The phenomenon of static electricity has been toyed with since antiquity. The Greeks called the fossil resin substance so often used to demonstrate the effects of static electricity elektron, but no extensive study was made of the subject until William Gilbert researched the event in 1600. In the years to follow, there was a continuing investigation of electrostatic charge by many individuals such as Otto von Guericke, who developed the first machine to generate large amounts of charge, and Stephen Gray, who was able to transmit electrical charge over long distances on silk threads. Charles DuFay demonstrated that charges either attract or repel each other, leading him to believe that there were two types of charge—a theory we subscribe to today with our defined positive and negative charges. There are many who believe that the true beginnings of the electrical era lie with the efforts of Pieter van Musschenbroek and Benjamin Franklin. In 1745, van Musschenbroek introduced the Leyden jar for the storage of electrical charge (the first capacitor) and demonstrated electrical shock (and therefore the power of this new form of energy). Franklin used the Leyden jar some seven years later to establish that lightning is simply an electrical discharge, and he expanded on a number of other important theories including the definition of the two types of charge as positive and negative. From this point on, new discoveries and theories seemed to occur at an increasing rate as the number of individuals performing research in the area grew. In 1784, Charles Coulomb demonstrated in Paris that the force between charges is inversely related to the square of the distance between the charges. In 1791, Luigi Galvani, professor of anatomy at the University of Bologna, Italy, performed experiments on the effects of electricity on animal nerves and muscles. The first voltaic cell, with its ability to produce electricity through the chemical action of a metal dissolving in an acid, was developed by another Italian, Alessandro Volta, in 1799. The fever pitch continued into the early 1800s with Hans Christian Oersted, a Swedish professor of physics, announcing in 1820 a relationship between magnetism and electricity that serves as the foundation for the theory of electromagnetism as we know it today. In the same year, a French physicist, André Ampère, demonstrated that there are magnetic effects around every current-carrying conductor and that current-carrying conductors can attract and repel each other just like magnets. In the period 1826 to 1827, a German physicist, Georg Ohm, introduced an important relationship between potential, current, and resistance which we now refer to as Ohm’s law. In 1831, an English physicist, Michael Faraday, demonstrated his theory of electromagnetic induction, whereby a changing current in one coil can induce a changing current in another coil, even though the two coils are not directly connected. Professor Faraday also did extensive work on a storage device he called the con
4 INTRODUCTION
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A BRIEF HISTORY 5
denser, which we refer to today as a capacitor. He introduced the idea of adding a dielectric between the plates of a capacitor to increase the storage capacity (Chapter 10). James Clerk Maxwell, a Scottish professor of natural philosophy, performed extensive mathematical analyses to develop what are currently called Maxwell’s equations, which support the efforts of Faraday linking electric and magnetic effects. Maxwell also developed the electromagnetic theory of light in 1862, which, among other things, revealed that electromagnetic waves travel through air at the velocity of light (186,000 miles per second or 3 108 meters per second). In 1888, a German physicist, Heinrich Rudolph Hertz, through experimentation with lower-frequency electromagnetic waves (microwaves), substantiated Maxwell’s predictions and equations. In the mid 1800s, Professor Gustav Robert Kirchhoff introduced a series of laws of voltages and currents that find application at every level and area of this field (Chapters 5 and 6). In 1895, another German physicist, Wilhelm Röntgen, discovered electromagnetic waves of high frequency, commonly called Xrays today. By the end of the 1800s, a significant number of the fundamental equations, laws, and relationships had been established, and various fields of study, including electronics, power generation, and calculating equipment, started to develop in earnest.
