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CONTENTS PREFACE .................................... ERROR! BOOKMARK NOT DEFINED. 1. INTRODUCTION TO CIRCUIT THEORY .. ERROR! BOOKMARK NOT DEFINED. 1.1. CIRCUIT VARIABLES - BASIC TERMS and DEFINITIONS.. Error! Bookmark not defined. 1.2. CLASSIFICATION of CIRCUIT THEORY PROBLEMS .......... Error! Bookmark not defined. 2. DC ANALYSIS ......................... ERROR! BOOKMARK NOT DEFINED. 2.1. CIRCUIT ELEMENTS ...................................................... Error! Bookmark not defined. CLASSIFICATION ............................................................. Error! Bookmark not defined. PASSIVE TWO-TERMINAL ELEMENTS ........................ Error! Bookmark not defined. Resistor ................................................................................ Error! Bookmark not defined. Voltmeter............................................................................. Error! Bookmark not defined. Ammeter .............................................................................. Error! Bookmark not defined. ACTIVE TWO-TERMINAL ELEMENTS ......................... Error! Bookmark not defined. Voltage source ..................................................................... Error! Bookmark not defined. Current source .................................................................... Error! Bookmark not defined. 2.2. CIRCUIT DIAGRAM and KIRCHHOFF’s LAWS ........ Error! Bookmark not defined. CIRCUIT DIAGRAM .......................................................... Error! Bookmark not defined. KIRCHHOFF’S LAWS ....................................................... Error! Bookmark not defined. 2.3. ANALYSIS of COMPLEX CIRCUITS ............................ Error! Bookmark not defined. GENERALIZED KIRCHHOFF’S ANALYSIS .................. Error! Bookmark not defined. NODE VOLTAGE (NODAL) ANALYSIS ........................ Error! Bookmark not defined. 2.4. ENERGY and POWER CONSERVATION PRINCIPLE............ Error! Bookmark not defined. 2.5. TWO-TERMINAL SUBCIRCUIT, THEVENIN’s/NORTON’s THEOREM .... Error! Bookmark not defined. PASSIVE TWO-TERMINAL SUBCIRCUIT ..................... Error! Bookmark not defined. Series connection of resistors, Voltage divider ................ Error! Bookmark not defined. Parallel connection of resistors, Current divider ............ Error! Bookmark not defined. ACTIVE TWO-TERMINAL SUBCIRCUIT ...................... Error! Bookmark not defined. Thevenin’s theorem ............................................................ Error! Bookmark not defined. Norton’s theorem................................................................ Error! Bookmark not defined. Practical sources ................................................................. Error! Bookmark not defined. 2.6. MAXIMUM POWER TRANSFER THEOREM ............. Error! Bookmark not defined. 2.7. TRANSFER FUNCTION, SUPERPOSITION PRINCIPLE ....... Error! Bookmark not defined. TRANSFER FUNCTION .................................................... Error! Bookmark not defined. One-dimensional case ......................................................... Error! Bookmark not defined. Multi-dimensional case ...................................................... Error! Bookmark not defined. SUPERPOSITION PRINCIPLE .......................................... Error! Bookmark not defined. 2.8. SEPARATION PRINCIPLE (SOURCE SUBSTITUTION THEOREM) .......... Error! Bookmark not defined. 2.9. MULTI-TERMINAL ELEMENTS ................................... Error! Bookmark not defined. ELEMENT DESCRIPTION – CONDUCTANCE MATRIX ............ Error! Bookmark not defined. Passive multi-terminal element ......................................... Error! Bookmark not defined. Two-terminal element (one-port) ............................................................. Error! Bookmark not defined. Three-terminal element ............................................................................ Error! Bookmark not defined. Two-port .................................................................................................. Error! Bookmark not defined. Active multi-terminal element ........................................... Error! Bookmark not defined. OTHER MATRICES OF MULTI-TERMINAL ELEMENT ............. Error! Bookmark not defined. ANALYSIS OF CIRCUITS WITH MULTI-TERMINAL ELEMENT(S) .................. Error! Bookmark not defined. 2.10. DEPENDENT (CONTROLLED) ELEMENTS ............. Error! Bookmark not defined. Arbitrary dependent element - description ..................... Error! Bookmark not defined. Controlled sources - description ....................................... Error! Bookmark not defined. Use of controlled sources to element modeling ................ Error! Bookmark not defined. Transistor ................................................................................................. Error! Bookmark not defined. Operational amplifier ............................................................................... Error! Bookmark not defined. Arbitrary three-terminal or two-port element .......................................... Error! Bookmark not defined. Analysis of circuits containing controlled sources........... Error! Bookmark not defined. 2.11. DESIGN TOLERANCES, SENSITIVITY ANALYSIS Error! Bookmark not defined. Designation of the maximum design deviation of circuit variableError! Bookmark not defined. Worst case analysis .................................................................................. Error! Bookmark not defined. Sensitivity analysis .................................................................................. Error! Bookmark not defined. Designation of parameter design tolerances .................... Error! Bookmark not defined. 