Lab Book Fayoum Doaa

‫المعمل المتطور لنظم القوي الكهربية‬ Advanced Laboratory for electric Power systems Faculty of Engineering Electrical Engineering Dept. ‫جامعة المنيا‬ Minia University ‫رؤيه المعمل‬ .‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‬ Electrical Engineering Dept. Introduction to Measurement and Laboratory (1) Instructor: Adel A. Elbaset , Ph.D. First year- communication department Contents Chapter 1 Measurement and Error Chapter 2 Measurement of Electrical Current Voltage and Resistance Chapter 2 Lab Experiments          Lab 0: Introduction : Introduction to electronic component: resistors capacitors, inductors and diodes. And learn how to read the component values and maximum ratings. Lab 1: DC Concepts and Measurement Lab 2: DC Measurements I: Series and Parallel Resistor Combinations and Current Measurements Lab 3: DC Measurements II: Circuit Laws and Voltage Dividers Lab 4: AC Concepts and Measurements I Lab 5: AC Concepts and Measurements II Lab 6: Introduction to Rectifying Diodes Half wave and full wave rectifier circuits Lab 7: Introduction to Transistors Lab 8: Introduction to Operational Amplifiers ‫ كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬،‫ "َسعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‬:‫رسانه انًعًم‬ ."ًٍ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعان‬ Tel: 01090343201 Fax: (086) 2346674 ‫ كلية الهندسة – جامعة المنيا‬- ‫ عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده‬.‫د‬.‫إعداد أ‬ Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com Page 1 of 58 ‫المعمل المتطور لنظم القوي الكهربية‬ Faculty of Engineering Electrical Engineering Dept. Advanced Laboratory for electric Power systems ‫جامعة المنيا‬ Minia University ‫رؤيه المعمل‬ .‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‬ Electrical Engineering Dept.    Lab 9: 555 Timer Lab 10: Arduino (Part 1) Lab 11: Arduino (Part 2) Chapter 1 Measurement and Error An engineer has to make a lot of measurements, collect and analyze data, and make decisions about the validity of his approaches and procedures. He must have a clear idea about the results he is going to obtain. In this respect, he may develop models of his expectations and compare the outcomes from the experiments to those from the model. He uses various measuring instruments whose reliabilities have outmost importance in successes of his decisions. Characteristics of measuring instruments that are used in selecting the proper ones are reviewed in the first section. Section 2 deals with analyses of measurement data. Section 3 handles the analyses of uncertainties and establishment of engineering tolerances. 1.1. Characteristics of Measuring Instruments 1.1.1. Definition of Terms The characteristics of measuring instruments are specified using terms shortly defined below. The full description of some of these terms will be provided later with examples. True value: standard or reference of known value or a theoretical value Accuracy: closeness to the true value; closeness with which an instrument reading approaches the true or accepted value of the variable (quantity) being measured. It is considered to be an indicator of the total error in the measurement without looking into the sources of errors. ‫ كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬،‫ "َسعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‬:‫رسانه انًعًم‬ ."ًٍ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعان‬ Tel: 01090343201 Fax: (086) 2346674 ‫ كلية الهندسة – جامعة المنيا‬- ‫ عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده‬.‫د‬.‫إعداد أ‬ Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com Page 2 of 58 ‫المعمل المتطور لنظم القوي الكهربية‬ Faculty of Engineering Electrical Engineering Dept. Advanced Laboratory for electric Power systems ‫جامعة المنيا‬ Minia University ‫رؤيه المعمل‬ .‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‬ Electrical Engineering Dept. Precision: a measure of the reproducibility of the measurements; given a fixed value of a variable, precision is a measure of the degree to which successive measurements differ from one another i.e., a measure of reproducibility or agreement with each other for multiple trials. Sensitivity: the ability of the measuring instrument to respond to changes in the measured quantity. It is expressed as the ratio of the change of output signal or response of the instrument to a change of input or measured variable. Resolution: the smallest change in measured value to which the instrument will respond, i.e. the smallest incremental quantity that can be reliably measured. Error: deviation from the true value of the measured variable. Linearity: the percentage of departure from the linear value, i.e., maximum deviation of the output curve from the best-fit straight line during a calibration cycle. Tolerance: maximum deviation allowed from the conventional true value. It is not possible to build a perfect system or make an exact measurement. All devices deviate from their ideal (design) characteristics and all measurements include uncertainties (doubts). Hence, all devices include tolerances in their specifications. If the instrument is used for highprecision applications, the design tolerances must be small. However, if a low degree of accuracy is acceptable, it is not economical to use expensive sensors and precise sensing components. 1.1.2. Static Calibration ‫ كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬،‫ "َسعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‬:‫رسانه انًعًم‬ ."ًٍ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعان‬ Tel: 01090343201 Fax: (086) 2346674 ‫ كلية الهندسة – جامعة المنيا‬- ‫ عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده‬.‫د‬.‫إعداد أ‬ Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com Page 3 of 58 ‫المعمل المتطور لنظم القوي الكهربية‬ Faculty of Engineering Electrical Engineering Dept. Advanced Laboratory for electric Power systems ‫جامعة المنيا‬ Minia University ‫رؤيه المعمل‬ .‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‬ Electrical Engineering Dept. The static calibration for a multi-input instrument is carried out by keeping all inputs except one at some constant values. The single input under study is varied over some range of constant values, causing the output(s) to vary over some range of constant values. The input-output relation developed in this way is called “static calibration”. A calibration curve for a dual-input single-output system is shown in figure 2.1. The static sensitivity (S) is the slope of Figure 1.1. Static calibration curves for a multi-input single-output system. the calibration curve and is defined as, S = ∂(output)/∂(input) ......................................(1.1) S is a constant for linear relation. Otherwise, S is a function of the input. 1.1.3. Accuracy and Precision A measurement isn‟t very meaningful without an error estimate! No measurement made is ever exact. The accuracy (correctness) and precision (number of significant figures) of a measurement are always limited by apparatus used, skill of the observer and the basic physics in the experiment and the experimental technique used to access it. The goal of the ‫ كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬،‫ "َسعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‬:‫رسانه انًعًم‬ ."ًٍ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعان‬ Tel: 01090343201 Fax: (086) 2346674 ‫ كلية الهندسة – جامعة المنيا‬- ‫ عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده‬.‫د‬.‫إعداد أ‬ Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com Page 4 of 58 ‫المعمل المتطور لنظم القوي الكهربية‬ Faculty of Engineering Electrical Engineering Dept. Advanced Laboratory for electric Power systems ‫جامعة المنيا‬ Minia University ‫رؤيه المعمل‬ .‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‬ Electrical Engineering Dept. experimenter is to obtain the best possible value of some quantity or to validate/falsify a theory. What comprises a deviation from a theory? Every measurement must give the range of possible value. In this section we will discuss the accuracy and precision with examples. 1.1.3.1 Accuracy Accuracy is defined as the degree of conformity of a measured value to the true (conventional true value – CTV) or accepted value of the variable being measured. It is a measure of the total error in the measurement without looking into the sources of the errors. Mathematically it is expressed as the maximum absolute deviation of the readings from the CTV. This is called the absolute accuracy. | | Example 1.1 A voltmeter is used for reading on a standard value of 50 volts, the following readings are obtained: 47V, 52 V, 51 V, 48V. Find accuracy of the voltmeter. Solution Conventional true value (CTV) = 50 volts, Maximum (VMAX) = 52 volts and Minimum (VMIN) = 47 volts. CTV – VMIN = 50 – 47 = 3 volts; ‫ كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬،‫ "َسعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‬:‫رسانه انًعًم‬ ."ًٍ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعان‬ Tel: 01090343201 Fax: (086) 2346674 ‫ كلية الهندسة – جامعة المنيا‬- ‫ عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده‬.‫د‬.‫إعداد أ‬ Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com Page 5 of 58 ‫المعمل المتطور لنظم القوي الكهربية‬ Faculty of Engineering Electrical Engineering Dept. Advanced Laboratory for electric Power systems ‫جامعة المنيا‬ Minia University ‫رؤيه المعمل‬ .‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‬ Electrical Engineering Dept. VMAX – CTV = 52 – 50 = 2 volts. Absolute accuracy = max of {3, 2} = 3 volts. Relative accuracy = 3/50 = 0.06 and % accuracy = 0.06x100 = 6% 1.1.3.2. Precision Precision is composed of two characteristics as conformity and the number of significant figures. Conformity The conformity is the ability of an instrument to produce the same reading, or it is the degree of agreement between individual measurements. So, it is also called repeatability or reproducibility. Mathematically it is expressed as “the absolute maximum deviation from the average of the readings”, i.e. Precision (Pr) = max {(VAV – VMIN ), (VMAX –VAV )}....................................... (2.5) Vav: Average Value 1.1.3.3. Bias The difference between CTV and average value (VAV) is called the bias. Ideally, the bias should be zero. For a high quality digital voltmeter, the loading error is negligible yielding bias very close to zero. Bias = CTV - VAV .............................................................................................. (2.6) In the previous example the average (VAV) = (47+48+51+52)/4 = 49.5 V Pr = max {(49.5 – 47), (52 – 49.5)} = 2.5 volts. Thus, Bias = 50 – 49.5 = 0.5 volt. ‫ كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬،‫ "َسعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‬:‫رسانه انًعًم‬ ."