اﳌﻤﻠﻜﺔ اﻟﻌﺮﺑﻴﺔ اﻟﺴﻌﻮدﻳﺔ KINGDOM OF SAUDI ARABIA Ministry of Higher Education وزارة اﻟﺘﻌﻠﻴﻢ اﻟﻌﺎﱄ - ﺟﺎﻣﻌﺔ أم اﻟﻘﺮى Umm Al-Qura University ﻛﻠﻴﺔ اﳍﻨﺪﺳﺔ و اﻟﻌﻤﺎرة اﻹﺳﻼﻣﻴﺔ College of Engineering and Islamic Architecture ﻗﺴﻢ اﳍﻨﺪﺳﺔ اﻟﻜﻬﺮ?ﺋﻴﺔ Electrical Engineering Department
ELECTRICAL AND ELECTRONIC MEASUREMENTS (802314-3)
Laboratory Manual
(Fall 2016: Term 1, 1437/1438H)
Prepared by: Dr. Makbul Anwari
Approved by: Control Sequence Committee Table of Contents
Page
1. Introduction 3
2. Laboratory Safety 3
3. Lab Report 5
4. Experiment # 1: 6
5. Experiment # 2: 11
6. Experiment # 3: 19
7. Experiment # 4: 25
8. Experiment # 5: 29
2 Introduction
This manual has been prepared for use in the course 802314-3, Electrical and Electronic Measurements. The laboratory exercises are devised is such a way as to reinforce the concepts taught in the lectures. Before performing the experiments the student must be aware of the basic laboratory safety rules for minimizing any potential dangers. The students must complete and submit the pre-lab report of each exercise before performing the experiment. The objective of the experiment must be kept in mind throughout the lab experiment.
Laboratory Safety:
∑ Safety in the electrical engineering laboratory, as everywhere else, is a matter of the knowledge of potential hazards, following safety regulations and precautions, and common sense. ∑ Observing safety precautions is important due to pronounced hazards in any electrical engineering laboratory. ∑ All the UQU Electrical Engineering Students, Teaching Assistants, Lab Engineers, and Lab technicians are required to be familiar with the LABORATORY SAFETY GUIDELINES FOR THE UQU ELECTRICAL ENGINEERING UNDERGRADUATE LAB AREAS published on the department web-page. ∑ Practice electrical safety at all times while constructing, analyzing and troubleshooting circuitry. ∑ Do not accompany any drinks or water with you inside the Lab. ∑ If you observed an electrical hazard in the lab area – NOTIFY THE INSTRUCTOR/LAB ASSISTANT IMMEDIATELY! ∑ Acquaint yourself with the location of the following safety items within the lab. a. Fire extinguisher b. First aid kit c. Fire-exit d. Telephone and emergency numbers
Department/Person Telephone Fire-Department Emergency 0 – 998 Dean College of Engineering & Islamic 0 - 5281155 / 1177 Architecture / Secretary EE Department Chair / Secretary 1024 / 1203 Dean of Students’ Affairs: 0 – 5561916 0 - 5563478 & 0 - 5562524 / x 6828 / x UQU University Service /Security 6027 UQU Medical Clinic/ Emergency/ 0 - 5589953/ x5658 / x5699 Reception
3 LABORATORY SAFETY REVIEW QUESTIONS:
1. YES or NO: Have you read the Laboratory Safety Guidelines for the UQU Electrical Engineering Undergraduate Lab Areas? 2. What should you do if an emergency situation occurs in the laboratory?
3. In the event of a fire, police, or medical emergency do you know the emergency telephone number? Write it down.
4. TRUE or FALSE: There is an increased risk of electric shock if you enter the lab area bare feet.
5. TRUE or FALSE: There is no increased risk of electric shock and the equipment is not affected in any way if food and drinks are allowed in the lab area.
6. TRUE or FALSE: The students may be allowed to work alone in any lab area without the supervision of Teaching Assistant (TA) or Course Professor.
7. Fill in the blanks: a. Voltages above ______Vrms AC are dangerous.
b. Voltages above ______DC are dangerous.