The Age of Electronics
Radio The true beginning of the electronics era is open to debate and is sometimes attributed to efforts by early scientists in applying potentials across evacuated glass envelopes. However, many trace the beginning to Thomas Edison, who added a metallic electrode to the vacuum of the tube and discovered that a current was established between the metal electrode and the filament when a positive voltage was applied to the metal electrode. The phenomenon, demonstrated in 1883, was referred to as the Edison effect. In the period to follow, the transmission of radio waves and the development of the radio received widespread attention. In 1887, Heinrich Hertz, in his efforts to verify Maxwell’s equations, transmitted radio waves for the first time in his laboratory. In 1896, an Italian scientist, Guglielmo Marconi (often called the father of the radio), demonstrated that telegraph signals could be sent through the air over long distances (2.5 kilometers) using a grounded antenna. In the same year, Aleksandr Popov sent what might have been the first radio message some 300 yards. The message was the name “Heinrich Hertz” in respect for Hertz’s earlier contributions. In 1901, Marconi established radio communication across the Atlantic. In 1904, John Ambrose Fleming expanded on the efforts of Edison to develop the first diode, commonly called Fleming’s valve—actually the first of the electronic devices. The device had a profound impact on the design of detectors in the receiving section of radios. In 1906, Lee De Forest added a third element to the vacuum structure and created the first amplifier, the triode. Shortly thereafter, in 1912, Edwin Armstrong built the first regenerative circuit to improve receiver capabilities and then used the same contribution to develop the first nonmechanical oscillator. By 1915 radio signals were being transmitted across the United States, and in 1918 Armstrong applied for a patent for the superheterodyne circuit employed in virtually every television and radio to permit amplification at one frequency rather than at the full range of
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6 INTRODUCTION
incoming signals. The major components of the modern-day radio were now in place, and sales in radios grew from a few million dollars in the early 1920s to over $1 billion by the 1930s. The 1930s were truly the golden years of radio, with a wide range of productions for the listening audience.
Television The 1930s were also the true beginnings of the television era, although development on the picture tube began in earlier years with Paul Nipkow and his electrical telescope in 1884 and John Baird and his long list of successes, including the transmission of television pictures over telephone lines in 1927 and over radio waves in 1928, and simultaneous transmission of pictures and sound in 1930. In 1932, NBC installed the first commercial television antenna on top of the Empire State Building in New York City, and RCA began regular broadcasting in 1939. The war slowed development and sales, but in the mid 1940s the number of sets grew from a few thousand to a few million. Color television became popular in the early 1960s.
Computers The earliest computer system can be traced back to Blaise Pascal in 1642 with his mechanical machine for adding and subtracting numbers. In 1673 Gottfried Wilhelm von Leibniz used the Leibniz wheel to add multiplication and division to the range of operations, and in 1823 Charles Babbage developed the difference engine to add the mathematical operations of sine, cosine, logs, and several others. In the years to follow, improvements were made, but the system remained primarily mechanical until the 1930s when electromechanical systems using components such as relays were introduced. It was not until the 1940s that totally electronic systems became the new wave. It is interesting to note that, even though IBM was formed in 1924, it did not enter the computer industry until 1937. An entirely electronic system known as ENIAC was dedicated at the University of Pennsylvania in 1946. It contained 18,000 tubes and weighed 30 tons but was several times faster than most electromechanical systems. Although other vacuum tube systems were built, it was not until the birth of the solid-state era that computer systems experienced a major change in size, speed, and capability.
The Solid-State Era
In 1947, physicists William Shockley, John Bardeen, and Walter H. Brattain of Bell Telephone Laboratories demonstrated the point-contact transistor (Fig. 1.3), an amplifier constructed entirely of solid-state materials with no requirement for a vacuum, glass envelope, or heater voltage for the filament. Although reluctant at first due to the vast amount of material available on the design, analysis, and synthesis of tube networks, the industry eventually accepted this new technology as the wave of the future. In 1958 the first integrated circuit (IC) was developed at Texas Instruments, and in 1961 the first commercial integrated circuit was manufactured by the Fairchild Corporation. It is impossible to review properly the entire history of the electrical/electronics field in a few pages. The effort here, both through the discussion and the time graphs of Fig. 1.2, was to reveal the amazing progress of this field in the last 50 years. The growth appears to be truly exponential since the early 1900s, raising the interesting question, Where do we go from here? The time chart suggests that the next few
FIG. 1.3 The first transistor. (Courtesy of AT&T, Bell Laboratories.)
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UNITS OF MEASUREMENT 7
decades will probably contain many important innovative contributions that may cause an even faster growth curve than we are now experiencing.