ًٍ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعان‬ Tel: 01090343201 Fax: (086) 2346674 ‫ كلية الهندسة – جامعة المنيا‬- ‫ عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده‬.‫د‬.‫إعداد أ‬ Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com Page 6 of 58 ‫المعمل المتطور لنظم القوي الكهربية‬ Faculty of Engineering Electrical Engineering Dept. Advanced Laboratory for electric Power systems ‫جامعة المنيا‬ Minia University ‫رؤيه المعمل‬ .‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‬ Electrical Engineering Dept. A consistent bias can be due to the presence of a systematic error or instrument loading. Hence, eliminating the causes removes the bias. However, if the bias is consistent and causes cannot be identified and/or eliminated, the bias can be removed by re-calibrating the instrument. Example 1.2 A known voltage of 100 volts (CTV = 100 V) is read five times by a voltmeter and following readings are obtained: 104V, 103V, 105V, 103V, 105V. Find Accuracy and Precision and write your comment on voltmeter. Solution Average reading = (1/5)x(104+103+105+103+105) = 104 volts. Pr = max {(VAV – VMIN), (VMAX – VAV)} = max {(104 – 103), (105 – 104)} = 1 volt Accuracy = max {(CTV – VMIN), (VMAX - CTV)} = max {(100 – 103), (105 – 100)} =5 V Bias = abs(average – CTV) = 104 – 100 = 4 volts. If we re-calibrated the instrument to remove the bias, then the average reading = CTV. The new readings would be 100, 99, 101, 99, 101 Hence, after re-calibration, average = CTV = 100 volts, and accuracy = precision = 1 volt. 1.1.4. Accuracy versus Precision The distinction between accuracy and precision can be illustrated by an example: two voltmeters of the same make and model may be compared. Both meters have knife-edged pointers and mirror-backed scales to avoid parallax, and they have carefully calibrated ‫ كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬،‫ "َسعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‬:‫رسانه انًعًم‬ ."ًٍ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعان‬ Tel: 01090343201 Fax: (086) 2346674 ‫ كلية الهندسة – جامعة المنيا‬- ‫ عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده‬.‫د‬.‫إعداد أ‬ Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com Page 7 of 58 ‫المعمل المتطور لنظم القوي الكهربية‬ Faculty of Engineering Electrical Engineering Dept. Advanced Laboratory for electric Power systems ‫جامعة المنيا‬ Minia University ‫رؤيه المعمل‬ .‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‬ Electrical Engineering Dept. scales. They may therefore be read to the same precision. If the value of the series resistance in one meter changes considerably, its readings may be in error by a fairly large amount. Thereforethe accuracy of the two meters may be quite different. To determine which meter is in error, a comparison measurement with a standard meter should be made. Accuracy refers to the degree of closeness or conformity to the true value at the quantity under measurement. Precision refers to the degree of agreement within a group of measurements or instruments. The target-shooting example shown in figure 2.2 illustrates the difference. Figure 1.2. An illustration of accuracy and precision. The high accuracy, poor precision situation occurs when the person hits all the bullets on a target plate on the outer circle and misses the bull‟s eye. In the second case, all bullets hit the bull‟s eye and spaced closely enough leading to high accuracy and high precision. The bullet hits are placed symmetrically with respect to the bull‟s eye in the third case but spaced apart yielding average accuracy but poor precision. In the last example, the bullets hit in a random manner, hence poor accuracy and poor precision. ‫ كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬،‫ "َسعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‬:‫رسانه انًعًم‬ ."ًٍ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعان‬ Tel: 01090343201 Fax: (086) 2346674 ‫ كلية الهندسة – جامعة المنيا‬- ‫ عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده‬.‫د‬.‫إعداد أ‬ Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com Page 8 of 58 ‫المعمل المتطور لنظم القوي الكهربية‬ Faculty of Engineering Electrical Engineering Dept. Advanced Laboratory for electric Power systems ‫جامعة المنيا‬ Minia University ‫رؤيه المعمل‬ .‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‬ Electrical Engineering Dept. The scatter graph in figure 2.3 shows an alternative way of presenting the accuracy and precision. Same quantity was measured three times by 5 different analyst or methods or measuring instruments. Distribution of readings around the true value indicates the most accurate, most precise and least accurate and least precise readings. The last reading is too far away from the true value and from other readings that may indicate a systematic error. Figure 1.3. An illustration of presenting the accuracy and precision. Precision is composed of two characteristics as stated: conformity and the number of significant figures to which a measurement may be made. Consider, for example, that the insulation resistance of a transformer has the true value 2,475,653 Ω. It is measured by an ohmmeter, which consistently and repeatedly indicates 2.5 MΩ. But can the observer "read" the true value from the scale? His estimates from the scale reading consistently yield ‫ كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬،‫ "َسعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‬:‫رسانه انًعًم‬ ."ًٍ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعان‬ Tel: 01090343201 Fax: (086) 2346674 ‫ كلية الهندسة – جامعة المنيا‬- ‫ عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده‬.‫د‬.‫إعداد أ‬ Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com Page 9 of 58 ‫المعمل المتطور لنظم القوي الكهربية‬ Faculty of Engineering Electrical Engineering Dept. Advanced Laboratory for electric Power systems ‫جامعة المنيا‬ Minia University ‫رؤيه المعمل‬ .‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‬ Electrical Engineering Dept. a value of 2.5 MΩ. This is as close to the true value as he can read the scale by estimation. Although there are no deviations from the observed value, the error produced by the limitation of the scale reading is a precision error. The example illustrates that conformity is a necessary, but not sufficient, condition for precision because of the lack of significant figures obtained. Similarly, precision is a necessary, but not sufficient condition for accuracy. Too often the beginning student is inclined to accept instrument readings at face value. He is not aware that the accuracy of a reading is not necessarily guarantied by its precision. In fact, good measurement technique demands continuous skepticism as to the accuracy of the results. In critical work, good practice dictates that the observer make an independent set of measurements, using different instruments or different measurement techniques, not subject to the same systematic errors. He must also make sure that the instruments function properly and are calibrated against a known standard, and that no outside influence affects the accuracy of his measurements. 1.1.6. Types of Errors (Uncertainties) No measurement can be made with perfect accuracy, but it is important to find out what the accuracy actually is and how different errors have entered into the measurement. A study of errors is a first step in finding ways to reduce them. Such a study also allows us to determine the accuracy of the final test result. Errors may come from different sources and are usually classified under three main headings as: Gross errors: largely human errors, among them misreading of instruments, incorrect adjustment and improper application of instruments, and computational mistakes. ‫ كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬،‫ "َسعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‬:‫رسانه انًعًم‬ ."ًٍ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعان‬ Tel: 01090343201 Fax: (086) 2346674 ‫ كلية الهندسة – جامعة المنيا‬- ‫ عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده‬.‫د‬.‫إعداد أ‬ Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com Page 10 of 58 ‫المعمل المتطور لنظم القوي الكهربية‬ Faculty of Engineering Electrical Engineering Dept. Advanced Laboratory for electric Power systems ‫جامعة المنيا‬ Minia University ‫رؤيه المعمل‬ .‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‬ Electrical Engineering Dept. Systematic (determinate) errors: shortcomings of the instruments, such as defective or worn parts, and effects of the environment on the equipment or the user. They are sometimes called bias due to error in one direction- high or low. They are generally originated from a known cause such as result from mis-calibrated device, experimental technique that always gives a measurement higher (or lower) than the true value, operator‟s limitations and calibration of glassware, sensor, or instrument. Their effects can be minimized by trying a different method for the same measurement. They can be corrected when determined. Systematic errors may be of a constant or proportional nature as illustrated in figure 2.5. The constant error influences the intercept while the proportional error influences the slope. Figure 1.5. Constant and proportional type error Random (indeterminate) errors: those due to causes that cannot be directly established because of random variations in the parameter or the system of measurement. Hence, we ‫ كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬،‫ "َسعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‬:‫رسانه انًعًم‬ ."