8. TRUE or FALSE: In the event of fire emergency use elevator to evacuate faster.
4 Lab Report:
A lab report for each experiment is to be submitted by each member (student) of a team one week after the lab session is completed. The lab report must be type written in the MSWord (Times-Roman 12 font) format and it must contain the following:
1. Cover page containing:
∑ Electrical and Electronic Measurements 802314-3 Experiment #______
∑ Experiment Title: ______
∑ Group #: ______
∑ Your Name: ______& I.D. #: ______
2. Objectives: Not copied from the lab manual
3. Specifications of Equipment Used:
4. Procedure: Steps you did in the lab. It is not copied from the lab manual
5. Block Diagram or Circuit Diagram should be included
6.Result or Analysis: Compare the Pre-lab results with those obtained in the experiment. Summary of what you discovered. (Attach the pre-lab with the lab report)
7. Answers to Questions: Answer to observation questions in the lab experiment,lab review questions and lab safety review questions at the end of the experiment in a written form (MSWord document).
8. Conclusion: The conclusions based on the experiment and other observationsmust be clearly discussed in the laboratory report.
9. Remarks or Comments: You may write your comments regarding your experience of each lab experiment.
(The laboratory report will be graded for content and written English)
5 (802314-3) EXPERIMENT #1 OSCILLOSCOPES
Objective:
To study the functions and operation of the Cathode Ray Oscilloscope (CRO) and to use it for the measurement of voltage, frequency, time period and phase difference.
Theory:
The oscilloscope is a very valuable device for making many measurements for voltage signals. It can show a scaled picture of one or more voltages applied to it. The picture (also called display) provides the following information:
q Peak and instantaneous value, q Frequency, q Period, q Phase angle between voltages.
Only steady or repetitive voltages can be measured with ordinary oscilloscope.
The scope can show two vertical inputs at the same time by connecting them alternately to the same set of vertical plates. The switching between them is done automatically based on the mode selected, i.e. chopped or alternate. It can also give algebraic sum or difference of two vertical inputs. Voltage can also be applied to the horizontal channel (normally used for time-sweep) so as to see it against the vertical voltage. This is called XY mode.
Pre-lab:
1. Briefly discuss each of the following oscilloscope controls: intensity, focus, position, volts/div, time/dive, and trigger level. 2. Explain how to determine peak-to-peak voltage, time period and frequency using oscilloscope.
Equipment Required:
q Oscilloscope. q RC Probe. q Function Generator. q Phase Shift Network (Resistor and Capacitor).
Procedure:
1) Locate the following switches and knobs on the oscilloscope and find out their functions: q Power on/off switch, 6 q Focus controls knob, q Beam find press button, q Intensity control knob, q Vertical shift control for each channel, q Channel-display switch (CH1/Both/CH2), q Vertical sensitivity control (Volts/cm) for each channel, q Input coupling switches (AC/GND/DC) for each channel, q Vertical input ports for each channel, q CH2-Invert press button, q Display-mode control switch (ADD/ALT/CHOP), q Horizontal-Shift control knob, q Sweep Rate control (Time/cm) and XY-mode switch, q External Synchronizing (Sync.) Input socket, q Internal-Trigger switch, q Trigger source switch, q Trigger slope press button, q Trigger level control knob.
2) Switch on the oscilloscope and set the sweep mode to free-run. Adjust focus and intensity to get a sharp but modestly bright trace.
Note: There should be ground line adjustment before making any measurements !
3) With the input coupling switch set to DC, apply a DC voltage of few volts in CH1. Set the sweep rate and sensitivity to a suitable sec/cm and volts/cm, setting to give a calibrated deflection of at least 4 cms from the ground reference. Calculate the voltage values as follows:
q Vertical Deflection, Y = ______
q Vertical Scale, S = ______
q Voltage, V = Y ∙ S = ______
4) Set the coupling to AC . Can you measure this way ? Why ? 5) Set the coupling switch to AC. Using the function generator; apply sinusoidal voltage of 50 Hz and a few (r.m.s.) volts to the vertical input of CH1. 6) Set the trigger selector to CH1 and the trigger level to give a stable picture. Set the sweep rate to 2msec/cm, don’t forget to put the red small knob at the calibrated position (fully clockwise). Adjust the vertical scale (volts/cm) to get a display of nearly 5 cm Peak to Peak. Center the display with the vertical shift control if necessary. 7) Calculate the peak to peak voltage as follows:
q Peak to Peak Voltage, V = (Peak to Peak vertical deflection, Y) * (vertical sensitivity, S)
8) Adjust the sweep rate to get just over one complete cycle of calibrated display of the waveform. 7 9) Measure the horizontal distance between any two points forming a complete cycle. 10) Calculate the period and the frequency as follows:
q Period, T = (Length of on cycle, L) × ( horizontal sensitivity, Z)
q Frequency, F = 1/ T.
