Introduction... 1 Part I: Getting Started with Circuit Analysis Part II: Applying Analytical Methods for Complex Circuits...

Transcription

1 Contents at a Glance Introduction... 1 Part I: Getting Started with Circuit Analysis... 5 Chapter 1: Introducing Circuit Analysis...7 Chapter 2: Clarifying Basic Circuit Concepts and Diagrams...15 Chapter 3: Exploring Simple Circuits with Kirchhoff s Laws...25 Chapter 4: Simplifying Circuit Analysis with Source Transformation and Division Techniques...41 Part II: Applying Analytical Methods for Complex Circuits Chapter 5: Giving the Nod to Node-Voltage Analysis...67 Chapter 6: Getting in the Loop on Mesh Current Equations...83 Chapter 7: Solving One Problem at a Time Using Superposition...95 Chapter 8: Applying Thévenin s and Norton s Theorems Part III: Understanding Circuits with Transistors and Operational Amplifiers Chapter 9: Dependent Sources and the Transistors That Involve Them Chapter 10: Letting Operational Amplifiers Do the Tough Math Fast Part IV: Applying Time-Varying Signals to First- and Second-Order Circuits Chapter 11: Making Waves with Funky Functions Chapter 12: Spicing Up Circuit Analysis with Capacitors and Inductors Chapter 13: Tackling First-Order Circuits Chapter 14: Analyzing Second-Order Circuits COPYRIGHTED MATERIAL Part V: Advanced Techniques and Applications in Circuit Analysis Chapter 15: Phasing in Phasors for Wave Functions Chapter 16: Predicting Circuit Behavior with Laplace Transform Techniques Chapter 17: Implementing Laplace Techniques for Circuit Analysis Chapter 18: Focusing on the Frequency Responses...313

2 Part VI: The Part of Tens Chapter 19: Ten Practical Applications for Circuits Chapter 20: Ten Technologies Affecting Circuits Index

3 Table of Contents 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 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 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

4 xii Circuit Analysis For Dummies 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 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 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

5 Table of Contents xiii Part II: Applying Analytical Methods for Complex Circuits Chapter 5: Giving the Nod to Node-Voltage Analysis 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 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 Discovering How Superposition Works...95 Making sense of proportionality...96 Applying superposition in circuits...98 Adding the contributions of each independent source Getting Rid of the Sources of Frustration Short circuit: Removing a voltage source Open circuit: Taking out a current source Analyzing Circuits with Two Independent Sources Knowing what to do when the sources are two voltage sources 103 Proceeding when the sources are two current sources Dealing with one voltage source and one current source Solving a Circuit with Three Independent Sources...108

6 xiv Circuit Analysis For Dummies Chapter 8: Applying Thévenin s and Norton s Theorems Showing What You Can Do with Thévenin s and Norton s Theorems Finding the Norton and Thévenin Equivalents for Complex Source Circuits Applying Thévenin s theorem Finding the Thévenin equivalent of a circuit with a single independent voltage source Applying Norton s theorem Using source transformation to find Thévenin or Norton A shortcut: Finding Thévenin or Norton equivalents with source transformation Finding the Thévenin equivalent of a circuit with multiple independent sources Finding Thévenin or Norton with superposition Gauging Maximum Power Transfer: A Practical Application of Both Theorems Part III: Understanding Circuits with Transistors and Operational Amplifiers Chapter 9: Dependent Sources and the Transistors That Involve Them Understanding Linear Dependent Sources: Who Controls What Classifying the types of dependent sources Recognizing the relationship between dependent and independent sources Analyzing Circuits with Dependent Sources Applying node-voltage analysis Using source transformation Using the Thévenin technique Describing a JFET Transistor with a Dependent Source Examining the Three Personalities of Bipolar Transistors Making signals louder with the common emitter circuit Amplifying signals with a common base circuit Isolating circuits with the common collector circuit Chapter 10: Letting Operational Amplifiers Do the Tough Math Fast The Ins and Outs of Op-Amp Circuits Discovering how to draw op amps Looking at the ideal op amp and its transfer characteristics Modeling an op amp with a dependent source Examining the essential equations for analyzing ideal op-amp circuits...159

7 Table of Contents xv Looking at Op-Amp Circuits Analyzing a noninverting op amp Following the leader with the voltage follower Turning things around with the inverting amplifier Adding it all up with the summer What s the difference? Using the op-amp subtractor Increasing the Complexity of What You Can Do with Op Amps Analyzing the instrumentation amplifier Implementing mathematical equations electronically Creating systems with op amps Part IV: Applying Time-Varying Signals to First- and Second-Order Circuits Chapter 11: Making Waves with Funky Functions Spiking It Up with the Lean, Mean Impulse Function Changing the strength of the impulse Delaying an impulse Evaluating impulse functions with integrals Stepping It Up with a Step Function Creating a time-shifted, weighted step function Being out of step with shifted step functions Building a ramp function with a step function Pushing the Limits with the Exponential Function Seeing the Signs with Sinusoidal Functions Giving wavy functions a phase shift Expanding the function and finding Fourier coefficients Connecting sinusoidal functions to exponentials with Euler s formula Chapter 12: Spicing Up Circuit Analysis with Capacitors and Inductors Storing Electrical Energy with Capacitors Describing a capacitor Charging a capacitor (credit cards not accepted) Relating the current and voltage of a capacitor Finding the power and energy of a capacitor Calculating the total capacitance for parallel and series capacitors Finding the equivalent capacitance of parallel capacitors Finding the equivalent capacitance of capacitors in series Storing Magnetic Energy with Inductors Describing an inductor Finding the energy storage of an attractive inductor...202