ًٍ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعان‬ Tel: 01090343201 Fax: (086) 2346674 ‫ كلية الهندسة – جامعة المنيا‬- ‫ عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده‬.‫د‬.‫إعداد أ‬ Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com Page 11 of 58 ‫المعمل المتطور لنظم القوي الكهربية‬ Faculty of Engineering Electrical Engineering Dept. Advanced Laboratory for electric Power systems ‫جامعة المنيا‬ Minia University ‫رؤيه المعمل‬ .‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‬ Electrical Engineering Dept. have no control over them. Their random nature causes both high and low values to average out. Multiple trials help to minimize their effects. We deal with them using statistics. Figure 2.6 provides a schematic summary of errors and their possible means of elimination. For example, errors caused by the loading effect of the voltmeter can be avoided by using it intelligently. A low-resistance voltmeter should not be used to measure voltages at the input of a voltage amplifier. In this particular measurement, a high-input impedance voltmeter (such as a digital voltmeter - DVM) is required. Gross and systematic errors cannot be treated mathematically. They can be avoided only by taking care in reading and recording the measurement data. Good practice requires making more than one reading of the same quantity, preferably by a different observer. Never place complete dependence on one reading but take at least three separate readings, preferably under conditions in which instruments are switched off-on. The error may be originated from the sampling of the source, preparation of the samples and measurement and analysis of the measurand. Care must be taken so that the sample is representative of the whole population (homogeneous vs. heterogeneous). No unwanted additions or deletions are allowed during the preparatory phase. Finally, calibration of the measuring instrument using standard measurands or standard solutions is done as frequent as defined by the equipment manufacturer. One way to assess total error is to treat a reference standard as a sample. The reference standard would be carried through the entire process to see how close the results are to the reference value. ‫ كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬،‫ "َسعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‬:‫رسانه انًعًم‬ ."ًٍ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعان‬ Tel: 01090343201 Fax: (086) 2346674 ‫ كلية الهندسة – جامعة المنيا‬- ‫ عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده‬.‫د‬.‫إعداد أ‬ Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com Page 12 of 58 ‫المعمل المتطور لنظم القوي الكهربية‬ ‫جامعة المنيا‬ ‫‪Minia University‬‬ ‫رؤيه المعمل‬ ‫‪Advanced Laboratory for electric‬‬ ‫‪Power systems‬‬ ‫‪Faculty of Engineering‬‬ ‫‪Electrical Engineering Dept.‬‬ ‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‪.‬‬ ‫‪Electrical Engineering Dept.‬‬ ‫‪Figure 1.6. A schematic summary of measurement errors.‬‬ ‫رسانه انًعًم‪َ" :‬سعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‪ ،‬كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬ ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعانًٍ"‪.‬‬ ‫‪Tel: 01090343201‬‬ ‫‪Fax: (086) 2346674‬‬ ‫إعداد أ‪.‬د‪ .‬عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده ‪ -‬كلية الهندسة – جامعة المنيا‬ ‫‪Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com‬‬ ‫‪Page 13 of 58‬‬ ‫المعمل المتطور لنظم القوي الكهربية‬ Faculty of Engineering Electrical Engineering Dept. Advanced Laboratory for electric Power systems ‫جامعة المنيا‬ Minia University ‫رؤيه المعمل‬ .‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‬ Electrical Engineering Dept. Example 1.3. Two different voltmeters are used to measure the voltage across resistor RB in the circuit of Figure 1. The meters are as follows. Meter A : S = 1k/V, Rm = 0.2k, range = 10V Meter B : S = 20k/V, Rm = 1.5k, range=10V Calculate: a) Voltage across RB without any meter connected across it. b) Voltage across RB when meter A is used. c) Voltage across RB when meter B is used d) Error in voltmeter readings. Solution (a) The voltage across resistor RB without either meter connected is found Using the voltage divider equation:  RB  VRB  E    R A  R B    5kΩ   30V    5V  25k  5k  (b) Starting with meter A, The total resistance presents to the circuit is RTA  S  Range  1k/V 10V  10kΩ The parallel combination of RB and meter A is ‫ كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬،‫ "َسعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‬:‫رسانه انًعًم‬ ."ًٍ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعان‬ Tel: 01090343201 Fax: (086) 2346674 ‫ كلية الهندسة – جامعة المنيا‬- ‫ عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده‬.‫د‬.‫إعداد أ‬ Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com Page 14 of 58 ‫المعمل المتطور لنظم القوي الكهربية‬ Faculty of Engineering Electrical Engineering Dept. Advanced Laboratory for electric Power systems ‫جامعة المنيا‬ Minia University ‫رؤيه المعمل‬ .‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‬ Electrical Engineering Dept. Re1  RB  RTA 5kΩ  10kΩ   3.33kΩ RB  RTA 5kΩ  10kΩ Therefore, the voltage reading obtained with meter A, determined by the voltage divider equation, is  Re1  3.33kΩ VRB  E   3.53V   30V  3.33kΩ  25kΩ  Re1  RA  (c) The total resistance that meter B presents to the circuit is RTB = S x Range = 20k/V x 10 V = 200 k The parallel combination of RB and meter B is Re2 = (RB x RTB)/(RB + RTB) = (5kx200k)/(5k+200k) = 4.88 k Therefore, the voltage reading obtained with meter B, determined by use of the voltage divider equation, is VRB = E(Re2)/(Re2+RA) = 30 V x (4.88k)/(4.88k+25k) = 4.9 V (d) Voltmeter A error = (5 V – 3.53 V)/5 V x (100%) = 29.4% Voltmeter B error = (5 V – 4.9 V)/5 V x (100%) = 2 % Problem 1.4:A set of independent voltage measurements taken by four observers was recorded as 117.02V, 117.11V, 117.08V, and 117.03V. Calculate a. The average voltage, b. The range of error. ‫ كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬،‫ "َسعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‬:‫رسانه انًعًم‬ ."ًٍ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعان‬ Tel: 01090343201 Fax: (086) 2346674 ‫ كلية الهندسة – جامعة المنيا‬- ‫ عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده‬.‫د‬.‫إعداد أ‬ Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com Page 15 of 58 ‫المعمل المتطور لنظم القوي الكهربية‬ Faculty of Engineering Electrical Engineering Dept. Advanced Laboratory for electric Power systems ‫جامعة المنيا‬ Minia University ‫رؤيه المعمل‬ .‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‬ Electrical Engineering Dept. Problem 1.5. A voltmeter, having a sensitivity of 1000V, reads 100 V on its 150-V scale when connected across an unknown resistor in series with a milliammeter. When the milliammeter reads 5mA, calculate a) Apparent resistance of the unknown resistor, b) Actual resistance of the unknown resistor, c) Error due to the loading effect of the voltmeter. Repeat Problem 3 if the milliammeter reads 800 mA and the voltmeter reads 40 V on its 150-V scale. ‫ كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬،‫ "َسعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‬:‫رسانه انًعًم‬ ."ًٍ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعان‬ Tel: 01090343201 Fax: (086) 2346674 ‫ كلية الهندسة – جامعة المنيا‬- ‫ عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده‬.‫د‬.‫إعداد أ‬ Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com Page 16 of 58 ‫المعمل المتطور لنظم القوي الكهربية‬ ‫جامعة المنيا‬ ‫‪Minia University‬‬ ‫رؤيه المعمل‬ ‫‪Advanced Laboratory for electric‬‬ ‫‪Power systems‬‬ ‫‪Faculty of Engineering‬‬ ‫‪Electrical Engineering Dept.‬‬ ‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‪.‬‬ ‫‪Electrical Engineering Dept.‬‬ ‫رسانه انًعًم‪َ" :‬سعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‪ ،‬كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬ ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعانًٍ"‪.‬‬ ‫‪Tel: 01090343201‬‬ ‫‪Fax: (086) 2346674‬‬ ‫إعداد أ‪.‬د‪ .‬عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده ‪ -‬كلية الهندسة – جامعة المنيا‬ ‫‪Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com‬‬ ‫‪Page 17 of 58‬‬ ‫المعمل المتطور لنظم القوي الكهربية‬ Faculty of Engineering Electrical Engineering Dept. Advanced Laboratory for electric Power systems ‫جامعة المنيا‬ Minia University ‫رؤيه المعمل‬ .‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‬ Electrical Engineering Dept. Errors caused by the loading effect of the voltmeter can be avoided by using it intelligently. For example, a low-resistance voltmeter should not be used to measure voltages in a vacuum tube amplifier. In this particular measurement, a high-input impedance voltmeter (such as VTVM or TVM) is required. A large number of gross errors can be attributed to carelessness or bad habits, such as improper reading of an instrument, recording the result differently from the actual reading taken, or adjusting the instrument incorrectly. Consider the case in which a multi-range voltmeter uses a single set of scale markings with different number designations for the various voltage ranges. It is easy to use a scale which does not correspond to the setting of the range selector of the voltmeter. A gross error may also occur when the instrument is not set to zero before the measurement is taken; then all the readings are off. Errors like these cannot be treated mathematically. They can be avoided only by taking care in reading and recording the measurement data. Good practice requires making more than one reading of the same quantity, preferably by a different observer. Never place complete dependence on one reading but take at least three separate readings, preferably under conditions in which instruments are switched off-on Problem 1.6. A set of independent current measurements was taken by six observers and recorded as 12.8 mA, 12.2 mA, 12.5 mA, 13.1 mA, 12.9 mA, and 12.4 mA. Calculate a) The arithmetic mean, b) The deviations from the mean. c) The average deviation for the data . ‫ كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬،‫ "َسعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‬:‫رسانه انًعًم‬ ."