1.3 UNITS OF MEASUREMENT
In any technical field it is naturally important to understand the basic concepts and the impact they will have on certain parameters. However, the application of these rules and laws will be successful only if the mathematical operations involved are applied correctly. In particular, it is vital that the importance of applying the proper unit of measurement to a quantity is understood and appreciated. Students often generate a numerical solution but decide not to apply a unit of measurement to the result because they are somewhat unsure of which unit should be applied. Consider, for example, the following very fundamental physics equation:
v velocity d distance (1.1) t time
Assume, for the moment, that the following data are obtained for a moving object:
d 4000 ft t 1 min
and v is desired in miles per hour. Often, without a second thought or consideration, the numerical values are simply substituted into the equation, with the result here that
As indicated above, the solution is totally incorrect. If the result is desired in miles per hour, the unit of measurement for distance must be miles, and that for time, hours. In a moment, when the problem is analyzed properly, the extent of the error will demonstrate the importance of ensuring that
the numerical value substituted into an equation must have the unit of measurement specified by the equation.
The next question is normally, How do I convert the distance and time to the proper unit of measurement? A method will be presented in a later section of this chapter, but for now it is given that
1 mi 5280 ft 4000 ft 0.7576 mi 1 min h 0.0167 h
Substituting into Eq. (1.1), we have
v 45.37 mi/h
which is significantly different from the result obtained before. To complicate the matter further, suppose the distance is given in kilometers, as is now the case on many road signs. First, we must realize that the prefix kilo stands for a multiplier of 1000 (to be introduced
0.7576 mi 0.0167 h
d t
1 60
v 4000 mi/h d t 4000 ft 1 min
v d t
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8 INTRODUCTION
in Section 1.5), and then we must find the conversion factor between kilometers and miles. If this conversion factor is not readily available, we must be able to make the conversion between units using the conversion factors between meters and feet or inches, as described in Section 1.6. Before substituting numerical values into an equation, try to mentally establish a reasonable range of solutions for comparison purposes. For instance, if a car travels 4000 ft in 1 min, does it seem reasonable that the speed would be 4000 mi/h? Obviously not! This self-checking procedure is particularly important in this day of the hand-held calculator, when ridiculous results may be accepted simply because they appear on the digital display of the instrument. Finally,
if a unit of measurement is applicable to a result or piece of data, then it must be applied to the numerical value.
To state that v 45.37 without including the unit of measurement mi/h is meaningless. Equation (1.1) is not a difficult one. A simple algebraic manipulation will result in the solution for any one of the three variables. However, in light of the number of questions arising from this equation, the reader may wonder if the difficulty associated with an equation will increase at the same rate as the number of terms in the equation. In the broad sense, this will not be the case. There is, of course, more room for a mathematical error with a more complex equation, but once the proper system of units is chosen and each term properly found in that system, there should be very little added difficulty associated with an equation requiring an increased number of mathematical calculations. In review, before substituting numerical values into an equation, be absolutely sure of the following:
1. Each quantity has the proper unit of measurement as defined by the equation. 2. The proper magnitude of each quantity as determined by the defining equation is substituted. 3. Each quantity is in the same system of units (or as defined by the equation). 4. The magnitude of the result is of a reasonable nature when compared to the level of the substituted quantities. 5. The proper unit of measurement is applied to the result.
