook. 7. Switch on the power supply to 10 V, and measure the voltage R for S TVOXOWO&#. Repeat for `ef TYOZTYO&#. Record values in Table 4.2 Calculated Measured L N LBN Table 4.2: Bridge data 8. By how much does the voltage R change when the 1000 # resistor changes to 1010 #. 9. Comment on your result, i.e. how accurately can you measure the change in output voltage (as percentage of output voltage R ) using the voltage divider and Wheatstone bridge. Discuss the results. 10. Hook up circuit shown in Fig Measure and record the resistances. 11. Do not apply power. Note the variable resistance (potentiometer) has been placed in the bridge. Which point is at a higher potential A or B?

30 26 LABORATORY 4. WHEATSTONE BRIDGE 12 V i+ R 1 10 kω h A B R 3 j 2.2 kω R 2 j 2.2 kω g Vo R x 10 kω Figure 4.3: Bridge circuit 12. Apply DC power. Monitor voltage between points A and B, LBN with a DMM, while adjusting the potentiometer `S until LBN is as close to zero as possible. 13. Remove the potentiometer, and measure its resistance 2. Record the result in your notebook. Record values in Table Calculate current k=bl and voltage =Bl for the load resistance 5m shown in the Fig V n+ R kω R 5 R 3 p 3.3 kω 10 kω R 2 o 6.2 kω V o R kω Figure 4.4: Bridge circuit 15. Hook up the circuit shown in Fig Measure the resistance and record values in the notebook. 16. Apply DC power to the circuit in Fig. 4.4, and measure = l and = l. Record the values in Table 4.4 and in the notebook 2q?rtsu CYv u A u >

31 4.5. PROCEDURE 27 Nominal Measured `w 5x S Calculated Measured Table 4.3: Bridge data Calculated Measured 6=Bl =Bl Table 4.4: Bridge data

32 28 LABORATORY 4. WHEATSTONE BRIDGE

33 Laboratory 5 Divider Circuits and LEDs In this lab, we analyze current divider circuits and currentvoltage (IV) characteristics of light emitting diode (LED). 5.1 Objectives To understand the theory of current divider circuits. To calculate currents in different branches of the current divider circuit. To measure currents to verify calculated values for the current divider circuit. To understand the operation of the light emitting diode (LED). To measure IVcharacteristics of a LED, and find its turnon voltage. To use current and voltage measurement techniques learned in previous experiments. To apply KVL and KCL. 5.2 Equipment Digital Multimeter (DMM) DC Power Supply Resistors: 470 #, 1 k#, and 10 k# Light emitting diode (LED) Protoboard Connecting cables and connecting wires 29

34 30 LABORATORY 5. DIVIDER CIRCUITS AND LEDS 5.3 Reading Assignment Pages 7273 of the textbook, Electric Circuits by Nillsson. Review Lab Procedure Current Divider Circuit 1. Obtain resistances and 5w of 10 k# value. Measure the resistance values using a DMM as an ohmmeter. 2. Hook up the circuit shown in Fig. 5.1 R 1 =10 k V 1 + R 2 R 3 10 kω 470 Ω Figure 5.1: Current divider 3. Set the power supply to 12V. Use DMM to measure the DC voltage; don t rely on the front panel display of the power supply. 4. Using a DMM as a voltmeter, measure voltage across the 10 k# resistor, and across resistors and w. Record the values and verify Kirchhoff s voltage law (KVL). 5. Using a DMM as an ammeter, measure the current through the 12V source. Remember you have to break the circuit, and insert the ammeter in series with 12V source. 6. Measure the current through and `w. 7. Verify Kirchhoff s current law (KCL) 8. Verify current divider circuit calculations. 9. Examine the accuracy of voltage measurement; consider the internal resistance of the voltmeter measured in Laboratory 2.