11) Record the result in table 1 below:
Table 1 Y V Waveform S L Z T F Peak to Peak to & Freq. (V/cm) (cm) (sec/cm) (sec) (Hz) Peak (cm) Peak (Volts)
50 Hz
1 kHz
5 kHz
50 Hz
1 kHz
5 kHz
12) Repeat for 1 kHz and 5 kHz frequencies. 13) Repeat for triangular wave at 50 Hz, 1 kHz and 5 kHz frequencies. 14) Wire the circuit shown in figure 1 below.
Figure 1: Phase Shift Network (LPF) 8 15) Set the channel display switch to Both . 16) Adjust the frequency and sweep rate to get a stable display of at least one cycle. 17) Adjust volts/cm settings on the two channels to get nearly equal peak to peak deflection of the two traces. Use the red (calibrate) knobs to compress the display if necessary. 18) Center the two traces, measure the distance between the Zero crossings of the two traces to calculate the phase difference as follows:
ÈDistancebetween zerocrossings,D˘ o q Phase Difference, f = Í ˙¥360 Î Length of onecompletecycle,L ˚
19) Turn the sweep rate control knob to XY position. 20) Adjust the volts/cm setting on CH1 to control the size of the horizontal deflection and on CH2 for vertical deflection. 21) Center the display and measure the phase f as follows:
-1Ê Distance,B, between Y - intercepts ˆ q f = SIN Á ˜ Ë Distance,A, of largest verticaldeflection¯ A B
Table 2 f f F D L A B sweep time XY- %Error (Hz) (cm) (cm) (cm) (cm) mode mode 1k 5k 200
22) Repeat the measurement for two other frequencies. 23) Record your readings and calculations in Table 2. 24) Set the scope to XY mode.
25) Apply sinusoidal voltage at frequency (fx = 120 Hz) to CH1.
26) Apply another sinusoidal voltage at any frequency (fy) to CH2. 27) Note the resulting Lissajous figure.
28) Calculate fy as follows:
9 ÈNumber of X - axis tangensions,nX ˘ q fy = Í ˙ ◊ fX ÎNumber of Y - axis tangensions,nY ˚
29) Measure fy using sweep time mode and find error. 30) Repeat for two more frequencies and fill table 3 below.
Table 3 F (Hz) F F (Hz) Y X n n Y sweep time %Error (Hz) X Y Calculated mode 120
31) Give your comments on the results in table 1, 2 and 3.
Instructor’s signature Date 10 Review Questions:
1. Briefly explain the VOLTS/DIV and TIME/DIV selector switches. 2. Explain what is Lissajous figure. 3. Define “deflection factor” and “deflection sensitivity” for an oscilloscope. 4. Determine the minimum time/division sensitivity for an oscilloscope that is to be used to investigate a 50MHz waveform. Assume that the time base magnifier expands the horizontal display by a factor of 5.
11 (802314-3) EXPERIMENT # 2 MOVING COIL VOLTMETER AND WAVEFORM ERROR
Objective:
To develop proficiency in the use of moving coil voltmeter (MCV) and to see its waveform error.
Theory:
When measuring AC voltages, we are usually interested in the RMS value because it represents the effectiveness of the different measured waveforms. Voltages can be measured by different types of meters. In this experiment, we use the following instruments:
q Moving Coil Voltmeter (MCV). q Digital Voltmeter (DVM). q Oscilloscope (CRO).