1.4 SYSTEMS OF UNITS
In the past, the systems of units most commonly used were the English and metric, as outlined in Table 1.1. Note that while the English system is based on a single standard, the metric is subdivided into two interrelated standards: the MKS and the CGS. Fundamental quantities of these systems are compared in Table 1.1 along with their abbreviations. The MKS and CGS systems draw their names from the units of measurement used with each system; the MKS system uses Meters, Kilograms, and Seconds, while the CGS system uses Centimeters, Grams, and Seconds. Understandably, the use of more than one system of units in a world that finds itself continually shrinking in size, due to advanced technical developments in communications and transportation, would introduce
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SYSTEMS OF UNITS 9
unnecessary complications to the basic understanding of any technical data. The need for a standard set of units to be adopted by all nations has become increasingly obvious. The International Bureau of Weights and Measures located at Sèvres, France, has been the host for the General Conference of Weights and Measures, attended by representatives from all nations of the world. In 1960, the General Conference adopted a system called Le Système International d’Unités (International System of Units), which has the international abbreviation SI. Since then, it has been adopted by the Institute of Electrical and Electronic Engineers, Inc. (IEEE) in 1965 and by the United States of America Standards Institute in 1967 as a standard for all scientific and engineering literature. For comparison, the SI units of measurement and their abbreviations appear in Table 1.1. These abbreviations are those usually applied to each unit of measurement, and they were carefully chosen to be the most effective. Therefore, it is important that they be used whenever applicable to ensure universal understanding. Note the similarities of the SI system to the MKS system. This text will employ, whenever possible and practical, all of the major units and abbreviations of the SI system in an effort to support the need for a universal system. Those readers requiring additional information on the SI system should contact the information office of the American Society for Engineering Education (ASEE).*
*American Society for Engineering Education (ASEE), 1818 N Street N.W., Suite 600, Washington, D.C. 20036-2479; (202) 331-3500; http://www.asee.org/.
°C 32 9 5
TABLE 1.1 Comparison of the English and metric systems of units.
English Metric
MKS CGS SI
Length: Meter (m) Centimeter (cm) Meter (m) Yard (yd) (39.37 in.) (2.54 cm 1 in.) (0.914 m) (100 cm) Mass: Slug Kilogram (kg) Gram (g) Kilogram (kg) (14.6 kg) (1000 g) Force: Pound (lb) Newton (N) Dyne Newton (N) (4.45 N) (100,000 dynes) Temperature: Fahrenheit (°F) Celsius or Centigrade (°C) Kelvin (K) Centigrade (°C) K 273.15 °C (°F 32) Energy: Foot-pound (ft-lb) Newton-meter (N•m) Dyne-centimeter or erg Joule (J) (1.356 joules) or joule (J) (1 joule 107 ergs) (0.7376 ft-lb) Time: Second (s) Second (s) Second (s) Second (s) 5 9
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10 INTRODUCTION
Figure 1.4 should help the reader develop some feeling for the relative magnitudes of the units of measurement of each system of units. Note in the figure the relatively small magnitude of the units of measurement for the CGS system. A standard exists for each unit of measurement of each system. The standards of some units are quite interesting. The meter was originally defined in 1790 to be 1/10,000,000 the distance between the equator and either pole at sea level, a length preserved on a platinum-iridium bar at the International Bureau of Weights and Measures at Sèvres, France.
The meter is now defined with reference to the speed of light in a vacuum, which is 299,792,458 m/s.
The kilogram is defined as a mass equal to 1000 times the mass of one cubic centimeter of pure water at 4°C.
This standard is preserved in the form of a platinum-iridium cylinder in Sèvres.
FIG. 1.4 Comparison of units of the various systems of units.
1 slug English 1 kg SI and MKS
1 g CGS
1 yd
1 m
1 ftEnglish
English
SI and MKS
1 yard (yd) = 0.914 meter (m) = 3 feet (ft)
Length:
Mass:
1 slug = 14.6 kilograms
Temperature:
English
(Boiling)
(Freezing)
(Absolute zero)
Fahrenheit Celsius or Centigrade
Kelvin – 459.7˚F –273.15˚C 0 K
0˚F
32˚F
212˚F
0˚C
100˚C
273.15 K
373.15 K
SI
MKS and CGS
K = 273.15 + ˚C
(˚F – 32˚)˚ C = 5 9 _
˚F =
9 5˚C + 32˚ _
English 1 ft-lb SI and MKS 1 joule (J)
1 erg (CGS)
1 dyne (CGS)
SI and MKS 1 newton (N)
1 ft-lb = 1.356 joules 1 joule = 107 ergs
1 pound (lb) = 4.45 newtons (N) 1 newton = 100,000 dynes (dyn)
1 m = 100 cm = 39.37 in. 2.54 cm = 1 in.
