# UnderstandableElectricCircuitsKeyconcepts,2ndEdition

IET MATERIALS, CIRCUITS AND DEVICES SERIES 47 Understandable Electric Circuits Other volumes in this series: Volume 2Analogue IC Design: The current-mode approach C. Toumazou, F.J. Lidgey and D.G. Haigh (Editors) Volume 3Analogue–Digital ASICs: Circuit techniques, design tools and applications R.S. Soin, F. Maloberti and J. France (Editors) Volume 4Algorithmic and Knowledge-based CAD for VLSI G.E. Taylor and G. Russell (Editors) Volume 5Switched Currents: An analogue technique for digital technology C. Toumazou, J.B.C. Hughes and N.C. Battersby (Editors) Volume 6High-frequency Circuit Engineering F. Nibler et al. Volume 8Low-power High-frequency Microelectronics: A unified approach G. Machado (Editor) Volume 9VLSI Testing: Digital and mixed analogue/digital techniques S.L. Hurst Volume 10Distributed Feedback Semiconductor Lasers J.E. Carroll, J.E.A. Whiteaway and R.G.S. Plumb Volume 11Selected Topics in Advanced Solid State and Fibre Optic Sensors S.M. Vaezi-Nejad (Editor) Volume 12Strained Silicon Heterostructures: Materials and devices C.K. Maiti, N.B. Chakrabarti and S.K. Ray Volume 13RFIC and MMIC Design and Technology I.D. Robertson and S. Lucyzyn (Editors) Volume 14Design of High Frequency Integrated Analogue Filters Y. Sun (Editor) Volume 15Foundations of Digital Signal Processing: Theory, algorithms and hardware design P. Gaydecki Volume 16Wireless Communications Circuits and Systems Y. Sun (Editor) Volume 17The Switching Function: Analysis of power electronic circuits C. Marouchos Volume 18System on Chip: Next generation electronics B. Al-Hashimi (Editor) Volume 19Test and Diagnosis of Analogue, Mixed-signal and RF Integrated Circuits: The system on chip approach Y. Sun (Editor) Volume 20Low Power and Low Voltage Circuit Design with the FGMOS Transistor E. Rodriguez-Villegas Volume 21Technology Computer Aided Design for Si, SiGe and GaAs Integrated Circuits C.K. Maiti and G.A. Armstrong Volume 22Nanotechnologies M. Wautelet et al. Volume 23Understandable Electric Circuits M. Wang Volume 24Fundamentals of Electromagnetic Levitation: Engineering sustainability through efficiency A.J. Sangster Volume 25Optical MEMS for Chemical Analysis and Biomedicine H. Jiang (Editor) Volume 26High Speed Data Converters Ahmed M.A. Ali Volume 27Nano-scaled Semiconductor Devices E. A. Gutie ′rrez-D (Editor) Volume 29Nano-CMOS and Post-CMOS Electronics: Devices and modelling Saraju P. Mohanty and Ashok Srivastava Volume 30Nano-CMOS and Post-CMOS Electronics: Circuits and design Saraju P. Mohanty and Ashok Srivastava Volume 32Oscillator Circuits: Frontiers in design, analysis and applications Y. Nishio (Editor) Volume 33High Frequency MOSFET Gate Drivers Z. Zhang and Y. Liu Volume 38System Design with Memristor Technologies L. Guckert and E.E. Swartzlander Jr. Volume 39Functionality-enhanced Devices: An alternative to Moore’s law P.-E. Gaillardon (Editor) Volume 43Negative Group Delay Devices: From concepts to applications B. Ravelo (Editor) Volume 60IP Core Protection and Hardware-assisted Security for Consumer Electronics A. Sengupta and S. Mohanty Understandable Electric Circuits Key concepts 2nd Edition Meizhong Wang The Institution of Engineering and Technology Published by The Institution of Engineering and Technology, London, United Kingdom The Institution of Engineering and Technology is registered as a Charity in England clearly presenting information and making studying/reviewing more effective. ●Key terms, properties, phrases, concepts, formulas, etc. are easily located. Clear step-by-step procedures for applying theorems. ●Summary at the end of each chapter to emphasize the key points and formulas in the chapter. Experiments after each chapter in the original edition have been replaced with practice problems, which will help students focus on the key principles, complete the connection between theory and practice, and assist readers in the learning process. Key concepts have been