Moving coil voltmeters are average type meters since they respond only to the DC value of the measured waveform. In order to measure alternating voltages using such instruments, the waveform should be rectified before applying it to the meter. Readings of moving coil voltmeters must be multiplied by waveform factor in order to be correct. Waveform factor is defined as RMS Value/DC value of rectified waveform.
In the case of pure sinusoidal voltages this factor is (p 2 2 ) for full wave rectification (FWR) and (p 2 ) for half wave rectification (HWR).
Most MCV’s use FWR and hence the reading is multiplied by p 2 2 = 1.11 to be correct. For ease, scales are adjusted to give correct reading without further multiplication when measuring voltages of pure sinusoidal waveforms. For other waveforms, error readings are obtained. The error in the reading can be calculated from:
ScaleReading of FWR (1.11¥average)- RMS q Error = ¥100% RMS
As an example, consider the triangular waveform shown in figure 1.
12 Figure 1: Triangular waveform
The FWR average and RMS values of this waveform equal Vm 2 and Vm 3 respectively. Therefore, the percentage error in measuring such waveforms using MCV is:
1.11¥Vm 2 - Vm 3 q Error = ¥100% = – 3.9% Vm 3
The error in measuring sinusoidal waveforms is equal to zero.
The oscilloscope can be used for voltage measurements by reading the values of the voltage waveform as displayed on the screen, and then calculating the RMS value.
Pre-lab:
1. Sketch the basic construction of a typical permanent magnet moving coil instrument. Identify each part of the instrument and explain its operation. 2. Sketch the circuit and waveforms for an ac voltmeter using a moving coil instrument and a full-wave bridge rectifier. Explain the circuit operation.
Equipment Required:
q Moving Coil Voltmeter. q Digital Voltmeter. q Oscilloscope. q Function Generator. q Resistance Box.
Procedure:
1) Identify the following controls on the MCV panel:
q Power ON/OFF switch. q Range knob. q Input and Output terminals. q Calibration Screen. 2) Calibrate your MCV so as to read zero when input is shorted. 3) Switch the instruments ON. 13 4) Adjust the function generator to give about 5 volts sinusoidal output at a frequency of 60 Hz. 5) Measure the voltage using the oscilloscope, the moving coil and digital voltmeters. 6) Record the readings on Table 1. 7) Repeat the last three steps for square and triangular voltage waveforms.
Table 1 MCV DVM Scope
l Reading a d i o
s Expected Error 0 % u n i S Actual Error
Reading e r a
u Expected Error 0 % q S Actual Error
Reading r a l u g
n Expected Error 0 % a i r T Actual Error
8) The expected RMS voltage for the different waveforms is as follows: Peak ◊ to ◊ Peak q V (sin wave) RMS 2 2 Peak ◊to◊ Peak q V (triangular - wave) RMS 2 3 Peak ◊to◊ Peak q V (square - wave) RMS 2 9) Repeat steps 5 and 7 at frequency 1 kHz. 10) Fill your results in table 2. 11) Write your comments on the experiments.
14 Table 2 MVC DVM Scope
l Reading a d i o s Expected Error 0 % u n i S Actual Error
Reading e r a u Expected Error 0 % q S Actual Error
Reading r a l u g
n Expected Error 0 % a i r T Actual Error
Instructor’s signature Date
15 Review Questions:
1. List three forces involved in the moving system of a deflection instrument. 2. Explain the function of “damping force” in permanent-magnet moving-coil instruments and how it is typically produced. 3. A permanent-magnet moving-coil instrument has full-scale deflection (FSD) of 100 µA and a coil resistance of 1 kΩ. Calculate the required shunt resistance value to convert the instrument into an ammeter with FSD = 100 mA. 4. Calculate the required shunt resistance value to convert instrument (in question 3) into an ammeter with FSD = 1 A.
16 (802314-3) EXPERIMENT #3 STUDY OF THE AVO METER
Objective:
To Study the design and use of AVO meter for both AC & DC measurements.
Theory:
The galvanometer (m-Ammeter) is a moving coil meter normally used to measure DC currents within its maximum Full Scale Deflection (FSD) value.