English
CGS 1 cm
1 in.
Actual lengths
English 1 pound (lb)
Force:
Energy:
1 kilogram = 1000 g
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SIGNIFICANT FIGURES, ACCURACY, AND ROUNDING OFF 11
The second was originally defined as 1/86,400 of the mean solar day. However, since Earth’s rotation is slowing down by almost 1 second every 10 years,
the second was redefined in 1967 as 9,192,631,770 periods of the electromagnetic radiation emitted by a particular transition of cesium atom.
1.5 SIGNIFICANT FIGURES, ACCURACY, AND ROUNDING OFF
This section will emphasize the importance of being aware of the source of a piece of data, how a number appears, and how it should be treated. Too often we write numbers in various forms with little concern for the format used, the number of digits that should be included, and the unit of measurement to be applied. For instance, measurements of 22.1 and 22.10 imply different levels of accuracy. The first suggests that the measurement was made by an instrument accurate only to the tenths place; the latter was obtained with instrumentation capable of reading to the hundredths place. The use of zeros in a number, therefore, must be treated with care and the implications must be understood. In general, there are two types of numbers, exact and approximate. Exact numbers are precise to the exact number of digits presented, just as we know that there are 12 apples in a dozen and not 12.1. Throughout the text the numbers that appear in the descriptions, diagrams, and examples are considered exact, so that a battery of 100V can be written as 100.0V, 100.00 V, and so on, since it is 100 V at any level of precision. The additional zeros were not included for purposes of clarity. However, in the laboratory environment, where measurements are continually being taken and the level of accuracy can vary from one instrument to another, it is important to understand how to work with the results. Any reading obtained in the laboratory should be considered approximate. The analog scales with their pointers may be difficult to read, and even though the digital meter provides only specific digits on its display, it is limited to the number of digits it can provide, leaving us to wonder about the less significant digits not appearing on the display. The precision of a reading can be determined by the number of significant figures (digits) present. Significant digits are those integers (0 to 9) that can be assumed to be accurate for the measurement being made. The result is that all nonzero numbers are considered significant, with zeros being significant in only some cases. For instance, the zeros in 1005 are considered significant because they define the size of the number and are surrounded by nonzero digits. However, for a number such as 0.064, the two zeros are not considered significant because they are used only to define the location of the decimal point and not the accuracy of the reading. For the number 0.4020, the zero to the left of the decimal point is not significant, but the other two are because they define the magnitude of the number and the fourth-place accuracy of the reading. When adding approximate numbers, it is important to be sure that the accuracy of the readings is consistent throughout. To add a quantity accurate only to the tenths place to a number accurate to the thousandths
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12 INTRODUCTION
place will result in a total having accuracy only to the tenths place. One cannot expect the reading with the higher level of accuracy to improve the reading with only tenths-place accuracy.
In the addition or subtraction of approximate numbers, the entry with the lowest level of accuracy determines the format of the solution.
For the multiplication and division of approximate numbers, the result has the same number of significant figures as the number with the least number of significant figures.
For approximate numbers (and exact, for that matter) there is often a need to round off the result; that is, you must decide on the appropriate level of accuracy and alter the result accordingly. The accepted procedure is simply to note the digit following the last to appear in the rounded-off form, and add a 1 to the last digit if it is greater than or equal to 5, and leave it alone if it is less than 5. For example, 3.186 3.19 3.2, depending on the level of precision desired. The symbol appearing means approximately equal to.
EXAMPLE 1.1 Perform the indicated operations with the following approximate numbers and round off to the appropriate level of accuracy. a. 532.6 4.02 0.036 536.656 536.7 (as determined by 532.6) b. 0.04 0.003 0.0064 0.0494 0.05 (as determined by 0.04) c. 4.632 2.4 11.1168 11 (as determined by the two significant digits of 2.4) d. 3.051 802 2446.902 2450 (as determined by the three significant digits of 802) e. 1402/6.4 219.0625 220 (as determined by the two significant digits of 6.4) f. 0.0046/0.05 0.0920 0.09 (as determined by the one significant digit of 0.05)
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