2.12. ANALYSIS OF NONLINEAR CIRCUITS .................... Error! Bookmark not defined. GRAPHICAL ANALYSIS .................................................. Error! Bookmark not defined. Series connection of elements .................................................................. Error! Bookmark not defined. Parallel connection of elements ............................................................... Error! Bookmark not defined. Single-loop circuit ................................................................................... Error! Bookmark not defined. Circuit with one nonlinear element .......................................................... Error! Bookmark not defined. ANALYSIS BASED ON PWL APPROXIMATION .......... Error! Bookmark not defined. ANALYSIS BASED ON NEWTON-RAPHSON ITERATION SCHEME ................ Error! Bookmark not defined. 2.13. NETWORK ANALOGIES – MAGNETIC CIRCUITS Error! Bookmark not defined. 3. TRANSIENT ANALYSIS .......... ERROR! BOOKMARK NOT DEFINED. 3.1. KIRCHHOFF’S LAWS and PASSIVE ELEMENT LAWS ......... Error! Bookmark not defined. KIRCHHOFF’S LAWS ....................................................... Error! Bookmark not defined. PASSIVE ELEMENT LAWS .............................................. Error! Bookmark not defined. Resistor ................................................................................ Error! Bookmark not defined. Capacitor ............................................................................. Error! Bookmark not defined. Coil (Inductor) .................................................................... Error! Bookmark not defined. Passive elements – Summary ............................................. Error! Bookmark not defined. 3.2. TRANSIENT ANALYSIS in CIRCUITS with STEP EXCITATION Error! Bookmark not defined. FORCED RESPONSE ......................................................... Error! Bookmark not defined. 1st order circuit – time-domain method ............................ Error! Bookmark not defined. 1st order circuit – s-domain method .................................. Error! Bookmark not defined. 1st order circuit – boundary values based method .......... Error! Bookmark not defined. 2nd order circuit – s-domain method ................................. Error! Bookmark not defined. NATURAL RESPONSE ...................................................... Error! Bookmark not defined. COMPLETE RESPONSE: NATURAL RESPONSE + FORCED RESPONSE.......... Error! Bookmark not defined. 3.3. TRANSIENT ANALYSIS in CIRCUITS with ARBITRARY EXCITATION ... Error! Bookmark not defined. TRANSFER FUNCTION – PROPERTIES and SELECTED EXAMPLES ................ Error! Bookmark not defined. Properties ............................................................................ Error! Bookmark not defined. Transfer functions of selected circuits .............................. Error! Bookmark not defined. Integrator ................................................................................................. Error! Bookmark not defined. Differentiator ........................................................................................... Error! Bookmark not defined. TRANSFER FUNCTION BASED TRANSIENT ANALYSIS - EXAMPLES ........... Error! Bookmark not defined. Practical step ............................................................................................ Error! Bookmark not defined. Practical pulse .......................................................................................... Error! Bookmark not defined. 4. AC STEADY-STATE ANALYSIS .............. ERROR! BOOKMARK NOT DEFINED. 4.1. ALTERNATING CURRENT – RMS VALUE, PHASOR NOTATION ............. Error! Bookmark not defined. 4.2. PHASOR ANALYSIS ......................................................... Error! Bookmark not defined. KIRCHHOFF’S LAWS ....................................................... Error! Bookmark not defined. ELEMENT LAWS ............................................................... Error! Bookmark not defined. Resistor ................................................................................ Error! Bookmark not defined. Inductor ............................................................................... Error! Bookmark not defined. Capacitor ............................................................................. Error! Bookmark not defined. GENERAL TWO-TERMINAL PHASOR CIRCUIT, PHASOR IMPEDANCE ........ Error! Bookmark not defined. ALGORITHM OF AC STEADY-STATE ANALYSIS ...... Error! Bookmark not defined. 4.3. AC STEADY-STATE POWER ......................................... Error! Bookmark not defined. MEASURES OF POWER ................................................... Error! Bookmark not defined. Instantaneous power .......................................................... Error! Bookmark not defined. Average or real power........................................................ Error! Bookmark not defined. Apparent power .................................................................. Error! Bookmark not defined. Reactive power.................................................................... Error! Bookmark not defined. Complex power ................................................................... Error! Bookmark not defined. MAXIMUM POWER TRANSFER ..................................... Error! Bookmark not defined. 4.4. FREQUENCY CHARACTERISTICS OF TWO-TERMINAL SUBCIRCUIT . Error! Bookmark not defined. IDEAL ELEMENTS – SUMMARY ................................... Error! Bookmark not defined. Resistor ................................................................................ Error! Bookmark not defined. Inductor ............................................................................... Error! Bookmark not defined. Capacitor ............................................................................. Error! Bookmark not defined. PRACTICAL COIL and PRACTICAL CAPACITOR ........ Error! Bookmark not defined. RESONANT CIRCUITS ..................................................... Error! Bookmark not defined. Series-resonant circuit RLC............................................... Error! Bookmark not defined. Parallel-resonant circuit RLC ........................................... Error! Bookmark not defined. Complex-resonant circuit .................................................. Error! Bookmark not defined. 4.5. TRANSFER FUNCTION APPROACH - FREQUENCY RESPONSE............... Error! Bookmark not defined. BODE (LOGARITHMIC) PLOT ........................................ Error! Bookmark not defined. FILTERS .............................................................................. Error! Bookmark not defined. Low-Pass Filter - LPF ........................................................ Error! Bookmark not defined. High-Pass Filter - HPF ....................................................... Error! Bookmark not defined. Band-Pass Filter - BPF ...................................................... Error! Bookmark not defined. Band-Stop Filter - BSF ...................................................... Error! Bookmark not defined. 4.6. ANALYSIS OF CIRCUIT RESPONSE WHEN ONE CIRCUIT CONSTANT VARIES ....................................................................................... Error! Bookmark not defined. 4.7. MUTUAL INDUCTANCE AND TRANSFORMERS ..... Error! Bookmark not defined. MUTUAL INDUCTANCE – BASIC TRANSFORMER ... Error! Bookmark not defined. IDEAL TRANSFORMER ................................................... Error! Bookmark not defined. PRACTICAL IRON-CORE TRANSFORMER .................. Error! Bookmark not defined. 4.8. THREE-PHASE CIRCUITS .............................................. Error! Bookmark not defined. WYE-WYE SYSTEMS ....................................................... Error! Bookmark not defined. DELTA-DELTA and WYE-DELTA SYSTEMS ................ Error! Bookmark not defined. COMBINATIONAL SYSTEMS ......................................... Error! Bookmark not defined. POWER IN THREE-PHASE SYSTEMS ............................ Error! Bookmark not defined. 5. TRANSMISSION LINE............. ERROR! BOOKMARK NOT DEFINED. 5.1. INTRODUCTION ............................................................... Error! Bookmark not defined. 5.2. TRANSIENT ANALYSIS .................................................. Error! Bookmark not defined. 5.3. AC ANALYSIS – STANDING WAVES ........................... Error! Bookmark not defined. MATCHED LOAD LINE .................................................... Error! Bookmark not defined. ARBITRARY TERMINATION .......................................... Error! Bookmark not defined. Open-circuited line ............................................................. Error! Bookmark not defined. Short-circuited line ............................................................. Error! Bookmark not defined. TRANSMISSION LINE as CIRCUIT ELEMENT, INPUT IMPEDANCE ................ Error! Bookmark not defined. APPENDIX A - LAPLACE TRANSFORM ..... ERROR! BOOKMARK NOT DEFINED. DEFINITION ....................................................................... Error! Bookmark not defined. PROPERTIES ...................................................................... Error! Bookmark not defined. INVERSE TRANSFORMATION - HEAVISIDE’S FORMULA ..... Error! Bookmark not defined. LAPLACE TRANSFORM DICTIONARY ......................... Error! Bookmark not defined. APPENDIX B – COMPLEX NUMBERS ........ ERROR! BOOKMARK NOT DEFINED. APPENDIX C – TERMS AND CONCEPTS .. ERROR! BOOKMARK NOT DEFINED. REFERENCES ............................ ERROR! BOOKMARK NOT DEFINED. INDEX .......................................... ERROR! BOOKMARK NOT DEFINED. PREFACE The aim of this book is to provide introductory, yet comprehensive, treatment of circuit analysis and design, to lay down some important and necessary foundations for subsequent use in later engineering courses, such as Signal Theory, Electronics Fundamentals and others. Since this book is designated primarily for the first or the second year introductory courses, the presentation is geared to students who are being exposed to the basic concepts of electric circuits for the first time. However, it is assumed that students have possessed some elementary knowledge of physics and have some understanding of freshman calculus, such as differential-integral calculus and vector-matrix formulation and solution of linear systems of equations. Other more complex mathematical topics, necessary to describe the considered circuit theory problems, such as i) Laplace transform and singularity functions, ii) algebraic manipulation of complex numbers, iii) solution of nonlinear systems of equations, are raised in a limited and self-contained manner, and are not required as prerequisite background. The first two are the subjects of appendices, the third is developed in the chapter in which it is needed. The book does not contain proofs of theorems, as they can be found in commonly available books dealing with the same subject. Resistance from expanding the length of the book to the extremes sometimes found in current practice was Author’s