ELECTRICAL MEASUREMENT LABORATORY

Transcription

1 DEPARTMENT OF ELECTRONIC ENGINEERING ELECTRICAL MEASUREMENT LABORATORY LECTURER: ASST. PROF. DR. GÖKHAN ÇINAR LAB ASSISTANTS: RES. ASST. ESRA SAATÇI RES. ASST. ERTUĞRUL BAŞAR 2007

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3 TABLE OF CONTENTS Lab Rules and Procedures i Laboratory Safety Rules ii Laboratory Report Rules iii Experiment 1 Errors in Measurement and Basic Statistical Sampling 1 Experiment 2 DC Current and Voltage Measurement 6 Experiment 3 Resistor Characteristics and Ohms Law 11 Experiment 4 Oscilloscope 16 Experiment 5 AC Voltage Measurement 22 Experiment 6 Measurement Using DC Bridges 29 Experiment 7 Measurement Using AC Bridges 34 Experiment 8 Measurement of Semiconductor Devices with Multimeter 40 Experiment 9 Thermistor Characteristics and Temperature Controlled Circuits 48

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5 LABORATORY RULES AND PROCEDURES 1. Students have to attend all the scheduled experiments. If anybody misses an experiment, he/she will make it up during the last week of the semester. Students who miss more than two experiments shall have to repeat the course; i.e. they will have an F grade automatically. 2. Experiments are done by groups of students (a maximum of three). 3. Experiments start at the scheduled time of the laboratory session when all the members of the group are ready. Any one who fails to join the group in 15 minutes will be assumed absent. 4. Experiment sheets is given to the students at least one week prior to the experiments. Students are supposed to study the experiment sheets, read the necessary references, do the preliminary calculations if necessary-, and collect enough knowledge about the experiment before coming to the laboratory. This will be checked by the instructor and will affect the student s grade. 5. Two copy of the, blank Experiment Data Sheet should be prepared before the experiment. Experiment Data Sheet is found at the end of each experiment section. All the experimental data (and graphics if necessary) must be written on these sheets. The laboratory instructor must sign the sheets. One copy of this sheet will be handed to the instructor after the experiment. The other will be kept by the students to be used in prepare the report. 6. Students must take all precautions for their own and instruments safety. They will be liable to replace the instruments or the components, which are damaged due to misuse. 7. Students should obey all the Laboratory Safety Rules in the lab. 8. Students should leave the bench clean and tidy after the experiment. Cleanliness and orderliness of the laboratory should always be maintained. All instruments should be switched off before leaving the lab. 9. Students repeating a course should attend laboratories fully including submitting the report. (They will not be exempted from the laboratories). i

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7 LABORATORY SAFTY RULES 1. Eating, drinking, smoking, sleeping are not allowed inside the laboratory. 2. Excessive noise must be avoided (i.e. when talking etc...) must be avoided. 3. Jewellery, ties and clothing which, in the opinion of the Laboratory Staff, is hazardous must not be worn while working with machinery in the Laboratory. All users must wear full shoes (not sandals) and at least a shirt and full-length trousers. Long hair must be held back securely with a head band or a net. Medallions or jewellery hanging from the neck must not be worn. 4. The bench is for experimental equipment only. Do not leave coats, sweaters, briefcases and other irrelevant personal belongings on the bench. 5. Keep your workspace tidy and set aside all equipment and leads that are not actually part of the test being conducted. 6. Move around slowly to avoid knocking things over. 7. Make sure that there are at least three persons in the lab all the time. 8. Never open (remove cover) of any equipment in the lab. 9. Use the proper power cord and correct fuse. Replace the power cord if it is cracked or broken or has any pins missing. Make sure that all devices are using a three-wire power cable when powered from a 220V outlet. Use extension cords only when necessary and only on a temporary basis. 10. Voltages above 50 V rms ac and 50 V dc are always dangerous. Extra precautions should be considered as voltage levels are increased. 11. Always be careful when electricity is applied to the experiment circuit. Some circuit elements such as capacitors and inductors may produce high voltages even when the power supply voltage is low. 12. Never handle live equipment when hands, feet, or body are wet or perspiring, when standing on a wet floor or on a metal surface. 13. While manipulating a circuit with an applied voltage or current, put one hand in your pocket or behind your back. 14. All accidents, including minor injuries and all hazardous conditions are to be reported immediately to the Laboratory Staff or the Director. 15. Laboratory shall remain locked other than laboratory hours. iii

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9 LABORATORY REPORTS RULES Each student of each group should submit a report of the experimental work with Experiment Data Sheet in one week after the experiment completion date. Grades will be reduced by 5 points-per-each delayed day. The reports will not be accepted after two weeks of delay. The first report will be given in a wired file for archiving whereas the rest will be given in the transparent file. The laboratory reports should include the following items: 1. Report cover page: Blank cover page of the experiment can be found at the appendix. Students should complete this page and make it the first page of the report. 2. Preliminary work: Should contain the short theory and method of the experiment. It must not be a repetition of the background section of the experiment, given in the Experiment sheets. Below items must be written in your own words: a. The technical objective of the experiment, b. Calculations and questions answers found in the Experiment sheets. 3. Experimental setup: This section should include following: a. Neat drawing of the experimental setup (indicating all the measuring instruments, with types and brand names), b. Equipment list: the list should include the names, manufacturer s brand names and model numbers of the instrument, c. List of the electronic components and other related tools, instruments used in the experiment. 4. Experimental results: This section should contain following: a. Calculated data in the preliminary work section in tabular form, b. All measured values in tabular form, c. All curves with suitable titles, units and scales on both coordinate axes, on each graph. 5. Conclusion: It includes: a. All discussion of the experimental results, b. Comments on differences between the experimental and theoretical results, c. Probable sources of errors and the ways of reducing these errors, d. Personal opinions about the experiments. Even though lab reports might be handwritten in pen or in ink, clarity and neatness are required. Marks can be lost for reports that are not presented in a convenient way. Marks are not given for the quantity of material written but for its quality. Comments, which show that you understand or have thought about what is going on, are valuable. Clarity of ideas, thoughts and understanding are essential for increasing your mark. Lack of these will reduce your mark. Your report should be legible but does not have to be a work of art. It is your ideas and experimental ability you will be graded on. v