35 5.4. PROCEDURE Examine the accuracy of ammeter measurement; consider the internal resistance of ammeter measured in Laboratory Light Emitting Diode (LED) A light emitting diode is a nonlinear device. When an LED is forward biased (i.e. large lead connected to the positive terminal and the negative lead connected to the negative terminal), exhibits low resistance. Current increases with the applied voltage, when the voltage across the LED is greater or equal to the turnon voltage. At the turnon voltage y3z, the LED will glow. The LED will glow around 1.49 V. In this part of the experiment, current (I) vs. voltage (V) characteristics of the LED will be measured and plotted. 1. Construct the circuit shown in Figure 5.2. Measure the resistance before connecting in the circuit. LED { V1 + I R 4 LED + 1 kω + V + Figure 5.2: LED circuit 2. Turn on DC power supply and vary the voltage from 3V to 2V in step of 0.5V. Measure the change in voltage with DMM used as voltmeter. Also monitor the current through the LED at every step of applied DC voltage. Remember to break the circuit to put DMM as an ammeter in series with LED. 3. Make a graph of IV Characteristics. Use software to plot I vs. V graph. No hand drawn graph will be accepted. A typical IVCharacteristics of a diode is shown in Fig Find on resistance of the LED from IVcharacteristics (I vs. V plot) 5. Verify KVL for the LED? What type of modifications will be required for LED circuit to verify KVL? 6. What did you notice in IVcharacteristics of LED? Is it linear? What happens for negative voltage? What is the voltage at which LED starts to glow, i.e., y z

36 32 LABORATORY 5. DIVIDER CIRCUITS AND LEDS Figure 5.3: Typical IVcharacteristic of a diode (Taken frfom Microelectronics Circuits by Sedra & Smith)

37 Laboratory 6 Equivalent Circuits In this laboratorywe will use Thévenin s theorem to analyze circuits. 6.1 Objectives To understand the concept of Thévenin and Superposition theorems. To find an equivalent circuit using Thévenin s theorem. To replace the circuit by its Thévenin s equivalent and measure its voltage and current Prove the equivalency of a network of several resistors to the Thévenin s circuit by comparing the results of various resistors Draw Norton s equivalent circuit 6.2 Equipment Digital Multimeter (DMM). DC Power Supply. Resistors. Potentiometer 5 k#. Protoboard. Connecting cables and connecting wires. 6.3 Reading Assignment Pages of the textbook, Electric Circuits by Nillsson. 33

38 34 LABORATORY 6. EQUIVALENT CIRCUITS 6.4 Procedure 1. Measure the resistance shown in Fig. 6.1 by using a DMM in Ohmmeter mode, and record the measured values in your notebook. 2. Calculate the load voltage (i.e. }6~ ) for each of the load resistances 5 Z ƒ #, Ô #, and X Ô #. Record the calculated values in your notebook. R 1 R 2 a 2 kω 2 kω + 12 V R 3 2 kω R L b Figure 6.1: Circuit to be replaced by Thévenin equivalent 3. Hook up the circuit shown in Fig. 6.1, and connect to DC supply. Make sure you have measured the voltage with DMM in voltmeter mode. Don t rely on the voltage indicated on the panel of DC power supply. Record the measured voltage in your notebook. 4. Connect the one load resistances at a time and measure load voltage for each resistance. Record the measured values in the notebook. The load resistances are 5 Z 5ƒ #, O&#. 5. Remove the load resistance from point terminal a and b. Calculate the open circuit voltage between terminals a and b. This is the open circuit voltage known as Thévenin Voltage 4 for the circuit. Record the Thévenin voltage value in the notebook. 6. Measure the actual Thévenin voltage and record in the notebook. 7. Calculate the resistance between terminal a and b, which is Thévenin equivalent resistance `4. Record in the notebook. 8. Disconnect the DC power supply, and replace it with a short using a jumper wire. Then measure the resistance between terminal a and b, which is the measured value of Thévenin s resistance 4. Record in the notebook. 9. Draw the Thévenin equivalent circuit in the notebook.

