Circuit Analysis For Dummies

John M. Santiago Jr., PhD, served in the United States Air Force (USAF) for 26 years. During that time, he held a variety of leadership positions in technical program management, acquisition development, and operation research support. While assigned in Europe, he spearheaded more than 40 international scientific and engineering conferences/workshops.

• Introduction 1About This Book 1Conventions Used in This Book 1What You’re Not to Read 2Foolish Assumptions 2How This Book is Organized 2Part I: Getting Started with Circuit Analysis 2Part II: Applying Analytical Methods for Complex Circuits 3Part III: Understanding Circuits with Transistors and Operational Amplifiers 3Part IV: Applying Time-Varying Signals to First- and Second-Order Circuits 3Part V: Advanced Techniques and Applications in Circuit Analysis 3Part VI: The Part of Tens 3Icons Used in This Book 4Where to Go from Here 4Part I: Getting Started with Circuit Analysis 5Chapter 1: Introducing Circuit Analysis 7Getting Started with Current and Voltage 7Going with the flow with current 8Recognizing potential differences with voltage 9Staying grounded with zero voltage 9Getting some direction with the passive sign convention 10Beginning with the Basic Laws 11Surveying the Analytical Methods for More-Complex Circuits 11Introducing Transistors and Operational Amplifiers 12Dealing with Time-Varying Signals, Capacitors, and Inductors 13Avoiding Calculus with Advanced Techniques 13Chapter 2: Clarifying Basic Circuit Concepts and Diagrams 15Looking at Current-Voltage Relationships 15Absorbing energy with resistors 16Applying Ohm’s law to resistors 16Calculating the power dissipated by resistors 18Offering no resistance: Batteries and short circuits 18Batteries: Providing power independently 19Short circuits: No voltage, no power 19Facing infinite resistance: Ideal current sources and open circuits 20All or nothing: Combining open and short circuits with ideal switches 20Mapping It All Out with Schematics 21Going in circles with loops 22Getting straight to the point with nodes 24Chapter 3: Exploring Simple Circuits with Kirchhoff’s Laws 25Presenting Kirchhoff’s Famous Circuit Laws 25Kirchhoff’s voltage law (KVL): Conservation of energy 26Identifying voltage rises and drops 26Forming a KVL equation 27Kirchhoff’s current law (KCL): Conservation of charge 29Tracking incoming and outgoing current 29Calculating KCL 30Tackling Circuits with KVL, KCL, and Ohm’s Law 31Getting batteries and resistors to work together 31Starting with voltage 32Bringing in current 32Combining device equations with KVL 33Summarizing the results 34Sharing the same current in series circuits 34Climbing the ladder with parallel circuits 36Describing total resistance using conductance 37Using a shortcut for two resistors in parallel 38Finding equivalent resistor combinations 38Combining series and parallel resistors 40Chapter 4: Simplifying Circuit Analysis with Source Transformation and Division Techniques 41Equivalent Circuits: Preparing for the Transformation 42Transforming Sources in Circuits 45Converting to a parallel circuit with a current source 45Changing to a series circuit with a voltage source 47Divvying It Up with the Voltage Divider 49Getting a voltage divider equation for a series circuit 49Figuring out voltages for a series circuit with two or more resistors 51Finding voltages when you have multiple current sources 52Using the voltage divider technique repeatedly 55Cutting to the Chase Using the Current Divider Technique 57Getting a current divider equation for a parallel circuit 57Figuring out currents for parallel circuits 59Finding currents when you have multiple voltage sources 60Using the current divider technique repeatedly 63Part II: Applying Analytical Methods for Complex Circuits 65Chapter 5: Giving the Nod to Node-Voltage Analysis 67Getting Acquainted with Node Voltages and Reference Nodes 67Testing the Waters with Node Voltage Analysis 69What goes in must come out: Starting with KCL at the nodes 70Describing device currents in terms of node voltages with Ohm’s law 70Putting a system of node voltage equations in matrix form 72Solving for unknown node voltages 73Applying the NVA Technique 74Solving for unknown node voltageswith a current source 74Dealing with three or more node equations 76Working with Voltage Sources in Node-Voltage Analysis 80Chapter 6: Getting in the Loop on Mesh Current Equations 83Windowpanes: Looking at Meshes and Mesh Currents 83Relating Device Currents to Mesh Currents 84Generating the Mesh Current Equations 86Finding the KVL equations first 87Ohm’s law: Putting device voltages in terms of mesh currents 87Substituting the device voltages into the KVL equations 88Putting mesh current equations into matrix form 89Solving for unknown currents and voltages 89Crunching Numbers: Using