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11 TC İSTANBUL KÜLTÜR UNIVERSITY FACULTY OF ENGINEERING AND ARCHITECTURE ELECTRONIC ENGINEERING ELECTRONIC MEASUREMENT LABORATORY REPORT EXPERIMENT NO : EXPERIMENT NAME : LABORATORY GROUP NO : LABORATORY PARTNERS : Prepeared by STUDENT NO : STUDENT NAME : Experiment Date: Report Submission Date: Submission Delay: Report Grade: Delay Grade: Result: Signature

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13 İSTANBUL KÜLTÜR UNIVERSITY DEPARTMENT OF ELECTRONIC ENGINEERING ELECTRICAL MEASUREMENT LABORATORY EXPERIMENT 1 ERRORS IN MEASUREMENT AND BASIC STATISTICAL SAMPLING OBJECTIVES To investigate sources of error in measurements, To observe the value of statistical analysis. EQUIPMENT & COMPONENTS composition resistors of the same color-coded value 2. 1 digital multimeter BACKGROUND Error is defined as the deviation of a reading (or set of readings) from the expected value of the measure variable. When we make measurements, some error is inevitable because no measurement can yield the exact value of any quantity. There are several sources of error in any experimental data. The primary concerns about analysing experimental data are the sources of error and the extent to which the error has affected the validity of the data. The error of measurement consists of three major components: 1. Gross error, 2. Systematic error, 3. Random error. 1

14 In order to eliminate gross error, good measurement practice must be applied. Always obey the rules of the measurement, do not relay on only one measurement, do many measurements and judge the results. Systematic errors are resulted from the measuring instruments (Instrumental error) and external conditions (Environmental error). Experiment 2 covers Instrumental errors A statistical analysis is performed on samples of very large quantities of the measurements to determine the probable variation in values of the entire measurement, which is resulted in Random errors. The percentage of the entire measurement, which will fall within a specific range of values, can be predicted quite accurately from the statistical analysis of the sample. Under ideal conditions, a very large number of measurements will provide a distribution of readings, with the greatest number of readings approximately equal to the actual value. On either side of the actual value, the frequency of readings will decrease, producing an approximately normal distribution as shown in Figure 1.1. Arithmetic mean of the n measurement is the best estimate of the true value. It can be formulated as: x + x + x x x = = n n i= 1 n n x i (1.1) Where n is the number of measurement, x i is the reading of the i th measurement. Standard Deviation or root-mean-square deviation of the n measurement is the best estimate of the precision. It can be formulated as: n d d d dn i= 1 σ 2 di = n 1 = for n n 1 (1.2) where n is the number of measurement, d i is the deviation from the mean ( d i = x i x). 2

15 Figure ( x x ) σ F( x) = e 2πσ PROCEDURE 1. Measure the value of each resistors by digital multimeter. Record the values in the Table 1.1 (Resistance values). 2. Select 8 resistors at random from the total lot and measure and record their values in Table 1.1 (Sample 1). 3. Mix all the resistors together and select, at random, any 12 resistors. Your selection may or may not include resistors from the previous sample. Measure and record the values of the 12 resistors in Table 1.1 (Sample 2). 4. Mix all the resistors together and select, at random, a sample of 16 resistors and measure an record their vales in Table 1.1 (Sample 3). 5. On one sheet of graph paper, plot the value of each resistor in the total lot and make a bar graph, or histogram. 6. Divide a second sheet of graph paper three ways vertically. Plot a histogram (resistance values versus frequency) for each of the three samples of the resistors. 7. Connect the maximum points of each histogram by a smooth curve. If the numbers of resistors in the samples were much larger, this would give an approximate normal distribution curve such as the one shown in Figure 1.1. However, your curves may be skewed because samples are small. 8. Compute and record in Table 1.1 the standard deviation σ for the entire lot and for each of the three samples. 9. Record in Table 1.2 which sample (1, 2, or 3) most neatly describes the total lot with regard to standard deviation. 3

16 QUESTIONS 1. What is average deviation? Calculate the average deviation of the samples in Table 1.1 and find out the best sample with regard the average deviation. 2. What is probable error? Calculate the probable error of the samples in Table 1.1 and find out the best sample with regard the probable error. 4

17 EXPERIMENT DATA SHEET Name of the Experiment :Errors in Measurement and Basic Statistical Sampling Group # : Names of the Students : Date of the Experiment : Name of the Lab Assistant : Signed : Experiment Data Resistance Values Table 1.1 Results Sample 1 Sample 2 Sample 3 Best sample Second Best Sample Worst Sample Sample 1 σ Sample 2 σ Sample 3 σ 5

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19 İSTANBUL KÜLTÜR UNIVERSITY DEPARTMENT OF ELECTRONIC ENGINEERING ELECTRICAL MEASUREMENT LABORATORY EXPERIMENT 2 DC CURRENT AND VOLTAGE MEASUREMENT OBJECTIVES To learn how to measure DC voltages and current through the circuit, To learn how to use multimeter properly. EQUIPMENT & COMPONENTS 1. Digital Multimeter 2. Analog Multimeter 3. DC Power Supply (12 V) 4. Resistors (100Ω, 1kΩ, 10kΩ) BACKGROUND The two most important commonly used quantities are the current and the voltage. The current is a serial quantity and measured by using ampermeter. The voltage is defined between two nodes and measured by connecting a voltmeter across those two nodes. 7