39 ƒ ƒ 6.4. PROCEDURE For the equivalent circuit drawn in step 9, connect the load resistances `Š 5ƒ #, T #, / O# one at a time, and calculate the voltage across each resitor (use voltage divider calculations). Record values in your notebook. 11. Hook up the circuit drawn in step 9. Use a 5 k# potentiometer to represent the Thévenin resistance. Set the potentiometer for the resistance in the equivalent circuit drawn in step 9. Adjust the voltage source for the Thévenin voltage. Place `ƒ each load resistance `ˆ #, T #, Ò # one at a time on the circuit and measure the voltage. Record the measured voltages in the notebook. 12. Remove the load resistance from the Thévenin equivalent circuit. Measure the open circuit voltage with no load, which is 4, and measure the setting on potentiometer, which will be Hook up the circuit shown in Fig. 6.2, and repeat steps 4 to 9. R 1 3 kω a 6 V + V 1 R L b Figure 6.2: Equivalent circuit 14. Compare the results of the two circuits, and comment on your results. 15. Find the Norton s equivalent for the circuits in Figs. 6.1 and 6.2. Compare the two Norton s Equivalent circuits.

40 36 LABORATORY 6. EQUIVALENT CIRCUITS

41 Laboratory 7 Superposition and Maximum Power Transfer We will analyze a circuit using the principle of superposition and maximum power transfer theorem. 7.1 Objectives Understand the principle of superposition. Analyze the circuit using superposition. Construct a circuit with two voltage sources, solve for currents and voltages, and verify calculations with measurements. Construct a model of a voltage source. Determine the maximum power obtainable from a voltage source of known internal resistance. Determine the significance of internal resistance of a voltage source. 7.2 Equipment Digital Multimeter (DMM). DC Power Supply. Resistors. Protoboard. Connecting cables and connecting wires. 37

42 38 LABORATORY 7. SUPERPOSITION AND MAXIMUM POWER TRANSFER 7.3 Reading Assignment Pages of the textbook, Electric Circuits by Nillsson. Maximum Power Transfer Theorem: The amount of power any source can supply to a load is limited by the internal resistance of the source and will be at a maximum value when the load resistance is equal to the internal resistance of the source. 7.4 Prelab Assignment Complete the calculations and circuit analysis of the lab before coming to the lab session. Record your calculated values in the notebook in tabulated form. Leave space in the table to enter the measured values. 7.5 Procedure 1. Consider circuit shown in Fig Measure the values of the resistances and record in your notebook. Using Superposition calculate the voltage across each resistance and the current through each resistance. Record the calculated values in your notebook. Record the calculations in a table in the notebook. a R 1 R 2 c 4.7 kω 6.2 kω 10 V + V 1 R 3 10 kω V V b d Figure 7.1: Circuit to be analyzed using superposition 2. Hook up circuit shown in Fig. 7.1, and connect the two DC power supplies. Remember to measure the DC voltage of the supplies with DMM in voltmeter mode. Don t rely on the voltages shown on DC power supply panel. 3. Measure the voltage across each resistance and record in your notebook. 4. Connect the circuit shown in Fig. 7.2

43 ƒ 7.5. PROCEDURE 39 a R 1 R 2 c 10 V + V kω R 3 10 kω 6.2 kω jumper wire b Œ d Figure 7.2: Source 2 is turned off 5. Note that the 12V source is replaced by a short (jumper wire) between points C and D. Calculate the total resistance seen by 10V power supply. Remove the 10 V power supply, and measure the resistance between points A and B. Compare the measured and calculated values. Calculate the currents and voltages in each branch of the circuit when the 10V power supply is connected to the circuit. 6. Reconnect the 10V power supply, and measure the current and voltages of each branch of the circuit. Record the measurements. 7. Connect the circuit shown in Fig. 7.3, and repeat steps 4 to 6. Make sure the 10V supply is replaced by a jumper wire in this case. a R 1 R 2 c Ž jumper wire 4.7 kω R 3 10 kω 6.2 kω V V b d Figure 7.3: Source 1 is turned off 8. From above data, verify the principle of superposition. 9. Connect the circuit shown in Figure 7.4. Set equal to 10 V and measure &ƒ resistances in the circuit. Use ` ctvowod#, X WOd#, / O&#, X WO&#, T #, T #,