Meshes to Analyze Circuits 90Tackling two-mesh circuits 90Analyzing circuits with three or more meshes 92Chapter 7: Solving One Problem at a Time Using Superposition 95Discovering How Superposition Works 95Making sense of proportionality 96Applying superposition in circuits 98Adding the contributions of each independent source 100Getting Rid of the Sources of Frustration 101Short circuit: Removing a voltage source 101Open circuit: Taking out a current source 102Analyzing Circuits with Two Independent Sources 103Knowing what to do when the sources are two voltage sources 103Proceeding when the sources are two current sources 105Dealing with one voltage source and one current source 107Solving a Circuit with Three Independent Sources 108Chapter 8: Applying Thévenin’s and Norton’s Theorems 113Showing What You Can Do with Thévenin’s and Norton’s Theorems 114Finding the Norton and Thévenin Equivalents for Complex Source Circuits 115Applying Thévenin’s theorem 117Finding the Thévenin equivalent of a circuit with a single independent voltage source 117Applying Norton’s theorem 119Using source transformation to find Thévenin or Norton 122A shortcut: Finding Thévenin or Norton equivalents with source transformation 122Finding the Thévenin equivalent of a circuit with multiple independent sources 122Finding Thévenin or Norton with superposition 124Gauging Maximum Power Transfer: A Practical Application of Both Theorems 127Part III: Understanding Circuits with Transistors and Operational Amplifiers 131Chapter 9: Dependent Sources and the Transistors That Involve Them 133Understanding Linear Dependent Sources: Who Controls What 134Classifying the types of dependent sources 134Recognizing the relationship between dependent and independent sources 136Analyzing Circuits with Dependent Sources 136Applying node-voltage analysis 137Using source transformation 138Using the Thévenin technique 140Describing a JFET Transistor with a Dependent Source 142Examining the Three Personalities of Bipolar Transistors 145Making signals louder with the common emitter circuit 146Amplifying signals with a common base circuit 149Isolating circuits with the common collector circuit 151Chapter 10: Letting Operational Amplifiers Do the Tough Math Fast 155The Ins and Outs of Op-Amp Circuits 155Discovering how to draw op amps 156Looking at the ideal op amp and its transfer characteristics 157Modeling an op amp with a dependent source 158Examining the essential equations for analyzing ideal op-amp circuits 159Looking at Op-Amp Circuits 160Analyzing a noninverting op amp 160Following the leader with the voltage follower 162Turning things around with the inverting amplifier 163Adding it all up with the summer 164What’s the difference? Using the op-amp subtractor 166Increasing the Complexity of What You Can Do with Op Amps 168Analyzing the instrumentation amplifier 168Implementing mathematical equations electronically 170Creating systems with op amps 171Part IV: Applying Time-Varying Signals to First- and Second-Order Circuits 173Chapter 11: Making Waves with Funky Functions 175Spiking It Up with the Lean, Mean Impulse Function 176Changing the strength of the impulse 178Delaying an impulse 178Evaluating impulse functions with integrals 179Stepping It Up with a Step Function 180Creating a time-shifted, weighted step function 181Being out of step with shifted step functions 182Building a ramp function with a step function 182Pushing the Limits with the Exponential Function 184Seeing the Signs with Sinusoidal Functions 186Giving wavy functions a phase shift 187Expanding the function and finding Fourier coefficients 189Connecting sinusoidal functions to exponentials with Euler’s formula 190Chapter 12: Spicing Up Circuit Analysis with Capacitors and Inductors 193Storing Electrical Energy with Capacitors 193Describing a capacitor 194Charging a capacitor (credit cards not accepted) 195Relating the current and voltage of a capacitor 195Finding the power and energy of a capacitor 196Calculating the total capacitance for parallel and series capacitors 199Finding the equivalent capacitance of parallel capacitors 199Finding the equivalent capacitance of capacitors in series 200Storing Magnetic Energy with Inductors 200Describing an inductor 201Finding the energy storage of an attractive inductor 202Calculating total inductance for series and parallel inductors 203Finding the equivalent inductance for inductors in series 203Finding the equivalent inductance for inductors in parallel 204Calculus: Putting a Cap on Op-Amp Circuits 205Creating an op-amp integrator 205Deriving an op-amp differentiator 207Using Op Amps to Solve Differential Equations Really Fast 208Chapter 13: Tackling First-Order Circuits  211Solving First-Order Circuits with Diff EQ 211Guessing at the solution with thenatural exponential function 213Using the