20 Figure 2.1 (a) The electronic circuit, (b) measuring current and (c) voltage: Current is measured by connecting the ammeter in series to the resistor; the voltage is measured by connecting the voltmeter in parallel to it. In order to eliminate the loading effect, the internal resistance of the ammeter should be very small and the resistance of the voltmeter should be very high compared to the circuit resistance. Otherwise the ammeter or the voltmeter changes the circuit operation conditions and an error is introduced. The error of measurement consists of three major components: 1. Gross error, 2. Systematic error, 3. Random error. In order to eliminate gross error, good measurement practice must be applied. Always obey the rules of the measurement, do not relay on only one measurement, do many measurements and judge the results. Systematic errors are resulted from the measuring instruments (Instrumental error) and external conditions (Environmental error). Instrumental error is given in the user s manual of the instrument for maximum reading: Δ ε0 = V V max (2.1) where ε 0 is the error or accuracy of the instrument. Error of the analogue instrument is usually expressed as the class of the instrument. The class of the instrument shows the relative error for full-scale deflection (maximum reading). Lading error is the other type of instrumental error. When measuring system is connected to the system to be measured, some loading effects happen due to the power sharing of the two 8

21 systems. The loading error for an ammeter and voltmeter can be calculated as follows, respectively. Δ I r = I r + R n ΔV Rth = V r + R th (2.2) (2.3) where r is the internal resistance of the meter and R n is the Norton and R th Thevenin equivalent resistance of the circuit. Since the internal resistance of analog voltmeter change with the selected range, instead of the internal resistance usually the sensitivity of the instrument, S (input resistance-per-volt), is given such as 20kΩ/V. This value is indicated on the panel of the instrument. If the range of the voltmeter is set to V R, then the internal resistance of analog voltmeter is: r = VR S (2.4) The internal resistance of a digital voltmeter is usually constant and greater than 1MΩ. The internal resistance of an ammeter changes with the range of the instrument and should be obtained from the users manual of the instrument. The relative worst case or limiting error of a measurement is the sum of the loading error and instrument (accuracy) error assuming other errors are negligible: ΔX ΔX ΔX = + (2.5) X X X worst case instrument loading PROCEDURE 1. Calculate the current and the voltages across the resistors R 1 and R 2 of Figure 2.2 for (a) R 2 =10kΩ and (b) R 2 =100Ω. Figure 2.2 9

22 2. Connect the circuit given in Figure 2.2. Set R 2 =10kΩ. Measure the exact value of the voltage source, using the digital voltmeter. 3. Open one end of R 1. Connect the analog ammeter in series and measure the current I Open one end of R 2. Connect the analog ammeter in series and measure the current I Connect the analog voltmeter across the resistor R 1 and measure V Connect the analog voltmeter across the resistor R 2 and measure V Repeat steps 3 to 6 using digital multimeter. 8. Set R 2 = 100Ω. Repeat steps 3 to Calculate the errors of measurements and fill in the Table 2-1, 2-2. QUESTIONS 1. Calculate the minimum input resistance of the voltmeter which will introduce a 1% loading error when measuring V 2 of Figure 2.2 with R 2 =100Ω. 2. What are other methods to measure a DC voltages? Explain their operation and compare with the simple voltmeter measurement method. 3. Is there a method to measure the current of a circuit without cutting the current carrying line? Explain the method(s) briefly. 10

23 EXPERIMENT DATA SHEET Name of the Experiment : DC Current and Voltage Measurement Group # : Names of the Students : Date of the Experiment : Name of the Lab Assistant : Signed : Experiment Data 2. V = Table 2.1 Results THEORICAL R 2 =10kΩ R 2 =100Ω Analog Meter EXPERIMENTAL R 2 =10kΩ R 2 =100Ω Digital Meter Analog Meter Digital Meter V 1 I 1 V 2 I 2 Table 2.2 Measurement Errors Instrument Error Analog Meter Loading Error Total Error R 2 =10kΩ Instrument Error Digital Meter Loading Error Total Error V 1 I 1 V 2 I 2 Instrument Error Analog Meter Loading Error Total Error R 2 =100Ω Instrument Error Digital Meter Loading Error Total Error V 1 I 1 V 2 I 2 11

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25 İSTANBUL KÜLTÜR UNIVERSITY DEPARTMENT OF ELECTRONIC ENGINEERING ELECTRICAL MEASUREMENT LABORATORY EXPERIMENT 3 RESISTOR CHARACTERISTICS AND OHM S LAW OBJECTIVES To learn how to use ohmmeter properly, To study characteristics of resistance, To learn how to use Ohm s Law in circuit analysis. EQUIPMENT & COMPONENTS 1. Digital Multimeter 2. Adjustable DC Power Supply 3. Potentiometer 4. Resistors BACKGROUND All materials possess electrical resistance which is the opposition to the flow of electrical current in a circuit. The unit of measure for electrical resistance is the ohms (Ω). One ohm may be defined as the electrical resistance of a copper wire which is 300 m long and 2.5 mm in diameter. The instrument used to measure electrical resistance is called an ohmmeter. The ohmmeter must be connected to any circuit element under no power conditions. The resistors can be simply divided into two types: fixed resistors and variable resistors. The fixed resistor has two terminals and its resistance is constant. A variable resistor (VR) or potentiometer has three terminals and its resistance is variable. 13

26 The circuit symbol of a variable resistor is shown in Figure 3.1. The three terminals are the end terminals A,C and a wiper terminal B. The resistance between the end terminals R AC is fixed and is always equal to its nominal value. The wiper resistances between the wiper terminal and the end terminals, R AB and R BC, are variable. The wiper resistances correspond to a given position of the potentiometer shaft. A B Figure 3.1 Symbol of a variable resistor C Ohm s law, discovered by a German physicist Simon Ohm ( ), is an important law that describes the relationship of voltage E to current I and resistance R. It is often referred to as the foundation of circuit analysis and can be expressed by three different ways: E I = R E = I R E R = I (3.1) where E is the potential difference from one end of a resistance element to the other (volt), I is the current through the same resistance element (amperes), R is the resistance of the same element (ohm). Remember that lowering the resistance raises the current, and raising the voltage also raises the current. PROCEDURE 1. Using the ohmmeter measure the resistance of resistors given to you and record the results in the column of measured value in Table Read the resistor values by using color codes. Compare the measured values with the reading values and tolerances for determining whether each measured value is within the tolerance or not. Complete Table