44 ƒ ƒ 40 LABORATORY 7. SUPERPOSITION AND MAXIMUM POWER TRANSFER #, dƒ #, TVO #. Use one ` value at a time for measurements. R 1 1 kω V s + R L V Figure 7.4: Variable load circuit 10. Switch on the DC power supply, with no connected (no load), measure the unloaded voltage. Record measured value in the notebook. 11. Connect each of the load resistance given in step 9 one by one. Measure the voltage across each (load resistance) and record in the notebook. 12. Calculate the power dissipated by each load resistance 5 using measured load voltage values. 13. Plot power dissipated in each load resistance RL vs. the load resistance RL values. (No hand drawn graphs will be accepted with the report). Find the maximum power dissipated in the load resistance ` from the graph. Compare the maximum power value obtained from the data with the calculations. What is the maximum power observed in this experiment? 14. What is the ratio of voltage across the load resistance 5 that dissipated the maximum power and the DC power supply voltage measured in step 10? 15. From the data verify the maximum power transfer theorem.

45 Laboratory 8 Operational Amplifiers We will evaluate the DC characteristics of operational amplifier in different configurations. 8.1 Objectives To learn the DC operation of an operational amplifier. To analyze the inverting operational amplifier circuit. To analyze the noninverting operational amplifier circuit. To analyze the summing operational amplifier circuit. 8.2 Equipment Digital Multimeter (DMM). 741 Operational Amplifier. DC Power Supply. Resistors. Protoboard. Connecting cables and connecting wires. 8.3 Reading Assignment Chapter5 of the textbook, Electric Circuits by Nillsson. 41

46 ƒ ƒ ƒ 42 LABORATORY 8. OPERATIONAL AMPLIFIERS 8.4 Prelab Assignment Complete the calculations and circuit analysis of the lab before coming to the lab session. Record your calculated values in the notebook in tabulated form. Leave space in the tables to enter the measured values. 8.5 Procedure 1. The Operational Amplifier (Op. Amp) to be used in this lab is the 741, which comes in a DIP (dual inline package) package shown in Fig Spend some time to understand the pin connection of the 741. Use Fig 8.1 to relate pin connections with that of the opamp symbol. Make sure you know the pin connections before connecting the device into the circuit. In case you are not sure about the pin connections, ask lab instructor to help you identify the pin connections. Pin 1, and 5 are used for nulling the offset voltage, this function will not be used in this lab. Pin 8 is not connected (NC) to the internal circuit of the op amp. šoffset null inverting input noninverting input V nc V + šoutput šoffset null V œ + V ž Figure 8.1: Operational amplifier 2. Fig. 8.2 shows the connections for the DC power supplies +VCC = +15V and VCC = 15V. Remember to measure voltage with a DMM in voltmeter mode. Don t rely on the power supply panel indicator. 3. Design the inverting operational amplifier shown in Fig. 8.3 to provide gains, RY of 100, 10, and 1 using the resistor values of TVOWO #, TYO #, T #, and TYOXO#. Measure these resistances with DMM in ohmmeter modeand record the values in the notebook. 4. Measure the output voltage for input voltage of 0.0V, +0.1V, +1V. Use DMM in voltmeter mode to measure the input and output voltages. 5. Plot output voltage R vs. input voltage Ÿ, and plot gain vs. input voltage. Explain your results. No hand drawn graph will be accepted. 6. Repeat step 3 through 6 for the noninverting operational amplifier shown in Fig. 8.4 for gains of +10 and +1. Combine the given resistances to obtain the specified gains.

47 8.5. PROCEDURE 43 + V 1 15 V V + 6 V o 2 V 4 LM V 2 15 V Figure 8.2: Biasing of a typical op amp R i V + V V CC Vo LM VCC 0 R f Figure 8.3: Inverting amplifier 7. Design a summing amplifier that has a gain of 10 for input E, and a gain of 5 for inputs w and x (assume w x ). The circuit for summing amplifier is shown in Fig Write the expression for the output voltage. Vo. 8. Build the circuit shown in Fig Remember to measure all resistances and DC power supply voltage +VP P = +15 V, VP P = 15 V, and record the values in the notebook. 9. Switch on the DC power supply, and verify the design done in step 8, and the expression for output voltage Vo. Remember to select a reasonable value of input voltage Ÿ which will keep the output R in the linear region of the operational amplifier.