ًٍ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعان‬ Tel: 01090343201 Fax: (086) 2346674 ‫ كلية الهندسة – جامعة المنيا‬- ‫ عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده‬.‫د‬.‫إعداد أ‬ Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com Page 18 of 58 ‫المعمل المتطور لنظم القوي الكهربية‬ ‫جامعة المنيا‬ ‫‪Minia University‬‬ ‫رؤيه المعمل‬ ‫‪Advanced Laboratory for electric‬‬ ‫‪Power systems‬‬ ‫‪Faculty of Engineering‬‬ ‫‪Electrical Engineering Dept.‬‬ ‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‪.‬‬ ‫‪Electrical Engineering Dept.‬‬ ‫‪Problem 1.7.‬‬ ‫‪Ten measurements of the resistance of a resistor gave 101.2 , 101.7 , 101.3 , 101.0 , 101.5 ,‬‬ ‫‪101.3 , 101.2 , 101.4 , 101.3 , and 101.1 Assume that only random errors are present.‬‬ ‫‪Calculate‬‬ ‫‪a) The arithmetic mean,‬‬ ‫‪b) The standard deviation of the readings,‬‬ ‫‪c) The probable error.‬‬ ‫رسانه انًعًم‪َ" :‬سعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‪ ،‬كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬ ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعانًٍ"‪.‬‬ ‫‪Tel: 01090343201‬‬ ‫‪Fax: (086) 2346674‬‬ ‫إعداد أ‪.‬د‪ .‬عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده ‪ -‬كلية الهندسة – جامعة المنيا‬ ‫‪Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com‬‬ ‫‪Page 19 of 58‬‬ ‫المعمل المتطور لنظم القوي الكهربية‬ Faculty of Engineering Electrical Engineering Dept. Advanced Laboratory for electric Power systems ‫جامعة المنيا‬ Minia University ‫رؤيه المعمل‬ .‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‬ Electrical Engineering Dept. Problem 1.8 Your laboratory has available a large number of 10F capacitors rated at 300 V. To design a capacitor bank of 40F rated at 600 V, how many 10F capacitors are needed and how would you connect them? Problem 1.9. Suppose your circuit laboratory has the following standard commercially available resistors in large quantities: 1.8 Ω 20 Ω 300 Ω 24 kΩ 56k Ω ‫ كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬،‫ "َسعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‬:‫رسانه انًعًم‬ ."ًٍ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعان‬ Tel: 01090343201 Fax: (086) 2346674 ‫ كلية الهندسة – جامعة المنيا‬- ‫ عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده‬.‫د‬.‫إعداد أ‬ Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com Page 20 of 58 ‫المعمل المتطور لنظم القوي الكهربية‬ Faculty of Engineering Electrical Engineering Dept. Advanced Laboratory for electric Power systems ‫جامعة المنيا‬ Minia University ‫رؤيه المعمل‬ .‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‬ Electrical Engineering Dept. Using series and parallel combinations and a minimum number of available resistors, how would you obtain the following resistances for an electronic circuit design? (a) 5Ω (b) 311.8 (c) 40k Ω (d) 52.32 k Ω Chapter-2 Measurement of Electrical Current Voltage and Resistance 2.1 Introduction A device called “the ammeter” measures the current in an electric circuit. It is connected in series with the circuit element in which the current is to be determined. The voltage is measured by “the voltmeter”. It is connected in parallel with the circuit element to determine the voltage across. Eventually, the ammeter requires breaking the current loop to place it into the circuit. The voltmeter connection is rather easy since it is connected without disturbing the circuit layout. Therefore, most electrical measurements prefer determination of the voltage rather than the current due the ease of measurement. Connections of ammeters and voltmeters are illustrated in figure 5.1. Resistance is defined by the Ohm‟s law as the ratio of voltage and current in a circuit element. The device that measures the resistance is called “the ohmmeter”. It applies a voltage from a constant (DC) voltage source (usually from an antennal battery) and measures the current passing through using an ammeter. ‫ كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬،‫ "َسعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‬:‫رسانه انًعًم‬ ."ًٍ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعان‬ Tel: 01090343201 Fax: (086) 2346674 ‫ كلية الهندسة – جامعة المنيا‬- ‫ عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده‬.‫د‬.‫إعداد أ‬ Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com Page 21 of 58 ‫المعمل المتطور لنظم القوي الكهربية‬ Faculty of Engineering Electrical Engineering Dept. Advanced Laboratory for electric Power systems ‫جامعة المنيا‬ Minia University ‫رؤيه المعمل‬ .‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‬ Electrical Engineering Dept. Figure 5.1. Connections for an ammeter and a voltmeter. 2.2 Instrument Loading Ideal ammeter has zero internal resistance and no voltage drop across it. Ideal voltmeter has infinite internal (meter) resistance and draws no current from the circuit. The practical ammeter can be symbolized by an ideal ammeter with an added series resistance that represents the meter resistance. Similarly, the practical voltmeter can be denoted by an ideal voltmeter in parallel with the meter resistance. These two models are illustrated in figure 5.2. Eventually the practical ammeter has a voltage drop across and the practical voltmeter has a current drawn from the circuit. All measuring instruments draw energy from the source of measurement. This is called “the loading effect of the instrument”. Hence, all measurements include errors due to instrument loading. If the energy extracted by the instrument is negligibly small compared to the energy that exists in the source, then the measurement is assumed to be close to perfect, and the loading error is ignored. ‫ كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬،‫ "َسعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‬:‫رسانه انًعًم‬ ."ًٍ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعان‬ Tel: 01090343201 Fax: (086) 2346674 ‫ كلية الهندسة – جامعة المنيا‬- ‫ عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده‬.‫د‬.‫إعداد أ‬ Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com Page 22 of 58 ‫المعمل المتطور لنظم القوي الكهربية‬ Faculty of Engineering Electrical Engineering Dept. Advanced Laboratory for electric Power systems ‫جامعة المنيا‬ Minia University ‫رؤيه المعمل‬ .‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‬ Electrical Engineering Dept. Figure 5.2. Models of practical ammeters and voltmeters. 2.2.1 Loading Errors in Ammeters Any electrical circuit can be modeled by a voltage source VT and a series resistance RT as illustrated in figure 5.3. The circuit is completed when the load resistance RL is connected across the output terminals and a load current IL flows through the load. An ammeter can be placed in series with the load to measure this current. Figure 5.3. Ammeter connection and it‟s loading effect. The current in the circuit can be calculated as ‫ كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬،‫ "َسعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‬:‫رسانه انًعًم‬ ."ًٍ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعان‬ Tel: 01090343201 Fax: (086) 2346674 ‫ كلية الهندسة – جامعة المنيا‬- ‫ عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده‬.‫د‬.‫إعداد أ‬ Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com Page 23 of 58 ‫المعمل المتطور لنظم القوي الكهربية‬ Faculty of Engineering Electrical Engineering Dept. Advanced Laboratory for electric Power systems ‫جامعة المنيا‬ Minia University ‫رؤيه المعمل‬ .‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‬ Electrical Engineering Dept. In the ideal condition, RM = 0 and the true value of the current is The error is the difference between the measured value and the true value, and generally expressed as the percentile error which is: Hence, the loading error due to the ammeter can be found as: Loading error can be ignored if RM<<(RT+RL) which is satisfied in most applications. 2.2.2 Loading Errors in Voltmeters In voltage measurement, the meter is connected in parallel with load resistor as shown in figure 5.4. The true value of the voltage across the resistor is (without the meter) Figure 5.4. Voltmeter connection and it‟s loading effect. ‫ كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬،‫ "َسعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‬:‫رسانه انًعًم‬ ."ًٍ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعان‬ Tel: 01090343201 Fax: (086) 2346674 ‫ كلية الهندسة – جامعة المنيا‬- ‫ عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده‬.‫د‬.‫إعداد أ‬ Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com Page 24 of 58 ‫المعمل المتطور لنظم القوي الكهربية‬ Faculty of Engineering Electrical Engineering Dept. Advanced Laboratory for electric Power systems ‫جامعة المنيا‬ Minia University ‫رؤيه المعمل‬ .‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‬ Electrical Engineering Dept. As the meter is connected, RM becomes in parallel with RL and effective load resistance becomes RLeff ≅ RL if RM>>RL. The voltage measured by the meter is 2.2.3 Instrument ‘loading’ effect Some measuring instruments depend for their operation on power taken from the circuit in which measurements are being made. Depending on the „loading‟ effect of the instrument (i.e. the current taken to enable it to operate), the prevailing circuit conditions may change. The resistance of voltmeters may be calculated since each have a stated sensitivity (or „figure ofmerit‟), often stated in „k Ω per volt‟ of f.s.d. A voltmeter should have as high a resistance as possible – ideally infinite. In a.c. circuits the impedance of the instrument varies with frequency and thus the loading effect of the instrument can change. Problem ‫ كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬،‫ "َسعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‬:‫رسانه انًعًم‬ ."ًٍ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعان‬ Tel: 01090343201 Fax: (086) 2346674 ‫ كلية الهندسة – جامعة المنيا‬- ‫ عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده‬.‫د‬.‫إعداد أ‬ Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com Page 25 of 58 ‫المعمل المتطور لنظم القوي الكهربية‬ ‫جامعة المنيا‬ ‫‪Minia University‬‬ ‫رؤيه المعمل‬ ‫‪Advanced Laboratory for electric‬‬ ‫‪Power systems‬‬ ‫‪Faculty of Engineering‬‬ ‫‪Electrical Engineering Dept.