explained clearly by detailed, worked examples in chapters and readers will be consistently made to apply and practice these theories in practice problems throughout the book. Practice problems allow readers to work similar problems and check their results against the odd-numbered answers pro- vided at the end of book, and thus, provide support for readers to complete the connection between theory and practice. Therefore, although the essential contents presented in the second edition of the book are the same as that in the first edition, the second edition contains some additions and enhancements that will ensure its applicability to readers today and for many years to come. Suitable readers This book is intended for college/university students, technicians, technologists, engineers, or any other professionals who require a solid foundation in the basics of electric circuits. It targets an audience of all sectors in the fields of electrical, electronic, and computer engineering such as electrical, electronics, computer, communications, control and automation, embedded systems, signal processing, power electronics, industrial instrumentation, power systems (including renewable energy), electrical apparatus and machines, nanotechnology, biomedical imaging, information tech- nology, artificial intelligence, and so on. It is also suitable to nonelectrical or electronics students. It provides readers with the necessary foundation for DC/AC circuits in related fields. To make this book more reader-friendly, the concepts, new terms, laws/rules and theorems are explained in an easy-to-understand style. Clear step-by-step procedures for applying methods of DC/AC analysis and network theorems make this book easy for readers to learn electric circuits themselves. xviiiUnderstandable electric circuits: key concepts, 2nd edition Acknowledgments Special thanks to Sarah Lynch, the commissioning editor, Olivia Wilkins, assistant editor, and Joanne Cordery, production controller for books at the Institution of Engineering and Technology (IET). I really appreciate their help and support in publishing a second edition of the book. I would also like to express my gratitude to N. Srinivasan (project manager of my production process from MPS Ltd.) for his work that has helped to refine the writing a second edition of this book. This page intentionally left blank Chapter R Quantities and units Chapter outline R.1 International system of units (SI).1 R.1.1SI units and circuit quantities.1 R.1.2Metric prefixes (SI prefixes)2 R.1.3Metric conversion.3 R.1.4The unit factor method.4 R.2 Scientific notation.6 R.2.1Write in scientific notation.6 R.3 Engineering notation.8 R.3.1Write in engineering notation 8 Summary10 Self-test12 Chapter R is a review of basic math fundamentals. There is a self-test at the end of the chapter that can test readers’ understanding of the material. Students can take the self-test before beginning the chapter to determine how much they know about the topic. Those who do well may decide to move on to the next chapter without reading the lesson. R.1International system of units (SI) R.1.1SI units and circuit quantities Metric system (SI – International System of Units): SI system is the world’s most widely used system of measurement. It is based on the basic units of meter, kilogram, second, etc. ●SI originates from the French ‘Le Syste `me International d’Unite ′s’, which means the International System of Units or the metric system to most people. ●Each physical quantity has an SI unit. There are seven basic units of the SI system and they are listed in Table R.1. SI Units – International System of Units (SI) is the world’s most widely used system of measurement. – There are seven base units of the SI system: m, kg, s, A, K, mol, and cd. Derived quantities: All other metric units can be derived from the seven SI basic units that are called ‘‘derived quantities.’’ Some derived SI Units for circuit quan- tities are given in Table R.2. R.1.2Metric prefixes (SI prefixes) Metric prefixes (SI prefixes) ●Sometimes, we come across very large or small numbers when doing circuit analysis and calculation. A metric prefix (or SI prefix) is often used in the circuit calculation to reduce the number of zeroes. ●Large and small numbers are made by adding SI prefixes. A metric prefix is a modifier on the root unit that is in multiples of 10. ●In general science, the most common metric prefixes such as milli, centi, and kilo are used. In circuit analysis, more metric prefixes such as nano and pico are used. Table R.3 contains a complete list of metric prefixes. Table R.1SI base units QuantityQuantity symbolUnitUnit symbol LengthlMeterm MassMKilogramkg TimetSeconds Electric currentIAmpereA TemperatureTKelvinK Amount of substancemMolemol Intensity of lightICandelacd Table R.2Some circuit quantities and their SI units QuantityQuantity symbolUnitUnit symbol VoltageVVoltV ResistanceROhmW ChargeQCoulombC PowerPWattW EnergyWJouleJ Electromotive forceE or VSVoltV ConductanceGSiemensS ResistivityrOhm ? meterW ? m . . 2Understandable electric circuits: key concepts, 2nd edition R.1.3Metric conversion Metric conversion table Power of 101031021011?10?110?210?3 PrefixkilohectodekaExample: meter, ampere, volt, etc. ?decicentimilli Symbolkhda?dcm Larger_____________________________________________________ Smaller Steps for metric conversion through decimal movement ●Identify the number of places to move on the metric conversion table. ●Move the decimal point. –Convert a smaller unit to a larger unit: move the decimal point to the left. –Convert a larger unit to a smaller unit: move the decimal point to the right. Table R.3Metric prefix table (the most commonly used prefixes are shown in bold.) PrefixSymbol (abbreviation) Exponential (power of 10) Multiple value (in full) yottaY10241,000,000,000,000,000,000,000,000 zettaZ10211,000,000,000,000,000,000,000 exaE10181,000,000,000,000,000,000 petaP10151,000,000,000,000,000 teraT10121,000,000,000,000 gigaG1091,000,000,000 megaM1061,000,000 myriamy10410,000 kilok1031,000 hectoh102100 dekada1010 decid10?10.1 centic10?20.01 millim10?30.001 microm10?60.000 001 nanon10?90.000 000 001 picop10?120.000 000 000 001 femtof10?150.000 000 000 000 001 attoa10?180.000 000 000 000 000 001 zeptoz10?210.000 000 000 000 000 000 001 yoctoy10?240.000 000 000 000 000 000 000 001 Note: m is a Greek letter called ‘‘mu’’ (see ‘‘Appendix A’’ for a list of Greek letters). Quantities and units3 Example R.1: 326 mm ?(?) m ●Identify mm (millimeters) and m (meters) on the conversion table. Count places from mm to m:3 places dmeter .cm 321 ●Move three decimal places.(1 m ?1,000 mm) Convertasmallerunit(mm)toalarger(m)unit:movethedecimalpointtotheleft. 326.mm = 0.326 m Move the decimal point three places to the left (326?326.). Example R.2: 4.675 kA?(?) A ●Identify kA (kilo amperes) and A (amperes) on the conversion table. Count places from kA to A:three places khda ampere ●Move three decimal places.(1 kA?1,000 A)123 Convertalargerunit(kA)toasmaller(A)unit:movethedecimalpointtotheright. 4.765 kA = 4,765 A Move the decimal point three places to the right. Example R.3: 30.5 mV ?(?) kV ●Identify mV (millivolts) and km (kilometers) on the conversion table. Count places from mV to kV: six places k hda volt. dc m ●Move six decimal places.(1 kV?1,000,000 mV)654321 Convertasmallerunit(mV)toalarger(kV)unit:movethedecimalpointtotheleft. 30.5 mV = 0.0000305 kV Move the decimal point six places to the left (add 0s). R.1.4The unit factor method Convert units using the unit factor method (or the factor-label method) ●Write the original term as a fraction (over 1).Example: 10 g can be written as 10g 1 ●Write the conversion formula as a fraction 1 e T or e T 1 : 4Understandable electric circuits: key concepts, 2nd edition Example:1 m ?100 cmcan be writtenas 1 m e100 cmT or e100 cmT 1m (Put the desired or unknown unit on the top.) ●Multiply the original term by 1 e T or e T 1 : (Cancel out the same units.) Metric conversion using the unit factor method: Example R.4: 1,200 V?