Electrical Circuits: A Primer

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 Electric Circuits: A Primer 1 Contents 6 Preface 14 I Static Circuits and Kirchhoff's Laws 2mm 16 Static Fields, Energy, and Power 18 Potential Energy Concepts 18 An Electric Field: Potential Source Model 20 A Conductor 21 Definition of a Voltage 22 Path Independence 24 Charged Particles in Motion: Current 25 Current Source 26 Power and Energy 26 Passive Sign Convention 27 Conservation of Power 28 Example: Conservation of Energy and Power 28 Demonstration of Conservation of Power 30 Discussion 30 Electrical Circuits and Circuit Elements 32 The Resistor 32 Concept of a Node 33 Dependent Voltage and Current Sources 35 A Model for the Bipolar Junction Transistor 35 The Operational Amplifier 37 Discussion 37 Kirchhoff's Loop and Current Laws 38 Concept of a Loop: Kirchhoff's Loop Law 39 Series and Parallel Circuit Elements 40 Conservation of Charge: Kirchhoff's Nodal or Current Law 41 Series Resistors and Voltage Division 41 Parallel Resistors and Current Division 43 Discussion 45 The Nodal Method of Circuit Analysis 46 Choosing the Potentials in the Circuit 46 Choosing the Currents 48 Applying the Kirchhoff Loop Law, Kirchhoff Current Law, and Ohm's Law 48 The Kirchhoff Loop Law 48 Ohm's Law 49 The Kirchhoff Current Law 49 Mathematical Solution 50 Power Consumed and Delivered in the Circuit 52 Software for Circuit Analysis 52 Octave 53 Combining Independent and Dependent Sources 54 A Worked Example 54 Discussion 57 Fixed Potential Between Nodes: Supernode 58 A Circuit Containing a Supernode 58 The Mesh Method for Circuit Analysis 62 An Example of the Application of the Mesh Method 62 Supermesh: Current Source in Common 64 Discussion 66 Linearity, Superposition, and Equivalence 68 Using Superposition: Analyze a Circuit 69 Turn off the Current Source (Source with 0 Amps) 70 Turn off the Potential Source (Source with 0 Volts) 70 Combine Two Separate Solutions 70 Equivalence 71 Discussion 74 Thevenin and Norton Equivalent Circuits 76 The Thevenin Model 76 Computing the Thevenin Equivalent Model 77 Thevenin Potential VTH 77 Thevenin Resistance RTH 79 The Norton Model 80 A Second Example 81 Comments 83 Maximum Power Transfer 84 Maximum Power Transfer Theorem 84 An Example: Maximum Power Transfer 86 Comments 88 II Dynamic Sources, Energy Storage, and Transients 2mm 90 The Capacitor and the Inductor 92 The Capacitor 92 Capacitors in Series and Parallel 96 Inductor 96 Inductors in Series and Parallel 98 Comments and Summary 98 The Source-Free RC Circuit 100 The Source-Free RC Circuit Prototype 100 A First Source-Free RC Circuit Example 102 A Second Source-Free RC Circuit Example 103 The Circuit for Negative Time 103 The Circuit for Positive Time 104 A Third Source-Free RC Circuit Example 105 The Circuit for Negative Time 107 The Circuit for Positive Time 107 Comments 109 The Source-Free RL Circuit 110 The Source-Free RL Circuit Prototype 110 A First Example of a Source-Free RL Circuit 111 The RL Circuit for Negative Time 112 The RL Circuit for Positive Time 113 Second Example of a Source-Free RL Circuit 114 Comments 117 Step Response of an RC Circuit 120 The Step Response RC Circuit Prototype 121 Negative Time Circuit and Its Analysis 121 Positive Time Circuit and Its Analysis 122 Numerical Solution Based on MATLAB 124 Numerical Solution 125 Numerical Results 127 Examples: Step Response of an RC Circuit 128 A First Example 128 Simplification and the Prototype Form 128 Solution Based on the Simplified Circuit 129 A Second Example 131 The Negative Time Circuit 132 The Positive Time Circuit 133 Discussion 134 Step Response of an RL Circuit 136 Negative Time 137 Positive Time 137 Discussion 137 Examples: Step Response of RL Circuits 140 A First Example: Step Response RL Circuit 140 Negative Time Circuit 140 Positive Time Circuit 141 The Solution for i(t) 141 A Second Example: Step Response RL Circuit 142 The Negative Time Circuit 142 The Positive Time Circuit 143 Series RLC Source-Free Circuits 146 Series RLC Prototype 147 Solution of the Second Order DE 148 is Real: The Overdamped Case 149 is Imaginary: The Underdamped Case 149 = 0: The Critically Damped Case 149 Numerical Solution Using MATLAB 150 Results 152 Appendix: Solution of Second Order DE 154 Examples: Series RLC Source-Free Circuits 158 A First Example 158 Negative Time Circuit 159 Positive Time Circuit 160 Discussion 161 A Second Example 161 The Circuit for Negative Time 162 The Circuit for Positive Time 162 Discussion 163 Source-Free Parallel RLC Circuits 164 Solution of the Second Order DE 165 is Real 166 is Imaginary 166 Discussion 166 Examples for a Parallel RLC Circuit 168 A First Example 168 A Second Example 169 Negative Time Circuit 170 Positive Time Circuit 171 The Use of Circuit Simulators 172 III AC: Sinusoidal Voltage and Current Sources 2mm 174 Sinusoidal Sources, the Phasor and Impedance 176 The Theory of the Phasor 177 A Resistor Using the Phasor Notation 178 Time to Phasor Domain Transformation 180 A Capacitor Using the Phasor: Impedance 181 An Inductor Using the Phasor: Impedance 183 Discussion 185 Circuit Analysis Based on Phasor Domain Representation 186 A First Example 186 Phasor Domain Analysis 188 Discussion 188 A Second Example 189 Comments 191 Dependent and Independent Sources: Phasor Domain 192 A First Example 192 A Second Example 194 Comments 195 Superposition: Phasors 196 Analysis Based on the AC Potential Source 197 Analysis Based on the AC Current Source 198 Analysis Based on the Static Voltage Source 200 Applying Superposition in the Time Domain 201 Comments 201 The Maximum Power Transfer Theorem and Resonance 202 Thevenin's Theorem for AC Circuits 202 Thevenin Potential 203 Thevenin Impedance ZTH 204 Maximum Power Transfer 204 Resonance 205 Series Resonance 205 Parallel Resonance 206 Summary 208 AC Power Concepts 210 Energy, Instantaneous and Average Power 210 Average Power for AC Circuits and Electrical Systems: Time Domain Analysis 211 Average Power for AC: Phasor Domain 212 Root Mean Square Power 214 Summary 214 Power Factor and Power Factor Correction 216 Power Absorbed by the Resistor 216 Power Absorbed by the Capacitor 217 Power Absorbed by the Inductor 218 Power Factor 219 Power Factor Correction 219 Power Factor Correction Example 222 Summary of Power Terminology 225 Magnetically Coupled Circuits 226 An Example: Circuit Making Use of Mutual Coupling 227 A Second Example: Mutual Coupling 229 Linear Transformer 231 The Ideal Transformer 233 Comments 235 Frequency Response and System Transfer Function 236 Example: Transfer Function for an RC Circuit 237 Example: Third Order Low Pass Filter 239 Analysis in the Time Domain 240 Bode Plot 243 Summary 243 Three Phase Systems: An Introduction 246 Balanced Three Phase System 246 Analysis of a Y-Y Balanced System 250 Analysis of a - Balanced System 251 Y and Transformations 253 Y to Transformation 254 to Y Transformation 254 Comments 254 Concluding Remarks and Further Reading 256 Digital Simulation and Design 257 History of EE 257 About the Author 260 Index 262 Electric,circuits;,Artech,House Electric circuits,Artech House 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 This book deals with electric circuit theory at an introductory level, and keeps derivations to a minimum. It is written in three parts, covering static circuits in the time domain, dynamic circuits, and sinusoidal sources and the so-called AC paradigm, in that order.