‬‬ ‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‪.‬‬ ‫‪Electrical Engineering Dept.‬‬ ‫‪Calculate the power dissipated by the voltmeter and by resistor R in Figure 10.9 when‬‬ ‫‪(a) R = 250Ω ,‬‬ ‫‪(b) R = 2 MΩ.‬‬ ‫‪Assume that the voltmeter sensitivity (sometimes called figure of merit) is 10 k Ω /V.‬‬ ‫‪Figure 10.9‬‬ ‫رسانه انًعًم‪َ" :‬سعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‪ ،‬كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬ ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعانًٍ"‪.‬‬ ‫‪Tel: 01090343201‬‬ ‫‪Fax: (086) 2346674‬‬ ‫إعداد أ‪.‬د‪ .‬عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده ‪ -‬كلية الهندسة – جامعة المنيا‬ ‫‪Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com‬‬ ‫‪Page 26 of 58‬‬ ‫المعمل المتطور لنظم القوي الكهربية‬ Faculty of Engineering Electrical Engineering Dept. Advanced Laboratory for electric Power systems ‫جامعة المنيا‬ Minia University ‫رؤيه المعمل‬ .‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‬ Electrical Engineering Dept. Problem 10. An ammeter has an f.s.d. of 100mA and a resistance of 50 Ω. The ammeter is used to measure the current in a load of resistance 500 Ω when the supply voltage is 10V. Calculate a. The ammeter reading expected (neglecting its resistance), b. The actual current in the circuit, c. The power dissipated in the ammeter and d. The power dissipated in the load. ‫ كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬،‫ "َسعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‬:‫رسانه انًعًم‬ ."ًٍ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعان‬ Tel: 01090343201 Fax: (086) 2346674 ‫ كلية الهندسة – جامعة المنيا‬- ‫ عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده‬.‫د‬.‫إعداد أ‬ Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com Page 27 of 58 ‫المعمل المتطور لنظم القوي الكهربية‬ ‫جامعة المنيا‬ ‫‪Minia University‬‬ ‫رؤيه المعمل‬ ‫‪Advanced Laboratory for electric‬‬ ‫‪Power systems‬‬ ‫‪Faculty of Engineering‬‬ ‫‪Electrical Engineering Dept.‬‬ ‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‪.‬‬ ‫‪Electrical Engineering Dept.‬‬ ‫‪Fig,‬‬ ‫‪Problem 5.‬‬ ‫‪A voltmeter having an f.s.d. of 100V and a sensitivity of 1.6 k Ω /V is used to measure‬‬ ‫‪voltage V1 in the circuit of Figure 10.11. Determine‬‬ ‫‪(a) the value of voltage V1 with the voltmeter not connected, and‬‬ ‫رسانه انًعًم‪َ" :‬سعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‪ ،‬كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬ ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعانًٍ"‪.‬‬ ‫‪Tel: 01090343201‬‬ ‫‪Fax: (086) 2346674‬‬ ‫إعداد أ‪.‬د‪ .‬عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده ‪ -‬كلية الهندسة – جامعة المنيا‬ ‫‪Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com‬‬ ‫‪Page 28 of 58‬‬ ‫المعمل المتطور لنظم القوي الكهربية‬ ‫جامعة المنيا‬ ‫‪Minia University‬‬ ‫رؤيه المعمل‬ ‫‪Advanced Laboratory for electric‬‬ ‫‪Power systems‬‬ ‫‪Faculty of Engineering‬‬ ‫‪Electrical Engineering Dept.‬‬ ‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‪.‬‬ ‫‪Electrical Engineering Dept.‬‬ ‫‪(b) the voltage indicated by the voltmeter when connected between A and B.‬‬ ‫‪Fig. 10.11‬‬ ‫رسانه انًعًم‪َ" :‬سعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‪ ،‬كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬ ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعانًٍ"‪.‬‬ ‫‪Tel: 01090343201‬‬ ‫‪Fax: (086) 2346674‬‬ ‫إعداد أ‪.‬د‪ .‬عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده ‪ -‬كلية الهندسة – جامعة المنيا‬ ‫‪Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com‬‬ ‫‪Page 29 of 58‬‬ ‫المعمل المتطور لنظم القوي الكهربية‬ ‫جامعة المنيا‬ ‫‪Minia University‬‬ ‫رؤيه المعمل‬ ‫‪Advanced Laboratory for electric‬‬ ‫‪Power systems‬‬ ‫‪Faculty of Engineering‬‬ ‫‪Electrical Engineering Dept.‬‬ ‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‪.‬‬ ‫‪Electrical Engineering Dept.‬‬ ‫‪The circuit is now effectively as shown in Figure 10.12(b). Thus the voltage indicated on‬‬ ‫‪the voltmeter is‬‬ ‫‪Vab= 100/(32+60)*32=34.78V‬‬ ‫‪A considerable error is thus caused by the loading effect of the voltmeter on the circuit. The‬‬ ‫‪error is reduced by using a voltmeter with a higher sensitivity.‬‬ ‫رسانه انًعًم‪َ" :‬سعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‪ ،‬كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬ ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعانًٍ"‪.‬‬ ‫‪Tel: 01090343201‬‬ ‫‪Fax: (086) 2346674‬‬ ‫إعداد أ‪.‬د‪ .‬عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده ‪ -‬كلية الهندسة – جامعة المنيا‬ ‫‪Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com‬‬ ‫‪Page 30 of 58‬‬ ‫المعمل المتطور لنظم القوي الكهربية‬ Faculty of Engineering Electrical Engineering Dept. Advanced Laboratory for electric Power systems ‫جامعة المنيا‬ Minia University ‫رؤيه المعمل‬ .‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‬ Electrical Engineering Dept. Problem 7. For the oscilloscope square voltage waveform shown in Figure 10.17, determine (a) the periodic time, (b) the frequency and (c) the peak-to-peak voltage. The „time/cm‟ (or timebase control) switch is on 100μs/cm and the „volts/cm‟ (or signal amplitude control) switch is on 20V/cm. Figure 10.17 assume that the squares shown are 1 cm by 1 cm. ‫ كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬،‫ "َسعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‬:‫رسانه انًعًم‬ ."ًٍ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعان‬ Tel: 01090343201 Fax: (086) 2346674 ‫ كلية الهندسة – جامعة المنيا‬- ‫ عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده‬.‫د‬.‫إعداد أ‬ Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com Page 31 of 58 ‫المعمل المتطور لنظم القوي الكهربية‬ ‫جامعة المنيا‬ ‫‪Minia University‬‬ ‫رؤيه المعمل‬ ‫‪Advanced Laboratory for electric‬‬ ‫‪Power systems‬‬ ‫‪Faculty of Engineering‬‬ ‫‪Electrical Engineering Dept.‬‬ ‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‪.‬‬ ‫‪Electrical Engineering Dept.‬‬ ‫‪Problem 9. A sinusoidal voltage trace displayed by an oscilloscope is shown in Figure‬‬ ‫‪10.19. If the „time/cm‟ switch is on 500μs/cm and the „volts/cm‟ switch is on 5V/cm, find,‬‬ ‫‪for the waveform, (a) the frequency, (b) the peak-to-peak voltage, (c) the amplitude, (d) the‬‬ ‫‪r.m.s. value.‬‬ ‫‪Figure 10.19‬‬ ‫رسانه انًعًم‪َ" :‬سعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‪ ،‬كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬ ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعانًٍ"‪.‬‬ ‫‪Tel: 01090343201‬‬ ‫‪Fax: (086) 2346674‬‬ ‫إعداد أ‪.‬د‪ .‬عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده ‪ -‬كلية الهندسة – جامعة المنيا‬ ‫‪Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com‬‬ ‫‪Page 32 of 58‬‬ ‫المعمل المتطور لنظم القوي الكهربية‬ ‫جامعة المنيا‬ ‫‪Minia University‬‬ ‫رؤيه المعمل‬ ‫‪Advanced Laboratory for electric‬‬ ‫‪Power systems‬‬ ‫‪Faculty of Engineering‬‬ ‫‪Electrical Engineering Dept.‬‬ ‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‪.‬‬ ‫‪Electrical Engineering Dept.‬‬ ‫‪Problem 11.‬‬ ‫‪For the double-beam oscilloscope displays shown in Figure 10.20, determine‬‬ ‫‪(a) their frequency,‬‬ ‫‪(b) their r.m.s. values,‬‬ ‫‪(c) their phase difference.‬‬ ‫‪The „time/cm‟ switch is on 100μs/cm and the „volts/cm‟ switch on 2V/cm.‬‬ ‫رسانه انًعًم‪َ" :‬سعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‪ ،‬كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬ ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعانًٍ"‪.‬‬ ‫‪Tel: 01090343201‬‬ ‫‪Fax: (086) 2346674‬‬ ‫إعداد أ‪.‬د‪ .‬عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده ‪ -‬كلية الهندسة – جامعة المنيا‬ ‫‪Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com‬‬ ‫‪Page 33 of 58‬‬ ‫المعمل المتطور لنظم القوي الكهربية‬ ‫جامعة المنيا‬ ‫‪Minia University‬‬ ‫رؤيه المعمل‬ ‫‪Advanced Laboratory for electric‬‬ ‫‪Power systems‬‬ ‫‪Faculty of Engineering‬‬ ‫‪Electrical Engineering Dept.‬‬ ‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‪.‬‬ ‫‪Electrical Engineering Dept.‬‬ ‫‪Figure 10.20‬‬ ‫رسانه انًعًم‪َ" :‬سعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‪ ،‬كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬ ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعانًٍ"‪.‬‬ ‫‪Tel: 01090343201‬‬ ‫‪Fax: (086) 2346674‬‬ ‫إعداد أ‪.‬د‪ .‬عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده ‪ -‬كلية الهندسة – جامعة المنيا‬ ‫‪Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com‬‬ ‫‪Page 34 of 58‬‬ ‫المعمل المتطور لنظم القوي الكهربية‬ ‫جامعة المنيا‬ ‫‪Minia University‬‬ ‫رؤيه المعمل‬ ‫‪Advanced Laboratory for electric‬‬ ‫‪Power systems‬‬ ‫‪Faculty of Engineering‬‬ ‫‪Electrical Engineering Dept.‬‬ ‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‪.‬‬ ‫‪Electrical Engineering Dept.‬‬ ‫رسانه انًعًم‪َ" :‬سعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‪ ،‬كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬ ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعانًٍ"‪.‬‬ ‫‪Tel: 01090343201‬‬ ‫‪Fax: (086) 2346674‬‬ ‫إعداد أ‪.‬د‪ .‬عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده ‪ -‬كلية الهندسة – جامعة المنيا‬ ‫‪Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com‬‬ ‫‪Page 35 of 58‬‬ ‫المعمل المتطور لنظم القوي الكهربية‬ Faculty of Engineering Electrical Engineering Dept. Advanced Laboratory for electric Power systems ‫جامعة المنيا‬ Minia University ‫رؤيه المعمل‬ .‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‬ Electrical Engineering Dept. Problem The current flowing through a resistor of 5 kΩ±0.4% is measured as 2.5mA with an accuracy of measurement of ±0.5%. Determine the nominal value of the voltage across the resistor and its accuracy. Solution Voltage, V = IR = (2.5×10−3)(5×103) =12.5V. The maximum possible error is 0.4% + 0.5% = 0.9% Hence the voltage, V =12.5V±0.9% of 12.5V = 0.9/100×12.5= 0.1125V = 0.11V correct to 2 significant figures. Hence the voltage V may also be expressed as 12.5±0.11 volts (i.e. a voltage lying between 12.39V and 12.61V). Problem 1 A current of 20 A flows through two ammeters A and B joined in series. Across A, the potential difference is 0.2 V and across B it is 0.3 V. Find how the same current will divide between A and B when they are joined in parallel. Solution Solution The two ammeters are connected in series in Fig. 2.6 ‫ كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬،‫ "َسعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‬:‫رسانه انًعًم‬ ."