However , using extra circuits , it can be to measure:
1. DC Currents higher than FSD value. 2. DC Voltages. 3. AC Currents. 4. AC Voltages. 5. Ohm Values.
Each class is going to be considered for analysis, where RM is the resistance of movement and iFSD is the full scale deflection current.
1. DC Currents higher than FSD Value :
Here , the circuit shown in figure 1 is used, where the new FSD Current IFSD is related to iFSD by :
iFSD R1
IFSD R1 + R M
Figure 1 : Current Shunt
Hence, to get the m-Ammeter to measure upto IFSD design R1 to be:
17 iFSD R1 ¥ R M (1) IFSD - iFSD and hence:
I New Scale Reading * FSD (2) iFSD
2. DC Voltage Measurements :
Here , the circuit shown in figure 2 is used, where the new FSD Voltage VFSD is related to iFSD by :
VFSD iFSD R 2 + R M
Figure 2 : Voltage Series
Hence, to get the m-Ammeter to measure upto VFSD design R2 to be:
VFSD R 2 - R M (3) iFSD and hence:
V NewScale Reading * FSD (4) iFSD
3. AC Current Measurements :
Figure 3 shows an RC filter and a bridge rectifier that are used to obtain from the applied sinusoidal signal a current balanced about zero level. The other end of the bridge have the shunt arrangements shown before in figure 1. If R3 = •, the movement will sense an average value (AV) related to the RMS of the ac part of the applied value by :
18 2 2 E ◊ E AV p RMS
Figure 3 : Bridge shunts.
Hence, the AC FSD will relate to the DC FSD :
p AC FSD ◊ DC FSD 1.11◊ DC FSD 2 2
When R3 is finite, IAC FSD is related to IFSD by :
iFSD R3
IACFSD ◊( 2 2 p ) R3 + R M
Hence,
iFSD R 3 ¥ R M (5) ( 2 2 p ) ◊ IFSD - iFSD
Hence, designing the AC ammeter to read a given IAC FSD requires an R3 value as given above.
Therefore, the AC new value scale is obtained by:
I New Scale Reading * ACFSD (6) iFSD
4. AC Voltage Measurements :
Here , the filter an bridge are used to balance and rectify the applied voltage input whereby a series circuit similar to that of figure 2 is then used to facilitate various voltage scales as shown in figure 4.
19 Figure 4 : Bridge Series
Hence,
VACFSD ◊( 2 2 p ) iFSD R 4 + R M
Hence,
VACFSD ◊( 2 2 p ) R 4 - R M (7) iFSD
Again, ac new scale is obtained by
V NewScale Reading * ACFSD (8) iFSD
5. Ohm Measurements :
This is achieved by either series or shunt arrangements. Both arrangements are shown in figure 5 and 6 . The circuit shown in figure 5 is more popular than that of figure 6, since it is consuming no battery power at measurement, while the other is.
Figure 5 : Series Ohmmeter
20 Figure 6 : Shunt Ohmmeter
At open circuit, indication is zero and we mark • on the W-scale and at short circuit indication should be:
E iFSD R5 + R M
Hence, R5 is designed to be :
E R5 - R M (9) iFSD
At any other measurement, R, the new scale is given by
E R - R - R (10) Reading M 5
Pre-lab:
1. For a galvanometer define current sensitivity, critical damping resistance, voltage sensitivity, and megohm sensitivity. 2. An instrument with FSD of 100 mA and a coil resistance of 1 kΩ is to be converted into a voltmeter. Determine the required multiplier resistance if the voltmeter is to measure 50 V at a full scale. Also calculate the applied voltage when the instrument indicates 0.8 of FSD.
Equipment Required:
q m Ammeter. q Resistors (1/4 watt). q 4 Diodes. q Connection Board. q DVM. q Function Generator.
