First and second order electric and electronic circuits contain energy storage elements, capacitors and inductors, fundamental to both time and frequency domain circuit response behavior, including exponential decay, overshoot, ringing, and frequency domain resonance. First and Second Order Circuits and Equations provides an insightful and detailed learning and reference resource for circuit theory and its many perspectives and duals, such as voltage and current, inductance and capacitance, and serial and parallel. Organized and presented to make each information topic immediately accessible, First and Second Order Circuits and Equations offers readers the opportunity to learn circuit theory faster and with greater understanding. First and Second Order Circuits and Equations readers will also find: Root locus charts of second order characteristic equation roots both in terms of damping factor ζ as well as damping constant α. Detailed treatment of quality factor Q and its relationship to bandwidth and damping in both frequency and time domains. Inductor and capacitor branch relationship step response insights in terms of calculus intuition. Derivations of voltage divider and current divider formulae in terms of Kirchhoff’s laws. First and Second Order Circuits and Equations is an essential tool for electronic industry professionals learning circuits on the job, as well as for electrical engineering, mechanical engineering, and physics students learning circuits and their related differential equations.

Table of Contents:
About the Author xvii Acknowledgments xix Part 1 Circuit Elements and Resistive Circuits 1 1 Ohm’s Law, Branch Relationships, and Sources 3 1.1 Chapter Summary and Polarity Reference 3 1.2 Branch Relationships and I–V Characteristics 5 1.3 Ohm’s Law, Resistance, and Resistors 8 1.4 Current, Voltage, and Sources Overview 11 1.5 Voltage Sources 12 1.6 Current and Current Sources 14 2 Kirchhoff’s Laws and Resistive Dividers 17 2.1 Kirchhoff’s Laws and Dividers Comparison Summary 17 2.2 Kirchhoff’s Laws Physical Analogies 18 2.3 Source Polarity in KVL – Time and Frequency Domains 19 2.4 Formulae Summary for Resistors in Series and Parallel 26 2.5 Resistors in Series 27 2.6 Voltage Dividers 32 2.7 Parallel Circuit Element Formulae 33 2.8 Current Dividers 36 2.9 Current and Voltage Intuitions 37 3 Opamp Models and Resistive Circuits 39 3.1 Introduction and Ideal Opamp Model Results Overview 39 3.2 Ideal Opamp Resistive Amplifier Circuits 41 4 Reactive Circuit Elements 45 4.1 Capacitor and Inductor Comparison Summary 45 4.2 Capacitors 47 4.3 Inductors 51 Part 2 First-Order Circuits 57 5 First-Order RC and RL Circuits Introduction 59 5.1 What are First-Order Circuits? 59 5.2 Intuitive First-Order Circuit Frequency Domain Examples 61 5.3 First-Order Natural and Step Response Overview 62 6 First-Order Frequency Domain Response 65 6.1 First-Order Frequency Response Overview 65 6.2 Series RC High-pass Filter Frequency Response 71 6.3 Series RL Low-pass Filter Frequency Response 89 6.4 Series RC Low-pass Filter Frequency Response 108 6.6 Parallel RL Low-pass Filter Frequency Response 128 6.7 Parallel RC High-pass Filter Frequency Response 139 7 Discharging and Charging First-Order RC and RL Circuits 149 7.1 Discharging RC and RL Circuits – Natural Response 149 7.2 Charging RC and RL Circuits – Step Response 153 7.3 The Exponential Time Constant τ (Tau) 155 7.4 Pulse Train Time Constants Simulation Example 156 8 Natural Response of RC and RL Circuits 159 8.1 RC and RL Circuits Natural Response Summary 159 8.2 RC and RL Natural Response Derivation 160 8.3 RC Natural Response (ZIR) Time Constants and Initial Current 166 8.4 Natural Response of Series RL with Voltage Source 167 8.5 First-Order RC and RL Natural Response Summary 171 9 First-Order Step Response of RC and RL Circuits 173 9.1 First-Order Step Response Summary Overview 173 9.2 Intuitive Analysis of RC and RL Step Response 177 9.3 Series RC Step Response Solution Using a Particular Solution 181 9.4 Series RL Step Response Solution Using a Particular Solution 184 9.5 Series RL Step Response with Voltage Source 188 9.6 First-Order Step Response Summary 190 10 Complete Response of First-Order RC and RL Circuits 191 10.1 First-Order Complete Response Summary Overview 191 10.2 Series RC Complete Response Examples 192 10.3 RL Complete Response Example and Intuitive Analysis 195 10.4 Complete Response with Switches 199 10.5 Complete Response General Derivation and Formulae 202 11 First-Order Opamp Integrator and Differentiator Circuits 207 11.1 RC Integrator Circuit Step Response 207 11.2 Opamp Integrator Circuit 208 11.3 Opamp Inverting Differentiator Circuit 210 Part 3 Second-Order Circuits 211 12 Second-Order RLC Circuits Overview 213 12.1 What are Second-Order Circuits? 213 12.2 Resonance in the Frequency Domain 215 12.3 Second-Order RLC Transfer Functions and Q 216 12.4 Two Time Domain Responses 217 13 Second-Order RLC Frequency Response 219 13.1 Series and Parallel RLC Impedance 219 13.2 Second-Order RLC Frequency Response 229 13.3 Second-Order RLC Bandwidth and Quality Factor 238 14 Second-Order RLC Circuit Natural Response 251 14.1 Second-Order Natural Response Introduction 251 14.2 Second-order Natural Response in Terms of R, L, and c 254 14.3 Second-order Damping Variables α and ω 0 283 14.4 Second-order Damping Ratio ζ – Zeta 291 15 Second-Order RLC Step and Complete Response 299 15.1 RLC Step Response Intuitive Overview 299 15.2 RLC Step Response Detailed Analyses 301 15.3 Parallel RLC Intuitive Step Response Example 303 15.4 Complete RLC Time Domain Response 305 Part 4 Technical Background Topics 307 16 Complex Numbers, Exponentials, and Phasors 309 16.1 Imaginary and Complex Numbers 309 16.2 Exponentials, Complex Numbers, and Trigonometry 311 16.3 Phasors and Sinusoidal Steady State 314 Index 319