27 3. Designate three terminals of VR1 on the KL as A (the right), B (the middle) and C (the left). 4. Using the ohmmeter, measure the resistance between terminals A and C and record the value on Table Turn the VR1 control knob completely to the left. Measure and record the resistance between terminals A and B, and A and C on Table Turn the VR1 control knob completely to the right. Measure and record the resistance between terminals A and B, and A and C on Table Turn the VR1 control knob to middle position. Measure and record the resistance between terminals A and B, and A and C on Table Set the circuit shown in Figure 3.2 by using R 1 = 100Ω and V s = 12 V. Using Ohm s Law calculate the current through resistor R 1. V s + R 1 I + V - Figure Connect the ammeter to the circuit shown in Figure 3.2. Measure the current through resistor R 1. and record the result on the Table 3.3 Is there good agreement between your measured and calculated current values? 10.Change V s as you read 150 ma on the ammeter. Measure the voltage across the resistor R 1 by using voltmeter. Calculate and record the voltage value (V) on the Table 3.3. Is there good agreement between your measured and calculated voltage values? 11. It is simple to build an equivalent ammeter by connecting a known resistor in parallel with a voltmeter, see Figure 3.3. According to this build your own ammeter with R A = 4.7 Ω. To measure the current in this ammeter you measure the voltage (V) and by using the Ohm s Law you calculate the current through R A ( I = V RA ). You assume that the internal resistance of voltmeter is very high and loading effect is negligible. 15

28 + R A V - Figure Connect your ammeter to the circuit shown in Figure 3.2 V (R 1 = 100Ω and V s = 12 V.). Calculate the current through the resistor R 1 by considering your ammeter connected to the circuit. Record the result on the Table Measure the current through resistor R 1 and record the result on the Table 3.4. Is there good agreement between your measured and calculated current values? QUESTIONS 1. How can you design a voltmeter with full scale of 100V by using an ammeter and a resistance. 2. Explain basic construction of an ohmmeter. 16

29 EXPERIMENT DATA SHEET Name of the Experiment : Resistor Characteristics and Ohm s Law Group # : Names of the Students : Date of the Experiment : Name of the Lab Assistant : Signed : Experiment Data Table 3.1 Resistor 1 st Band 2 nd Band 3 rd Band 4 th Band Reading Value (Ω) Tolerance (%) Measured Value (Ω) within Tolerance? R 1 R 2 R 3 R 4 Table 3.2 R AC =----- Shaft Position R AB R BC R AB +R BC Fully left Fully right At the middle Table 3.3 V s = 12 V R 1 = 100Ω I ca l I m V ca l V m I = 150 ma R 1 = 100Ω Table 3.4 V s = 12 V R 1 = 100Ω I ca l V m Im = Vm RA 17

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31 İSTANBUL KÜLTÜR UNIVERSITY DEPARTMENT OF ELECTRONIC ENGINEERING ELECTRICAL MEASUREMENT LABORATORY EXPERIMENT 4 OSCILLOSCOPE OBJECTIVES To learn how to use oscilloscope properly, To measure amplitude, frequency and phase angle by using oscilloscope, EQUIPMENT & COMPONENTS 1. Dual Trace Oscilloscope 2. Digital Multimeter 3. Signal Generator 4. Resistors 5. Capacitor BACKGROUND The cathode ray oscilloscope is the most versatile instrument to measure electrical quantities. It is possible to use an oscilloscope to measure the following quantities of a voltage; 1. Instantaneous value, v(t) 2. The positive and negative peak value, V p+, V p- 3. The peak-to-peak value, V pp 4. The average value, V A 5. The period, T 6. The phase difference between two voltages, φ 19

32 Figure 4.1. Sinusoidal wave. Probe: The imput impedance of an oscilloscope is very high. 1MΩ paralel 20pF input impedance is an industry standart for oscilloscopes. To compensate the large input capacitance and to increase the input resistance of an oscilloscope it is necessary to use a serial cable and circuit that is called PROBE. The probe is made of a co-axial shielded cable and compensated attenuator as shown in Figure 4.2. input C 1 Probe cable Oscilloscope R 1 C 2 R 2 ground x10 Figure 4.2. Oscilloscope probe. The large input time constant R 2 C 2 creates a low pass filter (with single pole) and attenuates all high frequency (HF) signals. To compensate this pole it is necessary to create a zero at the same frequency by R 1 C 1, satisfying: RC = RC (4.1)

33 To obtain x10 attenuation R 1 = 9MΩ is selected. It is necessary to adjust either C 1, to obtain the equality, since C 2 is not exactly known. This adjustment must be done once, for every oscilloscope and every probe connected to the specific input of this oscilloscope. Note: Compensation works only on x10 position. Therefore HF signals can only be used by using a compensated x10 probe. Measurement using an Oscilloscope Since it has a very large input resistance, an oscilloscope can only be used to measure voltages and time. The vertical axes of an oscilloscope are calibrated to indicate volts/cm and the horizontal axes are calibrated as s/cm. Instantaneous and peak value: Measuring the first three quantities, Instantaneous, Peak and Peak-to-Peak Voltage value is straightforward. Be sure that zero level adjustment is done properly and DC or AC input selection is correctly set. Average value: To measure the average value first the input connection is made AC coupled and one extreme of the waveform is set to the reference line. Then the input is set to Dc coupled mode and the voltage shift is measured. This shift is equal to the average value of the voltage. Period: The period can also be directly measured by measuring the time difference between two zero crossing points, and frequency can be easily calculated by taking the reciprocal of the period. Phase: The phase measurement can be performed in two different ways. 1. If the oscilloscope has dual trace facility two voltages are displayed simultaneously and the time difference, t D, is measured between two identical points of the waveforms. The phase difference is then: φ t T = 2π D (4.2) where T is the period of the signal. 21