21 Procedure:
1) Measure your m-ammeter parameters and note them down:
q iFSD = ______
q RM = ______
2) Wire the circuit in figure 1 using a suitable value of R1 to measure IFSD of 15 mA. Apply a dc voltage to resistor load so as to pass 10 mA measured by DMM. Replace the DMM by your ammeter and fill table 1 below:
Table 1 Required Your DMM I R Used R Reading %Error FSD 1 1 Reading Eq.(1) Eq.(2)
15 mA
3) Wire the circuit in figure 2 using a suitable value of R2 to measure VFSD of 3V. Apply a DC voltage of 2V to the DVM . Replace the DVM by your voltmeter and fill table 2 below:
Table 2 Required Your DVM V R Used R Reading %Error FSD 2 2 Reading Eq.(3) Eq.(4)
3 V
4) Wire the circuit in figure 3 using a suitable value of R3 to measure IACFSD of 50mA. Apply an AC voltage of 2V to a resistor load so as to pass 30mA measured by DMM . Replace the DMM by your ammeter and fill table 3 below:
Table 3 Required Your DMM I R Used R Reading %Error AC FSD 3 3 Reading Eq.(5) Eq.(6)
15mA
5) Wire the circuit in figure 4 using a suitable value of R4 to measure VACFSD of 10V. Apply an AC voltage to resistor load so as to be 2V measured by DVM . Replace the DVM by your voltmeter and fill table 4 below:
22 Table 4 Required Your DVM V R Used R Reading %Error ACFSD 4 4 Reading Eq.(7) Eq.(8)
10 V
6) Wire the circuit in figure 5 , use 5V for E. 7) Use the circuit to measure an unknown resistance. Fill table 5 below:
Table 5 Required Your DVM E R Used R Reading %Error DVM 5 5 Reading Eq.(9) Eq.(10)
5 V
8) Write your comments.
Instructor’s signature Date
23 Review Questions:
1. A galvanometer has a current sensitivity of 1µA/mm and a critical damping resistance of 1 kΩ. Calculate:
(a) the voltage sensitivity and (b) the megohm sensitivity.
2. Galvanometers are often employed as a “null meter” or “null detector”. Explain. 3. A galvanometer used as a “null meter” must be protected. Why? How to protect the galvanometer. 4. Explain voltmeter sensitivity, voltmeter loading effect, and voltmeter swamping resistance.
24 (802314-3) EXPERIMENT #4 ELECTRONIC FREQUENCY COUNTERS AND DIGITAL MULTIMETERS (DMM)
Objective:
To familiarize with the operation and use of electronic frequency counters in measuring frequencies, time periods , etc. and to use the digital multimeters ( DMM ).
Theory:
The electronic frequency counter is a digital instrument which can do the following functions:
q Totalizer : Where it counts the total no. of input pulses , whether square or not. q Frequency : Where the measures the frequency of the input single. q Period : Where the period of AC single is measured. q Some counters can also measure time interval between two events, ratio of two frequencies and can be used as a timer.
The DMM , on the other hand can be used to measure:
q DC / AC Volts. q DC / AC mAmps. q Resistance in W .
Pre-lab:
1. To what accuracy can a frequency counter determine an unknown frequency of 450 kHz, using a 1 s time base and a time-base accuracy of 0.01 per cent? 2. Explain methods can be used to increase the frequency range of a frequency counter.
Equipment Required:
q Electronic Frequency Counter. q DMM. q Scope, Probes, etc. q Function Generators. q Resistors.
Procedure:
1) Identify the following in the Electronic Frequency Counter:
q ON / OFF Press Button. q Period Button. 25 q Hold Button. q I / P Socket. q Display Screen.
2) Set the function generator to (Sinusoidal) at 10 Vp-p and 5KHz using scope. 3) Apply the signal to the I / P of the counter. 4) Press ( Freq.) button to set the counter to frequency measurement. 5) Fill table 2 below. 6) Press the ( Period ) button and fill table 3 below.
Table 2 Period by Period by Freq. by Freq. by Sensitivity Scope Scope Scope Counter %Error Remark (sec/ cm) (cm) ( sec ) ( Hz ) ( Hz ) ......
Table 3 Period by Period by Scope Counter %Error Remark ( sec ) ( sec )
......
7) Change the frequency to 20Hz at 10 Vp-p and fill table 4 below. What do you conclude ?
Table 4 Period by Period by Scope Counter %Error Remark ( sec ) ( sec )
......
