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 1

About This Book 1

Conventions Used in This Book 1

What You’re Not to Read 2

Foolish Assumptions 2

How This Book is Organized 2

Part I: Getting Started with Circuit Analysis 2

Part II: Applying Analytical Methods for Complex Circuits 3

Part III: Understanding Circuits with Transistors and Operational Amplifiers 3

Part IV: Applying Time-Varying Signals to First- and Second-Order Circuits 3

Part V: Advanced Techniques and Applications in Circuit Analysis 3

Part VI: The Part of Tens 3

Icons Used in This Book 4

Where to Go from Here 4

Part I: Getting Started with Circuit Analysis 5

Chapter 1: Introducing Circuit Analysis 7

Getting Started with Current and Voltage 7

Going with the flow with current 8

Recognizing potential differences with voltage 9

Staying grounded with zero voltage 9

Getting some direction with the passive sign convention 10

Beginning with the Basic Laws 11

Surveying the Analytical Methods for More-Complex Circuits 11

Introducing Transistors and Operational Amplifiers 12

Dealing with Time-Varying Signals, Capacitors, and Inductors 13

Avoiding Calculus with Advanced Techniques 13

Chapter 2: Clarifying Basic Circuit Concepts and Diagrams 15

Looking at Current-Voltage Relationships 15

Absorbing energy with resistors 16

Applying Ohm’s law to resistors 16

Calculating the power dissipated by resistors 18

Offering no resistance: Batteries and short circuits 18

Batteries: Providing power independently 19

Short circuits: No voltage, no power 19

Facing infinite resistance: Ideal current sources and open circuits 20

All or nothing: Combining open and short circuits with ideal switches 20

Mapping It All Out with Schematics 21

Going in circles with loops 22

Getting straight to the point with nodes 24

Chapter 3: Exploring Simple Circuits with Kirchhoff’s Laws 25

Presenting Kirchhoff’s Famous Circuit Laws 25

Kirchhoff’s voltage law (KVL): Conservation of energy 26

Identifying voltage rises and drops 26

Forming a KVL equation 27

Kirchhoff’s current law (KCL): Conservation of charge 29

Tracking incoming and outgoing current 29

Calculating KCL 30

Tackling Circuits with KVL, KCL, and Ohm’s Law 31

Getting batteries and resistors to work together 31

Starting with voltage 32

Bringing in current 32

Combining device equations with KVL 33

Summarizing the results 34

Sharing the same current in series circuits 34

Climbing the ladder with parallel circuits 36

Describing total resistance using conductance 37

Using a shortcut for two resistors in parallel 38

Finding equivalent resistor combinations 38

Combining series and parallel resistors 40

Chapter 4: Simplifying Circuit Analysis with Source Transformation and Division Techniques 41