48 «² ± ª 44 LABORATORY 8. OPERATIONAL AMPLIFIERS ² Ri 3 2 ª + «+ V «V ª + «VCC V o LM 741 ² Rf ª + «VCC ³ 0 Figure 8.4: Noninverting amplifier ª + V 1 «V2 V3 R 1 R 2 R3 3 2 LM 741 ª + «+ V V «VCC 6 ³ 0 R f V CC «Vo Figure 8.5: Adder circuit

49 Laboratory 9 Oscilloscopes and Function Generators This is an introduction to the oscilloscope and the function generator. We will perform measurements of voltage, time, and frequency of timevarying signal. 9.1 Objectives To understand the basic operation of the oscilloscope, and its controls. To display DC and AC waveforms on the oscilloscope. To measure timevarying signals with an oscilloscope. To measure the period and calculate the frequency of timevarying voltageswith the oscilloscope. To understand the operation of the function generator and its controls. 9.2 Equipment Digital Multimeter (DMM). Oscilloscope. Function Generator. DC Power Supply. Protoboard. Connecting cables and connecting wires. 45

50 46 LABORATORY 9. OSCILLOSCOPES AND FUNCTION GENERATORS 9.3 Introduction When voltages and currents in an electric circuit become timevarying, it is frequently desirable to be able to graphically display them as a function of time. In other words we would like to observe, and record plots of, circuit voltages and currents as a function of time. If the time variation occurs briefly in one short time interval, the signal is called transient. For signals that are periodic in time (regularly repetitive), we would like to measure the frequency or repetition time (the period) and shape of the function. The lab instrument for such time resolved measurements is known as an oscilloscope. Actually it is nothing more than a very simple black and white TV, or monitor, screen with a single (or at most several) voltage controlled raster line. In this laboratory exercise you will familiarize yourself with use of the oscilloscope for time resolved voltage measurements, and the function of the front panel controls on the instrument. At the same time you will observe the three timevarying functions provided by the laboratory function generator, namely sine wave, square wave, triangular wave. The instrument manual is located on top of your lab bench. 9.4 Oscilloscope 1. Sweep Sensitivity: the horizontal time axis crosses the screen from left to right, see Fig The time SCALE in fractional seconds per centimeter (or division) across the screen is set by the horizontal sweep time control knob. The spot of light that produces the display can sweep across the screen one time only (singleshot) or repetitively at a fixed rate (continuous), as set by the trigger control switches. 2. Vertical Sensitivity: The oscilloscope allows one to display two independent VOLTAGE signals simultaneously, on channel 1 (CH1) and channel 2 (CH2). The amplitude of the displayed time functions is controlled by the vertical sensitivity control knobs for each channel. The range of signal amplitudes that can be selected for display goes from millivolts to tens of volts per vertical division (centimeter). Each channel has a coupling control switch that either; (a) shorts the input to ground internally, (b) places a large capacitor in series with the input thereby blocking any DC voltage from the input (AC coupling), or (c) DC coupling that is a direct connection from input terminal to oscilloscope. A vertical MODE control switch allows one to display; (a) only CH 1, (b) only CH 2, (c) first CH 1 then CH 2, alternating continuously (NEVER USE THIS MODE), (d) both channels simultaneously displayed (chopped mode), (e) channel A input ADDED to CH 2 input and the sum displayed. A switch on CH 2 input can invert the voltage signal before displaying it. 3. Trace Position: The starting point onscreen for the horizontal axis (t = 0 point) is set by the horizontal position control knob. The relative vertical position of the V = 0 axis is adjusted with the vertical position control knob on each vertical channel.