8) Wire the circuit shown in figure 1. Use R = 1 kW. 9) Set the two DMM. to measure DC V and DC mA.
26 Figure 1
10) Fill table 5 below:
Table 5 E E E I R DMM R DMM by Scope by DMM %Error by DMM %Error IDMM (V) (V) (mA) Calculated Measured
11) Set the two DMM to measure AC V and AC mA. What do you notice? 12) Now set the function generator to sinusoidal and fill table 6 below.
Table 6 E E I I by Scope by DMM %Error by DMM Expected %Error (V) (V) (mA) (mA)
13) Give your comments on the results.
Instructor’s signature Date
27 Review Questions:
1. Explain how to obtain maximum accuracy of measurements using frequency counter? 2. What is the one very common instrumental error which occurs whenever frequency measurement are made? 3. How to determine the output frequency of the counter using prescaler method?
28 EXPERIMENT 5: BRIDGE MEASUREMENTS
Objective:
By the end of this experiment the student should be able to:
1. Use the DC Wheatstone Bridge to measure unknown resistance. 2. Use the AC Wheatstone Bridge to measure unknown inductance.
PART I THE DC WHEATSTONE BRIDE
Theory:
A bridge is a special class of circuits that can be used for measuring resistance, capacitance, or inductance. A resistance bridge is especially useful when a very accurate measurement of a resistance is required. The Wheatstone bridge or four arm bridge, invented by C. Wheatstone in 1843, is the most widely used resistance bridge for measuring resistance values above 1 Ω. Commercial Wheatstone bridges are accurate to about 0.1 percent, making the values of resistance obtained far more accurate than values obtained from many types of meters. For resistances below 1 Ω, a Kelvin Bridge can be used.
A Wheatstone bridge consists of a voltage source and two parallel voltage dividers, as shown in Figure 1. The bridge is said to be balanced when v12=0V. For the balanced condition, the voltage v3 is divided in the path containing resistors Raand Rbin the same ratio as in the path containing resistors Rcand Rx, which allows the unknown resistance Rxto be determined in terms of Ra, Rb and Rc.
We can find Rxin terms of Ra, Rband Rc as follows. Using the voltage divider relation,
For the balanced condition, v12=0 or v1=v2. Equating the above expressions for v1 and v2 gives:
Multiplying both sides by (Rx+Rc) and ( Rb+Ra), gives Rb(Rx+Rc)=Rx(Rb+Ra). Subtracting RbRxfrom both sides and solving for Rxgives:
29 In order to achieve balance for a specific unknown resistance Rx, let Raand Rchave fixed, known values, and let Rbbe a calibrated (adjustable) resistor. The procedure is to adjust Rb until v12=0, and then use the expression derived above to determine Rx.
Pre-lab:
1. Use Sinulink/Matlab to do the experiment by the same compounds. 2. What is the basic condition for balancing of DC bridges?
Procedure:
1. Construct the Wheatstone bridge shown in Figure 1. Use resistor values Ra=1kΩ, Rc=10kΩ, and Rs=10kΩ Use a decade resistance box for Rband a DC power supply adjusted to 5 volts. 2. Measure the value of an "unknown" resistance supplied by your lab GTA 1kΩ ≤Rx≤10kΩ. In adjusting Rbusing the decade resistance box, start with the coarsest scale and work toward the finest scale, while monitoring v12 with the You should observe some small deflection of galvanometer needle (if it is very large, or if there is no deflection, check with the instructor). 3. Calculate the unknown resistance. Next, perform one (or both, if time permits) of the following exercises (your choice): 4. Measure the resistance of a photo-resistor under various lighting conditions.
5. Measure the resistance of ten different 1 kΩ resistors and plot their values in terms of percent deviation from the nominal value. A bar graph is a convenient form for this plot. 30 Part II AC Wheatstone Bridge
Pre-lab:
1. What is the basic condition for balancing of AC bridges? 2. Test the circuit using Simulink/Matlab.
Next we will use the AC Wheatstone Bridge circuit shown in Figure 2 to measure an unknown inductor (with L somewhere between 15 and 25 mH).
