reading

Visit www.dummies.com/cheatsheet/circuitanalysis to view this book's cheat sheet.

Table of Contents

Introduction

About This Book

Conventions Used in This Book

What You’re Not to Read

Foolish Assumptions

How This Book Is Organized

Part I: Getting Started with Circuit Analysis

Part II: Applying Analytical Methods for Complex Circuits

Part III: Understanding Circuits with Transistors and Operational Amplifiers

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

Part V: Advanced Techniques and Applications in Circuit Analysis

Part VI: The Part of Tens

Icons Used in This Book

Where to Go from Here

Part I: Getting Started with Circuit Analysis

Chapter 1: Introducing Circuit Analysis

Getting Started with Current and Voltage

Going with the flow with current

Recognizing potential differences with voltage

Staying grounded with zero voltage

Getting some direction with the passive sign convention

Beginning with the Basic Laws

Surveying the Analytical Methods for More-Complex Circuits

Introducing Transistors and Operational Amplifiers

Dealing with Time-Varying Signals, Capacitors, and Inductors

Avoiding Calculus with Advanced Techniques

Chapter 2: Clarifying Basic Circuit Concepts and Diagrams

Looking at Current-Voltage Relationships

Absorbing energy with resistors

Offering no resistance: Batteries and short circuits

Facing infinite resistance: Ideal current sources and open circuits

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

Mapping It All Out with Schematics

Going in circles with loops

Getting straight to the point with nodes

Chapter 3: Exploring Simple Circuits with Kirchhoff’s Laws

Presenting Kirchhoff’s Famous Circuit Laws

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

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

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

Getting batteries and resistors to work together

Sharing the same current in series circuits

Climbing the ladder with parallel circuits

Combining series and parallel resistors

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

Equivalent Circuits: Preparing for the Transformation

Transforming Sources in Circuits

Converting to a parallel circuit with a current source

Changing to a series circuit with a voltage source

Divvying It Up with the Voltage Divider

Getting a voltage divider equation for a series circuit

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

Finding voltages when you have multiple current sources

Using the voltage divider technique repeatedly

Cutting to the Chase Using the Current Divider Technique

Getting a current divider equation for a parallel circuit

Figuring out currents for parallel circuits

Finding currents when you have multiple voltage sources

Using the current divider technique repeatedly

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

Testing the Waters with Node-Voltage Analysis

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

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

Putting a system of node voltage equations in matrix form

Solving for unknown node voltages

Applying the NVA Technique

Solving for unknown node voltageswith a current source

Dealing with three or more node equations

Working with Voltage Sources in Node-Voltage Analysis

Chapter 6: Getting in the Loop on Mesh Current Equations

Windowpanes: Looking at Meshes and Mesh Currents

Relating Device Currents to Mesh Currents

Generating the Mesh Current Equations

Finding the KVL equations first

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

Substituting the device voltages into the KVL equations

Putting mesh current equations into matrix form

Solving for unknown currents and voltages

Crunching Numbers: Using Meshes to Analyze Circuits

Tackling two-mesh circuits

Analyzing circuits with three or more meshes

Chapter 7: Solving One Problem at a Time Using Superposition

Discovering How Superposition Works

Making sense of proportionality

Applying superposition in circuits

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

Proceeding when the sources are two current sources

Dealing with one voltage source and one current source

Solving a Circuit with Three Independent Sources

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

Applying Norton’s theorem

Using source transformation to find Thévenin or Norton

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

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

Storing Magnetic Energy with Inductors

Describing an inductor

Finding the energy storage of an attractive inductor

Calculating total inductance for series and parallel inductors

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

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

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

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

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

555 Timer Circuits

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

Cheat Sheet

End User License Agreement

Circuit Analysis For Dummies^®

Published by
John Wiley & Sons, Inc.
111 River St.
Hoboken, NJ 07030-5774
www.wiley.com

Published by John Wiley & Sons, Inc., Hoboken, New Jersey

Published simultaneously in Canada

No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without the prior written permission of the Publisher. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http://www.wiley.com/go/permissions.

Trademarks: Wiley, the Wiley logo, For Dummies, the Dummies Man logo, A Reference for the Rest of Us!, The Dummies Way, Dummies Daily, The Fun and Easy Way, Dummies.com, Making Everything Easier, and related trade dress are trademarks or registered trademarks of John Wiley & Sons, Inc., and/or its affiliates in the United States and other countries, and may not be used without written permission. All other trademarks are the property of their respective owners. John Wiley & Sons, Inc., is not associated with any product or vendor mentioned in this book.

Limit of Liability/Disclaimer of Warranty: The publisher and the author make no representations or warranties with respect to the accuracy or completeness of the contents of this work and specifically disclaim all warranties, including without limitation warranties of fitness for a particular purpose. No warranty may be created or extended by sales or promotional materials. The advice and strategies contained herein may not be suitable for every situation. This work is sold with the understanding that the publisher is not engaged in rendering legal, accounting, or other professional services. If professional assistance is required, the services of a competent professional person should be sought. Neither the publisher nor the author shall be liable for damages arising herefrom. The fact that an organization or Website is referred to in this work as a citation and/or a potential source of further information does not mean that the author or the publisher endorses the information the organization or Website may provide or recommendations it may make. Further, readers should be aware that Internet Websites listed in this work may have changed or disappeared between when this work was written and when it is read.