ًٍ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعان‬ Tel: 01090343201 Fax: (086) 2346674 ‫ كلية الهندسة – جامعة المنيا‬- ‫ عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده‬.‫د‬.‫إعداد أ‬ Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com Page 36 of 58 ‫المعمل المتطور لنظم القوي الكهربية‬ Faculty of Engineering Electrical Engineering Dept. Advanced Laboratory for electric Power systems ‫جامعة المنيا‬ Minia University ‫رؤيه المعمل‬ .‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‬ Electrical Engineering Dept. (a) RA = 0.2/20 = 0.01 Ω , RB = 0.3/20 = 0.015 Ω The same two ammeters are connected in parallel in Fig.2.6 (b) Problem 2 A resistance of 10 Ω is connected in series with two resistances each of 15 Ω arranged in parallel. What resistance must be shunted across this parallel combination so that the total current taken shall be 1.5 A with 20V applied ? Solution. The original circuit is shown in Fig 2.7 Let R be the required resistance as shown in Fig 2.8. If Req is the equivalent resistance of the parallel group, then Fig.2.7 ‫ كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬،‫ "َسعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‬:‫رسانه انًعًم‬ ."ًٍ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعان‬ Tel: 01090343201 Fax: (086) 2346674 ‫ كلية الهندسة – جامعة المنيا‬- ‫ عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده‬.‫د‬.‫إعداد أ‬ Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com Page 37 of 58 ‫المعمل المتطور لنظم القوي الكهربية‬ Faculty of Engineering Electrical Engineering Dept. Advanced Laboratory for electric Power systems ‫جامعة المنيا‬ Minia University ‫رؤيه المعمل‬ .‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‬ Electrical Engineering Dept. Example 7.1 Two incandescent lamps with 80 Ω and 120 Ω resistances are connected in series with a 200 V dc source. Find the errors in measurement of power in the 80 Ω lamp using a voltmeter with internal resistance of 100 kΩ and an ammeter with internal resistance of 0.1 mΩ, when (a) the voltmeter is connected nearer to the lamp than the ammeter, and (b) when the ammeter is connected nearer to the lamp than the voltmeter Solution Assuming both the instruments to be ideal, i.e., the voltmeter with infinite internal impedance and ammeter with zero internal impedance, the current through the series circuit should be = 200/(80 + 120) = 1 A Hence, true power consumed by the 80 Ω lamp would have been = 12 X 80 = 80 Ω However, considering the internal resistance of the ammeter and voltmeter, the equivalent circuit will look like Figure 7.3. ‫ كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬،‫ "َسعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‬:‫رسانه انًعًم‬ ."ًٍ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعان‬ Tel: 01090343201 Fax: (086) 2346674 ‫ كلية الهندسة – جامعة المنيا‬- ‫ عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده‬.‫د‬.‫إعداد أ‬ Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com Page 38 of 58 ‫المعمل المتطور لنظم القوي الكهربية‬ ‫جامعة المنيا‬ ‫‪Minia University‬‬ ‫رؤيه المعمل‬ ‫‪Advanced Laboratory for electric‬‬ ‫‪Power systems‬‬ ‫‪Faculty of Engineering‬‬ ‫‪Electrical Engineering Dept.‬‬ ‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‪.‬‬ ‫‪Electrical Engineering Dept.‬‬ ‫)‪Supply current (ammeter reading‬‬ ‫رسانه انًعًم‪َ" :‬سعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‪ ،‬كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬ ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعانًٍ"‪.‬‬ ‫‪Tel: 01090343201‬‬ ‫‪Fax: (086) 2346674‬‬ ‫إعداد أ‪.‬د‪ .‬عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده ‪ -‬كلية الهندسة – جامعة المنيا‬ ‫‪Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com‬‬ ‫‪Page 39 of 58‬‬ ‫المعمل المتطور لنظم القوي الكهربية‬ ‫جامعة المنيا‬ ‫‪Minia University‬‬ ‫رؤيه المعمل‬ ‫‪Advanced Laboratory for electric‬‬ ‫‪Power systems‬‬ ‫‪Faculty of Engineering‬‬ ‫‪Electrical Engineering Dept.‬‬ ‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‪.‬‬ ‫‪Electrical Engineering Dept.‬‬ ‫‪Supply current‬‬ ‫رسانه انًعًم‪َ" :‬سعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‪ ،‬كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬ ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعانًٍ"‪.‬‬ ‫‪Tel: 01090343201‬‬ ‫‪Fax: (086) 2346674‬‬ ‫إعداد أ‪.‬د‪ .‬عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده ‪ -‬كلية الهندسة – جامعة المنيا‬ ‫‪Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com‬‬ ‫‪Page 40 of 58‬‬ ‫المعمل المتطور لنظم القوي الكهربية‬ ‫جامعة المنيا‬ ‫‪Minia University‬‬ ‫رؤيه المعمل‬ ‫‪Advanced Laboratory for electric‬‬ ‫‪Power systems‬‬ ‫‪Faculty of Engineering‬‬ ‫‪Electrical Engineering Dept.‬‬ ‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‪.‬‬ ‫‪Electrical Engineering Dept.‬‬ ‫رسانه انًعًم‪َ" :‬سعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‪ ،‬كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬ ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعانًٍ"‪.‬‬ ‫‪Tel: 01090343201‬‬ ‫‪Fax: (086) 2346674‬‬ ‫إعداد أ‪.‬د‪ .‬عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده ‪ -‬كلية الهندسة – جامعة المنيا‬ ‫‪Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com‬‬ ‫‪Page 41 of 58‬‬ ‫المعمل المتطور لنظم القوي الكهربية‬ Faculty of Engineering Electrical Engineering Dept. Advanced Laboratory for electric Power systems ‫جامعة المنيا‬ Minia University ‫رؤيه المعمل‬ .‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‬ Electrical Engineering Dept. Problem Find the total resistance for two resistors, R1 and R2 connected in (a) series, and (b) parallel. R1 = 50 Ω ± 5%, R2 = 100 Ω ± 5% Note: Assuming that the 5% tolerance values for each resistor are not correlated, the uncertainty values can be treated as independent uncertainties, which means they can be added in quadrature. The more conservative approach is to treat these uncertainties as correlated, so that they always combine in the same direction (upper/lower bound method or worst-case scenario). For this example, the uncertainties will be treated as uncorrelated. a) RT = R1 + R2 = (50 Ω± 2.5 Ω) + (100 Ω ± 5 Ω) = 150 Ω ± 5.6 Ω = 150 Ω ± 4% RT = (150 ± 6) Ω Note: The total resistance is larger than either of the individual resistors, but the relative uncertainty of RT (4%) is smaller than the tolerance of either resistor in series (5%). b) 1/RT = 1/R1 + 1/R2 = (1/50 ± 5%) Ω -1 + (1/100 ± 5%) Ω -1 1/RT = (0.02 ± 0.001) Ω -1 + (0.01 ± 0.0005) Ω -1 = (0.03 ± 0.0011) Ω -1 = 0.03 Ω -1 ± 3.7% RT = 33.3 Ω ± 3.7% = (33 ± 1) Ω Note: The total resistance is smaller than either of the individual resistors in parallel, and the relative uncertainty of RT (4%) is also less than the tolerance of either resistor. ‫ كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬،‫ "َسعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‬:‫رسانه انًعًم‬ ."ًٍ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعان‬ Tel: 01090343201 Fax: (086) 2346674 ‫ كلية الهندسة – جامعة المنيا‬- ‫ عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده‬.‫د‬.‫إعداد أ‬ Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com Page 42 of 58 ‫المعمل المتطور لنظم القوي الكهربية‬ Faculty of Engineering Electrical Engineering Dept. Advanced Laboratory for electric Power systems ‫جامعة المنيا‬ Minia University ‫رؤيه المعمل‬ .‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‬ Electrical Engineering Dept. Problem When two resistors are connected in parallel, their equivalent resistance is 2, and when they are connected in series, their equivalent resistance is 9. What are the values of the resistors? Solution When R1 and R2 are connected in parallel, the resulting resistance is (R1 x R2) / (R1 + R2). When connected in series the total resistance is R1 + R2. So Solve: (R1 x R2) / (R1 + R2) = 2 and R1 + R2 = 9 R1 = 9-R2 ((9-R2) x R2) / 9 = 2 9R2 - R2^2 = 18 -R2^2 + 9 R2 -18 =0 R2=6, R1=3 Chapter 3 Diode Diodes allow electricity to flow in only one direction. Diodes are the electrical version of a valve and early diodes were actually called valves. The schematic symbol of a diode is shown below. The arrow of the circuit symbol shows the direction in which the current can flow. The diode has two terminals, a cathode and an anode as shown in Figure 1. If a negative voltage is applied to the cathode and a positive voltage to the anode, the diode is forward biased and conducts. The diode acts nearly as a short circuit. If the polarity of ‫ كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬،‫ "َسعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‬:‫رسانه انًعًم‬ ."ًٍ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعان‬ Tel: 01090343201 Fax: (086) 2346674 ‫ كلية الهندسة – جامعة المنيا‬- ‫ عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده‬.‫د‬.‫إعداد أ‬ Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com Page 43 of 58 ‫المعمل المتطور لنظم القوي الكهربية‬ Faculty of Engineering Electrical Engineering Dept. Advanced Laboratory for electric Power systems ‫جامعة المنيا‬ Minia University ‫رؤيه المعمل‬ .‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‬ Electrical Engineering Dept. the applied voltage is changed, the diode is reverse biased and does not conduct. The diode acts very much as an open circuit. Finally, if the voltage vD is more negative than the Reverse Breakdown voltage (also called the Zener voltage, VZ), the diode conducts again, but in a reverse direction. The voltage versus current characteristics of a silicon diode is shown in Figure 2. Fig. 1 Diode Operation Figure 2: Voltage-current characteristics of a Silicon diode 3.1.1 Forward Voltage Drop Electricity uses up a little energy pushing its way through the diode, rather like a person pushing through a door with a spring. This means that there is a small voltage across a ‫ كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬،‫ "َسعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‬:‫رسانه انًعًم‬ ."ًٍ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعان‬ Tel: 01090343201 Fax: (086) 2346674 ‫ كلية الهندسة – جامعة المنيا‬- ‫ عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده‬.‫د‬.