The arrangement of the AC Bridge is shown in Figure 2.
1. Show that when the bridge is balanced the resistance R4 and inductance L are given by the determination of L is not very precise for low frequencies because the voltage across L and L comparable.
(General Radio) resistors for R2 and R3 and the Eico resistors for R1 and R4. Use the Eico capacitance box and the numbered inductor board. Use the function generator with the voltage source. Set the DMM null meter to read AC voltage. Now adjust C and R1 to minimize the DMM reading. (Because of noise pickup you may only be able to null the bridge to a few mV. You can test whether you have nulled the f = 1 kHz signal by turning the function generator amplitude to zero and observing what happens to the null reading.) Record the results and calculate L. Also, record the number on the inductor board. 3. Change f by a factor of 2 and rebalance the bridge to verify that the balance equations do not depend on Ω.
4. Check with your lab instructor to get the actual value of L for the board you used. How close was your measurement to the actual value?
31 Figure 2
Instructor’s signature Date
32 Review Questions:
1. List the main parts of a bridge. 2. What are the main sourcesof errors when we use a bridge? 3. What is the main difference between a dc and an ac bridge?
33 Experiment (6) Spectrum Analyzers
6.1 Introduction: Spectrum analyzers are used to measure the spectral characteristics of signals. Knowing signal's spectrum helps identifying the specifications of systems that process such signals. The spectrum of a signal could be identified by either using Fourier theorems to get an analytical description of the signal in frequency domain or using a device to measure the spectral components. Such device is called spectrum analyzer. In this experiment, students are going to be first familiarized with the spectrum analyzer they are going to use and its various controls then to do some measurements on various signal types as well as measurement on the input and output of a given circuit so as to be able to identify the circuit's transfer function.
6.2 Objectives By the end of this experiment, the student should be able to: 1. Identify the various controls of the Spectrum analyzer 2. Use the Spectrum analyzer to measure the spectrum of various signals 3. Use the measurements above to identify the transfer function of a given circuit
6.3 Equipments Spectrum analyzer Function generator Oscilloscope Resistance box Capacitance box
6.4 Procedure A. Spectrum analyzer familiarization Use the attached manual pages of the Spectrum analyzer to identify the various controls of the instrument.
B. Measurement of signal's spectrum 1. Adjust the function generator to produce a 1Vp 200 kHz square wave. Use the CRO to check the signal's amplitude and frequency. 2. Move the marker in the Spectrum analyzer to 200 KHz. And record the reading in the first row of table 1. This represents the fundamental component of the square wave. 3. Continue moving the marker to the frequencies specified in the first raw of table 1 and record your readings. These are the harmonics of the square wave. 4. Sketch the spectrum of the square wave. 5. Repeat steps 1-4 for the different frequencies specified in table 1. 6. Repeat the above steps for a triangular wave with the frequencies specified in table 2 and sketch the spectrum for each row. 7. Compare the results with the analytical counterparts by applying Fourier series to the signals in both tables. Use the CRO to identify the time-domain description to help you in applying Fourier analysis. 34 Table 1 Square wave spectrum Frequency Fundamental Second H. Third H. Fourth H. Fifth H. 200 KHz. 500 KHz. 1 MHz.
Table 2 Triangular wave spectrum Frequency Fundamental Second H. Third H. Fourth H. Fifth H. 200 KHz. 500 KHz. 1 MHz.
C. Determination of a circuit's transfer function 1. Connect the circuit shown below
2. Apply a 200 KHz sine wave to the input of the circuit. 3. Measure the spectrum of both the input and output. 4. Record the ratio Vo(f)/Vi(f) in the corresponding entry of table 3. 5. Repeat the above steps for the rest of frequencies in table 3. 6. Plot the circuit's transfer function; H(f)= Vo(f)/Vi(f) versus the frequency; f. 7. Using the plot obtained above describe the given circuit.
Table 3 Circuit's Transfer function Frequency 200 KHz 500 KHz 1 MHz 2 MHz 5 MHz 10 MHz Vi(f) Vo(f) H(f)= Vo(f)/Vi(f)
Instructor’s signature Date
35