characteristic equation for a first-order equation 214Analyzing a Series Circuit with a Single Resistor and Capacitor 215Starting with the simple RC series circuit 215Finding the zero-input response 217Finding the zero-state response byfocusing on the input source 219Adding the zero-input and zero-state responses to find the total response 222Analyzing a Parallel Circuit with a Single Resistor and Inductor 224Starting with the simple RL parallel circuit 225Calculating the zero-input response for an RL parallel circuit 226Calculating the zero-state response for an RL parallel circuit 228Adding the zero-input and zero-state responses to find the total response 230Chapter 14: Analyzing Second-Order Circuits 233Examining Second-Order Differential Equations with Constant Coefficients 233Guessing at the elementary solutions: The natural exponential function 235From calculus to algebra: Using the characteristic equation 236Analyzing an RLC Series Circuit 236Setting up a typical RLC series circuit 237Determining the zero-input response 239Calculating the zero-state response 242Finishing up with the total response 245Analyzing an RLC Parallel Circuit Using Duality 246Setting up a typical RLC parallel circuit 247Finding the zero-input response 249Arriving at the zero-state response 250Getting the total response 251Part V: Advanced Techniques and Applications in Circuit Analysis 253Chapter 15: Phasing in Phasors for Wave Functions 255Taking a More Imaginative Turn with Phasors 256Finding phasor forms 256Examining the properties of phasors 258Using Impedance to Expand Ohm’s Law to Capacitors and Inductors 259Understanding impedance 260Looking at phasor diagrams 261Putting Ohm’s law for capacitors in phasor form 262Putting Ohm’s law for inductors in phasor form 263Tackling Circuits with Phasors 263Using divider techniques in phasor form 264Adding phasor outputs with superposition 266Simplifying phasor analysis with Thévenin and Norton 268Getting the nod for nodal analysis 270Using mesh-current analysis with phasors 271Chapter 16: Predicting Circuit Behavior with Laplace Transform Techniques 273Getting Acquainted with the Laplace Transform and Key Transform Pairs 273Getting Your Time Back with the Inverse Laplace Transform 276Rewriting the transform with partial fraction expansion 276Expanding Laplace transforms with complex poles 278Dealing with transforms with multiple poles 280Understanding Poles and Zeros of F(s) 282Predicting the Circuit Response with Laplace Methods 285Working out a first-order RC circuit 286Working out a first-order RL circuit 290Working out an RLC circuit 292Chapter 17: Implementing Laplace Techniques for Circuit Analysis 295Starting Easy with Basic Constraints 296Connection constraints in the s-domain 296Device constraints in the s-domain 297Independent and dependent sources 297Passive elements: Resistors, capacitors, and inductors 297Op-amp devices 299Impedance and admittance 299Seeing How Basic Circuit Analysis Works in the s-Domain 300Applying voltage division with series circuits 300Turning to current division for parallel circuits 302Conducting Complex Circuit Analysis in the s-Domain 303Using node-voltage analysis 303Using mesh-current analysis 304Using superposition and proportionality 305Using the Thévenin and Norton equivalents 309Chapter 18: Focusing on the Frequency Responses 313Describing the Frequency Response and Classy Filters 314Low-pass filter 315High-pass filter 316Band-pass filters 316Band-reject filters 317Plotting Something: Showing Frequency Response à la Bode 318Looking at a basic Bode plot 319Poles, zeros, and scale factors: Picturing Bode plots from transfer functions 320Turning the Corner: Making Low-Pass and High-Pass Filters with RC Circuits 325First-order RC low-pass filter (LPF) 325First-order RC high-pass filter (HPF) 326Creating Band-Pass and Band-Reject Filters with RLC or RC Circuits 327Getting serious with RLC series circuits 327RLC series band-pass filter (BPF) 327RLC series band-reject filter (BRF) 330Climbing the ladder with RLC parallel circuits 330RC only: Getting a pass with a band-pass and band-reject filter 332Part VI: The Part of Tens 335Chapter 19: Ten Practical Applications for Circuits  337Potentiometers 337Homemade Capacitors: Leyden Jars 338Digital-to-Analog Conversion Using Op Amps 338Two-Speaker Systems 338Interface Techniques Using Resistors 338Interface Techniques Using Op Amps 339The Wheatstone Bridge 339Accelerometers 339Electronic Stud Finders 340555 Timer Circuits 340Chapter 20: Ten Technologies Affecting Circuits 341Smartphone Touchscreens 341Nanotechnology 341Carbon Nanotubes 342Microelectromechanical Systems 342Supercapacitors 343The Memristor 343Superconducting Digital Electronics 343Wide Bandgap Semiconductors 343Flexible Electronics 344Microelectronic Chips that Pair Up with Biological Cells 344Index 345