Using Complex Numbers in Circuit Analysis and （在电路分析和使用复数）.pdf

Physics 160 Practical Electronics Spring 2014 Using Complex Numbers in Circuit Analysis and Review of the Algebra of Complex Numbers The purpose of this note is to review the algebra of concept numbers and show how they can be used to simplify analyses of linear circuits. This is the basic theory behind how PSpice handles linear circuits (and linear small-signal approximations of non-linear circuits). The basic techniques are also widely used in many types of linear analysis found in physics and engineering (electrical or mechanical), so if you are majoring in one of those fields, you will need to become familiar with these techniques and concepts sooner or later, even though we will not use them extensively in this course. I illustrate the technique with a simple, standard LRC circuit and then with a non-trivial example, and I show how the same example can be easily solved by PSpice. At the end I discuss briefly how PSpice can handle much more complicated circuits, including non- linear circuits, by extending the same mathematical techniques. Complex numbers are commonly used in electrical engineering, as well as in physics. In general they are used when some quantity has a phase as well as a magnitude. Such a situation occurs when one deals with sinusoidal oscillating voltage and current (other examples in physics include optics, where wave interference is important, and quantum mechanical wave functions). I want to emphasize that complex numbers are used to make calculations easier! Do not be intimidated by trying to imagine what