34 2. If one of the signals applied to the horizontal input while the other is connected to vertical input an elliptical trace is obtained on the screen as shown in Figure 4.3. The phase difference can be calculated using this trace as follows: φ = arcsin b (4.3) a V Y (Ө) Y Ө 0 Ф 2п b a X b = V ( φ) = a sin( φ) Y φ = arcsin( ba) V X (Ө) 2п Ө Figure 4.3. The Lissajou curve. PROCEDURE 1. Read the short instruction for the oscilloscope given in appendix Set all push buttons to OUT position. Then turn on the oscilloscope according to the procedures in appendix. 3. Connect the x10 probe to the CAL output of the oscilloscope. Adjust the TIME/DIV. and VOLT/DIV. knobs to obtain a suitable square wave on the screen. Then adjust the compensation capacitor by using a suitable screwdriver. Try to obtain an ideal square wave. 22

35 Over compensated Under compensated Critically compensated CR CR = CR 1 1 > CR 2 2 CR 1 1 < CR Apply 1 khz sinewave to the INP.-I input of the oscilloscope. Adjust the TIME/DIV. to obtain approximately one full period, and set VOLTS/DIV.-I to 0.2V/cm and adjust the output of the signal generator to obtain 1.2V peak-to-peak amplitude. Measure the period of the waveform and calculate the frequency. 5. Measure RMS output voltage of the signal generator using the digital voltmeter. Calculate peak-to-peak amplitude. Compare the result with the oscilloscope. 6. Connect the circuit in Figure 4.4. using R = 1kΩ and C = 100nF. Connect node A to vertical input CH.I and node B to vertical input CH.II. Adjust VOLTS/DIV.-II to obtain reasonable amplitude. Measure the time difference between the zero crossing points of the waveforms and calculate the phase difference for (i) f=100hz, (ii) f=1khz, (iii)=f=10khz. Oscilloscope B A CH.I GND CH.II Signal Generator R C Figure Push Hor/MENU button and obtain the Lissajou pattern. Measure the phase using Equation 4.3 for (i) f=100hz, (ii) f=1khz, (iii)=f=10khz. QUESTIONS 1. Calculate the theoretical errors for the measurement done in steps 4 and 5. Compare the results with the measured values. Explain the reasons for disagreements (if there are any). 2. Explain the operation of Digital Storage Oscilloscope by drawing block diagrams. 3. Draw the Lissajou curve if v ( t) = 5sin(628 t) and v ( t) = 5sin(942 t). x y 23

36 EXPERIMENT DATA SHEET Name of the Experiment : Oscilloscope Group # : Names of the Students : Date of the Experiment : Name of the Lab Assistant : Signed : Experiment Data 4. T = f = V RMS = V PP (calculated) = V PP (set) = V PP = f = 100Hz t = Ф = f = 1kHz t = Ф = f = 10kHz t = Ф = f = 100Hz a = b= Ф = f = 1kHz a = b= Ф = f = 10kHz a = b= Ф =

37 İSTANBUL KÜLTÜR UNIVERSITY DEPARTMENT OF ELECTRONIC ENGINEERING ELECTRICAL MEASUREMENT LABORATORY EXPERIMENT 5 AC VOLTAGE MEASUREMENT OBJECTIVES To learn how to measure AC voltages, To become familiar with the use of AC voltmeters. EQUIPMENT & COMPONENTS 1. Dual Trace Oscilloscope 2. Digital Multimeter 3. Analog Multimeter 4. Signal Generator BACKGROUND The important parameters of a time varying AC voltage, v(t), to be measured are the following; 1. Instantaneous value, v(t) 2. The positive and negative peak value, V p+, V p- 3. The peak-to-peak value, V pp 4. The average value, V A 5. The RMS value, V RMS 5. The period, T 6. The frequency, f 25

38 Figure 5.1. Sinusoidal wave. The oscilloscope is the most versatile instrument to measure most of these electrical quantities. An oscilloscope can measure all of the above mentioned properties except the RMS value and the frequency. The frequency may be easily calculated after measuring the period since f = 1T. The phase diffrence between two voltages may be also measured by an oscilloscope. Measurement using a Voltmeter: To measure the average value, V A, of an AC signal a DC voltmeter may be used directly. An AC voltmeter must be used for measuring the RMS value. However, an AC voltmeter can work properly only in a limited frequency range for which it is designed. Outside of this range, the measuremnet results will be wrong. Therefore, for AC measurements, it is important to know the ferquency of the signal to be measured and the frequency characteristics of the voltmeter to be used. The waveform also effects the measurement s result. Ordinary AC voltmeters are designed and calibrated to measure the RMS values of sinisoidal signals only. For other waveforms the result is not usually correct. The RMS value of a waveform is defined as follows: T 1 2 VRMS v ( t) dt T 0 = (5.1) 26