‫إعداد أ‬ Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com Page 44 of 58 ‫المعمل المتطور لنظم القوي الكهربية‬ Faculty of Engineering Electrical Engineering Dept. Advanced Laboratory for electric Power systems ‫جامعة المنيا‬ Minia University ‫رؤيه المعمل‬ .‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‬ Electrical Engineering Dept. conducting diode, it is called the forward voltage drop and is about 0.7V for all normal diodes which are made from silicon. The forward voltage drop of a diode is almost constant whatever the current passing through the diode so they have a very steep characteristic (refer to current-voltage graph). 3.1.2 Reverse Voltage Though we say that a diode does not conduct in the reverse direction, there are limits to the reverse electrical pressure that can be applied. The manufacturers of diodes specify a peak inverse voltage (PIV) that the diode can safely withstand. If this is exceeded, the diode will fail and allow a large current to flow in the reverse direction. This voltage is also called the Reverse Breakdown voltage. 3.1.3 Ideal Diode For most practical applications, the operating voltage is high, and the forward voltage drop is negligible in comparison. The voltage-current characteristics of a diode (shown in figure 3) suggest that we can use the following model of an ideal diode for all practical purposes (i.e., ignoring the forward voltage drop). The ideal diode acts as a short circuit for forward currents and as an open circuit with reverse voltage applied. ‫ كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬،‫ "َسعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‬:‫رسانه انًعًم‬ ."ًٍ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعان‬ Tel: 01090343201 Fax: (086) 2346674 ‫ كلية الهندسة – جامعة المنيا‬- ‫ عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده‬.‫د‬.‫إعداد أ‬ Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com Page 45 of 58 ‫المعمل المتطور لنظم القوي الكهربية‬ Faculty of Engineering Electrical Engineering Dept. Advanced Laboratory for electric Power systems ‫جامعة المنيا‬ Minia University ‫رؤيه المعمل‬ .‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‬ Electrical Engineering Dept. Figure 3: Ideal characteristics 3.2 Diode Rectifier Circuits One of the important applications of a semiconductor diode is in rectification of AC signals to DC. Diodes are very commonly used for obtaining DC voltage supplies from the readily available AC voltage. There are many possible ways to construct rectifier circuits using diodes. The three basic types of rectifier circuits are: 1. The Half Wave Rectifier 2. The Full Wave Rectifier 3. The Bridge Rectifier In the remaining sections of this chapter, we will study the operation of these circuits in detail, and study their application in power supply circuits. 3.3 Half-wave Rectifier The easiest rectifier to understand is the half wave rectifier. A simple half-wave rectifier using an ideal diode and a load is shown in Figure 4. Circuit operation ‫ كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬،‫ "َسعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‬:‫رسانه انًعًم‬ ."ًٍ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعان‬ Tel: 01090343201 Fax: (086) 2346674 ‫ كلية الهندسة – جامعة المنيا‬- ‫ عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده‬.‫د‬.‫إعداد أ‬ Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com Page 46 of 58 ‫المعمل المتطور لنظم القوي الكهربية‬ Faculty of Engineering Electrical Engineering Dept. Advanced Laboratory for electric Power systems ‫جامعة المنيا‬ Minia University ‫رؤيه المعمل‬ .‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‬ Electrical Engineering Dept. Let‟s look at the operation of this single diode rectifier when connected across an alternating voltage source vs. Since the diode only conducts when the anode is positive with respect to the cathode, current will flow only during the positive half cycle of the input voltage. Figure 4: Simple half-wave rectifier circuit The supply voltage is given by: (1) where is the angular frequency in rad/s. We are interested in obtaining DC voltage across the “load resistance” RL. During the positive half cycle of the source, the ideal diode is forward biased and operates as a closed switch. The source voltage is directly connected across the load. During the negative half cycle, the diode is reverse biased and acts as an open switch. The source voltage is disconnected from the load. As no current flows through the load, the load voltage vo is zero. Both the ‫ كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬،‫ "َسعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‬:‫رسانه انًعًم‬ ."ًٍ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعان‬ Tel: 01090343201 Fax: (086) 2346674 ‫ كلية الهندسة – جامعة المنيا‬- ‫ عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده‬.‫د‬.‫إعداد أ‬ Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com Page 47 of 58 ‫المعمل المتطور لنظم القوي الكهربية‬ Faculty of Engineering Electrical Engineering Dept. Advanced Laboratory for electric Power systems ‫جامعة المنيا‬ Minia University ‫رؤيه المعمل‬ .‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‬ Electrical Engineering Dept. load voltage and current are of one polarity and hence said to be rectified. The waveforms for source voltage vS and output voltage vo are shown in figure 5. Figure 5: Source and output voltages We notice that the output voltage varies between the peak voltage Vm and zero in each cycle. This variation is called “ripple”, and the corresponding voltage is called the peak-topeak ripple voltage, Vp-p. Average load voltage and current If a DC voltmeter is connected to measure the output voltage of the half-wave rectifier (i.e., across the load resistance), the reading obtained would be the average load voltage Vave, also called the DC output voltage. The meter averages out the pulses and displays this average. ‫ كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬،‫ "َسعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‬:‫رسانه انًعًم‬ ."ًٍ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعان‬ Tel: 01090343201 Fax: (086) 2346674 ‫ كلية الهندسة – جامعة المنيا‬- ‫ عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده‬.‫د‬.‫إعداد أ‬ Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com Page 48 of 58 ‫المعمل المتطور لنظم القوي الكهربية‬ Faculty of Engineering Electrical Engineering Dept. Advanced Laboratory for electric Power systems ‫جامعة المنيا‬ Minia University ‫رؤيه المعمل‬ .‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‬ Electrical Engineering Dept. The output voltage waveform and average voltage are shown in figure 6. Figure 6: Output voltage and average voltage for half-wave rectifier The output vo may be viewed as a DC voltage plus a ripple voltage. As we can see, the output has a large amount of ripple. Average Load Current Just as we can convert a peak voltage to average voltage, we can also convert a peak current to an average current. The value of the average load current is the value that would be measured by a DC ammeter. ‫ كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬،‫ "َسعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‬:‫رسانه انًعًم‬ ."ًٍ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعان‬ Tel: 01090343201 Fax: (086) 2346674 ‫ كلية الهندسة – جامعة المنيا‬- ‫ عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده‬.‫د‬.‫إعداد أ‬ Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com Page 49 of 58 ‫المعمل المتطور لنظم القوي الكهربية‬ Faculty of Engineering Electrical Engineering Dept. Advanced Laboratory for electric Power systems ‫جامعة المنيا‬ Minia University ‫رؤيه المعمل‬ .‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‬ Electrical Engineering Dept. where IL is the average current passing through the load resistance. Peak Inverse Voltage The maximum amount of reverse bias that a diode will be exposed to is called the peak inverse voltage or PIV. For the half wave rectifier, the value of PIV is: The reasoning for the above equation is that when the diode is reverse biased, there is no voltage across the load. Therefore, all of the secondary voltage (Vm) appears across the diode. The PIV is important because it determines the minimum allowable value of reverse voltage for any diode used in the circuit. Example ‫ كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬،‫ "َسعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‬:‫رسانه انًعًم‬ ."ًٍ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعان‬ Tel: 01090343201 Fax: (086) 2346674 ‫ كلية الهندسة – جامعة المنيا‬- ‫ عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده‬.‫د‬.‫إعداد أ‬ Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com Page 50 of 58 ‫المعمل المتطور لنظم القوي الكهربية‬ Faculty of Engineering Electrical Engineering Dept. Advanced Laboratory for electric Power systems ‫جامعة المنيا‬ Minia University ‫رؤيه المعمل‬ .‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‬ Electrical Engineering Dept. A 50Ω load resistance is connected across a half wave rectifier. The input supply voltage is 230V (rms) at 50Hz. Determine the DC output (average) voltage, peak-to-peak ripple in the output voltage (Vp-p), and the output ripple frequency (fr). Solution The peak amplitude of the source voltage can be calculated as: √ Output DC voltage: The peak-to-peak ripple voltage is the difference between the maximum and the minimum in the vo waveform. Therefore, Vp-p = Vm- 0= 325.3V Percentage ripple = (Vp-p/Vave) x 100 = 314% The ripple is at the supply frequency of 50 Hz. Hence fr=50 Hz We notice that the “percentage ripple” is 314%, which is very large, and undesirable. This ripple can be reduced by adding a capacitor across the load resistor. The capacitor acts to filter (reduce) the ripple voltage, as we will see later. 3.4 Diode rectifier for power supply ‫ كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬،‫ "َسعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‬:‫رسانه انًعًم‬ ."ًٍ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعان‬ Tel: 01090343201 Fax: (086) 2346674 ‫ كلية الهندسة – جامعة المنيا‬- ‫ عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده‬.‫د‬.