A Handbook of Circuit Mathematics for Technical Engineers is designed to provide students and practicing engineers a reference regarding the background and technique for solving most problems in circuit analysis. Using hundreds of equations and examples, the book covers topics ranging from the analysis of simple resistive and reactive networks to complex filters in both the analog and digital domain. The book also presents the characteristics and analysis of input forcing functions from batteries through sine, square, pulse and impulse waves; diodes and transistors, transformers, and operational amplifiers; and the transient response methods of Laplace, Fourier, and the Z-Transform. The appropriate input functions and networks, both passive and active, are illustrated in their simple, complex, and exponential forms so that readers can understand and use each form on problems encountered in day-to-day circuit analysis.
Table of Contents
AN INTRODUCTION. Mathematics, the Language of Engineering. Information is Power. Voltage, Current and the Relationship Between the Two. Thinking and Models-Words, Graphs and Equations. Graphing-Placement of Coordinates and Graphical Representation, the Graphical Solution. Input/Output, Transfer Function, Block Diagrams. FUNDAMENTAL MODELS-RESISTORS IN SERIES AND PARALLEL. An Introduction. Fundamental Networks and Network Laws. Circuit Examples Showing Loop and Branch Currents. Solving Network Equations Using Determinants. Network Theorems. The Analysis of Two-Port, Four Terminal Black Box Networks. An Introduction to Computer Circuit Analysis. BATTERIES, SINE WAVES AND OTHER NICE INPUTS. About This Chapter. Constant Output Generators. Thevenin and Norton Equivalents. Sine and Cosine Wave Generators. Square-Wave Generators. Sawtooth Generators. Unit-Step Generators. Unit-Pulse Generators. RC AND RL CIRCUITS-AN INTRODUCTION TO AC AND TRANSIENT CIRCUIT FUNCTIONS. About This Chapter. Inductors in Series and Parallel. Capacitors in Series and Parallel. The Reactance (AC Resistance) of Inductors and Capacitors. VECTORS, PHASORS, & COMPLEX NUMBERS-THE ICONS OF AC. About This Chapter. Phase Notation and Sinusodial (or Cosinusodial) Waveforms. Real, Imaginary, and Complex Number Arithmetic. The j Operator. The Polar Form. The Exponential Form and Euler's Identity. Complex Number Mathematical Operations. The Complex Variable or S Plane-Poles and Zeros. FILTER MODELS. About This Chapter. The Transfer Function. The Bode Plot. Simple RC and RL Low-Pass Filters. Simple RC and RL High-Pass Filters. Simple RLC Band-Pass Filters. Transmission-Line Originated Constant-K Filters. Transmission-Line Originated M-Derived Filters. Polynomial Filters. Active Filters. Designing Active Filters. RLC CIRCUITS-THERE IS MORE HERE THAN YOU REALIZE. NATURAL AND FORCED RESPONSE. About This Chapter. The Series RC or RL Circuit. The Parallel RC or RL Circuit. An Introduction to the Response of RLC Circuits. The Response of Series RLC Circuits. The Response of Parallel RLC Circuits. The Use of Computers in Calculating and Plotting Resonance Response. DIODES AND TRANSISTORS. An Introduction. The Conceptual Diode. The Operating Parameters and Limitations of Diodes. Diode Models. The Conceptual Two-Junction Transistor. The Common Emitter (CE) Transistor Amplifier. Transistor Biasing. Common Emitter Small-Signal Amplifiers. The Common Base Amplifier. The Common Collector Amplifier. Junction Transistor Equivalent Circuits. Junction Field-Effect Transistors or JFETs. Metal-Oxide Semiconductor Field Effect Transistors-MOSFETs. JFET and MOSFET Equivalent Circuits. TRANSFORMERS AND EQUIVALENT CIRCUITS. About This Chapter. Magnetic Fields and Circuits. Ohm's Law for Magnetic Circuits. The Universal Linearity Problem. Transformer DC, AC, and High Frequency Equivalent Circuit Models Including Losses. Computer Transformer Design. THE OPERATIONAL AMPLIFIER-INTRODUCTION TO OPERATIONAL MATHEMATICS. About This Chapter-The Ideal Operational Amplifier. The Differential Amplifier-The Input Stage of the Operational Amplifier. Errors in the Non-Idea Differential Amplifier. Integrated (IC) Differential Amplifiers. Voltage Level Shifters and the Output Stage-the Complete Op Amp. The Open-Loop Characteristics of Operational Amplifiers. The Closed-Loop (Feedback) Characteristics of Operational Amplifiers. An Introduction to Analog Computing-Analog Computing Circuits. FOURIER SERIES-A MANY SPLENDORED THING. About This Chapter-Analysis, Synthesis, Composition, and Decomposition. Infinite Series. An Introduction to Fourier Series. Finding Fourier Coefficients Using Graphical Techniques. The Exponential Form of the Fourier Series. The Coefficients of Typical Waveforms. The Fourier Spectrum. TRANSIENT ANALYSIS-THE LAPLACE TRANSFORM. About This Chapter. TRANSIENT ANALYSIS-THE FOURIER TRANSFORM AND ITS FFT. About This Chapter. DIGITAL CIRCUITS-SAMPLING, SIMPLE DIGITAL FILTERS AND THE Z TRANSFORM. About This Chapter. CALCULUS FOR TECHNICAL ENGINEERS. About This Chapter. PROBLEM MODELS IN CIRCUIT ANALYSIS. About This Chapter.