39 It is fairly difficult to perform the squaring operation to obtain the true RMS value. Only expensive voltmeters measure the true RMS value. The ordinary voltmeters measure the absolute average of a voltage, which is defined: VAA T 1 vt ( ) dt T (5.2) 0 as the average of the absolute value. The absolute average value can be easily be obtained by a full wave rectifying the input voltage. The The converison from the absolute average to the RMS value can be done by scaling the readout (or the input voltage) by a factor called the shape factor. But a Shape Factor is only valid for a certain waveform. For a sinusoidal waveform thsi factor is VRMS π SF = = 1.11 (for sinewave) (5.3) V 2 2 AA After measuring the Absolute Average voltage, the RMS value can be easily determined if the waveform is known. For complex waveforms, such as speech and noise, it is not possible to determine the shape factor and it is necessary to use a True RMS voltmeter. AC Voltmeter must be connected in parallel with the terminals of the circuit elements whose ac voltages will be measured. Besides the polarity, AC voltmeters use the same rules as DC voltmeters do. Since AC voltage reverses its polarity periodically, AC voltmeters are therfore designed without limit in polarity. Measurement using an Oscilloscope Since it has a very large input resistance, an oscilloscope can only be used to measure voltages and time. The vertical axes of an oscilloscope are calibrated to indicate volts/cm and the horizontal axes are calibrated as s/cm. Instantaneous and peak value: Measuring the first three quantities, Instantaneous, Peak and Peak-to-Peak Voltage value is straightforward. Be sure that zero level adjustment is done properly and DC or AC input selection is correctly set. Average value: To measure the average value first the input connection is made AC coupled and one extreme of the waveform is set to the reference line. Then the input is set to Dc coupled mode and the voltage shift is measured. This shift is equal to the average value of the voltage. 27

40 Period: The period can also be directly measured by measuring the time difference between two zero crossing points, and frequency can be easily calculated by taking the reciprocal of the period. Phase: The phase measurement can be performed in two different ways. 1. If the oscilloscope has dual trace facility two voltages are displayed simultaneously and the time difference, t D, is measured between two identical points of the waveforms. The phase difference is then: φ t T = 2π D (5.4) where T is the period of the signal. 2. If one of the signals applied to the horizontal input while the other is connected to vertical input an elliptical trace is obtained on the screen as shown in Figure 5.3. The phase difference can be calculated using this trace as follows: φ = arcsin b (5.5) a V Y (Ө) Y Ө 0 Ф 2п b a X b = V ( φ) = a sin( φ) Y φ = arcsin( ba) V X (Ө) 2п Ө Figure 5.2. The Lissajou curve. 28

41 CALCULATIONS Calculate the shape factor of a triangular and square wave. The standard AC voltmeters are calibrated to indicate the RMS value of a sine wave. Using the calculated shape factors calculate the voltage to be displayed by an absolute average reading meter when the input is 10 V peak (i) sine, (ii) square and (iii) triangular waveform. Calculate the theoretical RMS values for the procedure steps 4, 5 and fill in the blanks in table. PROCEDURE 1. Read the short instruction for the oscilloscope given in appendix 1. Set all push buttons to OUT position. Then turn on the oscilloscope according to the procedures in appendix 2. Apply 1 khz sinewave to the INP.-I input of the oscilloscope. Adjust the TIME/DIV. to obtain approximately one full period, and set VOLTS/DIV.-I to 2V/cm and adjust the output of the signal generator to obtain 12V peak-to-peak amplitude. Measure the period of the waveform and calculate the frequency. 3. Connect the analog and digital voltmeters and the oscilloscope to the signal generator as shown in Figure 5.3. Set the waveform to Sinewave, output voltage to 12V peak-to-peak on the oscilloscope. Change the frequency and note the voltmeter readings in Table 5.1 (Check the voltage on the oscilloscope to remain constant, 12V, peak-to-peak for every frequency). Figure Set the frequency to 50 Hz. Adjust the output voltage to 10V peak-to-peak on the oscilloscope. Then read the voltage with digital and analog voltmeter. Compare the result with the theoretical values. Complete Table

42 5. Change the signal to square and triangular waveforms then repeat step-4. Complete Table Draw the frequency response of the voltmeters, using the measured values (Table 5.1), for the sinusoidal input, on a lin-log graph-paper. QUESTIONS 1. Is it possible to measure the phase difference of two sine waves with a single-input oscilloscope? Explain how. 2. Which instrument is more accurate at 500 Hz and 5000 Hz? Explain the reason. 3. Are Digital and analog Voltmeters used in the Experiment True RMS Voltmeter? 30

43 EXPERIMENT DATA SHEET Name of the Experiment : AC Voltage Measurement Group # : Names of the Students : Date of the Experiment : Name of the Lab Assistant : Signed : Experiment Data 2. T = f = Oscilloscope Analog VM Digital VM Table 5.1. The Frequency response of the instruments Frequency (Hz) K 2K 5K 10K 20K 50K 4. Sine Wave Table 5.2. Sinewave measurement of the instruments Digital VM Analog VM Oscilloscope Theoretical Measured 5. Square Wave Triangle Wave Table 5.3. Square and Triangle Wave measurement of the instruments Digital VM Analog VM Oscilloscope Theoretical Measured Theoretical Measured 31

44 32

45 İSTANBUL KÜLTÜR UNIVERSITY DEPARTMENT OF ELECTRONIC ENGINEERING ELECTRICAL MEASUREMENT LABORATORY EXPERIMENT 6 MEASUREMENT USING DC BRIDGES OBJECTIVES To study resistance measurement techniques using DC Bridge circuits EQUIPMENT & COMPONENTS 1. Digital Multimeter 2. 12V DC power supply 3. Potentiometer 4. Resistors BACKGROUND Accurate measurements of resistances may be performed by using impedance-measuring Bridges. There are a number of bridges, which are called usually by their inventor s name, to measure different type of resistances and impedances. Typical bridge circuit is given in Figure

46 Z1 Z2 + - A B Z3 Z4 Figure 6.1. The basic impedance bridge. When the equation ZZ = ZZ (6.1) is satisfied, the voltages of nodes A and B are equal and the current of the detector, is zero. The unknown impedance, Z 4 is: Z 4 Z 2 = Z3 (6.2) Z1 For measuring real impedances, i.e. resistors, all impedances are resistors and the bridge is called Wheastone Bridge. For measuring capacitance, inductance or complex impedances at least one of the Z 1, Z 2, Z 3 must also be complex in order to satisfy the balance equation. Resistance Measurement using the Wheastone Bridge The basic bridge circuit called Wheastone Bridge is suitable to measure medium range resistance. A DC voltage source and DC meter may be used in this case, since the impedances to be used are real. R1 R2 E A G B R3 Rx Figure 6.2 Wheastone Bridge. 34