(?) kV ●Write the original term (the left side) as a fraction: 1;200 V ? 1;200 V 1 ●Writetheconversionformulaas afraction.1kV ? 1;000 V: 1 kV e1;000 VT ‘‘kV’’ is the desired unit. ●Multiply:1;200 V ? 1;200V 1 ? 1 kV e1;000VT ? 1;200 kV 1;000 ? 1:2 kV The units ‘‘V’’ cancel out. Example R.5: 30 cm ?(?) mm ●Write the original term (the left side) as a fraction: 30 cm ? 30 cm 1 ●Write the conversion formula as a fraction. 1cm ? 10 mm : e10 mmT 1cm ‘‘mm’’ is the desired unit. ●Multiply:30 cm ? 30cm 1 ? 10 mm e1cmT ? e30Te10Tmm 1 ? 300 mm The units ‘‘cm’’ cancel out. Quantities and units5 Adding and subtracting SI measurements: Example R.6:3 A3,000 mA1 A?1,000 mA ? 2;000 mA?2;000 mA 1;000 mA Combine after converting to the same unit. Example R.7:25 kW25,000 W1 kW? 1,000 W t4 Wt4 W 25;004 W R.2Scientific notation R.2.1Write in scientific notation Scientific notation is a special way of concisely expressing very large and small numbers. Example R.8:300,000,000?3?108m/sThe speed of light. 0.00000000000000000016 ?1.6?10?19CAn electron. Scientific notation It is a product of a number between 1 and 10 and power of 10. N × 10±n Scientific notationExample N? 10?n1 ? N 1076 is not between 1 and 10. 8.2? 10130.82? 10140.82 1053.7 is not between 1 and 10. Writing a number in scientific notation Example R.9:Step ●Move the decimal point after the first nonzero digit. 0.0079 37213000. n?3n?7 ●Determine n (the power of 10) by counting the number of places you moved the decimal. ●If the decimal point is moved to the right: ?10?n 0.0079 = 7.9 × 10-3 3 places to the right ●If the decimal point is moved to the left: ?10n 37213000. = 3.7213×107 7 places to the left Example R.10: Write in scientific notation. 1.2340000 ? 2340000: ? 2:34 ? 1066 places to the left;?10n 2.0:000000439 ? 4:39 ? 10?77 places to the right;?10?n Example R.11: Write in standard (or ordinary) form. 1.6:4275 ? 104? 64;2752.2:9 ? 10?3? 0:0029 Quantities and units7 Example R.12: Simplify and write in scientific notation. 1. e4:9?10?3Te3:82?108T ? e4:9?3:82Te10?3t8T Multiply coefficients of10?n; aman? amtn ? e18:718?105T18:718 10; this is not in scientific notation: ? e1:8718?106T 1:8718 0), the actual current direction is consistent with the assumed or reference direction. –If I 0), the actual voltage polarity is consistent with the assumed reference polarity. ●If V 0: the actual current direction is consistent with the reference current direction. – If I 0: the actual voltage polarity is consistent with the reference voltage polarity. – If V 0, actual current direction is consistent with the reference current direction. ●If I 0: actual voltage polarity is consistent with the reference voltage polarity. ●If V 0, meaning the component absorption (or consumption) of energy. ●When a component in a circuit has non-mutually related reference polarity of current and voltage, power is negative, i.e., P 0 (absorption energy). –If a circuit has non-mutually related reference polarity of current and voltage: P 0 , the resistor absorbs energy. (a) P 0(b) P 0, the resistor absorbs energy. ●Power for R1and R2(a to c): P3? ?EeTI ? ?20 VeT 2 AeT ? ?40 WP I1 I3must be current entering node A to satisfy SIin?SIout i.e., I1tI3? I2or5AtI3?6A,therefore,I3? 1 A I1I2 A ab Figure 2.21Supernode B BC I7 = ? I5 = 4 A I2 = 6 A I1 = 5 A I3 I6 = 1 A A I4 D Figure 2.22Circuit for Example 2.15 Basic laws of electric circuits61 ●At node B:Since current entering node B is I2?6 A currents exiting node B isI5?4 A,soI2I5 I4must be current exiting node B to satisfy SIin?SIout i.e., I2?I4tI5or6A?I4t4A,therefore,I4? 