‫إعداد أ‬ Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com Page 51 of 58 ‫المعمل المتطور لنظم القوي الكهربية‬ Faculty of Engineering Electrical Engineering Dept. Advanced Laboratory for electric Power systems ‫جامعة المنيا‬ Minia University ‫رؤيه المعمل‬ .‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‬ Electrical Engineering Dept. The purpose of a power supply is to take electrical energy in one form and convert it into another. There are many types of power supply. Most are designed to convert high voltage AC mains electricity to a suitable low voltage supply for electronics circuits and other devices such as computers, fax machines and telecommunication equipment. In Singapore, supply from 230V, 50Hz AC mains is converted into smooth DC using AC-DC power supply. A power supply can by broken down into a series of blocks, each of which performs a particular function. A transformer first steps down high voltage AC to low voltage AC. A rectifier circuit is then used to convert AC to DC. This DC, however, contains ripples, which can be smoothened by a filter circuit. Power supplies can be „regulated‟ or „unregulated‟. A regulated power supply maintains a constant DC output voltage through „feedback action‟. The output voltage of an unregulated supply, on the other hand, will not remain constant. It will vary depending on varying operating conditions, for example when the magnitude of input AC voltage changes. Main components of a regulated supply to convert 230V AC voltage to 5V DC are shown below. ‫ كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬،‫ "َسعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‬:‫رسانه انًعًم‬ ."ًٍ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعان‬ Tel: 01090343201 Fax: (086) 2346674 ‫ كلية الهندسة – جامعة المنيا‬- ‫ عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده‬.‫د‬.‫إعداد أ‬ Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com Page 52 of 58 ‫المعمل المتطور لنظم القوي الكهربية‬ Faculty of Engineering Electrical Engineering Dept. Advanced Laboratory for electric Power systems ‫جامعة المنيا‬ Minia University ‫رؤيه المعمل‬ .‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‬ Electrical Engineering Dept. Figure 7: Block diagram of a regulated power supply Power supplies are designed to produce as little ripple voltage as possible, as the ripple can cause several problems. For Example 1. In audio amplifiers, too much ripple shows up as an annoying 50 Hz or 100 Hz audible hum. 2. In video circuits, excessive ripple shows up as “hum” bars in the picture. 3. In digital circuits it can cause erroneous outputs from logic circuits. 3.5 Half-wave Rectifier with Capacitor Filter The capacitor is the most basic filter type and is the most commonly used. The half-wave rectifier for power supply application is shown below. A capacitor filter is connected in parallel with the load. The rectifier circuit is supplied from a transformer. Circuit operation The operation of this circuit during positive half cycle of the source voltage is shown in figure 8. During the positive half cycle, diode D1 will conduct, and the capacitor charges rapidly. As the input starts to go negative, D1 turns off, and the capacitor will slowly discharge through the load (figure 9). ‫ كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬،‫ "َسعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‬:‫رسانه انًعًم‬ ."ًٍ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعان‬ Tel: 01090343201 Fax: (086) 2346674 ‫ كلية الهندسة – جامعة المنيا‬- ‫ عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده‬.‫د‬.‫إعداد أ‬ Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com Page 53 of 58 ‫المعمل المتطور لنظم القوي الكهربية‬ Faculty of Engineering Electrical Engineering Dept. Advanced Laboratory for electric Power systems ‫جامعة المنيا‬ Minia University ‫رؤيه المعمل‬ .‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‬ Electrical Engineering Dept. Figure 8: Half wave rectifier with capacitor filter – positive half cycle Figure 9: Half wave rectifier with capacitor filter – negative half cycle Using the previous half wave rectifier as an example, figure 10 examines what is happening with our filter. (a) Unfiltered output from the half wave rectifier ‫ كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬،‫ "َسعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‬:‫رسانه انًعًم‬ ."ًٍ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعان‬ Tel: 01090343201 Fax: (086) 2346674 ‫ كلية الهندسة – جامعة المنيا‬- ‫ عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده‬.‫د‬.‫إعداد أ‬ Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com Page 54 of 58 ‫المعمل المتطور لنظم القوي الكهربية‬ Faculty of Engineering Electrical Engineering Dept. Advanced Laboratory for electric Power systems ‫جامعة المنيا‬ Minia University ‫رؤيه المعمل‬ .‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‬ Electrical Engineering Dept. (b) When the next pulse does arrive, it charges the capacitor back to full charge as shown on the right. The thick line shows the charge – discharge waveform at the capacitor. (c) The load sees a reasonably constant DC voltage now, with a ripple voltage on top of it. The operation can be analyzed in detail using figure 11. During each positive half cycle, the capacitor charges during the interval t1 to t2. During this interval, the diode will be forward biased. Due to this charging, the voltage across the capacitor vo will be equal to the AC peak voltage Vm on the secondary side of the transformer at t2 (assuming diode forward voltage drop is zero). The capacitor will supply current to load resistor RL during time interval t2 to t3. During this interval, diode will be reverse biased since the AC voltage is less than the output voltage vo. Due to the large energy stored in the capacitor, the capacitor voltage will not reduce much during t2 to t3, and the voltage vo will remain close to the peak value. As can be seen, addition of the capacitor results in much better quality output voltage. ‫ كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬،‫ "َسعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‬:‫رسانه انًعًم‬ ."ًٍ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعان‬ Tel: 01090343201 Fax: (086) 2346674 ‫ كلية الهندسة – جامعة المنيا‬- ‫ عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده‬.‫د‬.‫إعداد أ‬ Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com Page 55 of 58 ‫المعمل المتطور لنظم القوي الكهربية‬ Faculty of Engineering Electrical Engineering Dept. Advanced Laboratory for electric Power systems ‫جامعة المنيا‬ Minia University ‫رؤيه المعمل‬ .‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‬ Electrical Engineering Dept. Figure 11: Output voltage waveform of half-wave rectifier with capacitor filter Average load voltage In practical applications, a very large capacitor is used so that the output voltage is close to the peak value. The average voltage (also called DC output voltage) across the load can therefore be approximated to: Calculation of capacitance The voltage waveforms show a small AC component called “ripple” present in the output voltage. This ripple can be minimized by choosing the largest capacitance value that is practical. The capacitor is typically “electrolytic” type, and is very large (several hundreds or even thousands of microfarads). We can calculate the required value of the filter capacitor as follows. The charge removed from the capacitor during the discharge cycle (i.e., t2 to t3) is: ‫ كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬،‫ "َسعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‬:‫رسانه انًعًم‬ ."ًٍ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعان‬ Tel: 01090343201 Fax: (086) 2346674 ‫ كلية الهندسة – جامعة المنيا‬- ‫ عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده‬.‫د‬.‫إعداد أ‬ Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com Page 56 of 58 ‫المعمل المتطور لنظم القوي الكهربية‬ Faculty of Engineering Electrical Engineering Dept. Advanced Laboratory for electric Power systems ‫جامعة المنيا‬ Minia University ‫رؤيه المعمل‬ .‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‬ Electrical Engineering Dept. Where IL is the average load current and T is the period of the AC voltage. As the interval t1 to t2 is very small, the discharge time can be approximated to T. If Vp-p is the peak-to-peak ripple voltage, and C is the capacitance, the charge removed from the capacitor can also be expressed as: From these two equations, capacitance C can be calculated as: Example 2 In the circuit of example 1, a 10000µF filter capacitor is added across the load resistor. The voltage across the secondary terminals of the transformer is 230V (rms). Determine the DC output voltage (i.e. average voltage), load current, peak-to-peak ripple in the output voltage, and the output ripple frequency. ‫ كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬،‫ "َسعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‬:‫رسانه انًعًم‬ ."ًٍ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعان‬ Tel: 01090343201 Fax: (086) 2346674 ‫ كلية الهندسة – جامعة المنيا‬- ‫ عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده‬.‫د‬.‫إعداد أ‬ Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com Page 57 of 58 ‫المعمل المتطور لنظم القوي الكهربية‬ ‫جامعة المنيا‬ ‫‪Minia University‬‬ ‫رؤيه المعمل‬ ‫‪Advanced Laboratory for electric‬‬ ‫‪Power systems‬‬ ‫‪Faculty of Engineering‬‬ ‫‪Electrical Engineering Dept.‬‬ ‫أٌ َكىٌ انًعًم انًتطىر نُظى انقىٌ انكهربُت يركزاً بحثُا ً وخذيُا ً واستشارَا ً يتًُزاً ورائذاً عهٍ انًستىٌ انقىيٍ وانعانًٍ فٍ يجال َظى انقىٌ انكهربُت‪.‬‬ ‫‪Electrical Engineering Dept.‬‬ ‫‪Prof. Dr. Adel Abd Elbaset‬‬ ‫‪With Best wishes‬‬ ‫رسانه انًعًم‪َ" :‬سعً انًعًم انًتطىر نُظى انقىٌ انكهربُت نتطبُق َظاو نهجىدة يتىافق يع انًعاَُر انذونُت‪ ،‬كًا َهذف انًعًم نهُهىض بانصُاعت انىطُُت‬ ‫وتقىَه وتفعُم انعالقت بٍُ كهُت انهُذست وانًجتًع اإلَتاجٍ وانًساهًت بذور فعال فٍ تحسٍُ انعًهُت انبحثُت وانخذيُت عهً انًستىي انقىيٍ وانعانًٍ"‪.‬‬ ‫‪Tel: 01090343201‬‬ ‫‪Fax: (086) 2346674‬‬ ‫إعداد أ‪.‬د‪ .‬عادل عبدالباسط محمد أستاذ وإستشاري نظم الطاقة الجديدة والمتجدده ‪ -‬كلية الهندسة – جامعة المنيا‬ ‫‪Email: AdeL.Soliman@mu.edu.eg & DR_AdeL72@yahoo.com‬‬ ‫‪Page 58 of 58‬‬

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