motivation. On the other hand all the theorems and definitions are illustrated by many practical examples. It should be emphasized, that while presenting basic components of electric circuits and introducing different techniques of circuit analysis, particular attention is given to the practical aspects and the physical interpretation of results. The main aim of the book is to provide students with essential tools of analysis of circuits together with many important concepts underlying the theory of electronic circuits. Care has been taken to fashion the selection and order of content to be of use to the electrical engineering baccalaureate students, but also to students of other engineering disciplines, as the analysis and design of electric circuits is a critical skill for all engineers. Nowadays, English is the binding language in engineering world and the book provides complete vocabulary of terms and concepts used in the Circuit Theory. They are collected in the Appendix C glossary, together with Polish equivalents. This makes the book a very useful educational aid, addressed not only to English speaking students, but also to Polish speaking students having some minor fluency in written English – indispensable for today’s engineers. The book consists of five basic parts – chapters and three appendices. The general order of the content has been selected so that students may learn as many of the techniques of circuit analysis and design as possible in the simplest context. These logically divide into i) real numbers domain - DC analysis), ii) time-domain and Laplace transform domain - transient analysis), iii) phasor or frequency domain - AC analysis. These analyses are discussed first for circuits with lumped constants, next the transmission line transient and AC analyses are considered. In the brief introductory Chapter 1, the electric variables used to describe circuit elements are revised and problems of circuit analysis and design are classified. The second Chapter is intended to provide a thorough treatment of circuit analysis based on direct current (dc) circuits. First, linear circuits are discussed. Then, nonlinear resistive circuits and their network analogy (magnetic circuits) are studied. Many important definitions and fundamental principles are given. Various computational techniques are presented with numerous practical examples, such that the student is expected to be conversant with the principles of circuits before entering the next Chapter 3. The third Chapter and the fourth Chapter are intended to provide a thorough treatment of transient analysis and alternate current (ac) analysis, respectively. Some of the concepts taught in Chapter 1 are revised and extended to more useful and general practical application in time domain and in frequency domain. The fifth Chapter is intended to provide a thorough treatment of circuits with distributed in place (not lumped) constants. Transmission line is discussed, first its transient response to aperiodic input, then, steady-state sinusoidal response. It is recommended to organize the material here into a two-semester introductory course, with 30 hours in Semester 1 and 30-45 hours in Semester 2, and to proceed chapter by chapter. Appendix A on Laplace transform and singularity functions should be reviewed before studying Chapter 3, Appendix B on complex numbers should be reviewed before studying Chapter 4, which relies heavily on complex and phasor algebra. The major results of the theory may appear quite subtle or even abstract, and to make them easy to comprehend numerous practical problems have been provided. The problems are organized into: i) examples and ii) drill problems. Each section of each chapter has numerous step-by-step solved examples and ends with drill problems which are designed to range over all topics of the section and they are generally simple. They can be well used as the formative assessment test or final examination test problems. In all there are near 80 exercises and near 300 drill problems. APPENDIX C – TERMS AND CONCEPTS Acceptability region Region in the parameter space P with boundaries Obszar sprawności designated by the design constraints on circuit variables: F jmin , F jmax . Active circuit Obwód aktywny Active element Admittance in s-domain Y (s ) Admittance in phasor-domain Y ( j ) Element aktywny Alternating current i Admitancja operatorowa Reciprocal of Z (s ) . Admitancja symboliczna Reciprocal of Z ( j ) , Y ( j ) G ( ) jB( ) Prąd sinusoidalny Apparent power S Artificial or temporary magnet Attenuation constant Sinusoidally time-varying current i I m sin( t i ) , I m - amplitude or peak value, - angular frequency, i - initial phase angle. Ampere Amper A Ampere-turns Amperozwoje At Amplitude Amplituda (peak value) (wartość szczytowa) Im , Um Angular (radian) Pulsacja (częstotliwość frequency Circuit that contains at least one active element, independent source. Element that may deliver energy to a circuit. kątowa) Moc pozorna See Current See Magnetomotive force See Alternating current See Alternating current, Frequency Power that defines the maximum capacity of the sinusoidal source, S P pf 1 UI . Unit: volt-ampere [ V A ] . Elektromagnes Tłumienność Autotransformer Autotransformator Average or real power P Moc czynna See Electromagnet or solenoid coil See Propagation constant Transformer that has windings both magnetically and electrically interconnected. Average value of the instantaneous power in the ac circuit. Represents the power delivered by the source or absorbed by the circuit. Unit: watt [W]. T P 1 / T pdt UI cos , 0 cos pf is the so called power factor.