47 For the resistive case the Equation 6.2 becomes: R R 2 x = R3 (6.3) R1 For the maximum sensitivity of the bridge all resistance values should be in the same range (as close to each other as possible) as a result of maximum power transfer theorem. Resistance Measurement using the Kelvin Double Bridge G b a Figure 6.3. The Kelvin Double Bridge. The Kelvin Double Bridge is a modification of the Wheatstone Bridge and provides greatly increased accuracy in the measurement of low-value resistances, generally below 1Ω. The term double bridge is used because the circuit contains a second set of ratio arms.. The unknown resistance R x can be calculated as follows: R x = R R 1 R br y R a 1 ( a + b + R ) y R2 b (6.4) where R y is the yoke resistance measured between the node connecting R 3 and b and the node connecting R x and a. PROCEDURE 1. Connect the Wheatstone bridge circuit shown in Figure 6.2. Set R 1 =R 2 = 1kΩ. Use an unkown resistor with a relatively low resistance value, a potentiometer for R 3 and 12V DC power supply for the voltage source. Connect a DC voltmeter between nodes A-B as the detector. 2. By adjusting R v obtain the balance of the bridge. 35

48 3. Calculate the value of unknown resistance R x 4. Replace R 1 =R 2 = 100Ω and repeat steps 2, Connect the Kelvin double bridge circuit shown in Figure 6.3. Set R 1 =R 2 =R 3 =a=b= 1kΩ and an unknown resistor having a relatively low resistance value. Connect a 12V DC power supply for the voltage source. 6. Calculate the value of unknown resistance R x. QUESTIONS 1. Compare the accuracy of the Wheatstone and Kelvin double bridges. 2. Which bridge would you prefer to use for the measurement of a test resistor having a value around 50 kω? 36

49 EXPERIMENT DATA SHEET Name of the Experiment : Measurement using DC Bridges Group # : Names of the Students : Date of the Experiment : Name of the Lab Assistant : Signed : Experiment Data 2. R 3 = R x = ± R 3 = R x = ± R x = ±

50 38

51 İSTANBUL KÜLTÜR UNIVERSITESI DEPARTMENT OF ELECTRONIC ENGINEERING ELECTRICAL MEASUREMENT LABORATORY EXPERIMENT 7 MEASUREMENT USING AC BRIDGES OBJECTIVES To study impedance measurement techniques using AC Bridge circuits EQUIPMENT & COMPONENTS 1. Digital Multimeter 2. Signal Generator 3. Potentiometers 4. Resistors, Capacitors and Inductors BACKGROUND Accurate measurements of complex impedances and frequencies may be performed by using impedance-measuring AC Bridges. There are a number of bridges, which are called usually by their inventor s name, to measure different types of impedances and frequencies. Typical bridge circuit is given in Figure

52 Z1 Z2 + - A B Z3 Z4 Figure 7.1. The basic impedance bridge. When the equation ZZ = ZZ (7.1) is satisfied, the voltages of nodes A and B are equal and the current of the detector, is zero. The unknown impedance, Z 4 is: Z 4 Z 2 = Z3 (7.2) Z1 For measuring capacitance, inductance or complex impedances at least one of the Z 1, Z 2, Z 3 must also be complex in order to satisfy the balance equation. Capacitance Measurement using the Schering Bridge R1 C1 R2 + E - A Detector B C3 Rx Cx Figure 7.2. The Schering Bridge. The Schering Bridge is a complex impedance bridge to measure capacitance. The complex balance equation yields two real equation. Using these two equations the unknown capacitance and its equivalent series resistor (which corresponds to the losses of the capacitor) can be calculated as follows: 40

53 C R R 1 x = C3 (7.3) R2 C 1 x = R2 (7.4) C3 The error of measurement can be calculated as: ΔC ΔR ΔR ΔC C R R C x = + + (7.5) x The relative error on the C x should be treated as the sum of the accuracy of the component Δ C C, which is given by the manufacturer and the minimum relative variation, Δ C x x det x acc C, that can be detected by the detector. x ΔCx ΔCx ΔCx det = + (7.6) C C C x x acc x The accuracy of the detector does not effect the error of measurement. But its sensitivity determines the minimum detectable difference between the voltages of the nodes A and B, hence, minimum detectable variation of adjustable components, C xdet. The best sensitivity is obtained if the values of the impedances of the arms of the bridge on the operating frequency are close to each other. The losses of a capacitor can either be represented by a shunt or series equivalent resistors. The Schering Bridge measures the series equivalent capacitor and resistor. To obtain the parallel equivalent capacitor and leakage resistor (representing the losses): 1 1 D = wcsrs Q = = wc R (7.7) D D 1 Cp = Cs D D Rp = Rs D 2 (7.8) The result of measurement should be given as: C = C ±Δ C (7.9) 41

54 Inductance Measurement using the Maxwell Bridge The Maxwell Bridge is a complex impedance bridge to measure an unknown inductance in terms of a known capacitance. The complex balance equation yields two real equation. Using these two equations the unknown inductance and the resistor in series with it can be calculated as follows: R3 Lx Figure 7.3 Maxwell Bridge. L x = R (7.10) 2R3C1 and R 2 3 R x = (7.11) R R 1 respectively. PROCEDURE 1. Connect the Schering bridge circuit shown in Figure 7.2. Set C 3 to 47nF, R 1 to 1kΩ. and oscillator frequency to 1kHz. Connect an AC voltmeter between nodes A-B as the detector. 2. Set C 1 as 22nF and by adjusting R 2 obtain the balance of the bridge. Can you balance the bridge? Then change C 1 to 47nF and adjust R 2 to obtain balance of the bridge. Can you balance the bridge? 3. Calculate the value of unknown capacitor C x and equivalent resistance R x. 4. Calculate the value of unknown capacitor C p and equivalent resistance R p. 42