Equivalent Circuits: Preparing for the Transformation 42

Transforming Sources in Circuits 45

Converting to a parallel circuit with a current source 45

Changing to a series circuit with a voltage source 47

Divvying It Up with the Voltage Divider 49

Getting a voltage divider equation for a series circuit 49

Figuring out voltages for a series circuit with two or more resistors 51

Finding voltages when you have multiple current sources 52

Using the voltage divider technique repeatedly 55

Cutting to the Chase Using the Current Divider Technique 57

Getting a current divider equation for a parallel circuit 57

Figuring out currents for parallel circuits 59

Finding currents when you have multiple voltage sources 60

Using the current divider technique repeatedly 63

Part II: Applying Analytical Methods for Complex Circuits 65

Chapter 5: Giving the Nod to Node-Voltage Analysis 67

Getting Acquainted with Node Voltages and Reference Nodes 67

Testing the Waters with Node Voltage Analysis 69

What goes in must come out: Starting with KCL at the nodes 70

Describing device currents in terms of node voltages with Ohm’s law 70

Putting a system of node voltage equations in matrix form 72

Solving for unknown node voltages 73

Applying the NVA Technique 74

Solving for unknown node voltageswith a current source 74

Dealing with three or more node equations 76

Working with Voltage Sources in Node-Voltage Analysis 80

Chapter 6: Getting in the Loop on Mesh Current Equations 83

Windowpanes: Looking at Meshes and Mesh Currents 83

Relating Device Currents to Mesh Currents 84

Generating the Mesh Current Equations 86

Finding the KVL equations first 87

Ohm’s law: Putting device voltages in terms of mesh currents 87

Substituting the device voltages into the KVL equations 88

Putting mesh current equations into matrix form 89

Solving for unknown currents and voltages 89

Crunching Numbers: Using Meshes to Analyze Circuits 90

Tackling two-mesh circuits 90

Analyzing circuits with three or more meshes 92

Chapter 7: Solving One Problem at a Time Using Superposition 95

Discovering How Superposition Works 95

Making sense of proportionality 96

Applying superposition in circuits 98

Adding the contributions of each independent source 100

Getting Rid of the Sources of Frustration 101

Short circuit: Removing a voltage source 101

Open circuit: Taking out a current source 102

Analyzing Circuits with Two Independent Sources 103

Knowing what to do when the sources are two voltage sources 103

Proceeding when the sources are two current sources 105

Dealing with one voltage source and one current source 107

Solving a Circuit with Three Independent Sources 108

Chapter 8: Applying Thévenin’s and Norton’s Theorems 113

Showing What You Can Do with Thévenin’s and Norton’s Theorems 114

Finding the Norton and Thévenin Equivalents for Complex Source Circuits 115

Applying Thévenin’s theorem 117

Finding the Thévenin equivalent of a circuit with a single independent voltage source 117

Applying Norton’s theorem 119

Using source transformation to find Thévenin or Norton 122

A shortcut: Finding Thévenin or Norton equivalents with source transformation 122

Finding the Thévenin equivalent of a circuit with multiple independent sources 122