For general information on our other products and services, please contact our Customer Care Department within the U.S. at 877-762-2974, outside the U.S. at 317-572-3993, or fax 317-572-4002.

For technical support, please visit www.wiley.com/techsupport.

Wiley publishes in a variety of print and electronic formats and by print-on-demand. Some material included with standard print versions of this book may not be included in e-books or in print-on-demand. If this book refers to media such as a CD or DVD that is not included in the version you purchased, you may download this material at http://booksupport.wiley.com. For more information about Wiley products, visit www.wiley.com.

Library of Congress Control Number: 2013932101

ISBN 978-1-118-49312-0 (pbk); ISBN 978-1-118-59050-8 (ebk); ISBN 978-1-118-59052-2 (ebk); ISBN 978-1-118-59056-0 (ebk)

Manufactured in the United States of America

10 9 8 7 6 5 4 3 2 1

About the Author

John Santiago retired from the military in 2003 with 26 years of service in the United States Air Force (USAF). John has served in a variety of leadership positions in technical program management, acquisition development, and operation research support. While assigned in Europe for three years with the USAF, he spearheaded more than 40 international scientific and engineering conferences/workshops as a steering committee member.

John has experience in many engineering disciplines and missions, including control and modeling of large, flexible space structures; communications systems; electro-optics; high-energy lasers; missile seekers/sensors for precision-guided munitions; image processing/recognition; information technologies; space, air, and missile warning; missile defense; and homeland defense.

One of John’s favorite assignments was serving as an associate professor at the USAF Academy during his tour from 1984 through 1989. John is currently a professor of Electrical and Systems Engineering at Colorado Technical University, where he has taught 26 different undergraduate and graduate courses in electrical and systems engineering.

Some of his awards include Faculty of the Year at Colorado Technical University in 2008; USAF Academy Outstanding Military Educator in 1989; and USAF Academy Outstanding Electrical Engineering Educator in 1998.

During his USAF career, John received his PhD in Electrical Engineering from the University of New Mexico; his Master of Science in Resource Strategy at the Industrial College of the Armed Forces; his Master of Science in Electrical Engineering from the Air Force Institute of Technology, specializing in electro-optics; and his Bachelor of Science from the University of California, Los Angeles.

On February 14, 1982, John married Emerenciana F. Manaois.

More information about John’s background and experience is available at www.FreedomUniversity.TV.

Dedication

To my heavenly Father, thank you for all the many blessings, especially the gift of family and friends.

To my lovely Emily, thank you for your loving and continued support, always and forever.

To my parents, who bravely immigrated here from the Philippines to live in this great nation.

To the Founding Fathers, who were engineers and visionary leaders in creating this great country called the United States. To their creative genius and to all those standing on their shoulders, especially the next generation of engineers.

To all those who wondered if there’s anything more to circuit analysis than Ohm’s law and Kirchhoff’s laws.

Author’s Acknowledgments

Many people have been involved in this book, and I thank them all. First, to all the former cadets at the United States Air Force Academy, the students at the University of West Florida, and the students at the Colorado Technical University who endured my class lessons and asked a gazillion questions over the years as I continued to learn to become a better teacher.

I’d like to thank a team of players who’ve made my writing presentable. First, I’d like to thank Matt Wagner, my agent, who contacted me about writing this book. I’d also especially like to thank the folks at Wiley who made this book possible: Erin Mooney, my acquisitions editor; Jennifer Tebbe, my project editor; and Danielle Voirol, my copy editor.

I’d again like to thank my wife for her encouragement and for keeping me straight about the things going on at home and in the community as I went through this writing adventure.

Publisher’s Acknowledgments

We’re proud of this book; please send us your comments at http://dummies.custhelp.com. For other comments, please contact our Customer Care Department within the U.S. at 877-762-2974, outside the U.S. at 317-572-3993, or fax 317-572-4002.

Some of the people who helped bring this book to market include the following:

Acquisitions, Editorial, and Vertical Websites

Project Editor: Jennifer Tebbe

Acquisitions Editor: Erin Calligan Mooney

Senior Copy Editor: Danielle Voirol

Assistant Editor: David Lutton

Editorial Program Coordinator: Joe Niesen

Technical Editor: Chang Liu, Dan Moore

Editorial Manager: Christine Meloy Beck

Editorial Assistant: Alexa Koschier, Rachelle S. Amick

Composition Services

Project Coordinator: Katherine Crocker

Layout and Graphics: Carl Byers, Carrie A. Cesavice, Amy Hassos, Joyce Haughey, Christin Swinford

Proofreaders: Tricia Liebig, Dwight Ramsey

Indexer: Ty Koontz

Publishing and Editorial for Consumer Dummies

Kathleen Nebenhaus, Vice President and Executive Publisher

David Palmer, Associate Publisher

Kristin Ferguson-Wagstaffe, Product Development Director

Publishing for Technology Dummies

Andy Cummings, Vice President and Publisher

Composition Services

Debbie Stailey, Director of Composition Services

Introduction

Circuit analysis is often one of those weed-out classes in engineering schools. Either you pass the class to study engineering, or you don’t pass and start thinking about something else. Well, I don’t want you to get weeded out, because engineering is such a rewarding field. This book is here to help you make sense of circuit analysis concepts that may be puzzling you. Along the way, you explore a number of analytical tools that give you shortcuts and insight into circuit behavior.