51 9.5. FUNCTION GENERATOR 47 Figure 9.1: Oscilloscope 4. Brightness and focus: Both are independently adjustable. The trace should be just barely visible on the screen for best measurement resolution. Never allow a bright spot to trace slowly across the screen. 9.5 Function Generator The function generator (FG) can provide many different sorts of repetitive and transient time functions. We will only be interested in the three primary periodic functions; sine wave, square wave and triangular wave. The function switch selects between them, see Fig A DC offset switch allows one to insert an internal DC voltage source in series with the timevarying voltage. There is one BNC coax output terminal on the Figure 9.2: Function generator unit. A trigger output signal is also available which is a very short pulse occurring a few nanoseconds before the function generator output passes through 0 volts. 1. The signal frequency is set by decade pushbutton switches and a continuously adjustable control knob within the decade range. Frequency is given in Hz.

52 48 LABORATORY 9. OSCILLOSCOPES AND FUNCTION GENERATORS 2. Peak Amplitude of the periodic signal is set by a continuously adjustable 0 30 V control knob. The amplitude can be further adjusted downward by power of ten attenuator pushbutton switches, or by a rotary decade switch knob; 20db, 40db, 60db, etc. 9.6 Procedure Measuring Sine and Nonsinusoidal Waveform with Oscilloscope 1. Connect a BNC cable from the FG output to the CH2 of oscilloscope input. 2. Connect another cable from the FG trigger output (located at the back of the FG) to the oscilloscope trigger input. 3. Set up the FG for triangle wave, at 20.0 KHz, and 0.3 V peak output. Do not proceed unless you are sure it is correctly set up. 4. Adjust the scope controls to display 23 complete triangle wave cycles with amplitude nearly filling the screen. Set the trigger control switch to automatic. Use chop mode and ground CH1 input, 0V. Record all relevant settings on both FG and oscilloscope. 5. Record accurately the function you see on the screen. Measure the period of the triangle wave on the screen and check it against frequency measured with the (yellow) Fluke multimeter. Measure the + and peak values of the function on screen. Check the zero volt trace position on screen by grounding input. 6. Now change ALL of the settings on the oscilloscope to see how they affect the display. Record. 7. Return the scope to the conditions in step3. Switch the FG to sine wave and then square wave repeating step4 in each case. Repeat step5 for the square wave. See an easy way to measure peak voltage? 8. Set the oscilloscope CH 2 vertical sensitivity to 1.V /cm and sweep to 20 micro seconds/cm. Now change most of the settings on the FG to see how they affect the display. Use a sine waveform only Measuring DC Voltage with Oscilloscope 1. Establish the ground reference for CH 1 and CH 2 by setting the input coupling switch to ground (GND). Use vertical POS switch for channel 1 and 2 to place the trace at different level on the screen of the oscilloscope. 2. Move input coupling switch to DC

53 9.6. PROCEDURE Switch on DC the power supply and measure 2 V with a DMM in voltmeter mode. Connect the 2V power supply to the input of the oscilloscope using the proper scope probe. The trace on the screen will shift with respect to the reference established in step 1. The magnitude of the voltage is equal to (=Volts/Div x No. of divisions). Reverse the polarity of the DC voltage, describe what you see?

54 50 LABORATORY 9. OSCILLOSCOPES AND FUNCTION GENERATORS

55 Laboratory 10 Evaluation of Equivalent Circuits via SPICE Analysis of circuits consisting of independent and dependent sources, and its verification by simulation using PSPICE. Verification of Thevenin s, Norton s theorem and maximum power transfer theorem using PSPICE Objectives Understand the basic commands for different type of dependent sources. Verify the hand calculation with PSPICE for a circuit containing independent and dependent sources. Verify Thevenin s theorem and maximum power transfer theorem using PSPICE. Verify Norton s theorem and maximum power transfer theorem using PSPICE. Compare the current source (Norton s) and voltage source (Thevenin s) theorem analysis Equipment PC with student version of PSPICE or similar Prelab Assignment Chapters 2 and 4 of the recommended book, SPICE (3rd Edition), by Paul W. Tuinenga 51