8 xvi Circuit Analysis For Dummies Calculating total inductance for series and parallel inductors Finding the equivalent inductance for inductors in series Finding the equivalent inductance for inductors in parallel Calculus: Putting a Cap on Op-Amp Circuits Creating an op-amp integrator Deriving an op-amp differentiator Using Op Amps to Solve Differential Equations Really Fast Chapter 13: Tackling First-Order Circuits Solving First-Order Circuits with Diff EQ Guessing at the solution with the natural exponential function Using the characteristic equation for a first-order equation Analyzing a Series Circuit with a Single Resistor and Capacitor Starting with the simple RC series circuit Finding the zero-input response Finding the zero-state response by focusing on the input source Adding the zero-input and zero-state responses to find the total response Analyzing a Parallel Circuit with a Single Resistor and Inductor Starting with the simple RL parallel circuit Calculating the zero-input response for an RL parallel circuit Calculating the zero-state response for an RL parallel circuit Adding the zero-input and zero-state responses to find the total response Chapter 14: Analyzing Second-Order Circuits Examining Second-Order Differential Equations with Constant Coefficients Guessing at the elementary solutions: The natural exponential function From calculus to algebra: Using the characteristic equation Analyzing an RLC Series Circuit Setting up a typical RLC series circuit Determining the zero-input response Calculating the zero-state response Finishing up with the total response Analyzing an RLC Parallel Circuit Using Duality Setting up a typical RLC parallel circuit Finding the zero-input response Arriving at the zero-state response Getting the total response...251

9 Table of Contents xvii Part V: Advanced Techniques and Applications in Circuit Analysis Chapter 15: Phasing in Phasors for Wave Functions Taking a More Imaginative Turn with Phasors Finding phasor forms Examining the properties of phasors Using Impedance to Expand Ohm s Law to Capacitors and Inductors Understanding impedance Looking at phasor diagrams Putting Ohm s law for capacitors in phasor form Putting Ohm s law for inductors in phasor form Tackling Circuits with Phasors Using divider techniques in phasor form Adding phasor outputs with superposition Simplifying phasor analysis with Thévenin and Norton Getting the nod for nodal analysis Using mesh-current analysis with phasors Chapter 16: Predicting Circuit Behavior with Laplace Transform Techniques Getting Acquainted with the Laplace Transform and Key Transform Pairs Getting Your Time Back with the Inverse Laplace Transform Rewriting the transform with partial fraction expansion Expanding Laplace transforms with complex poles Dealing with transforms with multiple poles Understanding Poles and Zeros of F(s) Predicting the Circuit Response with Laplace Methods Working out a first-order RC circuit Working out a first-order RL circuit Working out an RLC circuit Chapter 17: Implementing Laplace Techniques for Circuit Analysis Starting Easy with Basic Constraints Connection constraints in the s-domain Device constraints in the s-domain Independent and dependent sources Passive elements: Resistors, capacitors, and inductors Op-amp devices Impedance and admittance Seeing How Basic Circuit Analysis Works in the s-domain Applying voltage division with series circuits Turning to current division for parallel circuits...302

10 xviii Circuit Analysis For Dummies Conducting Complex Circuit Analysis in the s-domain Using node-voltage analysis Using mesh-current analysis Using superposition and proportionality Using the Thévenin and Norton equivalents Chapter 18: Focusing on the Frequency Responses Describing the Frequency Response and Classy Filters Low-pass filter High-pass filter Band-pass filters Band-reject filters Plotting Something: Showing Frequency Response à la Bode Looking at a basic Bode plot Poles, zeros, and scale factors: Picturing Bode plots from transfer functions Turning the Corner: Making Low-Pass and High-Pass Filters with RC Circuits First-order RC low-pass filter (LPF) First-order RC high-pass filter (HPF) Creating Band-Pass and Band-Reject Filters with RLC or RC Circuits Getting serious with RLC series circuits RLC series band-pass filter (BPF) RLC series band-reject filter (BRF) Climbing the ladder with RLC parallel circuits RC only: Getting a pass with a band-pass and band-reject filter Part VI: The Part of Tens Chapter 19: Ten Practical Applications for Circuits Potentiometers Homemade Capacitors: Leyden Jars Digital-to-Analog Conversion Using Op Amps Two-Speaker Systems Interface Techniques Using Resistors Interface Techniques Using Op Amps The Wheatstone Bridge Accelerometers Electronic Stud Finders Timer Circuits...340

11 Table of Contents xix Chapter 20: Ten Technologies Affecting Circuits Smartphone Touchscreens Nanotechnology Carbon Nanotubes Microelectromechanical Systems Supercapacitors The Memristor Superconducting Digital Electronics Wide Bandgap Semiconductors Flexible Electronics Microelectronic Chips that Pair Up with Biological Cells Index

12 xx Circuit Analysis For Dummies