Finding Thévenin or Norton with superposition 124

Gauging Maximum Power Transfer: A Practical Application of Both Theorems 127

Part III: Understanding Circuits with Transistors and Operational Amplifiers 131

Chapter 9: Dependent Sources and the Transistors That Involve Them 133

Understanding Linear Dependent Sources: Who Controls What 134

Classifying the types of dependent sources 134

Recognizing the relationship between dependent and independent sources 136

Analyzing Circuits with Dependent Sources 136

Applying node-voltage analysis 137

Using source transformation 138

Using the Thévenin technique 140

Describing a JFET Transistor with a Dependent Source 142

Examining the Three Personalities of Bipolar Transistors 145

Making signals louder with the common emitter circuit 146

Amplifying signals with a common base circuit 149

Isolating circuits with the common collector circuit 151

Chapter 10: Letting Operational Amplifiers Do the Tough Math Fast 155

The Ins and Outs of Op-Amp Circuits 155

Discovering how to draw op amps 156

Looking at the ideal op amp and its transfer characteristics 157

Modeling an op amp with a dependent source 158

Examining the essential equations for analyzing ideal op-amp circuits 159

Looking at Op-Amp Circuits 160

Analyzing a noninverting op amp 160

Following the leader with the voltage follower 162

Turning things around with the inverting amplifier 163

Adding it all up with the summer 164

What’s the difference? Using the op-amp subtractor 166

Increasing the Complexity of What You Can Do with Op Amps 168

Analyzing the instrumentation amplifier 168

Implementing mathematical equations electronically 170

Creating systems with op amps 171

Part IV: Applying Time-Varying Signals to First- and Second-Order Circuits 173

Chapter 11: Making Waves with Funky Functions 175

Spiking It Up with the Lean, Mean Impulse Function 176

Changing the strength of the impulse 178

Delaying an impulse 178

Evaluating impulse functions with integrals 179

Stepping It Up with a Step Function 180

Creating a time-shifted, weighted step function 181

Being out of step with shifted step functions 182

Building a ramp function with a step function 182

Pushing the Limits with the Exponential Function 184

Seeing the Signs with Sinusoidal Functions 186

Giving wavy functions a phase shift 187

Expanding the function and finding Fourier coefficients 189

Connecting sinusoidal functions to exponentials with Euler’s formula 190

Chapter 12: Spicing Up Circuit Analysis with Capacitors and Inductors 193

Storing Electrical Energy with Capacitors 193

Describing a capacitor 194

Charging a capacitor (credit cards not accepted) 195

Relating the current and voltage of a capacitor 195

Finding the power and energy of a capacitor 196

Calculating the total capacitance for parallel and series capacitors 199

Finding the equivalent capacitance of parallel capacitors 199

Finding the equivalent capacitance of capacitors in series 200

Storing Magnetic Energy with Inductors 200

Describing an inductor 201

Finding the energy storage of an attractive inductor 202

Calculating total inductance for series and parallel inductors 203

Finding the equivalent inductance for inductors in series 203

Finding the equivalent inductance for inductors in parallel 204

Calculus: Putting a Cap on Op-Amp Circuits 205

Creating an op-amp integrator 205

Deriving an op-amp differentiator 207

Using Op Amps to Solve Differential Equations Really Fast 208

Chapter 13: Tackling First-Order Circuits  211

Solving First-Order Circuits with Diff EQ 211

Guessing at the solution with the

natural exponential function 213

Using the characteristic equation for a first-order equation 214

Analyzing a Series Circuit with a Single Resistor and Capacitor 215

Starting with the simple RC series circuit 215

Finding the zero-input response 217

Finding the zero-state response by

focusing on the input source 219

Adding the zero-input and zero-state responses to find the total response 222

Analyzing a Parallel Circuit with a Single Resistor and Inductor 224

Starting with the simple RL parallel circuit 225

Calculating the zero-input response for an RL parallel circuit 226

Calculating the zero-state response for an RL parallel circuit 228

Adding the zero-input and zero-state responses to find the total response 230

Chapter 14: Analyzing Second-Order Circuits 233

Examining Second-Order Differential Equations with Constant Coefficients 233

Guessing at the elementary solutions: The natural exponential function 235

From calculus to algebra: Using the characteristic equation 236

Analyzing an RLC Series Circuit 236

Setting up a typical RLC series circuit 237

Determining the zero-input response 239

Calculating the zero-state response 242

Finishing up with the total response 245

Analyzing an RLC Parallel Circuit Using Duality 246

Setting up a typical RLC parallel circuit 247

Finding the zero-input response 249

Arriving at the zero-state response 250

Getting the total response 251

Part V: Advanced Techniques and Applications in Circuit Analysis 253

Chapter 15: Phasing in Phasors for Wave Functions 255

Taking a More Imaginative Turn with Phasors 256

Finding phasor forms 256

Examining the properties of phasors 258

Using Impedance to Expand Ohm’s Law to Capacitors and Inductors 259

Understanding impedance 260

Looking at phasor diagrams 261

Putting Ohm’s law for capacitors in phasor form 262

Putting Ohm’s law for inductors in phasor form 263

Tackling Circuits with Phasors 263

Using divider techniques in phasor form 264

Adding phasor outputs with superposition 266

Simplifying phasor analysis with Thévenin and Norton 268

Getting the nod for nodal analysis 270

Using mesh-current analysis with phasors 271

Chapter 16: Predicting Circuit Behavior with Laplace Transform Techniques 273

Getting Acquainted with the Laplace Transform and Key Transform Pairs 273

Getting Your Time Back with the Inverse Laplace Transform 276

Rewriting the transform with partial fraction expansion 276

Expanding Laplace transforms with complex poles 278

Dealing with transforms with multiple poles 280

Understanding Poles and Zeros of F(s) 282

Predicting the Circuit Response with Laplace Methods 285

Working out a first-order RC circuit 286

Working out a first-order RL circuit 290

Working out an RLC circuit 292

Chapter 17: Implementing Laplace Techniques for Circuit Analysis 295

Starting Easy with Basic Constraints 296

Connection constraints in the s-domain 296

Device constraints in the s-domain 297

Independent and dependent sources 297

Passive elements: Resistors, capacitors, and inductors 297

Op-amp devices 299

Impedance and admittance 299

Seeing How Basic Circuit Analysis Works in the s-Domain 300

Applying voltage division with series circuits 300

Turning to current division for parallel circuits 302

Conducting Complex Circuit Analysis in the s-Domain 303

Using node-voltage analysis 303

Using mesh-current analysis 304

Using superposition and proportionality 305

Using the Thévenin and Norton equivalents 309

Chapter 18: Focusing on the Frequency Responses 313

Describing the Frequency Response and Classy Filters 314

Low-pass filter 315

High-pass filter 316

Band-pass filters 316

Band-reject filters 317

Plotting Something: Showing Frequency Response à la Bode 318

Looking at a basic Bode plot 319

Poles, zeros, and scale factors: Picturing Bode plots from transfer functions 320

Turning the Corner: Making Low-Pass and High-Pass Filters with RC Circuits 325

First-order RC low-pass filter (LPF) 325

First-order RC high-pass filter (HPF) 326

Creating Band-Pass and Band-Reject Filters with RLC or RC Circuits 327

Getting serious with RLC series circuits 327

RLC series band-pass filter (BPF) 327

RLC series band-reject filter (BRF) 330

Climbing the ladder with RLC parallel circuits 330

RC only: Getting a pass with a band-pass and band-reject filter 332

Part VI: The Part of Tens 335

Chapter 19: Ten Practical Applications for Circuits  337

Potentiometers 337

Homemade Capacitors: Leyden Jars 338

Digital-to-Analog Conversion Using Op Amps 338

Two-Speaker Systems 338

Interface Techniques Using Resistors 338

Interface Techniques Using Op Amps 339

The Wheatstone Bridge 339

Accelerometers 339

Electronic Stud Finders 340

555 Timer Circuits 340

Chapter 20: Ten Technologies Affecting Circuits 341

Smartphone Touchscreens 341

Nanotechnology 341

Carbon Nanotubes 342

Microelectromechanical Systems 342

Supercapacitors 343

The Memristor 343

Superconducting Digital Electronics 343

Wide Bandgap Semiconductors 343

Flexible Electronics 344

Microelectronic Chips that Pair Up with Biological Cells 344

Index 345