# Basic Laws and Analytical Methods for Circuit Analysis by John Santiago

The Basic Laws

A circuit is basically a collection of electrical devices, such as resistors, batteries, capacitors, and inductors, arranged to perform a certain function. Each component of a circuit has its own constraints. When you connect devices in any circuit, the devices follow certain laws:

• Ohm's law: This law describes a linear relationship between the voltage and current for a resistor.

• Kirchhoff's voltage law (KVL): KVL says the algebraic sum of the voltage drops and rises around a loop of a circuit is equal to zero.

• Kirchhoff's current law (KCL): KCL says the algebraic sum of incoming and outgoing currents at a node is equal to zero.

With these three laws, you can solve for the current or voltage in any device.

Surveying the Analytical Methods for More-Complex Circuits

When you have many simultaneous equations to solve or too many inputs, you can use the following techniques to reduce the number of simultaneous equations and simplify the analysis:

• Node-voltage analysis: A node is a point in the circuit. This technique has you apply Kirchhoff's current law (KCL), producing a set of equations that you use to find unknown node voltages. When you know all the node voltages in a circuit, you can find the voltage across each device.

• Mesh-current analysis: Mesh-current analysis deals with circuits that have many devices connected in many loops. You use Kirchhoff's voltage law (KVL) to develop a set of equations with unknown mesh currents. Because you can describe the device currents in terms of the mesh currents, finding the mesh currents lets you calculate the current through each device in the circuit.

• Superposition: When you have multiple independent power sources in a linear circuit, superposition comes to your rescue. Analyzing linear circuits involves using only devices (such as resistors, capacitors, and inductors) and independent sources. By applying superposition, you can take a complex circuit that has multiple independent sources and break it into simpler circuits, each with only one independent source. The circuit's total output then is the algebraic sum of output contributions due to the input from each independent source.

• Thevenin's and Norton's theorems: Thevenin and Norton equivalent circuits are valuable tools when you're connecting and analyzing two parts of a circuit. The interaction between the source circuit (which processes and delivers a signal) and load circuits (which consume the delivered signal) offers a major challenge in circuit analysis. Thevenin's theorem simplifies the analysis by replacing the source circuit's complicated arrangement of independent sources and resistors with a single voltage source connected in series with a single resistor. Norton's theorem replaces the source circuit with a single current source connected in parallel with a single resistor.

I don't know about you, but I hate using calculus when I don't have to, which is why I'm a fan of the advanced circuit analysis techniques that allow you to convert calculus-based problems into problems requiring only algebra. Phasors make your life simple when you're dealing with circuits that have capacitors and inductors, because you don't need differential equations to analyze circuits in the phasor domain. Phasor analysis investigates circuits that have capacitors and inductors in the same way you analyze circuits that have only resistors. This technique applies when your input is a sine wave (or a sinusoidal signal).

Analyzing Circuits with Software

When circuits get too complex to analyze by hand, today's software offers many capabilities. Here are some commonly used software tools:

• SPICE: This software was originally developed at the Electronics Research Laboratory of the University of California, Berkeley. SPICE stands for Simulation Program for Integrated Circuit Emphasis. PSpice is a PC version of SPICE, and several companies, such as Cadence (cadence.com) and Linear Technology (linear.com), produce various versions of SPICE. Both companies offer demos and free versions of their software.

• National Instrument's Multisim: This is one of the granddaddies of circuit analysis oftware as well as a great tool for beginners. It also has a cool feature that shows changing voltages in real time of the circuit. The trial version pretty much lets you do anything you want. A student version is available as well. Visit ni.com/multisim/ for more information.

• Ngspice: This tool is a widely used open source circuit simulator from Sourceforge. The free Ngspice software (available at ngspice.sourceforge.net) is developed by many users, and its code is based on several major open-source software packages.

John Santiago retired from the military in 2003 with 26 years of service in the United States Air Force (USAF) traveling over 23 countries. John has served in a variety of leadership positions in technical program management, acquisition, 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 lasters; 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 associate professor at the USAF Academy during his tour from 1984 though 1989. John is currently a professor of Electrical and Systems Engineering at Colorado Technical University, where he has taught over 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 National 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 from the University of California, Los Angeles (UCLA). More information about John's background and experience is available at FreedomUniversity.TV

Circuits Overloaded from Electric Circuit Analysis?

Many universities require that students pursuing a degree in electrical or computer engineering take an Electric Circuit Analysis course to determine who will "make the cut" and continue in the degree program. Circuit Analysis For Dummies will help these students to better understand electric circuit analysis by presenting the information in an effective and straightforward manner.

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Whether you're pursuing a degree in electrical or computer engineering or are simply interested in circuit analysis you can enhance you knowledge of the subject with Circuit Analysis For Dummies

A reader in the United Kingdom says,"This book is a lovely, rich and clear exploration of the basics of circuit analysis using mathematical and engineering techniques and eventually solving first and second differential equations. The usage of Ohm's, Kirchhoff's voltage and current laws, Nodal analysis, superposition techniques is very well explained. The aim, being to grasp small circuits with components modelling by differential equations. These good bits are held back to the latter half of the book. I thought initially this was lacking in some way, but this book held the best for last. Can i explain i have learned to use these in other books but this book is as well designed as any I have encountered prior to this book. The only downside being is there are few questions and answers in this book to practice these skill on and to test your comprehension with. So you may need to work with other sources for questions." Click here to learn more.