55 5. Set the frequency of the generator to 50 Hz and repeat step 3 and Connect the Maxwell bridge circuit shown in Figure 7.2. Set C 1 to 47nF, R 2 to 1kΩ. and oscillator frequency to 1kHz. Connect an AC voltmeter between nodes A-B as the detector. 7. By adjusting R 1 and R 3 obtain the balance of the bridge. Can you balance the bridge? 8. Calculate the value of unknown capacitor L x and resistance R x. 9. Calculate the value of unknown capacitor L p and resistance R p. 10. Set the frequency of the generator to 50 Hz and repeat step 8 and 9. QUESTIONS 1. Derive the balance equations of the Schering Bridge. 2. Can an inductor be measured by using a Schering Bridge?Why? 3. Derive the balance equations of the Maxwell Bridge. 4. Can a capacitor be measured by using a Maxwell Bridge?Why? 43

56 EXPERIMENT DATA SHEET Name of the Experiment : Measurement using AC Bridges Group # : Names of the Students : Date of the Experiment : Name of the Lab Assistant : Signed : Experiment Data 2. R 2 = C 1 = C x = ± R x = ± C p = ± R p = ± C x = ± R x = ± C p = ± R p = ± R 1 = R 3 = L x = ± R x = ± L p = ± R p = ± L x = ± R x = ± L p = ± R p = ±

57 İSTANBUL KÜLTÜR UNIVERSITY DEPARTMENT OF ELECTRONIC ENGINEERING ELECTRICAL MEASUREMENT LABORATORY EXPERIMENT 8 MEASUREMENT OF SEMICONDUCTOR DEVICES WITH MULTIMETER OBJECTIVES To understand the construction of the analog and digital multimeter, To learn how to test semiconductor devices by using the multimeter EQUIPMENT & COMPONENTS 1. KL 100 main unit KL KL 100 breadboard module 2. KL 100 module KL analog multimeter N4001 diode, 1 2N3906 BJT BACKGROUND The analog (VOM - Volt-Ohm-Miliammeter) and digital (DMM) multimeters is the most popular instruments for electrical parameter measurements. As the name implies, the multimeter can be considered as a test instrument which assembles some separate instruments such as the ac voltmeter, dc voltmeter, dc miliammeter, and the ohmmeter into a unit. Each separate function can be accomplished through the control of a selector switch. With specific circuits and scales added, the multimeter can also perform the measurements of inductance, capacitance and db. In this experiment the use of the multimeter will be exercised in the tests for diode, bipolar junction transistor (BJT) and Field Effect Transistor (FET). 45

58 Analog and Digital meters behave quite differently when testing nonlinear devices like diodes and transistors. DMMs can result in false readings as the current may be too low to adequately bias the junctions of diodes and transistors. Thus, VOM may be most suitable for semiconductor device test. However, since lowest resistance range of VOM may put out too much current for smaller devices possibly damaging them, next higher resistance range should be considered first. Testing Diode with VOM. A diode is a two-terminal element, usually made by using a p-n junction. The symbol for a diode is shown in Figure 8.1(a). Which terminal is which matters very much in a diode. Usually, the terminal indicated by a horizontal line in Fig. 8.1 (a), called the cathode, is marked on a real diode (Fig. 8.1 (b)). Voltage (v D ) and the current (i D ) of a diode are defined as shown in Figure 8.1(c). When the voltage v D is positive, the diode is said to be forward-biased; a large current can then flow, and the diode is said to conduct. When the voltage v D is negative, the diode is said to be reverse-biased; the diode current is extremely small, and it is assumed to be zero; the diode is then said to be turned off. Thus, the diode effectively conducts current in only one direction; it refuses to conduct current in the other direction. Figure 8.1. (a) the symbol of the diode, (b) real diode, (c) i-v characteristic of a diode. To test the functionality and polarity of the diode are very important. Battery powered VOM can be used to test the diode and determine the way it conducts the current. To test the diode, VOM is used on low scale range. When black probe (GND probe) is connected to the cathode and red probe to anode of the diode, the diode is forward biased by the battery inside the VOM and should show very low resistance, for instance couple of ohms for regular diode (but not zero). On the contrary, if the probes are interchanged, the VOM measures very high resistance (nearly infinite resistance) as VOM battery reverse 46

59 bised the diode. However, it should be emphasized that the measured resistance is a resistance at particular (at low current) operating point. On a (digital) DMM, there will usually be a diode test mode, which displays the actual forward voltage drop of the diode in volts, rather than a "resistance" figure in ohms. These meters work by forcing a small current through the diode and measuring the voltage dropped between the two test leads. Using this, a silicon diode should read between 0.5 to 0.8 V in the forward direction and open in reverse. Testing BJT with WOM A Bipolar Junction Transistor (BJT) has three terminals connected to three doped semiconductor regions. In n-p-n transistor, a thin and lightly doped p-type material is sandwiched between two thicker n-type materials; while in a pnp transistor, a thin and lightly doped n-type material is sandwiched between two thicker p-type materials (Figure 8.2). Figure 8.2. Bipolar transistor types. The three terminals of a transistor are typically used as the input, output and the common terminal of both input and output. Depending on which of the three terminals is used as common terminal, there are three different configurations: common emitter (CE), common base (CB) and common collector (CC). The common emitter (CE) is the most typical configuration: Two voltages V BE and V CB are applied to the base and collector of the transistor with respect to the common emitter. In normal operation, the BE junction is forward biased while the CB junction is reverse biased (Figure 8.3). 47