You can take the tools you find here and apply them to whatever high-tech gizmo or craze is out there. And not only can you pass your class, but you can also take these concepts to the real world, enriching human lives with comfort and convenience and rewarding you with more time to do useful activities.

About This Book

Like all other For Dummies books, Circuit Analysis For Dummies isn’t a tutorial. Rather, it’s a reference book, which means you don’t have to read it from cover to cover, although you certainly can if that’s your preference. You can jump right to the topics or concepts you’re having trouble with. Either way, you’ll find helpful information along with some real-world examples of electrical concepts that may be hard to visualize otherwise.

Conventions Used in This Book

I use the following conventions throughout the text to make things consistent and easy to understand:

New terms appear in italics and are closely followed by an easy-to-understand definition. Variables likewise appear in italics.

Bold is used to highlight keywords in bulleted lists and the action parts of numbered steps. It also indicates vectors.

Lowercase variables indicate signals that change with time, and uppercase variables indicate signals that are constant. For example, v(t) and i(t) denote voltage and current signals that change with time. If, however V and I are capitalized, then those signals don’t vary in time.

What You’re Not to Read

Although it’d be great if you read every word, you’re welcome to skip the sidebars (the shaded boxes sprinkled throughout the book) and paragraphs flagged with a Technical Stuff icon.

Foolish Assumptions

I may be going out on a limb, but as I wrote this book, here’s what I assumed about you:

You’re currently taking an introductory circuit analysis course, and you need help with certain concepts and techniques. Or you’re planning to take a circuit analysis course in the next semester, and you want to be prepared with some supplementary material.

You have a good grasp of linear algebra and differential equations.

You’ve taken an introductory physics class, which exposed you to the concepts of power, positive and negative charges, voltage, and current.

How This Book Is Organized

Circuit analysis integrates a variety of topics from your math and physics courses, and it introduces a variety of techniques to solve for circuit behavior. To help you grasp the concepts in manageable bites, I’ve split the book into several parts, each consisting of chapters on related topics.

Part I: Getting Started with Circuit Analysis

This part gives you the engineering lingo, concepts, and techniques necessary for tackling circuit analysis. Here, I help you quickly grasp the main aspects of circuit analysis so you can analyze circuits, build things, and predict what’s going to happen. If you’re familiar with current, voltage, power, and Ohm’s and Kirchhoff’s laws, you can use this part as a refresher.

Part II: Applying Analytical Methods for Complex Circuits

This part looks at general analytical methods to use when dealing with more complicated circuits. When you have many simultaneous equations to solve or too many inputs, you can use various techniques to reduce the number of equations and simplify circuits to a manageable level.

Part III: Understanding Circuits with Transistors and Operational Amplifiers

This part deals with two devices that require power to make them work. You can use transistors as current amplifiers, and you can use operational amplifiers as voltage amplifiers.

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

This part gets tougher because you’re dealing with changing signals and with circuits that have passive energy-storage devices such as inductors and capacitors. You also need to know differential equations in order to analyze circuit behavior for first- and second-order circuits.

Part V: Advanced Techniques and Applications in Circuit Analysis

This part takes the problems described in Part IV and changes a calculus-based problem into one requiring only algebra. You do this conversion by using phasor and Laplace techniques. You can gather additional insight into circuit behavior from the poles and zeros of an equation, which shape the frequency response of circuits called filters.

Part VI: The Part of Tens

Here you find out about ten applications and ten technologies that make circuits more interesting.

Icons Used in This Book

To make this book easier to read and simpler to use, I include some icons to help you find key information.

Anytime you see this icon, you know the information that follows will be worth recalling after you close this book — even if you don’t remember anything else you just read.

This icon appears next to information that’s interesting but not essential. Don’t be afraid to skip these paragraphs.

This bull’s-eye points out advice that can save you time when analyzing circuits.

This icon is here to prevent you from making fatal mistakes in your analysis.

Where to Go from Here

This book isn’t a novel — you can start at the beginning and read it through to the end, or you can jump right in the middle. If you like the calculus approach to solving circuits, head to the chapters on first- and second-order circuits. If calculus doesn’t suit your fancy or if you’re itching to find out what the Laplace transform is all about, flip straight to Chapter 16.

If you’re not sure where to start, or you don’t know enough about circuit analysis to even have a starting point in mind yet, no problem — that’s exactly what this book is for. Just hop right in and get your feet wet. I recommend starting with the chapters in Part I and moving forward from there.

Circuit Analysis For Dummies®

Circuit Analysis For Dummies^®