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 Thevenin’s and Norton’s Theorems 113
Showing What You Can Do with Thevenin’s and Norton’s Theorems 114
Finding the Norton and Thevenin Equivalents for Complex Source Circuits 115
Applying Thevenin’s theorem 117
Finding the Thevenin equivalent of a circuit with a single independent voltage source 117
Applying Norton’s theorem 119
Using source transformation to find Thevenin or Norton 122
A shortcut: Finding Thevenin or Norton equivalents with source transformation 122
Finding the Thevenin equivalent of a circuit with multiple independent sources 122
Finding Thevenin 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 Thevenin 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 Thevenin 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 Thevenin 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 a 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
