Electric Circuits: A Primer

Description

This new resource provides a comprehensive and concise introduction of the underpinnings and fundamentals of electrical circuits. Models, the limitations of models, and examples are clearly explained. The book examines circuits with static sources and explains how to reduce any circuit to a system of linear equations. Moreover, the book presents dynamic sources that exhibit transient phenomena that require the solution of linear differential equations. MATLAB code is used throughout the book to help solve key problems and assist engineers in the field. Additionally, this hands-on volume explores circuits with sinusoidal sources also known as the AC paradigm. The book provides another key mathematical tool known as a phasor which are mathematical objects based on complex number theory. The book emphasizes solutions for computing power, interpreting power and energy, and compensating electrical systems if the power factor is too low. Professionals are offered design guidance throughout the book with many real-world examples. Electric Circuits: A Primer......Page 1 Contents......Page 6 Preface......Page 14 I Static Circuits and Kirchhoff's Laws 2mm......Page 16 Potential Energy Concepts......Page 18 An Electric Field: Potential Source Model......Page 20 A Conductor......Page 21 Definition of a Voltage......Page 22 Path Independence......Page 24 Charged Particles in Motion: Current......Page 25 Power and Energy......Page 26 Passive Sign Convention......Page 27 Example: Conservation of Energy and Power......Page 28 Discussion......Page 30 The Resistor......Page 32 Concept of a Node......Page 33 A Model for the Bipolar Junction Transistor......Page 35 Discussion......Page 37 Kirchhoff's Loop and Current Laws......Page 38 Concept of a Loop: Kirchhoff's Loop Law......Page 39 Series and Parallel Circuit Elements......Page 40 Series Resistors and Voltage Division......Page 41 Parallel Resistors and Current Division......Page 43 Discussion......Page 45 Choosing the Potentials in the Circuit......Page 46 The Kirchhoff Loop Law......Page 48 The Kirchhoff Current Law......Page 49 Mathematical Solution......Page 50 Software for Circuit Analysis......Page 52 Octave......Page 53 A Worked Example......Page 54 Discussion......Page 57 A Circuit Containing a Supernode......Page 58 An Example of the Application of the Mesh Method......Page 62 Supermesh: Current Source in Common......Page 64 Discussion......Page 66 Linearity, Superposition, and Equivalence......Page 68 Using Superposition: Analyze a Circuit......Page 69 Combine Two Separate Solutions......Page 70 Equivalence......Page 71 Discussion......Page 74 The Thevenin Model......Page 76 Thevenin Potential VTH......Page 77 Thevenin Resistance RTH......Page 79 The Norton Model......Page 80 A Second Example......Page 81 Comments......Page 83 Maximum Power Transfer Theorem......Page 84 An Example: Maximum Power Transfer......Page 86 Comments......Page 88 II Dynamic Sources, Energy Storage, and Transients 2mm......Page 90 The Capacitor......Page 92 Inductor......Page 96 Comments and Summary......Page 98 The Source-Free RC Circuit Prototype......Page 100 A First Source-Free RC Circuit Example......Page 102 The Circuit for Negative Time......Page 103 The Circuit for Positive Time......Page 104 A Third Source-Free RC Circuit Example......Page 105 The Circuit for Positive Time......Page 107 Comments......Page 109 The Source-Free RL Circuit Prototype......Page 110 A First Example of a Source-Free RL Circuit......Page 111 The RL Circuit for Negative Time......Page 112 The RL Circuit for Positive Time......Page 113 Second Example of a Source-Free RL Circuit......Page 114 Comments......Page 117 Step Response of an RC Circuit......Page 120 Negative Time Circuit and Its Analysis......Page 121 Positive Time Circuit and Its Analysis......Page 122 Numerical Solution Based on MATLAB......Page 124 Numerical Solution......Page 125 Numerical Results......Page 127 Simplification and the Prototype Form......Page 128 Solution Based on the Simplified Circuit......Page 129 A Second Example......Page 131 The Negative Time Circuit......Page 132 The Positive Time Circuit......Page 133 Discussion......Page 134 Step Response of an RL Circuit......Page 136 Discussion......Page 137 Negative Time Circuit......Page 140 The Solution for i(t)......Page 141 The Negative Time Circuit......Page 142 The Positive Time Circuit......Page 143 Series RLC Source-Free Circuits......Page 146 Series RLC Prototype......Page 147 Solution of the Second Order DE......Page 148 = 0: The Critically Damped Case......Page 149 Numerical Solution Using MATLAB......Page 150 Results......Page 152 Appendix: Solution of Second Order DE......Page 154 A First Example......Page 158 Negative Time Circuit......Page 159 Positive Time Circuit......Page 160 A Second Example......Page 161 The Circuit for Positive Time......Page 162 Discussion......Page 163 Source-Free Parallel RLC Circuits......Page 164 Solution of the Second Order DE......Page 165 Discussion......Page 166 A First Example......Page 168 A Second Example......Page 169 Negative Time Circuit......Page 170 Positive Time Circuit......Page 171 The Use of Circuit Simulators......Page 172 III AC: Sinusoidal Voltage and Current Sources 2mm......Page 174 Sinusoidal Sources, the Phasor and Impedance......Page 176 The Theory of the Phasor......Page 177 A Resistor Using the Phasor Notation......Page 178 Time to Phasor Domain Transformation......Page 180 A Capacitor Using the Phasor: Impedance......Page 181 An Inductor Using the Phasor: Impedance......Page 183 Discussion......Page 185 A First Example......Page 186 Discussion......Page 188 A Second Example......Page 189 Comments......Page 191 A First Example......Page 192 A Second Example......Page 194 Comments......Page 195 Superposition: Phasors......Page 196 Analysis Based on the AC Potential Source......Page 197 Analysis Based on the AC Current Source......Page 198 Analysis Based on the Static Voltage Source......Page 200 Comments......Page 201 Thevenin's Theorem for AC Circuits......Page 202 Thevenin Potential......Page 203 Maximum Power Transfer......Page 204 Series Resonance......Page 205 Parallel Resonance......Page 206 Summary......Page 208 Energy, Instantaneous and Average Power......Page 210 Average Power for AC Circuits and Electrical Systems: Time Domain Analysis......Page 211 Average Power for AC: Phasor Domain......Page 212 Summary......Page 214 Power Absorbed by the Resistor......Page 216 Power Absorbed by the Capacitor......Page 217 Power Absorbed by the Inductor......Page 218 Power Factor Correction......Page 219 Power Factor Correction Example......Page 222 Summary of Power Terminology......Page 225 Magnetically Coupled Circuits......Page 226 An Example: Circuit Making Use of Mutual Coupling......Page 227 A Second Example: Mutual Coupling......Page 229 Linear Transformer......Page 231 The Ideal Transformer......Page 233 Comments......Page 235 Frequency Response and System Transfer Function......Page 236 Example: Transfer Function for an RC Circuit......Page 237 Example: Third Order Low Pass Filter......Page 239 Analysis in the Time Domain......Page 240 Summary......Page 243 Balanced Three Phase System......Page 246 Analysis of a Y-Y Balanced System......Page 250 Analysis of a - Balanced System......Page 251 Y and Transformations......Page 253 Comments......Page 254 Concluding Remarks and Further Reading......Page 256 History of EE......Page 257 About the Author......Page 260 Index......Page 262