2 A ●Prove it at node C: I4?I3tI6, 2 A?1 At1 A, 2 A?2 A (proved)SIin?SIout (I3is the current entering node A; I4is the current exiting node B.) 2.3.6Some important circuit terminologies Several important circuit terminologies ●Node: The intersectional point of two or more current paths where current has several possible paths to flow. ●Branch: A current path between two nodes where one or more circuit com- ponents is in series. ●Loop: A complete current path where current flows back to the start. ●Mesh: A loop in the circuit that does not contain any other loops (non-redun- dant loop). Note ●A mesh is always a loop, but a loop is not necessarily a mesh. ●A mesh can be analogized as a windowpane, and a loop may include several such windowpanes. Example 2.16: List the nodes, branches, meshes, and loops in Figure 2.23. Solution: ●Node:four nodes—A, B, C, and D ●Branch:six branches—AB, BD, AC, BC, CD, and AD ●Mesh:1, 2, and 3 ●Loop:1, 2, 3, A-B-D-C-A, A-B-D-A, etc. A B C D 12 3 Figure 2.23Illustration for Example 2.16 62Understandable electric circuits: key concepts, 2nd edition 2.4Voltage source and current source 2.4.1Ideal voltage source Power supply It is a circuit device that provides electrical energy to drive the system. ●A power supply is a source that can provide EMF (electromotive force) and current to operate the circuit. ●The power supply can be classified into two categories: voltage source and current source. Ideal voltage source It is a two-terminal circuit device that can provide a constant output voltage Vab, across its terminals, and is shown in Figure 2.24(a). ●Voltage of the ideal voltage source, VS, will not change even if an external circuit such as a load RL, is connected to it as shown in Figure 2.24(b), so it is an independent voltage source. ●The voltage of the ideal voltage source is independent of variations in its external circuit or load. ●The ideal voltage source has a zero internal resistance (RS?0), and it can provide maximum current to the load. The characteristic curve of an ideal voltage source ●Current in the ideal voltage source is dependent on the variations in its external circuit. ●When the load resistance RLchanges, the current in the ideal voltage source also changes since I? V/RL. ●The characteristic curve of an ideal voltage source is shown in Figure 2.24(c). The terminal voltage Vabfor an ideal voltage source is a constant, and same as the source voltage (Vab?VS), regardless of its load resistance RL. Ideal voltage source – It can provide a constant terminal voltage that is independent of the variations in its external circuit, Vab? VS. – Its internal resistance, RS? 0. – Its current depends on the variations in its external circuit. a b Ideal voltage source Ideal voltage source with a load Characteristic curve I RL V + + – + – – VS V 0 (c)(b) (a) VSVS I or t Figure 2.24Ideal voltage source Basic laws of electric circuits63 2.4.2Real voltage source Real voltage source (or voltage source) ●Usually a real-life application of a voltage source such as a battery, DC gen- erator, or DC power supply will not reach a perfect constant output voltage after it is connected to an external circuit or load, since nothing is perfect. ●The realvoltagesourcesallhaveanonzerointernalresistanceRS.Vab?VS?IRS ●The real voltage source (or voltage source) can be represented as an ideal vol- tage source VSin series with an internal resistor RSas shown in Figure 2.25(a). ●Once a load resistor RLis connected to the voltage source (Figure 2.25(b)), the terminal voltage of the source Vabwill change if the load resistance RLchanges. Small internal resistance RS ●Since the internal resistance RSis usually very small, Vabwill be a little bit lower than the source voltage VS(Vab?VS– IRS). I ? VS RSt RL ●A smaller internal resistance can also provide a higher current through the external circuit of the real voltage source because I “? VS RS#tRL (apply Ohm’s law in Figure 2.25(b)). ●Once the load resistance RLchanges, current I in this circuit will change, and the terminal voltage Vabalso changes. This is why the terminal voltage of the real voltage source is not possible to keep at an ideal constant level (Vab6? VS). ●The internal resistance of a real voltage source usually is much smaller than the load resistance, i.e., RS? RL, so the voltage drop on the internal resistance (IRS